Two-step beam-forming using space-frequency transformation in a time-multiplexed phased array receiver Deng, W.

Transcription

1 Two-step beam-forming using space-frequency transformation in a time-multiplexed phased array receiver Deng, W. DOI: /IR73153 Published: 01/01/011 Document Version Publisher s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. The final author version and the galley proof are versions of the publication after peer review. The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication Citation for published version (APA): Deng, W. (011). Two-step beam-forming using space-frequency trans-formation in a time-multiplexed phased array receiver Eindhoven: Technische Universiteit Eindhoven DOI: /IR73153 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal? Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 15. Dec. 018

2 Two-Step Beam-Forming Using Space-Frequency Transformation in a Time-Multiplexed Phased-Array Receiver Wei Deng

3 Front cover: Chip photo of the system presented in Chapter 8 Back cover: Wei Deng photo and short Curriculum Vitae

4 Two-Step Beam-Forming Using Space-Frequency Transformation in a Time-Multiplexed Phased-Array Receiver PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op maandag 8 november 011 om uur door Wei Deng geboren te Wuhan, China

5 Dit proefschrift is goedgekeurd door de promotor: prof.dr.ir. A.H.M. van Roermund Copromotor: dr.ir. R. Mahmoudi A catalogue record is available from the Eindhoven University of Technology Library. CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN Wei Deng Two-Step Beam-Forming Using Space-Frequency Transformation in a Time-Multiplexed Phased-Array Receiver / by Wei Deng. Eindhoven : Technische Universiteit Eindhoven, 011. Proefschrift. ISBN: NUR 959 Key words: 30GHz / SiGe mm wave integrated circuit design / phased array / receiver / beam forming / multiplexing / switching Copyright 011 by Wei Deng, Eindhoven All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic, mechanical, including photocopy, recording, or any information storage and retrieval system without the prior written permission of the copyright owner.

6 To my parents, and to my wife, Yan Huang.

7 Samenstelling van de promotiecommissie: prof. dr. ir. A.C.P.M. Backx, prof. dr. ir. A.H.M. van Roermund, dr. ir. R. Mahmoudi, prof. dr. ir. D.M.W. Leenaerts, prof. dr. ir. F.E. Vliet, prof. ir. A. van Ardenne, prof. dr. ir. A.B. Smolders, dr. ir. G.H.C. van Werkhoven, Technische Universiteit Eindhoven, voorzitter Technische Universiteit Eindhoven, promotor Technische Universiteit Eindhoven, co-promotor Technische Universiteit Eindhoven University of Twente Chalmers University of Technology Technische Universiteit Eindhoven Thales Nederland.

8 Contents Contents... vii Glossary... xi 1 Introduction Motivation Background Problem statement and research strategy Thesis outline... 5 Basic concepts Receiver system basics Noise Non-linearity Dynamic Range Phase modulation basics Phased-array basics Single and multipath receiver: a system approach Translating ADC parameters to RF domain ADC model... 7 vii

9 viii Contents 3.1. ADC noise ADC non-linearity Mapping ADC parameters to system design Receiver system optimization method Receiver signal flow diagram Optimization method Analog beam-forming Digital beam-forming General case of beam-forming Conclusion Two-step beam-forming: multiplexing architecture Multiplexing architecture introduction Spatial to frequency mapping Two steps of spatial filtering Phased-array analog and digital co-design Generalized phased-array system design Multiplexing architecture, ideal behavior Analog multiplexing Properties of the switching signal Pulse modulation Combination in the analog domain Spatial to frequency mapping Space to frequency mapping coefficient D n Translation from voltage to power domain, D n to Px n Coarse beam pattern Rx N by frequency selectivity Digital de-multiplexing and phase-shifting Array pattern Conclusion... 89

10 Contents ix 6 Multiplexing architecture, non-ideal behavior Angle deviation Non-ideal switches Noise in a multiplexing system Frequency mixing System simulations Power flow diagram for a multiplexed architecture Conclusion Designs for the 30GHz components Design requirements LNA and Multiplexer Circuit design Measurements LNA-multiplexer-mixer combination Circuit design Measurements Clock generator Circuit design Measurements Input delay line Circuit design Measurements Power amplifier Circuit design Measurements Trouble shooting Conclusion System integration and verification System with one channel

11 x Contents 8. System with four channels Demonstration with one input signal Demonstration with two input signals Conclusion Conclusions and future works Conclusion Future works Original contributions References Publications Summary Samenvatting Acknowledgement Curriculum vitae

12 Glossary Symbol Description Unit A Signal amplitude V BW Bandwidth Hz c n Complex Fourier coefficients for generic switching signal c n Complex Fourier coefficients for equal time slot duration τ d Adjacent antenna distance m D n Coefficient function of the n-th order harmonic V f C Carrier frequency Hz f MUL Sampling rate for multiplexer in the multiplexing system Hz f S Sampling rate for each path in the multiplexing system Hz k Antenna number K Number of antennas L Power rejection ratio of desired viewing angle to un-desired viewing angle n Harmonic number N Number of harmonics Px n Power contained in the n-th pair of side frequency mw Py n Power transferred to the fundamental frequency from the n-th pair mw RxN Array coarse pattern mw RxN Array final pattern mw SNR Signal to noise ratio ts Starting time delay of the switching signal s TS Period of the switching signal s N Angle deviation degree D FE Distortion contribution by the RF front-end referred to ADC output N FE Noise contribution by the RF front-end referred to ADC input P 1 Margin to the ADC full scale range power P Energy reduction from one tone input to two tone inputs (by each tone) S Distance difference for adjacent channels in the wave propagation direction m t Progressive time delay between two adjacent channels, caused by θ s α 1 Positive amplitude of the switch signal V α 1 Negative amplitude of the switch signal V β 1 Interference suppression flexibility of the general beam-forming system Noise reduction flexibility of the general beam-forming system β xi

13 xii Glossary φ Electric phase difference between two adjacent channels caused by θ rad/degree θ Angle of incidence in spatial domain degree Ø Angle of electric phase shifter γ in spatial domain degree γ Electric phase shifter between two adjacent channels rad/degree λ Wavelength m τ Duration for each time slot (pulse width) in the multiplexing system s χ1 Interference suppression flexibility of the multiplexed architecture Noise reduction flexibility of the multiplexed architecture χ

14 C h a p t e r 1 1 Introduction 1.1 Motivation Silicon-based technology has had a dramatic impact on the world of wireless technology. Wireless devices have become part of our life: smart phones, satellite navigation system, home wireless network, etc, and it is getting more and more popular. Today we can access digital information in virtually every corner of the globe. This trend has made the wireless communication one of the fastest growing segments of the modern technology industry. The vast majority of today s wireless standards and applications are accommodated around 1 to 6GHz. This is initially due to the early technology access. Along with the technology progress indicated by Moore s law [1], the components expenses around these frequencies are getting cheaper, leading to a rapid expansion of these systems. One of the downsides of this expansion is the resulting limitations of available bandwidth. The defined systems are capable of supporting light or moderate levels of wireless data traffic. As in Bluetooth [], its maximum data rate is 3Mbps at.4ghz. 1

15 Chapter 1. Introduction Driven by the customer demands, especially the fast growing wireless portable devices market, the requirement of supporting multi-standard applications has been recognized. Lacking of channel capacity has become one of the bottlenecks of low frequency applications. Furthermore, as predicted by Edholm s law [3], the required data rates (and associated bandwidths) have doubled every eighteen months over the last decade. This trend is shown in Fig. 1.1 for cellular, wireless local area networks and wireless personal area networks for last sixteen years. Fig. 1.1: Data rate trend predicted by Edholm s law Applications operating at 1 to 6GHz are suitable for long distance communications. However, the spectrum congestion and data rate limitation motive designers exploring new solutions. As stated by Shannon [4], the maximum available capacity of a communication system increases linearly with channel bandwidth and logarithmically with the signal-to-noise ratio. Therefore, one of the choices is to look upwards in the high frequencies where more bandwidth could be available. One of the high frequency applications is the indoor personal communications and wireless fidelity at 60GHz [5]. Around 7GHz spectral spaces has been allocated worldwide for unlicensed use. In order to design circuits at 60GHz, the transistor cut-off frequency f T needs to be typically around 00GHz. At this moment, the process for making such a device is still relatively expensive than lower frequency transistors. On contrary, making transistors with f T around 100GHz is quite matured in worldwide foundries increasing availability at low cost. Therefore and in order

16 1. Background 3 to demonstrate the principles outlined in this thesis, the system and circuits are implemented at 30GHz. Besides, there are two applications defined by the Federal Communications Commission (FCC) around 30GHz. Local Multipoint Distribution Services (LMDS) [6], can be considered as one of these applications. It is a broadband wireless access technology originally designed for digital television transmission (DTV). It was conceived as a fixed wireless, point-to-multipoint technology for utilization in the last mile. LMDS commonly operates on microwave frequencies across the 6GHz and 31GHz bands. Another application is the satellite Ka-band communication [7]. Ka-band transmission is viewed as a primary means for meeting the increasing demands for high data rate services of space exploration missions. At Ka-band, deep space communications is allocated 500MHz of bandwidth compare to the 50MHz of bandwidth allocated to the X-band [8]; leading to even greater increase in throughput when using Ka-band. 1. Background At 30GHz, the wave propagation path loss, the noise of the receiver, and the output power of the transmitter are more problematic to cope with than low frequencies. However, at this frequency, the millimeter-wave operation can facilitate very small antenna apertures for the array receptors, since the electromagnetic wavelength is very short. This property allows highly miniaturized, lightweight phased-array to be manufactured, a key for compensating the path loss and alleviating the RF transceiver front-end requirements. The ability to individually control both amplitude and phase of each element in the array is known as beam-forming 1 [9]. Beam-forming can be separated into two categories: analog beam-forming, and digital beam-forming. As indicated by its name, analog beam-forming controls the amplitude and phase of each element in the analog part of the receiver chain. Phase shifters are commonly used in the analog beam-forming phased-array architecture for adjusting the phase of each antenna path and steering the beam [10-11]. Phase shifter can be implemented in different parts of a transceiver, such as at RF [1-15], at IF [16-19], or at LO [0-]. On the other hand, digital beam-forming controls the amplitude and phase of each element in the digital part of the receiver chain. As a result, the phase shifter is implemented in the digital domain by various algorithms [3-7]. In practice, these two beam-forming techniques have their own pros and cons. The analog beam-forming technique enhances the SNR and rejects the interferences before the ADC and the ADC dynamic range is relaxed. However, due to the phase compensation in the analog domain, the phase information of the incidence signal is not available for digital signal processing. On the other hand, the digital beam-forming technique conveys the incidence signal amplitude and phase information into the digital domain, which provides more 1 Phased-array architecture is usually used together with beam-forming technique. Sometimes, we also use beam-steering or beam-patterning. In this thesis, we only use beam-forming for simplicity.

17 4 Chapter 1. Introduction flexibility. Nevertheless, the hardware implementation per antenna channel, especially the power hungry ADCs, will increase the overall power consumption, area and cost. The demand for a flexible phased-array architecture that takes advantage of both analog and digital beam-forming is enormous. In the past few years, research has been performed in this area. Reference [8] presents a technique for realizing phase-amplitude weighting for phased-array antennas using sampling of antenna elements signals. In this architecture, beam-forming is achieved in the analog domain. Traditional phase shifters are replaced by programmable switches that improve the flexibility of the analog beam-forming. The drawback for this architecture is similar as other analog beam-forming structures: phase information of the incidence signal is lost before the digital signal processing, which limits the further flexibility improvement. Reference [9] presents a code-modulating path-sharing multi-antenna receiver for spatial multiplexing and beam-forming. It uses code modulation in the RF domain to distinguish antenna signals before combining them and sending the resulting signal through a single path, so it is possible to recover the signals in the digital domain. This architecture realizes beam-forming in the digital domain, and compared to digital beam-forming, it reduces hardware consumption in the analog domain. The drawbacks for this architecture are that the signal bandwidth expansion after the channel coding requires a very demanding ADC, and the coding complexity makes it not suitable for a large number of arrays. Instead of code modulation, reference [30] presents a similar concept using a time division multiplexed scheme for digital beam-forming which achieves a reduction of RF hardware by multiplexing several individual elements of the antenna array into a single RF channel prior to the LNA, and de-multiplexing the combined signal before the analog low pass filter and ADC. This architecture has only limited improvement on the hardware consumption, and it achieves no improvement on the use of multiple ADCs. It introduces a noise problem because the pin diode multiplexer is placed before the LNA. 1.3 Problem statement and research strategy As previously mentioned, current literature mostly focuses on phased-array circuit implementations. A system approach analysis method is lacking. This leads to a non-optimized result. Furthermore, a flexible phased-array receiver that can relax the ADC design in the analog domain (advantage of analog beam-forming), and still preserves the initial phase information in the digital domain (advantage of digital beam-forming) is needed. Moreover, from implementation point of view, the possibility to realize this idea at 30GHz with low-cost technology is of particular interested. Hence, the main research objectives of this thesis are therefore: provide a system approach analysis method for phased-array receivers. investigate a flexible phased-array structure with both analog and digital beam-forming properties.

18 1.4 Thesis outline 5 investigate a real low-cost integrated solution of the 30GHz phased-array front-end system and verify its performance and to draw conclusions on future work. The research strategy for the first objective is to introduce a system optimization method for a single path receiver; mapping a phased-array receiver to an equivalent single path receiver model; and then apply the optimization method to the equivalent model. The research strategy for the second objective is shown in Fig. 1.. It shows a functional block diagram of such a phased-array receiver. It combines K paths into one path by an analog combination block, with initial phase information preserved. Then, an analog signal processing block processes the combined signal to relax the ADC design. After the ADC, the digital signal processing block separates the combined signal into the original K paths, and the initial phase information is recovered. The phase shifters are implemented in the digital domain just like a traditional digital beam-forming. And, at last, the phase compensated signals are added together to form the desired beam-pattern. Fig. 1.: Flexible phased-array receiver shown in functional blocks. The research strategy for the third objective is: based on the provide technology, identify the critical components of the system and characterize them individually at 30GHz before complete system integration; implement system firstly with only one channel to check the initial integration performance; implement the complete phased-array system with four channels and verify the measurement result with pre-developed theory. 1.4 Thesis outline This thesis is organized in the following way. Chapter introduces some basics concepts and required theories that will be used in the following chapters. To be more particular, it includes

19 6 Chapter 1. Introduction receiver system basics, phase modulation basics, and phased-array basics. Chapter 3 provides a system approach analysis method for single and multi-path receivers, which is the answer to the first objective of this thesis. The research strategy is applied to analog and digital beam-forming in this chapter. Using the results from the previous analysis, the system approach for the general case of beam-forming is extracted. Chapters 4, 5, and 6 provide a multiplexing architecture with analog and digital beam-forming properties, which is the answer to the second objective of this thesis. Chapter 4 introduces the architecture, and the tagged along new concepts. Chapter 5 provides a detailed analysis for the multiplexing architecture. Chapter 6 studies the non-ideal behaviors of this architecture. Chapters 7 and 8 are about the circuit and system implementation of the multiplexing phased-array architecture, which is the answer to the third objective of this thesis. Chapter 7 addresses the component design at 30GHz. Chapter 8 discusses the system integration of the individual components listed in chapter 7. Note that this thesis mainly covers the multiplexing phased-array receiver part. For the transmitter part, only a power amplifier component design is described in section 7.6 to explore the feasibility. Chapter 9 is reserved for conclusions and future work recommendations. Chapter 10 summarizes the original contributions of this work.

20 C h a p t e r Basic concepts This chapter introduces some basics concepts and required theories that will be used in the following chapters. Section.1 explains basic concepts in communication systems, including noise, linearity, and dynamic range which will be frequently used in chapter 3 and 4. Section. explains phase modulation basics, which will be used as the guideline to analysis and explain the multiplexing phased-array system in chapter 4. Section.3 discusses the basic theory of phased-array..1 Receiver system basics Noise and linearity are the most frequently used concepts in receiver designs. Low noise and high linearity are desired and demanded in most communication systems. However, to achieve low noise and high linearity is not always easy. 7

21 8 Chapter. Basic concepts.1.1 Noise The noise performance of the receiver is measured with noise factor (F), which is a measure of how much the signal-to-noise ratio is degraded through the system [31]. We note that F SNR SNR in in in, source out, total out, added = = = = 1+ (.1) out S ( S G) / N N Nout, source in / N out, total N out, source N where S in is the available input signal power, G is the available power gain, N out,total is the total noise power at the output, N out,source is the noise power at the output originating at the source, and N out,add is the noise power at the output added by the electronic circuitry. This shows that the minimum possible noise factor, which occurs if the electronics adds no noise, is equal to 1. Noise figure NF is related to noise factor F by NF = 10log10 F (.) It can be derived that NF is the ratio of the receiver s signal-to-noise ratio (SNR) at the output to that at the input, which can be expressed in db format as follows SNR out, db = SNRin, db NF (.3) Equation (.3) indicates that the NF represents the amount of SNR degradation after the signal is processed by the receiver. G 1 G G 3 NF 1 NF NF 3 G n NF n Fig..1: Noise cascading system In Fig..1, assuming that all stages are matched to the system characteristic impedance, the overall noise factor of the system is determined by the gain and noise factor of each stage as in (.4), and the overall gain of the system is shown in (.5)

22 .1 Receiver system basics 9 F total = F 1 F 1 F3 1 Fn (.4) G G G G G G n 1 G total = G1 G Gn 1 Gn (.5) Equation (.4) is known as Friis s formula [3], which indicates that the noise factor of the first stage is most critical to the system noise performance because the noise due to each cascade stage is suppressed by the available power gain preceding it. Fig.. shows the equivalent noise model of a single receiver stage. N eq,in is the input equivalent noise, and N eq,out is the output equivalent noise. N eq,in G NF N eq,out Fig..: Equivalent noise model of a single receiver stage The output equivalent noise can be expressed as N eq, out, dbm = N = N eq, in, dbm floor, dbm + G db + NF + G db (.6) where N floor represents the noise floor of the stage. In a cascaded system (Fig..1), the output of one stage feeds the input of the next. The total output equivalent noise can be expressed as ( ) ( ) N = 10log kt BW + NF + G total, eq, out, dbm total total, db = 174dBm + 10 log BW + NF + G total total, db (.7) where kt*bw is the receiver input noise floor, and NF total and G total are the system total noise figure and gain, respectively. In (.7), k=1.38*10-3 J/K is the Boltzmann s constant [33]. T is the temperature. BW is the bandwidth in Hertz. kt corresponds to the minimum equivalent noise per Herz for a receiver at room temperature (90K), that is -174dBm/Hz. NF total is the total noise figure of the system, and it is derived in (.4). G total is the total available gain (in db) of the system, and it is derived in (.5).

23 10 Chapter. Basic concepts.1. Non-linearity Any unwanted signal fed into a receiver is called interference and it generally degrades the signal to noise ratio of the wanted signal. Most interference comes from the signals intended for other users or other applications. The interference power can be orders of magnitude higher than the desired signal power and may corrupt the signal as a result of receiving non-linear behavior. Any real receiver is a nonlinear system that responses linearly only if the input signal is sufficiently small. When the input signal increases beyond some extent, the nonlinear behavior of the receiver becomes evident. If a sinusoid is applied to a nonlinear system, the output generally exhibits frequency components that are integer multiples of the input frequency. They are called harmonics of the input frequency. Fig..3: Nonlinear system, one tone input For simplicity, assuming nonlinear property of the system can be written as Taylor expansion, we limit our analysis to third order, and assume nonlinear terms above the third order are negligible, y(t) in Fig..3 can be derived as y( t) = α A cos ( ωt) + α A cos ( ωt) + α A cos ( ωt) 3 α A 3α A 3 = + α A cos DC fundamental 3 3 α A α A 4 3 ( ωt) + cos( ωt ) + cos( 3ωt ) harmonics (.8) One figure of merit for receiver linearity is the gain compression point. Theoretically, the receiver s output power increases linearly with the injected input power regardless of the input power level, as shown in Fig..4 [34] by the dashed line. The solid line in Fig..4 depicts a typical input/output transfer function of a real receiver.

24 .1 Receiver system basics 11 P out [dbm] OCP 1dB 1dB ICP 1dB P in [dbm] Fig..4: 1-dB compression point It can be seen that at low input power level, the real I/O curve can be approximated with the straight line. As P in increases, P out gradually deviates from the linear curve and is eventually saturated. The point at which Pout is 1dB lower than its linear theoretical value is called the input 1-dB compression point (ICP1dB). The importance of this point is that it indicates where the receiver starts to leave the linear region and the saturation becomes a potentially serious problem. The receiver also generates spurs at the harmonics of the signal frequency when the receiver goes into compression. Fig..5: Nonlinear system, two tone input Fig..5 shows two closely spaced interferences at f 1 and f in the vicinity of signal band, where the strongest interference commonly originates. After passing the nonlinear system, the output signal y two (t) can be derived as

25 1 Chapter. Basic concepts y two ( t) = α x 1 two = α A 9 + A α1 + α 3 A α A + α A 1 + α 3 A α 3 A 4 ( t) + α x ( t) + α x ( DC) ( t) [ cosω t + cosω t] ( Fundamental ) [ cosω t + cosω t] ( HD) [ cos( ω + ω ) t + cos( ω ω ) t] ( IM ) 3 3 two 1 1 [ cos3ω t + cos3ω t] ( HD3) 1 [ cos( ω1 + ω ) t + cos( ω1 ω ) t] [ cos( ω + ω ) t + cos( ω ω ) t] two ( IM 3) (.9) One of the important linearity specifications in (.9) is the third-order intermodulation point (IM3). When the interference power is high enough, the receiver generates noticeable spurs at ±nf 1 ±mf due to intermodulation, where n and m are integers including zero. Two of these spurs, located at f 1 - f and f -f 1, are particularly threatening to the received signal because they can fall into the signal band and become impossible to eliminate by filtering. The power of the 3rd order distortion increases 3dB per 1dB increase of the input power. Fig..6 shows the typical curves of the main tone and the third-order intermodulation power as a function of P in. P out [dbm] 1st 3rd IIP 3 P in [dbm] Fig..6: Third order input intercept point The third-order interception point is obtained by extrapolating the main-tone output at the slope of 1dB/1dB and the third-order distortion curve at 3dB/1dB from the low input power level

26 .1 Receiver system basics 13 until they intersect with each other, as shown in Fig..6. The x-coordinate of the intersection point is called the input referred third-order interception point (IIP3), and the y-coordinate is called the output referred third-order interception point (OIP3). In a cascaded system as shown in Fig..1, the overall IIP 3 of the system is given by G G G G G G G (.10) n 1 = IIP 3, total IIP3,1 IIP3, IIP3,3 IIP3, n It can be seen from (.10) that in a cascade system the linearity requirements on the receiver components at the back-end are more stringent because their effects on the overall system are magnified by the preceding gain. We should emphasize that (.10) is merely an approximation. In practice, more precise calculations or simulations must be performed to predict the overall IP Dynamic Range Dynamic range (DR) is defined as the ratio of the maximum input power level that the circuit can tolerate to the minimum input power level that the circuit can properly detect [35]. DR specifies how well the system can handle signals with various power levels. The lower bound of the dynamic range is set by the receiver sensitivity, defined as the lowest input signal power a receiver can appropriately process. To calculate the receiver sensitivity, one starts from the maximum bit error rate (BER) the data transmission can tolerate in the absence of interference. To achieve this BER, the receiver must provide a minimum SNR out to the subsequent demodulator. Therefore, a minimum SNR in must be achieved at the receiver input, which is given by SNR + in, min. db = SNRout, min, db NFtotal (.11) Assuming the receiver input is impedance matched to the antenna, the receiver sensitivity can be obtained as ( ) P = NF + 10log kt BW + SNR in,min, dbm total out,min, db = NF 174dBm + 10log( BW ) + SNR total out,min, db (.1)

27 14 Chapter. Basic concepts The upper limit of the dynamic range has various definitions that result in different bounds [36], but all are related to the linearity of the receiver. For instance, the most common definition, the spurious-free dynamic range (SFDR), defines the maximum allowed input signal power as the one causing the maximum intermodulation product equal to the output noise power. From Fig..6, this input power level can be solved by using the graphical method, which is given by 1 Pin, max, dbm = IIP3, total, db + [ NFtotal 174dBm + 10log( BW )] (.13) 3 3 From (.1) and (.13), the receiver dynamic range can be found by DR db = P = 3 in,max, dbm P in,min, dbm [ IIP3, total, db NFtotal + 174dBm 10log( BW )] SNRout,min, db (.14). Phase modulation basics Modulation is the process of modifying a high-frequency signal (called the carrier signal) with low-frequency information (called the modulating signal). The two most common types of modulation are amplitude modulation (AM) and frequency modulation (FM) [37]. These two forms of modulation modify the carrier s amplitude or frequency, respectively, according to the instantaneous value of the modulating signal. Phase modulation (PM) is similar to frequency modulation (FM) except that the phase of the carrier waveform is varied, rather than its frequency. Assume carrier signal v c (t) and modulating signal v m (t) υ c ( t) = Vc cos[ θc ( t) ] = V cos( πf t + φ ) c c c (.15) m ( t) V cos( πf t) υ = (.16) m m where V, f, and Ø are the amplitude, frequency and phase, respectively. Combining (.15) and (.16), the phase modulated signal in time domain is given by υ pm [ ] ( t) = V πf t + φ + k υ ( t) c cos (.17) c c p m

28 . Phase modulation basics 15 The instantaneous phase Ø i of the carrier is ( ) t k m p c i υ φ φ + = (.18) where k p is the change in carrier phase per volt of modulating signal, called phase sensitivity (rad/volt). Ø c is usually 0. Defining β as the phase deviation, the max amount by which the carrier phase deviates from its unmodulated value, we get ( ) m p m p V k t k = = max υ β (.19) Substituting (.19) into (.17), the phase modulated signal can be expressed as ( ) ( ) [ ] ( ) [ ] t f t f V t f V k t f V t m c c m m p c c pm π β π π π υ cos cos cos cos + = + = (.0) Expanding the above equation with Fourier analysis, and using the Bessel function [38] to determine the spectrum of a phase modulated signal, we achieve ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] ( ) [ ] { } ( ) ( ) ( ) ( ) ( ) [ ] ( ) [ ] { } ( ) ( ) ( ) = 5 cos 5 cos 4 cos 4 cos 3 cos 3 cos cos cos cos cos cos π π π π β π π β π π π π β π π π π β π π π π β π β υ t f f t f f J V t f f t f f J V t f f t f f J V t f f t f f J V t f f t f f J V t f J V t m c m c c m c m c c m c m c c m c m c c m c m c c c c pm (.1)

29 16 Chapter. Basic concepts Fig..7 shows the Bessel function J n (β) versus β for n=0 to n=6. Fig..7: Bessel functions for n=0 to n=6 Some properties of the Bessel function can be discovered as follows: The higher side frequencies are insignificant in the PM spectrum when β is low. When β 0.5, only J 0 (β), J 1 (β) have a significant value. The power in a sinusoidal signal depends only on its amplitude and is independent of frequency and phase. It follows that the power in a PM signal equals the power in the un-modulated carrier P 1 = (.) PM V c

30 . Phase modulation basics 17 The total power in a PM signal is the sum of the power of the sidebands and the carrier power. Hence, for the 1-tone modulation, the total power can also be obtained by summing the power in all spectral components in the PM spectrum P PM 1 1 = = ( ) + Vc Vc J 0 β J n ( β ) (.3) n=1 Obviously, the power in the side frequencies is obtained only at the expense of the carrier power J ( ) ( β ) J n = n= 1 β (.4) Power contained in the carrier frequency and the first N pairs of side frequencies is given by r N N = J J n n= 1 ( ) + ( ) 0 β β (.5) Because the exact spectrum of the phase modulated signals is difficult to evaluate in general, formulas for the approximation of the spectra are very useful. As a rule-of-thumb, when N=β+1 β 1 1 = 0 + β + J J n = n= 1 ( β ) + ( β ) r (.6) Equation (.6) indicates that approximately 98% of the power of a phase modulated signal lies within the bandwidth covered by the first N=β+1 pairs of side frequencies. It is the minimum number of pairs of side frequencies that along with f c., account for 98% of the total PM power. Carson s bandwidth can be defined as BW c ( + ) f m = β 1 (.7) This formula gives a rule-of-thumb expression for evaluating the transmission bandwidth of PM signals; it is called Carson s rule [39]. It gives an easy way to compute the effective bandwidth of PM signals from power perspective. In later chapters, this method will be used to evaluate the effective bandwidth of the time multiplexed receiver.

31 18 Chapter. Basic concepts.3 Phased-array basics Phased-array antenna systems is one of the widely used multiple antenna systems in high frequency applications. In wave theory, a phased-array is a group of antennas in which the relative phases of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern of the array is reinforced in a desired direction and suppressed in undesired directions [40]. Comparing with a conventional single path antenna system, two of the main benefits that a phased-array can provide are signal to noise ratio (SNR) enhancement and interference suppression [41-47] as a result of beam-forming. A phased-array receiver consists of several signal paths, each connected to a separate antenna. Generally, radiated signal arrives at spatially separated antenna elements at different times. An ideal phased-array compensates for the time-delay difference between the elements and combines the signal coherently to enhance the reception from the desired direction, while rejecting emissions from other directions. The antenna elements of the array can be arranged in different spatial configurations. θ θ d S Fig..8: (a) Simplified phased-array system model. (b) Time and phase relation. Fig.8 (a) shows a simplified phased-array system model. For a plane wave, the signal arrives at each antenna element with a progressive time delay t as in Fig..8(b). This delay difference between two adjacent elements is related to their distance d and the signal angle of incidence θ by d sinθ t = (.8) c where c is the speed of light. While an ideal delay can compensate the arrival time differences at all frequencies, in narrow-band applications it can be approximated via other means. For a narrow-band signal, the amplitude and phase change slowly relatively to the carrier frequency. Therefore, we only need to compensate for the progressive phase difference

32 .3 Phased-array basics 19 π ϕ = β S = d sinθ (.9) λ Where φ is the electric phase difference between two adjacent channels; β is the phase constant; S is the distance difference for adjacent channel in the wave propagation direction; λ=c/f is the wave-length in the air. Assume that d= λ/, ϕ = π sinθ sinθ t = f (.30) For example, the incoming angle of 7. corresponds to an electrical phase shift of.5. From the above equation, we can also find the relation between φ and t as t ϕ = π (.31) T where Ts is the period of the propagation wave. Fig..8(b) shows the relation between time and phase. In a receiver chain, for a given modulation scheme, a maximum acceptable bit error rate (BER) translates to a minimum signal-to-noise ratio (SNR) at the base band output of the receiver (input of the demodulator). For a given receiver sensitivity, the output SNR sets an upper limit on the noise figure of the receiver. The noise figure (NF) is defined as the ratio of the total output noise power to the output noise power caused only by the source, as shown in (.11), which cannot be directly applied to multiport systems, such as phased-arrays. Consider the n-path phased-array system, shown in Fig..9. S in is the input signal power; N in is the input noise power; N 1 and N are the 1 st and nd stage added noise power, respectively; G 1 and G are the available power gain of the 1 st and nd stage, respectively; k is the antenna number; K is the number of antennas; Ø is the phase difference between two adjacent channels to compensate the phase difference introduced by angle of incidence θ. We assume here that the noise power N in and N 1 are equal for all channels. S

33 0 Chapter. Basic concepts S in N in S in 1 G 1 3Ø N 1 N in G 1 Ø S in N 1 G S out N in k G 1 Ø N N out S in N 1 N in K G 1 0 N 1 Fig..9: Simplified model for n channels phased-array Since the input signals are added coherently, taking into account the weighting factor for each channel when combiners are implemented in analog domain [48], then Sout KG1G S in = (.3) The antenna s noise contribution is primarily determined by the temperature of the object(s) at which it is pointed. When antenna noise sources are uncorrelated, such as in indoor environment, and also the front-end noise sources are uncorrelated, the output total noise power is given by N ( Nin + N1) G1G N G = (.33) out + Thus, compared to the output SNR of a single-path receiver, the output SNR of the array is improved by a factor between K and K, depending on the noise and gain contribution of different stages. The array noise factor can be expressed as F = K ( N + N ) in SNR = K SNR 1 G1G + N G KN G G in out in 1 (.34)

34 .3 Phased-array basics 1 which shows that the SNR at the phased-array output can be even larger than the SNR at the input if K>F. For a given NF, an n-array receiver improves the sensitivity by 10log(K) in decibels compared to a single-path receiver. For instance, an 8 element phased array can improve the receiver sensitivity by 9dB. P 0 At the main beam direction P 0 1 3Ø P 0 Ø P 0 k Ø P0 + 0 log K P 0 K 0 Fig..10: Simplified model of phased-array receiving system Phased-array can enhance the receiving signal power, as shown in Fig..10. Assume each antenna of a phased-array receives P 0 power form the main beam direction. After phase shift and combining, assuming no loss in between, the combined power in the main beam direction is P 0 +0log(K). An additional advantage of a phased array is its ability to significantly attenuate the incident interference power from other directions. In a single-chain receiver, the linearity performance reflects on the third order input intercept point (IIP3). It is in many cases dominated by the interferer instead of the desired signal. A phased-array receiver has the advantage of enhancing the desired signal by adding the path signals in-phase, and reject the unwanted interferer (from another angle) by adding the path signals out-of-phase. This can be expressed as SUM K j π fct j( k 1) ϕ j( k 1) γ ( ) (.35) s = A t e e e k = 1 Where s SUM is the signal at the output; A(t) is the amplitude of the incoming signal and f C is the carrier frequency; φ is the input signal electric phase difference (can be either desired or unwanted signal), and γ is the electric phase compensation (for desired signal) on each path and γ=ϖ*sinø; k is the antenna number; K is the number of antennas. Furthermore, assuming antenna spacing

35 Chapter. Basic concepts d=λ/ (λ is the signal wavelength), the space angle θ(deg) can be transferred to a phase difference by π ϕ = d sinθ = π sinθ (.36) λ Combining (.35) and (.36), and taking only the absolute amplitude of s SUM, the normalized array gain, A SUM, can be expressed as (for normalized signal amplitude, A(t)=1V) SUM K j( k 1) sin j( k 1) π sin (.37) k= 1 A = e e When K=1, it is a single antenna receiver without any directivity. Hence, the array gain is unity for all angles of incidence. When K 1, multiple antennas produce antenna patterns which are a function of K, desired viewing angle θ d, and un-desired viewing angle θ i. Assuming θ d =0, adjusting Ø to the desired signal results Ø=0. A SUM can be expressed in (.38), and plotted in Fig..11 with K=1,, 4, 8 as examples. A SUM, db K j( k 1) π sinθ = 0log e (.38) k = 1 Fig..11: Phased-array antenna gain patterns, when K=1,,4,8.

36 .3 Phased-array basics 3 Here, we define a suppression factor L that describes the power rejection for θ i relatively to the power at θ d ( n,θ, θ ) L = f (.39) i For example, assume K=4 and θ i =35 as shown in Fig..11, the suppression from the peak (K=4) is 1dB-(-5dB)=17dB, hence L= f(n=4, θ i =35, θ d =0 )=-17dB (note that L in terms of db is always a negative number, corresponding to a power loss or power gain smaller than one). d

37 4 Chapter. Basic concepts

38 C h a p t e r 3 3 Single and multipath receiver: a system approach There are many ways to categorize receiver architectures. One of them is to categorize them into single-path receiver and multi-path receivers. A multi-path receiver is composed of many single-path receivers, hence they have some properties in common. Nevertheless, multi-path gives another dimension of design freedom to the receiver structure: the spatial dimension. In other words, a multi-path receiver has more properties than a single-path receiver. In this chapter, we will discuss single- and multi-path receivers from a system point of view. We will start with single-path receiver analysis. As we know that a receiver chain can be separated into RF and ADC parts, at section 3.1, ADC parameters are translated into the RF domain, so that we can have a fair comparison/trade-off between them on system level. After that, the design trade-offs are discussed in section 3.. The discussions are based on noise and linearity. An optimization method is introduced in section 3.3 to optimize the system for different applications and purposes. The two categories of phased-array receivers: analog beam-forming and digital beam-forming are discussed in section 3.4 and 3.5, respectively. Both of them are first made equivalent to a single-path receiver, and then analyzed by the method in sections

39 6 Chapter 3. Single and multipath receiver: a system approach Section 3.6 introduces receiver structure that takes optimum advantage of both analog and digital beam-forming. Section 3.7 concludes this chapter. 3.1 Translating ADC parameters to RF domain The rapid growth of wireless communication has resulted in a shift of RF applications towards high frequencies. The increased bandwidth and dynamic range requires a systematic design strategy for RF receivers. RF system engineers are mainly focusing on the performance and power consumption of RF front-ends. The lack of a proper relation between RF blocks and ADC has led to the over-specifications of these blocks and a non-optimized system [49-58]. Fig. 3.1: Simplified receiver chain Fig. 3.1 shows a simplified receiver chain including both RF front-end and ADC, where the interferers cause the dominant distortion. RF front-ends are usually characterized by noise figure (NF), power gain, third order input intercept point (IIP3) and power consumption [59]. The established theory enables the calculation of overall NF and IIP3 in cascaded RF blocks through the transformation of NF and IIP3 of each individual block. An extension of this theory enables the optimization of the overall power consumption through proper dimensioning of the individual RF blocks [60]. However, the main obstacles to a systematic design strategy for overall optimization are the lack of: a proper translation of ADC parameters into RF domain; a proper design flow reflecting the relation between RF and ADC blocks; a set of variables, enabling the proper dimensioning of individual block performance.

40 3.1 Translating ADC parameters to RF domain ADC model Fig. 3. shows the simplified front-end and ADC model. The main task of the Nyquist filter and the VGA consists in reducing the dynamic range of the ADC by providing some filtering of the blocking signals and the adjacent channels interference, and adjusting the signal level to the input range of the ADC. Fig. 3.: Simplified front-end and ADC model The ADC component is modeled by two blocks: the non-linearity block and the ADC noise block. It is assumed that the transferred output signal has a unity gain, and no offset errors, compared to the input analog signal ADC noise In ADC design, the parameters of interest are peak-to-peak full scale voltage (v FS ), sampling frequency (f sample ), and number of bits (n). When noise is the product of quantization, the signal to quantization noise ratio (SQNR) of an ideal ADC with full scale sinusoid wave as input is given by SQNR=6.0n+1.76 [61]. Fig. 3.3 shows the ADC quantization mechanism, where q S is the ADC quantization noise in fundamental interval (f sample /). Without loss of generality, we assume here that the output of the ADC is a voltage

41 8 Chapter 3. Single and multipath receiver: a system approach v peak q s v FS v peak Fig. 3.3: ADC quantization mechanism In case of oversampling, the signal bandwidth (BW) is less than f sample /. Hence the ADC quantization noise in the signal bandwidth BW can be further reduced as a result of the process gain, which is indicated by f sample /(*BW). Fig. 3.4 shows the voltage relations. BW f sample BW SQNR v FS Fig. 3.4: Voltage relations in ADC design However, in practice, the ADC is not a stand-alone component; it is used in combination with the RF blocks in a receiver chain. From this perspective, assuming the input impedance of the ADC is 50Ω, the parameters of interest can be described as full scale input signal power 3 (P FS ), sampling frequency (f sample ), ADC signal to noise ratio (SNR ADC ), channel bandwidth (BW), and ADC noise factor (F ADC ). Fig. 3.5 shows the conceptual translation from ADC noise design parameters in volt to RF design parameters in mw. Note that this translation assumes a 50Ω matching at the input of the ADC, and the ADC noise factor (F ADC ) contains the contribution of quantization as well as thermal noise. 3 Assume a pure sine wave input

42 3.1 Translating ADC parameters to RF domain 9 BW f sample BW SQNR v FS f sample kt BW F ADC N ADC BW SNR ADC P FS Fig. 3.5: Conceptual translation of ADC noise parameters to RF domain It is more suitable to use effective number of bits (ENOB noise ) instead of n, because it includes both ADC quantization noise (Q noise) and thermal noise (T noise), assuming that quantization noise behaves the same as thermal noise and has no correlation with the signal. In this case, one can write: SNR ADC =6.0ENOB noise After proper derivation, the noise figure of the ADC, NF ADC, can be expressed as f sample NFADC = PFS, dbm 10log ( kt BW ) + 10log + SNR ADC, db BW 6.0ENOBnoise (3.1) With the help of (3.1), we can directly include ADC noise into cascaded noise calculations of receiver systems ADC non-linearity Non-linearity is the other major concern in ADC design. In a typical design, there are two parameters of interest. Firstly, the effective full scale range voltage (v FS,eff ), and secondly, the harmonic distortion. For simplicity, we limit our analysis to memory-less, time-variant systems and assume then 3 y( t) α x( t) + α x ( t) + α x ( ) (3.) 1 3 t

43 30 Chapter 3. Single and multipath receiver: a system approach Fig. 3.6 visualizes the non-linearity model of the ADC. vinput v h 1 v h v h3 Fig. 3.6: Non-linearity model of ADC where v input is the magnitude of the fundamental of the analog input spectrum, note that v input<v FS,eff.. v h1 is the magnitude of the fundamental at the output. v h and v h3 is the magnitude of the second and third harmonic at the output, respectively. In (3.), if v input =A, and x(t)=acosωt, then y( t) = α Acosωt + α A cos ωt + α A cos ωt αa 3α 3A αa α3a = + α1a + cosωt + cos ωt + cos 3ωt 4 4 v vh vh3 h1 (3.3) However, from RF system perspective, interferer signals often cause the dominant distortion (see Fig. 3.1). Thus the third order input intercept point IIP3 ADC can be used to describe the ADC global nonlinear property. IIP3 ADC is a function of the fundamental output interference signal (I out ), output third order intermodulation distortion product (D IM3,adc ). Considering the unity transfer of the ADC (G ADC =1), one can express IIP3 ADC as IIP3 = OIP3 ADC, dbm ADC, dbm IM = + = 1 3ADC, db 3 1 Iout, dbm Iout, dbm DIM 3, ADC, dbm (3.4) where OIP3 ADC is the ADC output 3 rd order intercept point, and (IM3 ADC ) -1 is the ratio between I out and D IM3,ADC. Fig. 3.7 shows intermodulation in an ADC system. The input two tone signals allocate in frequency f 1 and f, respectively. They pass through an ADC system with nonlinear

44 3.1 Translating ADC parameters to RF domain 31 property described in Fig. 3.6, and the output third order intermodulation product falls in frequency f 1 -f and f -f 1, respectively. v input v fund v IM 3, ADC Fig. 3.7: Intermodulation in an ADC system Similar to (3.3), v input =A. Assuming input x(t)=(a/)*(cosω 1 t+ cosω t), then 9 A y( t) = α1 + α3 A cosω1t + cosωt 4 v fund IM 3, ADC 3 ( ) 3 A + α3 cos ( ω ω1 ) t + cos( ω1 ω ) t + 4 v (3.5) From (3.3) and (3.5), we can find the relation between v h3 and v IM3,ADC as 3 3 A 3 v IM 3, ADC = α 3 = vh3 (3.6) 4 8 Hence, (3.4) can be re-written in terms of 3 rd order harmonic power as IIP3ADC, dbm = Iout, dbm H 3ADC, dbm 10 log (3.7) 8 where H3 ADC is the power of the ADC 3 rd order harmonics. To guarantee the integrity of the signal, two auxiliary parameters, P 1 and P are usually introduced.

45 3 Chapter 3. Single and multipath receiver: a system approach P 1 is the margin to the ADC full scale range power, for example DC offset and overloading behavior, which depends on the ADC architecture. P FS / P 1 indicates the ADC effective input full scale power, which is the counterpart of v FS,eff. P is the energy reduction from one tone input to two tone inputs (by each tone), which is usually half of voltage (6 db). Hence, P FS /( P 1 * P ) is the input interferer power (by each tone). Fig. 3.8 shows the conceptual translation from ADC non-linearity design parameters in volt to RF design parameters in dbm. Note that this translation assumes a 50Ω matching at the input of ADC. v h3 v FS, eff v FS 1 IM 3 ADC D IM 3, ADC ( = D ADC ) H 3 ADC Iout ( = I in ) P P 1 P FS OIP3 ADC ( = IIP3 ADC ) Fig. 3.8: Conceptual translated ADC non-linearity parameters to RF domain. In the following chapters, it is assumed that interference signals are the dominant causes for ADC distortion in the desired channel, which means that D IM3,ADC is the dominant distortion component. Moreover, D IM3,ADC is replaced by D ADC which means ADC distortion power. 3. Mapping ADC parameters to system design In many cases, the system performance is defined in terms of BER, which is a function of signal to noise and distortion ratio (SNDR). SNDR can be separated into signal to noise ratio (SNR) and signal to distortion ratio (SDR), in order to distinguish the contribution of noise and distortion, and to enable the possibility of a trade-off for an optimum performance. From this perspective, it is very important to analyze the impact of ADC noise and distortion on the

46 3. Mapping ADC parameters to system design 33 performance of the system SNR and SDR. Assuming the phases of the distortion components of different stages uncorrelated [6], the equivalent total noise and distortion power of the system can be formulated as (first order approach) N = N + N (3.8) tot, dbm ADC, dbm FE, db D = D + D (3.9) tot, dbm ADC, dbm FE, db where N tot,dbm is the equivalent total noise power of the system referred to ADC input; D tot,dbm is the equivalent total distortion power of the system referred to the ADC output; N FE,dB and D FE,dB are the noise and distortion contribution by the RF front-end referred to ADC input and output, respectively. Defining S ADC and S out as the signal power at the ADC input and output, one can formulate SNR and SDR as ( ) SNR = S N = S N + N (3.10) db ADC, dbm tot, dbm ADC, dbm ADC, dbm FE, db ( ) SDR = S D = S D + D (3.11) db out, dbm tot, dbm out, dbm ADC, dbm FE, db Combining equation (3.10) and (3.11) with the results achieved in previous sections, enables the embedding of the ADC into the overall system characterization as depicted in Fig The X1- axis is the ADC block noise parameters. It has been explained in Fig The Y1- axis is the ADC block non-linearity parameters. It has been explained in Fig The X- axis represents the signal and noise relation at the input of ADC on a system level. N ADC is the noise contribution of the ADC; N FE is the noise contribution by the RF front-end referred to the ADC input; N tot is the equivalent total noise power of the system referred to ADC input; SNR is the signal to noise ratio; S ADC is the input signal power; I ADC is the remaining input interferer power after the filter and the VGA. The Y- axis represents the signal and distortion relation at the output of ADC on a system level. I out is the output interferer level; S out is the output signal power; SDR is the signal to distortion ratio; D tot is the equivalent total distortion power of the system referred to the ADC output; D FE is the distortion contribution by the RF front-end referred to the ADC output;

47 34 Chapter 3. Single and multipath receiver: a system approach OIP3 ADC, dbm P P,dB P FS, dbm 1, db I out, dbm IM 1 3 ADC, db S out, dbm D tot, dbm SDRdB D FE, db H3 ADC, dbm D ADC, dbm D IM 3, ADC, dbm ( = ) N FE, db SNR db N N ADC, dbm tot, dbm S ADC, dbm I ADC, dbm 10 log ( kt BW ) NF ADC fsample 10log BW, SNR ADC db P FS, dbm IIP3 ADC, dbm Fig. 3.9: ADC to system power 4 (dbm) mapping for noise and distortion Assuming the ADC has a unity transfer as indicated by line A, we have S ADC =S out ; I ADC =I out ; IIP3 ADC =OIP3 ADC. Line B shows the power of the third order intermodulation product, which grows at three times the rate at which the main components increases, and we see that D ADC is generated from I ADC. From Fig. 3.9, we can rewrite SNR and SDR for the total system as ( ) SNRdB = SADC, dbm 10log kt BW + NFADC + NFE, db (3.1) ( ) SDR = S 3 P P P IIP3 + D db out, dbm FS, dbm 1, db, db ADC, dbm FE, db (3.13) 4 In this figure, to keep the 3rd order intermodulation product a straight line, we need to use dbm coordinate scale.

48 3.3 Receiver system optimization method 35 Equation (3.1) and (3.13) link system parameters (SNR, SDR) with ADC parameters (NF ADC, IIP3 ADC ). 3.3 Receiver system optimization method The predefined specifications of wireless standards are the starting point for the design strategy. Standards usually include: bandwidth of the signal (BW), signal to noise ratio (SNR) (derived from BER and modulation scheme), desired input signal power (S in ) and input interferer power (I in ) for intermodulation characterization. This allows us to determine the receiver total noise figure and total input intercept point, as NFtot = Sin, dbm SNRdB 10log( kt BW ) (3.14) IIP3 I S + SNR = + I (3.15) in, dbm in, dbm db tot, dbm in, dbm Furthermore, the type of ADC dictates P FS, P 1 and P, which in turn (P FS - P 1 - P ) fixes the interferer power level at the input of the ADC (I ADC ) Receiver signal flow diagram Optimizing the overall performance of the receiver chain demands a design flow, containing fixed parameters and variables. Fig represents such a flow diagram for receiver signal, noise and distortion.

49 36 Chapter 3. Single and multipath receiver: a system approach IIP3 ADC OIP3 ADC IIP3 FE IIP3 tot IADC P + P 1 P FS I o u t I max I in G FE S ADC S out N to t D to t S in D FE N to t, in N F E N FE F t o t D FE N ADC D ADC F FE F ADC kt BW Fig. 3.10: Receiver signal, noise and distortion power flow diagram This flow consists of three fronts: Antenna front, which is at the input of the receiver. IIP3 FE, IIP3 tot, and I in are non-linearity related parameters, where IIP3 FE and IIP3 tot are 3 rd order input intercept point of front-end and total receiver, respectively; I max is the adjacent channel interference power, I in is the in-band interference power (by each tone). S in is the minimum input signal power. N tot,in and N FE are noise related parameters, where N tot,in is the equivalent total receiver noise referring to the antenna; N FE is the equivalent front-end noise referring to the antenna. F FE and F tot are front-end and total receiver noise factor, respectively. After the LNA, the adjacent channel interference I max is processed by the filter and VGA. As a result, I max is amplified to the same power level as I in at the input of ADC. To simplify the later analysis, we only assume the presence of I in. ADC input front, which is at the input of the ADC. It is the same as X- axe in Fig ADC output front, which is at the output of the ADC. It is the same as Y- axe in Fig Note that P 1 is the margin to the ADC full scale range power, and P is the energy reduction from one tone input to two tone inputs (by each tone), which is usually 6dB (1/ of voltage).

50 3.3 Receiver system optimization method 37 From antenna to ADC input, the available power gain is represented by G FE. From ADC input to ADC output, it is assumed that the ADC has a unity transfer. From Fig. 3.10, N FE can be expressed as F G tot FE N FE = (3.16) FADC Utilizing the noise factor relation of a cascade (RF front-end plus ADC), and using equation (3.16), the noise factor of front-end and ADC can be derived in (3.17) and (3.18), respectively F FE 1 1 = Ftot 1 + N (3.17) FE GFE F ADC F tot FE = (3.18) N G FE As expected, we can see that F FE has a direct 5 relation with N FE, and F ADC has an inverse 6 relation with N FE. Keeping F tot, G FE constant, adjusting N FE can result in the trade-off between front-end and ADC noise. Similarly, from Fig. 3.10, D FE can be expressed as IIP3 ADC D = 3 FE (3.19) IIP tot GFE Through the cascade relations of IIP3 and equation (3.19), the 3 rd order input intercept point of front-end and ADC can be derived in (3.0) and (3.1), respectively IIP IIP3 1 1 D tot 3 FE = (3.0) FE IIP3 = IIP3 G D (3.1) ADC tot FE FE It shows that IIP3 FE has an inverse relation with D FE, and IIP3 ADC has a direct relation with D FE. Keeping IIP3 tot, G FE constant, adjusting D FE can result in the trade-off between 5 With direct relation, we mean when NFE increases, FFE also increases. 6 With inverse relation, we mean when NFE increases, FADC decreases

51 38 Chapter 3. Single and multipath receiver: a system approach front-end and ADC linearity. Instead of tuning four parameters (F FE, IIP3 FE, F ADC, IIP3 ADC ) to achieve system optimization, we can now reduce to two tuning parameters ( N FE, D FE ), and it simplifies the system design Optimization method Two variables, N FE and D FE, can be used to trade-off between RF front-ends and ADC to achieve the system requirements. These variables enable: the trade-off between the RF front-end and ADC performance. the adaption of RF front-end and ADC performance for different system specifications. If the functions of these variables versus power consumption of their described blocks are given, they further more enable: the trade-off between RF front-end and ADC performance for minimum system power consumption. the comparison of individual block with different designs or different technologies, to find minimum system power consumption. The impact of the choice between different scenarios on the system power consumption can be investigated through the following relation [63]: P sys IIP3 IIP3 FE ADC = PC, FE + PC, ADC (3.) N FE N ADC where P C,FE and P C,ADC by definition denote the power coefficient of the front-end and ADC, respectively. Fig shows the system design flow chart of the above presented method.

52 3.4 Analog beam-forming 39 Fig. 3.11: System design flow chart 3.4 Analog beam-forming Depending on the location where the required phase shifters are placed, the beam-forming of a phased-array can be classified as RF, LO, IF or digital beam-forming. In this section, we take the IF beam-forming architecture as an example. Fig. 3.1(a) shows a phased-array receiver in which signal and noise power level at the antenna inputs are S in and N FL ( FL stands for floor ), respectively. The front-end block includes LNA and mixer. To simplify the analysis, we assume the filter and VGA are ideal and they amplify the adjacent channel interference to the same power level as the in-band interference at the input of the ADC.

53 40 Chapter 3. Single and multipath receiver: a system approach G FE N FL N FE G FE N FL N FE N ADC G = 1 ADC N FL N FE G FE G FE N FL N FE 1 N FL K 1 N FE K K GFE N ADC G = 1 ADC Fig. 3.1: (a) Analog phased-array receiver on block level. (b) Equivalent single-path structure for (a) regards noise and gain. The front-end (FE) equivalent noise power (N FE ) is the noise power referred to the input. The front-end gain (G FE ) enlarges the signal as well as the noise. The analog to digital converter (ADC) converts the analog signal into the digital domain, but also adds quantization noise (N ADC ). Assuming a unity gain ADC and a lossless and noise-free phase shifter and combination of signal and noise from each path, at point A, the correlated signals from all antenna inputs are added in voltage, nevertheless, the uncorrelated noise from each path are added in power 7, taking into account the weighting factor for each channel when combiners are implemented in analog domain, yielding S = S ( K G ) (3.3) A in FE 7 Assuming the distance between adjacent antenna elements is equal to λ/, so the antennas are decoupled with each other. Hence the thermal noise can be considered as un-correlated.

54 3.4 Analog beam-forming N = A ( N + FL N FE ) G = FE ( N FL N FE ) ( K GFE ) K + K (3.4) From (3.3) and (3.4), we are able to project phased-array receiver in Fig. 3.1(a) into an equivalent single-path structure in Fig. 3.1(b). The equivalent values for N FL, N FE and G FE are (1/K) N FL, (1/K) N FE and K G FE, respectively. All the blocks after point A are maintained. Note that K G FE consists by two parts, antenna array gain K, and front end gain G FE. From Fig. 3.1(b), we can derive the input referred total noise power as N = N + N + N tot, in FL FE ADC K K K GFE (3.5) Hence, the total noise factor (F tot ) of the phased-array receiver is F tot Ntot, in 1 N FE 1 N = = 1+ + N K N K G N ADC FL FL FE FL (3.6) The equivalent Friis noise equation for the phased-array receiver is F tot 1 1 FADC 1 = FFE + (3.7) K K G FE where F FE and F ADC represent noise factor of the front-end and ADC, respectively. It is obvious that thanks to the antenna array gain, both front-end and ADC input referred noises are reduced.

55 4 Chapter 3. Single and multipath receiver: a system approach N tot N tot, in K G FE N FE 1 N FE K 1 K F FE F tot FADC N ADC kt BW Fig. 3.13: Analog phased-array noise power flow diagram A design flow for a single-path receiver which indicates two variables that can be used for the trade-off between RF and ADC blocks was introduced in Fig Similarly, Fig. 3.1(b) is the equivalent single-path structure for an analog phased-array receiver, so applying the same design flow for Fig. 3.1(b), we can generate the analog phased-array noise power (mw) flow diagram in Fig The difference is that N FE, F FE, and G FE are replaced by (1/K)* N FE, (1/K)* F FE, and K* G FE, respectively. At the antenna front, number K indicates the system has K antennas. Before the ADC input front, the dashed line Analog Combine means that the mutipath input signals are combined at this place, and form only one path further on. Similar to (3.16), N FE in Fig can be expressed as F K G tot FE NFE = (3.8) FADC Combining (3.7) and (3.8), the noise factor of front-end and ADC can be derived in (3.9) and (3.30), respectively F FE 1 1 = K Ftot 1 + NFE G FE (3.9) F ADC = F tot K G N FE FE (3.30)

56 3.4 Analog beam-forming 43 F FE has a direct relation with N FE, and F ADC has an inverse relation with N FE. Keeping F tot, G FE, and K constant, adjusting N FE can result in the trade-off between front-end and ADC noise. IIP3 ADC IIP3 FE IIP3 tot K G FE L I ADC I ou t I in D tot D FE D FE D ADC kt BW Fig. 3.14: Analog phased-array distortion power flow diagram Similar to Fig. 3.13, we can generate the phased-array distortion power (mw) flow diagram in Fig Compared with Fig. 3.10, G FE is replaced by K*G FE *L, where L is the power rejection factor in (.39). After analog combination, the distortion power from K channels is added together. Taking into account the weighting factor during analog combination, the combined distortion power is denoted by D FE. Assuming interferers power I in dominate the receiver non-linearity performance, the equivalent Friis linearity equation for a phased-array is D FE in Fig can be expressed as 1 1 K GFE L = + (3.31) IIP3 IIP3 IIP3 tot FE ADC IIP3 ADC DFE = IIP3tot K GFE L (3.3) Combining (3.31) and (3.3), the IIP3 FE and IIP3 ADC can be derived in (3.33) and (3.34), respectively

57 44 Chapter 3. Single and multipath receiver: a system approach IIP3 FE IIP3tot = (3.33) 1 1 D FE IIP3 = IIP3 K G L D (3.34) ADC tot FE FE It shows that IIP3 FE has an inverse relation with D FE, and IIP3 ADC has a direct relation with D FE. Keeping IIP3 tot, G FE, and L constant, adjusting D FE can result in the trade-off between front-end and ADC linearity. Fig and 3.14 can be combined in Fig. 3.15, which shows the signal, noise and distortion power (mw) flow of an analog phased-array receiver. IIP3 FE IIP3 ADC IIP3 tot K G FE L I ADC I o u t I in SADC S out K G FE N tot S in N tot, in N FE D tot 1 N FE K 1 F FE K F tot D FE FADC N ADC D FE DADC kt BW Fig. 3.15: Analog phased-array signal, noise and distortion power flow diagram Note that in Fig. 3.15, after the dashed line Analog Combination, the flow is the same as the single-path flow shown in Fig In brief, there are two types of power flow in Fig. 3.15,

58 3.5 Digital beam-forming 45 The flow of the interference signal from I in to I ADC, suppressed due to the power rejection factor L. The flow of the desired signal from S in increased to S ADC, due to signal addition in voltage domain. 3.5 Digital beam-forming With digital beam-forming (DBF), a signal from each channel is carried from antenna to digital domain, where the beam-forming algorithms are implemented. The flexibility of beam-forming algorithms is its main advantage. As shown in Fig. 3.16(a), a DBF combines the signal in the digital domain, after the ADC. The front-end block includes LNA and mixer. To simplify the analysis, we assume the filter and VGA are ideal and they amplify the adjacent channel interference to the same power level as the in-band interference at the input of the ADC. NFL N FE G FE N ADC G FE N FL N FE N ADC G FE N FL N FE N ADC G FE N FL N FE N ADC 1 N FL K 1 N FE K K G FE N ADC K Fig. 3.16: (a) Digital phased-array receiver on block level. (b) Equivalent single-path structure for (a) regards noise and gain.

59 46 Chapter 3. Single and multipath receiver: a system approach At point B, the signal is added in voltage and noise is added in power 8. The total output signal power, S B, and noise power, N B, can be formulated as S = S K G = S ( K G ) K (3.35) B in FE in FE ( ) N = N + N K G + N K B FL FE FE ADC 1 1 = NFL + NFE ( K GFE ) + N ADC K K K (3.36) From (3.35) and (3.36), we are able to project the phased-array receiver in Fig. 3.16(a) onto an equivalent single-path structure in Fig. 3.16(b). The equivalent values for N FL, N FE and G FE are (1/K) N FL, (1/K) N FE and K G FE, respectively. From Fig. 3.16(b), we can derive the input referred total noise power as N = N + N + N tot, in FL FE ADC K K K GFE (3.37) Hence, the total noise factor (F tot ) of the phased-array receiver is F tot Ntot, in 1 N FE 1 N = = 1+ + N K N K G N ADC FL FL FE FL (3.38) The equivalent Friis noise equation for phased-array is F tot = F + 1 ADC FFE K GFE 1 (3.39) where F FE and F ADC represent noise factor of the front-end and ADC, respectively. It is obviously that thanks to the antenna array gain, both front-end and ADC input referred noises are reduced. 8 Assuming the distance between adjacent antenna elements is equal to λ/, so the antenna is decoupled with each other. Hence the thermal noise can be considered as un-correlated. Also assuming thermal noise is equal to or larger than quantization noise, as it then de-correlates the quantization noise of various ADCs.

60 3.5 Digital beam-forming 47 MULTI ANTENNA ADC INPUT ADC OUTPUT K K K K G FE N tot N tot, in 1 N FE K 1 F FE K F tot N FE K F ADC K N ADC kt BW Digital Combination Fig. 3.17: Digital phased-array noise power flow diagram Based on the equivalent single-path structure for digital phased-array shown in Fig. 3.16(b), we can generate the phased-array noise power (mw) flow diagram in Fig Comparing with Fig. 3.10, the difference is that N FE, F FE, and G FE are replaced by (1/K)* N FE, (1/K)* F FE, and K * G FE, respectively. At the antenna, ADC input, and ADC output front, number K indicates the system has K antennas. Noise of ADC at ADC input front is the sum of ADC noise from K channels, denote by K*N ADC and K*F ADC. After the ADC output front, the dashed line Digital Combination means that the multipath input signals are combined at this place, and forms only one path further on. Similar to (3.16), N FE can be expressed as F K G tot FE NFE = (3.40) FADC Combining (3.39) and (3.40), the noise figure of front-end and ADC can be derived in (3.41) and (3.4), respectively F FE 1 1 = K Ftot 1 + N FE G FE (3.41) F ADC = F tot K G N FE FE (3.4)

61 48 Chapter 3. Single and multipath receiver: a system approach One can see that NF FE has a direct relation with N FE, and NF ADC has a reverse relation with N FE. Keeping NF tot, G FE, and K constant, adjusting N FE can result in the trade-off between front-end and ADC noise. IIP3 FE I ADC IIP3 ADC K L IIP3 tot I in G FE I o u t D tot K D FE D FE kt BW K D ADC Fig. 3.18: Digital phased-array distortion power flow diagram Similar to Fig. 3.17, we can generate the phased-array distortion power (mw) flow diagram in Fig From ADC input to Digital Combine front, interference signal power is suppressed by a factor of K *L, where L is the power rejection factor in (.39). Both front-end and ADC distortion power are added together from K channels, denoted by K*D FE and K*D ADC, respectively. Assuming interferers power I in dominant the receiver linearity performance, equivalent Friis linearity equation for phased-array is D FE in Fig can be expressed as 1 K K GFE = + (3.43) IIP3 IIP3 IIP3 tot FE ADC IIP3 ADC 1 DFE = IIP3tot GFE K (3.44) Combining (3.43) and (3.44), the IIP3 FE and IIP3 ADC can be derived in (3.45) and (3.46), respectively

62 3.5 Digital beam-forming 49 IIP3 FE = IIP3tot K (3.45) 1 1 D IIP3 = IIP3 G K D (3.46) ADC tot FE FE It shows that IIP3 FE has a reverse relation with D FE, and IIP3 ADC has a direct relation with D FE. Keeping IIP3 tot, and G FE constant, adjusting D FE can result in the trade-off between front-end and ADC linearity. Fig and 3.18 can be combined in Fig. 3.19, which shows the signal, noise and distortion power (mw) flow of a digital phased-array receiver. Note that beam-forming is placed in digital domain, hence the suppression factor L is in the right part of the plane. IIP3 FE IIP3 tot G FE I ADC IIP3 ADC K L I ou t I in K G FE S ADC S out S in N tot N tot, in N FE D tot 1 K N FE 1 F FE K kt BW F tot K D FE K N ADC K F ADC DFE K D ADC Fig. 3.19: Digital phased-array signal, noise and distortion power flow diagram

63 50 Chapter 3. Single and multipath receiver: a system approach There are two types of power flow in Fig. 3.19, The flow of interference signal from I in increase to I ADC with single-path front-end gain G FE. Then from I ADC suppressed to I out due to power rejection factor L. The flow of desired signal from S in increased to S out, due to signal added in voltage. 3.6 General case of beam-forming As explained in the previous sections, beam-forming can be implemented in the analog domain or digital domain. Analog beam-forming (ABF) combines the signal from the antennas in the analog domain and relaxes the dynamic range of the following receiver blocks. However, the phase information from each antenna is also lost after the combination. On the other hand, digital beam-forming (DBF) conveys signal amplitude and phase into the digital domain, which provides more flexibility and control of the signal in terms of applying various algorithms. Nevertheless, the hardware replication, especially the power hungry ADCs, will increase the overall power consumption, area and cost. For a more general case of beam-forming, instead of either analog or digital beam-forming, one can think of a way in between, which means beam-forming is partly done in analog domain, and partly done in digital domain. In section 3.4, Fig shows a signal, noise and distortion power flow diagram of an analog phased-array system, where the signals combine occurs before ADC. In section 3.5, Fig shows a power flow diagram of a digital phased-array system, where the signals combine occurs after ADC. Using properties from both Fig and 3.19, one can design a power flow diagram for general case beam-forming, which is shown in Fig. 3.0.

64 3.6 General case of beam-forming 51 IIP3 FE IIP3 ADC IIP3 tot I in β G 1 FE β1 GFE L I o ut S out N tot S in N tot, in N FE D tot 1 N FE K 1 F FE K F tot β DFE β FADC β N ADC D FE β DADC kt BW Fig. 3.0: Signal, noise and distortion power flow diagram of a general beam-forming system One can notice that except for parameters that has been explained previously, there are two extra parameters: β 1 and β. They indicate the flexibility of the beam-forming system. Analog Beam-forming Digital Beam-forming β 1 K K β 1 K Table 3.1: Parameter difference with analog and digital beam-forming As shown in Table 3.1, when β 1 =K and β =1, the system is analog beam-forming system, which is the same as Fig. 3.15; When β 1 = K and β =K, the system is digital beam-forming system, which is the same as Fig. 3.19, When K<β 1 < K and 1<β <K, the system is partly analog, and partly digital beam-forming. On system design level, β 1 and β can be used as another design dimension to perform system optimization with various applications.

65 5 Chapter 3. Single and multipath receiver: a system approach 3.7 Conclusion This chapter has presented system approaches to both single- and multi-path receivers. With single-path receiver, a design flow for trade-off between RF front-end and ADC block performance by translating ADC parameters into RF domain is introduced. This approach indicates two variables, N FE and D FE, for achieving optimum dynamic range in a receiver chain. Associating these variables to the power consumption enables the trade-off between RF and ADC block for minimum overall power consumption. After that, two types of multi-path receiver, namely, analog beam-forming and digital beam-forming are analyzed as a single chain receiver with their equivalent model. It started with analyzing the difference between phased-array and single-chain receivers from noise and linearity perspectives and the result indicates that for both cases, the total noise figures are reduced due to non-correlated noise adding, and the total IIP3 are increased due to interference cancellation. At last, this chapter provided a general case of beam-forming analysis, and two parameters β 1 and β are introduced to indicate the flexibility of the beam-forming. When K<β 1 < K and 1<β <K, the system is partly analog, and partly digital beam-forming. On system design level, β 1 and β can be used as another design dimension to perform system optimization with various applications.

66 C h a p t e r 4 4 Two-step beam-forming: multiplexing architecture A multiplexing phased-array architecture combines K antenna paths into one path by dividing the signal into different time slots. The signals from the antennas are received in rapid succession, one after the other, each using its own time slot. After mixing, filtering, and analog to digital conversion, the multiplexed signal is de-multiplexed in the digital domain, and digital phase shifters are applied to compensate the phase differences for each channel. In the end, signals are combined again in the digital domain, and the desired signal is picked up by means of digital filtering. This chapter presents the concept of multiplexing phased-array architecture and its major properties. The detailed analysis of this architecture is discussed in chapter 5 and Multiplexing architecture introduction Fig. 4.1 shows a flexible phased-array receiver architecture matches with Fig. 1.. The analog combination block is implemented by an K:1 multiplexer, which chops up the channel into se- 53

67 54 Chapter 4. Two-step beam-forming: multiplexing architecture quential time slices. As such, the phase information from each channel is carried to the digital domain. The analog signal processing block is implemented by a mixer and a band-pass filter. In digital domain, the combined signal is separated again by a de-multiplexer which is synchronized with the multiplexer. After that, the phase difference of each channel is compensated by a digital phase shifter, where the beam-forming algorithms can be applied. f S BWana log BWdigital f MUL Fig. 4.1: Multiplexing system structure The major properties of the multiplexing system can be summarized as the following: No analog phase shifter is implemented at the RF front-end. The phase shifter is only implemented in digital domain. The multiplexer can be seen as a beam-forming component in itself, because the clock generator generates switching pulses with phase delays. But, assuming the analog filter is not present, then the de-multiplexer in digital domain compensates the previous generated phase delays, and the original input phase information are preserved for the digital phase-shifter. The analog band pass filter is used to relax the following ADC design in two aspects. Firstly, ADC bandwidth is relaxed. The band pass filter bandwidth will determine the ADC bandwidth. And secondly, it creates a coarse spatial filter (because of the combination usage with the multiplexer) which filters out the spatial interferences, to relax the ADC dynamic range. The details will be explained in chapter 5. The digital phase shifter provides the flexibility to compensate the non-ideal phase influences in the analog path, and formalize the final array patter in digital domain with high speed and accuracy.

68 4.1 Multiplexing architecture introduction 55 Fig. 4. shows the simplified model for multiplexing structure to explain the frequency spectrum transformation from point A to B, where θ is the angle of incidence, BW analog is the analog filter bandwidth, and Ø is the digital phase compensation. Point A and B are located right after multiplexer and de-multiplexer, respectively. At point A, the frequency spectrum for θ=0 has only one component located in the fundamental tone (n=0). The frequency spectrum for θ 0 has multiple components located throughout the spectrum. Depending on the condition applied to parameters BW analog and Ø, the spectrum at point B for different angle of incidence behaves differently. The detailed explanation of this transformation will be explained in chapter 5. θ Ø θ=0 k A BWanalog k Ø Ø B BWdigital K K 0 θ=0 Ø=θ n=0 Ø θ n=0 θ 0 BW analog = Ø=θ n=0 BW n=0 Fig. 4.: Simplified model for multiplexing structure to explain the frequency spectrum transformation from point A to B. The time division multiplexing phased-array receiver uses a clock controlled multiplexer to combine K paths into one. The switch-driving waveform is shown in Fig At time slot one, channel one is connected, and all other channels are disconnected. At time slot two, channel two is connected, and all other channels are disconnected, etc. The time slot for each channel is designed to be equal.

69 56 Chapter 4. Two-step beam-forming: multiplexing architecture τ TS Fig. 4.3: Switch driving waveform for multiplexing system In Fig. 4.3, τ represents the duration for each time slot, and T S represents one period in which all the channels have been connected once. We have TS = K τ (4.1) 1 K fmul = = = K fs (4.) τ T To recover the signal from each path correctly in the digital domain, the sampling rate for each path (f S ) must fulfill the Nyquist sampling theory [64] S fs > BW (4.3) where BW is the single side bandwidth of the incoming modulated signal. As a result, the multiplexer sampling rate f MUL can be expressed as f MUL = K f > K BW (4.4) S

70 4. Spatial to frequency mapping 57 which means that the larger the signal bandwidth BW, or the larger the antenna number K, the faster the sampling speed f MUL. On the other hand, for a dedicated technology, the sampling speed f MUL has a upper limit, which also limits the incoming signal bandwidth when K is fixed, or limits the total antenna number if the incoming signal bandwidth BW is fixed. 4. Spatial to frequency mapping The phased-array multiplexing architecture can achieve spatial domain to frequency domain mapping in the following way: In the spatial domain, the angular information θ (in degrees) at the antenna front is translated to a wave-front time delay t (in second) between adjacent channels. In time domain, the time delay t can be modeled (assuming narrow band) as a waveform phase difference φ (in rad) between adjacent channels. The multiplexer is acting like a kind of phase modulation. Through the K:1 multiplexing, an input signal with phase difference φ is modulated to the carrier. Using Fourier transform, the phase modulated signal is presented in the frequency domain with a unique frequency pattern. The detailed spatial domain to frequency domain mapping is explained in chapter Two steps of spatial filtering The phased-array multiplexing architecture can achieve two steps of spatial filtering in the following way: The coarse spatial filtering is realized by the analog band-pass filter as shown in Fig Because of the unique mapping from spatial to frequency domain, a filter in frequency domain can result in a filter in spatial domain. This filter is used to filter out the spatial interferences far away from the desired angle of incidence, to relax the specification requirement for the following ADC. Note that it is called coarse spatial filtering, because it is a coarse-selectivity. The final spatial filtering is realized after the digital band-pass filter as shown in Fig It is the place where the final array pattern is formed. After de-multiplexer and phase-shifter,

71 58 Chapter 4. Two-step beam-forming: multiplexing architecture the achieved final array pattern is similar to a conventional phased-array pattern. Note that the final selectivity can only be applied within the region that is defined by the coarse-selectivity. The detailed coarse and final spatial filtering is explained in chapter 5. to Phased-array analog and digital co-design As previously explained, the design of the phased-array multiplexing architecture can be separated in two parts: the coarse spatial filtering in analog domain, and the final spatial filtering in digital domain. Hence, the phased-array functionality is achieved by a co-design in the analog and digital domain with different design focus. In the analog part, the focus of the design is the coarse spatial filtering bandwidth. If the bandwidth is too small, the final array pattern in the digital domain cannot be achieved. (Note that the final selectivity can only be applied within the region that is defined by the coarse-selectivity.) If the bandwidth is too large, the coarse-selectivity is not effective, and the ADC design specification cannot be relaxed, because of the interference. Hence it is a trade-off, and it is determined by the number of antennas K, the analog filter bandwidth BW a, and the switching frequency f S. In the digital part, the focus of the design is on the digital beam-steering speed and accuracy. It is determined by the implementation of the digital phase-shifter. The idea of phased-array analog and digital co-design is to make both analog and digital designs programmable, so that we can achieve phased-array functionality with more flexibility. 4.5 Generalized phased-array system design With a programmable phased-array structure, the separation between analog and digital beam-forming is not so sharp anymore. Besides the phase-shifter, we can take more design parameters into considerations, so the phased-array functionalities can be achieved partly in analog and partly in digital domain. In chapter 3.6, a generalized beam-forming model is presented. The phased-array multiplexing architecture is one of the realizations of such a generalized beam-forming model. From interference point of view, the array pattern is partly formed in analog and partly in digital domain.

72 4.5 Generalized phased-array system design 59 From noise point of view, in analog domain, the multiplexing phased-array has a similar structure as analog phased-array, in terms of K:1 combination. Hence the noise behavior is also similar to a analog phased-array. But with such a noise cost, we still keep the flexibility to perform the final phase-steering in the digital domain. The detailed flow diagram of a multiplexing phased-array is presented in chapter 6.6.

73 60 Chapter 4. Two-step beam-forming: multiplexing architecture

74 C h a p t e r 5 5 Multiplexing architecture, ideal behavior Fig. 4.1 shows the block diagram of a multiplexing phased-array receiver. The signal is processed in the following different steps: analog switching, analog combining, analog mixing, analog filtering, AD conversion, digital switching, digital phase shifting, digital combining, and in the end filtering. In this chapter, we will mathematically analyze this architecture in detail. Section 5.1 discusses the architecture upto the first combination which is the analog combination. The properties of the combined signal will be discussed using traditional phase modulation theory. Based on the result, a new coefficient function D n will be introduced in section 5. to explain the properties of the combined signal. Based on the properties of the combined signal, we introduce a new concept, which is a frequency to space filtering transformation. Section 5.3 discusses the digital part of the architecture. A mathematical analysis is applied to the digital de-multiplexing and phase shifting. After the second combination, in digital domain, the array pattern of the multiplexing architecture is simulated in section 5.4. Section 5.5 concludes what has been discussed in this chapter. 61

75 6 Chapter 5. Multiplexing architecture, ideal behavior 5.1 Analog multiplexing As shown in Fig. 4.1, the multiplexing phased-array architecture starts with transferring signals from multiple channels into one channel. This process can be separated into two steps, namely switching and combining. In this section, we will first introduce the idea of a pulse modulated phased-array signal of a single channel, and then extend the model into multiple channels and the combination of them Properties of the switching signal Switching is a fundamental part of a multiplexing architecture. In time domain, the switching signal can be represented by a square wave, as shown in Fig. 5.1, where T S =1/f S is the period of the pulse train; t S is the starting time delay of the pulse; α 1 and α are the positive and negative amplitude, respectively; τ is the pulse width of the pulse. u( t) α 1 τ 0 α t S t T S Fig. 5.1: Switching signal In one period [0, Ts), u(t) can be expressed as α t < t S u( t) = α 1 ts t < t S + τ (5.1) α ts + τ t < TS 0

76 5.1 Analog multiplexing 63 As we know, this waveform can be represented over (-, + ) by the complex exponential Fourier series as [65] u n= jn πfst ( t) = cne (5.) n= where n is the harmonic order number, f S =(1/T S ), and the complex Fourier coefficients c n can be expressed in two different situations, for n=0, c 0 1 = T 1 = T = S S ( t ) ( α α ) 1 0 T S T t 0 S u S α dt dt + τ + α t + τ t S S α 1 dt + T S t + τ S α dt (5.3) and for n 0, 1 ( ) TS jn π f S t c n = u t e dt T 0 S t S t S + τ T jn π f S ( 0 ) S t jn π f 1 S t jn π f S t α e dt α e dt α e dt t t + τ 1 = + + T S S S α α n π (5.4) ( τ ) 1 jnπ f S t S + = sin ( π τ ) e n f Substituting c n from (5.3) and (5.4) into (5.), u(t) can be further expressed as S u( t) = = n= 0 c n e jn πf St + n= n= ( α1 α ) τ α1 α sin( n πf Sτ ) jn πf S ( ts + τ ) + α + e T S c n n= n 0 e jn πf St π n= n 0 n e jn πfst (5.5) Fig. 5. shows the amplitude part of the frequency spectrum of u(t), for the positive part of the frequency axis.

77 64 Chapter 5. Multiplexing architecture, ideal behavior f MUL fs f S TS fs τ T S fs τ Fig. 5.: Amplitude part of the frequency spectrum of u(t). At each integer multiples of harmonic T S /τ, the envelope of u(t) drops to zero Pulse modulation According to communication theory [66], any physical band-pass waveform can be represented by { ( ) e } j π f C m t t s( t) = Re (5.6) Where Re{.} denotes the real part of {.}, m(t) is called the complex envelope of s(t), and f C is the associated carrier frequency. In a phased-array receiving system, the signals arriving in each channel are the original signal with different phase shifts. The signals received by the k-th antenna element can be written as { ( ) j f t+ ( k 1) } C s ( t) = Re m t e π ϕ (5.7) k where φ is the differential carrier phase change between two consecutive antenna elements. The value of φ (rad) can be written in the form π ϕ = d sin ( θ ) = π sin ( θ ) (5.8) λ

78 5.1 Analog multiplexing 65 where d is the distance between two adjacent antennas, and assuming d=λ/; λ is the wavelength of the incoming signal; θ is the incoming space angle in degrees. Furthermore, in a multiplexing phased-array receiving system, the signal in each channel is modulated by a pulse function u(t) which is described in equation (5.5). The behavior model of this modulation is shown in Fig jπ fct Re m( t) e u1( t) Re ( ) j π fct + j ϕ m t e u( t) ( 1) Re ( ) j π fct + j k ϕ m t e uk ( t) ( 1) Re ( ) j π fct + j K ϕ m t e uk ( t) Fig. 5.3: Model of multiplexing phased-array pulse modulation From Fig. 5.3, in general situation, the modulated signal in the k-th channel can be expressed as ( ) x t m t e u t j π fct+ j( k 1) ϕ k ( ) = Re k ( ) [ π ϕ] n= = m( t) cos f t + ( k 1) c e C n= n, k jn π fst 1 n= n= ( ) j π fct j( k 1) ϕ jn π fst j π fct j( k 1) ϕ jn π fst = m t e e cn, ke + e e cn, ke n= n= positive frequency negative frequency (5.9) where c n,k is the complex Fourier coefficients for the k-th channel. In the frequency domain, the modulated signal has both positive and negative frequencies. Here, we consider only positive frequencies. Substituting c n from (5.3) and (5.4) into (5.9), x k (t) positive can be expressed as

79 66 Chapter 5. Multiplexing architecture, ideal behavior 1 xk ( t) = m( t) e e c e positive j π fct n= j( k 1) ϕ n, k jn π fst n= ( ) α α τ = + = 1 ( ) j π fct j ( k 1) ϕ 1 k m t e e α ( n 0) TS n= 1 ( 1) 1 (, ) ( ) π C j k ϕ α α jn π f sin S ts k + τ k + m t e e ( n π fsτ k ) e e n= nπ n 0 j f t jn π fst (5.10) ( n 0) The above equation can be expanded into different frequency components.

80 5.1 Analog multiplexing 67 Table 5.1 lists the components until the n=±4 harmonic. Number Frequency n=0 f C Component ( α α ) τ k j 1 ( ) 1 j( k 1) ϕ m t + α e e TS π fct 1 α α m ( t ) sin π fsτ k e e π 1, n=1 f C +f S ( ) 1, n= f C +f S ( ) j ( k 1) ϕ π fsts k π fsτ k j π ( fc + fs ) t 1 α α m ( t ) sin π fsτ k e e π 1, n=3 f C +3f S ( ) j ( k 1) ϕ 4π fsts k π fsτ k j π ( fc + fs ) t 1 α α m ( t ) sin 3 π fsτ k e e 3π 1, n=4 f C +4f S ( ) j ( k 1) ϕ 6π fsts k 3π fsτ k j π ( fc + 3 fs ) t 1 α α m ( t ) sin 4 π fsτ k e e 4π 1, n=-1 f C -f S ( ) j ( k 1) ϕ 8π fsts k 4π fsτ k j π ( fc + 4 fs ) t 1 α α m ( t ) sin π fsτ k e e π 1, n=- f C -f S ( ) j ( k 1) ϕ + π fsts k + π fsτ k j π ( fc fs ) t 1 α α m ( t ) sin π fsτ k e e π 1, n=-3 f C -3f S ( ) j ( k 1) ϕ + 4π fsts k + π fsτ k j π ( fc fs ) t 1 α α m ( t ) sin 3 π fsτ k e e 3π 1, n=-4 f C -4f S ( ) j ( k 1) ϕ + 6π fsts k + 3π fsτ k j π ( fc 3 fs ) t 1 α α m ( t ) sin 4 π fsτ k e e 4π j ( k 1) ϕ + 8π fsts k + 4π fsτ k j π ( fc 4 fs ) t Table 5.1: Component expansion of the k-th channel pulse modulated signal Each frequency component is uniquely defined, and can be identified by four different properties: frequency component, harmonic number, amplitude, and phase. Closely investigating which parameters of the square wave (Fig. 5.1) and incoming signal (Fig. 5.3) contribute to the above frequency spectrum, we can break equation (5.10) down into three different properties: fre-

81 68 Chapter 5. Multiplexing architecture, ideal behavior quency, amplitude, and phase. Assuming a normalized case, 0.5* m(t) =1 in (5.10), we can list how these properties are influenced: Parameters that can influence the frequency: f C ; f S ; n Parameters that can influence the amplitude: α 1 ; α ; f S ; τ k Parameters that can influence the phase: K; φ; f S ; τ k ; t S,k The square wave amplitudes (α 1, α ) directly relate to the component amplitude. The channel number (k), phase difference between two adjacent channel (φ), and starting time delay of the pulse (t S,k ) directly relate to the component phase. Amplitude and phase are correlated by f S and τ k. In frequency domain, summing all the channels means summing of all spectrum components from each frequency of all channels. With a given system application target in mind, we can design the above mentioned parameters such that the properties of the summed signal are as needed. For example, in [8], these parameters are designed to reach maximum amplitude at frequency f C -f S Combination in the analog domain In a multiplexing receiver system, the channels are conducting one after each other, sequentially. When one channel is conducting, other channels must be isolated. Moreover, the conducting time during of each channel is evenly distributed in period T S. Fig. 5.4 describes such a square wave.

82 5.1 Analog multiplexing 69 α 1 τ 1 α 0 τ t S, τ k t S, k τ K t S, K T S Fig. 5.4: Multiplexing pulses For simplicity, assuming all paths τ k equal to 1/(K f S ), and assuming also α 1 =1, α =0, t S,1 =0/(K f S ), t S, =1/(K f S ), t S,k =(k-1)/(k f S ), t S,K =(K-1)/(K f S ), equation (5.10) simplifies to x k (t) equal-paths as n= 1 j π fct j( k 1) ϕ jn π fst xk ( t) = m( t) e e c equal paths n, ke n= 1 1 = m t e e n = K j π fct j( k 1) ϕ ( ) ( 0) n= k 1 1 ( 1) 1 jn j fct j k n π π ϕ π K jn π fst + m( t) e e sin e e ( n 0) n= nπ K n 0 (5.11) Note that for this specific situation of all equal paths, we use c n,k as the complex Fourier coefficients. Note also that φ is the differential carrier phase change between two consecutive antenna elements. As shown in Fig. 5.3, the pulse modulated signals from all channels are summed together. Substituting φ from (5.8) into (5.11), the summed signal in the time domain can be expressed as 1 x t x t m t e c e e K n= K j π fct j( k 1) π sin( θ ) jn π fst sum ( ) = k ( ) = ( ) equal path n, k k = 1 n= k = 1 (5.1)

83 70 Chapter 5. Multiplexing architecture, ideal behavior 5. Spatial to frequency mapping Define D n as the coefficient function of the n-th order harmonic D ( K, θ ) = c e n K n, k j( k 1) π sin( θ ) (5.13) k = 1 D n is determined by two variables, K and θ, in which K is the number of antennas and θ is the incoming signal angle of incidence. Substituting (5.13) into (5.1), x sum (t) can be expressed as 1 xsum ( t) = m( t) e D ( K, ) e (5.14) n= jπ fct jn π fst n θ n= Taking the Fourier transform of (5.14), we obtain n= 1 X sum( f ) = M ( f ) Dn ( K, θ ) δ ( fc n fs ) (5.15) n= The above equation (5.15) indicates that the frequency spectrum of x sum (t) is modulated by the incoming signal angle of incidence θ. In another word, a multiplexing phased-array architecture transfers space angle information into frequency information. This property will be discussed in detail in section Space to frequency mapping coefficient D n To understand the summed phase modulated signal x sum (t), it is important to understand function D n (K,θ) first. In the following analysis, we assume four antennas, normalized input signal, and normalized and equal paths, we get: K=4, τ 4 =1/(4 f S ), α 1 =1, α =0, t S,1 =0/(4 f S ), t S, =1/(4 f S ), t S,3 =/(4 f S ), t S,4 =3/(4 f S ; 0.5* m(t) =1. Taking all these assumptions into account, the summed signal in (5.1) can be re-written as 4 n= 4 C S xsum ( t) = xk ( t) = e cn k e e k= 1 n= k = 1 j π f t j( k 1) π sin( θ ) jn π f t equal path, (5.16) From (5.13), the D n (K,θ) for four antennas can be expressed as

84 5. Spatial to frequency mapping 71 D (4, θ ) = c e n 4 j( k 1) π sin( θ ) n, k (5.17) k = 1 Substituting equation (5.3) and (5.4) into (5.17), and expending the amplitude of D n (4,θ) and ignore the phase component, we have D (4, θ ) n 4 1 j( k 1) π sin( θ ) e n = 0 4 k = 1 = π e e n nπ 4 k = 1 nπ 4 1 n j 4 j ( k 1) sin( ) n f sin π θ π S ts, k 0 (5.18) Substituting φ from (5.8) into (5.18), table 5. extends the relation of harmonic number n and D n (4,θ), until the ±4 th harmonic.

85 7 Chapter 5. Multiplexing architecture, ideal behavior when n=0 (f C ) D 0 j j j3 ( ) D 1 D -1 D D - D 3 D -3 1/ 4 1+ e + e + e when n=1 (f C +f S ) ( / ( π )) ϕ ϕ ϕ π j j π j π ϕ ϕ j 3ϕ π e + e + e + e when n=-1 ((f C -f S ) ( / ( π )) π j j π j π ϕ ϕ j 3ϕ π e + e + e + e when n= (f C +f S ) ( 1/ ( π )) π j j π j π ϕ ϕ j 3ϕ π e + e + e + e when n=- (f C -f S ) ( 1/ ( π )) π j j π j π ϕ ϕ j 3ϕ π e + e + e + e when n=3 (f C +3f S ) ( / (6 π )) 3π j j π j π ϕ ϕ j 3ϕ π e + e + e + e when n=-3 (f C -3f S ) ( / (6 π )) 3π j 4 when n=4 (f C +4f S ) D 4 0 when n=-4 (f C -4f S ) D j π j π ϕ ϕ j 3ϕ π e + e + e + e Table 5.: Relation of n and D n (4,θ) From the above table, for given n, D n (4,θ) is a function of φ, and thus, via (5.8), of θ. Hence, we can make a two dimensional table based on Table 5. to look up the value of D n (4,θ). Table 5.3 shows the value of D n (4,θ) for different θ and n combinations. Table column represents the harmonic (amplitude) distribution for a certain angle of incidence θ. For example, 0 means the fundamental tone f C, ±1 means sidebands f C +fs and f C -f S, etc.

86 5. Spatial to frequency mapping 73 Θ n Table 5.3: Values of D n (4,θ) with different θ and n combinations. The dashed line (within) indicates the minimum required harmonics to have at least 90% of total power. The dashed line (within) indicates the minimum required harmonics to have at lease 90% (as an example) of total power for a certain angle of incidence θ. For example, if θ=30, 0.9 =0.81 has not reached 90% of total power; =0.9 has reached exactly 90% of total power, so the dashed line is drawn at n=±3. From the above analysis, D n (4,θ) has the property of D n ( 4, θ ) = D n (4, θ ) (5.19) Moreover, at even harmonic number, when n=0,, 4, 6, 8 D ( 4, θ) D (4, θ) = D (4, θ ) (5.0) n = n n

87 74 Chapter 5. Multiplexing architecture, ideal behavior (5.19) and (5.0) is also true for other k values. So we have D n (4, θ ) = D (4, θ ) = D n D (4, θ ) n n (4, θ ) = D n (4, θ ) ( n =,4,6 ) (5.1) Fig. 5.5 shows the spectrum of x sum (t) with incidence angels of 0, 30, 60, 90 degree.

88 5. Spatial to frequency mapping 75 X sum f C X sum f C f S f C f C + f S X sum f C f S f C f C + f S X sum f C Fig. 5.5: Amplitude part of the spectrum of X sum (f) for (a) θ=0 (b) θ=10 (c) θ=30 (d) θ=60

89 76 Chapter 5. Multiplexing architecture, ideal behavior For different angle of incidence, the spectrum looks differently. At 0 degree, the peak is centered at f C ; at 10 degree, the energy is spreading from f C to f C +f S and f C -f S ; at 30 degree, the peak is centered at f C +f S, and energy of f C goes to zero. At 60 degree, the energy is spreading to many harmonics in the spectrum. The spectrum of x sum (t) is phase modulated. As section 4. explained, a multiplexing phased-array architecture transfers space angle information into frequency information. Furthermore, there is a unique translation from incoming angle of incidence θ to frequency spectrum pattern. 5.. Translation from voltage to power domain, D n to Px n Power in a sinusoidal signal depends only on its amplitude, and is independent of frequency and phase [67]. Remember that in section., we have discussed in (.4) that the power of the carrier is spread over the various side components as a function of θ. Hence, we also have (, ) D 1 n K θ = (5.) n= Define Px n (K,θ) as the power contained in the n-th pair of side frequency Px0 K θ = D0 K θ n = (, ) (, ) 0 Pxn ( K, θ) = Dn ( K, θ) + D n( K, θ) n 1 (5.3) Thus, (5.) can also be written as Px (, ) 1 n K θ = (5.4) n= 0 Note that (5.4) does not mean physically adding the power. It is a power property indication over all harmonics. Table 5.4 shows the value of Px n (K,θ) with different θ and n combination, when K=4. Table row represents the harmonic power distribution for a certain angle of incidence θ. For example, 0 means the fundamental tone f C, 1 means sidebands f C ±fs, etc.

90 5. Spatial to frequency mapping 77 n θ Table 5.4: Values of Px n (K,θ) with different θ and n combinations (when K=4). The dashed line (within) indicates the minimum required harmonics to have at lease 90% of total power. The dashed line (at left) indicates the minimum required harmonics to have at lease 90% (as an example) of total power. Fig. 5.6(a) plots the values from Table 5.4. For θ sweeping from 0 to 90 degree, the value of Px n (K,θ) is shown, with n as a parameter (n from 0 to 6).

91 78 Chapter 5. Multiplexing architecture, ideal behavior Fig. 5.6: Px n (K,θ) as a function of θ, n=0,1,,3,4,5,6 (a) when K=4, (b) when K=16. Table 5.4 and Fig. 5.6(a) show that at different angles of incidence, the energy concentrates in different side frequencies. For example, at 0 degree, all energies are stored in n=0, which is the fundamental frequency. At 30 degree, 81% of the energies are stored in n=1, and the rest of the energies are only stored in the odd harmonics. At 90 degree, 81% of the energies are stored in n=, and the rest of the energies are only stored in the even harmonics. The above properties give the translation from space/angle difference into frequencies spectrum/energy difference. Fig. 5.6(b) again shows the Px n (K,θ) plot, but now for 16 antennas. Comparing with Fig. 5.6(a), the side frequency energy is more concentrated around the corresponding spatial angle, which indicates a better spatial resolution.

92 5. Spatial to frequency mapping Coarse beam pattern Rx N by frequency selectivity The normalized power sum of the first N pairs of harmonics is given by Rx ( K, θ ) = Px ( K, θ ) N N n= 0 n N = D0 ( K, θ ) + Dn ( K, θ ) + D n( K, θ ) n= 1 (5.5) Note that (5.5) does not mean physically adding the power. It is a power property indication over harmonic pairs up until number N. For example, in case of four antenna elements (K=4), and 10 of angle of inciedence (θ=10 ) Rx Rx Rx Rx = Px = Px 0 0 = Px = Px 0 0 = ( N = 0) + Px 1 + Px 1 + Px 1 = ( N = 1) + Px + Px = Px 3 ( N = = ) ( N = 3) (5.6) Following (5.6), we can mark in Table 5.3 and 5.4 dashed line representing the boundary of the minimum required harmonics to have at lease 90% of total power. Two plots of Rx N (K,θ) (in db) as a function of θ are shown in Fig. 5.7.

93 80 Chapter 5. Multiplexing architecture, ideal behavior Fig.5.7: Rx N (K,θ) as a function of θ, N=0,1,,3, (a) when K=4, (b) when K=16. From Fig. 5.7(a), one can notice that the array coarse-pattern looks differently for various N. If N increases, the array coarse-pattern in space becomes less selective, meaning less spatial filtering effect. Note that N denotes the first N pairs of sideband frequencies which are preserved after analog band-pass filtering, as in (5.5), which represent the effect of the frequency filter. Hence, the above figure shows that a filter in the frequency domain results in a filter in space domain. This phenomenon is shown more clearly in Fig Fig. 5.7(b) again shows the Rx n (K,θ) plot, but for 16 antennas. Comparing with Fig. 5.7(a), with we see that for equal step of filter bandwidth increase in frequency domain, the spatial filter bandwidth is increasing with better resolution. It confirms our analysis in Fig. 5.6.

94 5.3 Digital de-multiplexing and phase-shifting 81 x ( ) sum t x ( ) sum t x ( ) sum t Fig. 5.8: Frequency to space filtering, with array coarse-pattern, for K=4, (a) N=0, (b) N=1, (c) N=. Fig. 5.8(a) shows that the band-pass filter passes only the 0 th order harmonic signal. The corresponding array coarse-pattern Rx 0 (4,θ) is displayed, and the -3dB spatial bandwidth is θ=[-13, 13 ]. It means that signals coming from -13 to 13 in space are allowed to pass (attenuation less than 3dB), and the signals coming from other degrees are attenuated. Similarly, Fig. 5.8(b) shows that a band-pass filter that passes the 0 th and 1 st order signals. The corresponding array coarse-pattern Rx 1 (4,θ) is displayed, and the -3dB spatial bandwidth is θ=[-48, 48 ]. Fig. 5.8(c) shows that a band-pass filter that passes the 0 th, 1 st, and nd order signals. The corresponding array coarse-pattern Rx (4,θ) is displayed, and the -3dB spatial bandwidth is θ=[-90, 90 ], which means almost no spatial selectivity applied. Note that in this thesis, we only discuss the brick-wall filter [68]. Taking other filters (meaning different weight function for the spectrum components), one can get different spatial patterns. Small part of the desired signal that located outside the filter bandwidth is blocked by the band-pass filter. This part of the missing signal can not be calibrated or compensated in the digital domain, so after the digital demodulation, the bit error rate (BER) of the desired signal will slightly degrade. To choose the filter bandwidth, there is a trade-off between interference suppression requirement and BER requirement. In this thesis, we choose filter bandwidth based on the interference suppression specification. In practice, we should always check the influence to BER degradation.

95 8 Chapter 5. Multiplexing architecture, ideal behavior 5.3 Digital de-multiplexing and phase-shifting Fig. 5.5 shows that the multiplexing phased-array architecture translates the input signal for each angle of incidence θ to a specific frequency spectrum pattern. Fig. 5.8 shows that a filter in frequency domain results in a filter in space domain and hence forms the array coarse-pattern. Fig. 5.9 shows how the signal is further processed in the digital domain. First, the signal is de-multiplexed from one path back to four paths, and then these four signals are phase shifted according to the desired viewing angle and combined. At last, a band-pass filter is used to clean up the frequency spectrum. Fig. 5.9: Signal processing in digital domain In practice, the summed multiplexed signal from (5.14) passes through the mixer, the filter, and the ADC to reach at the input of de-multiplexer. To simplify the analysis, we assume a normalized situation, 0.5* m(t) =1, and the transfer functions of the mixer, the filter, and the ADC equal to one. So the complex envelope of the input signal is D n (K,θ), as shown in Fig The input signal is further processed by de-multiplexer and digital phase shifter. Note that the de-multiplexer is using the same switching frequency f S as the multiplexer. Fig (a)-(e) shows the frequency mixing of each input harmonic component due to de-multiplexing. This process can be understood by the following steps: First, due to de-multiplexing, the frequency components for each channel at the de-multiplexer input are mixing to other locations with step size f S. Next, the digital phase delay component (per channel) applies a desired phase shift to the fundamental tone in order to add them in-phase (n=0). Thirdly, the phase adjusted fundamental tones from the previous step are added in-phase (per channel). And finally, fundamental components from all four channels are added together.

96 5.3 Digital de-multiplexing and phase-shifting 83 y,k ( t ) (a) y 1,k ( t ) (b) y0,k ( t) (c) Harmonic Order y1,k ( t) (d) y,k ( t) (e) Fig. 5.10: Frequency mixing and spectrum reformation of one channel, (a) n=- (b) n=-1 (c) n=0 (d) n=1 (e) n=

97 84 Chapter 5. Multiplexing architecture, ideal behavior For example, at Fig. 5.10(a), the n=- component is transferred to: the -4 th order component via the - nd (n=-) harmonic term the -3 rd order component via the -1 st (n=-1) harmonic term the - nd order component via the DC term the -1 st order component via the 1 st (n=1) harmonic term the fundamental component via the nd (n=) harmonic term of the switching function in (5.5). The same frequency mixing mechanism applies to input harmonic components n=-1, n=0, n=1, and n= in Fig. 5.10(b), (c), (d), and (e), respectively. However, not all the mixing products are of interest. The digital phase shifters are designed for maximizing the signal amplitude at the fundamental frequency (n=0). So only the mixing products which fall into the fundamental frequency needs to be further processed, as highlighted in Fig Note that the above figure only shows the mixing result of one channel. In case of K channels, the above analysis happens K times and the K results are then summed together. In Fig. 5.9, y n,k (t) is defined as the complex envelope after mixing the n-th harmonic component to the fundamental frequency (n=0) form the k-th channel. For example, after frequency mixing in Fig. 5.10(a), the complex envelope at the fundamental frequency (n=0) is y -,k (t). Table 5.5 displays a two dimensional parameter matrix, assuming the number of channels is four (K=4). y -,sum (t) means the sum of the fundamental tones (n=0) from 4 channels, from which the fundamental tone is converted from n=- harmonic for each channel. This definition can be extended for all other y n,sum (t). The column of Table 5.5 is matched to the Fig explanation. n k sum n=- y -,1 (t) y -, (t) y -,3 (t) y -,4 (t) y -,sum (t) n=-1 y -1,1 (t) y -1, (t) y -1,3 (t) y -1,4 (t) y -1,sum (t) n=0 y 0,1 (t) y 0, (t) y 0,3 (t) y 0,4 (t) y 0,sum (t) n=1 y 1,1 (t) y 1, (t) y 1,3 (t) y 1,4 (t) y 1,sum (t) n= y,1 (t) y, (t) y,3 (t) y,4 (t) y,sum (t) Table 5.5: Parameter matrix of y n,k (t), when K=4

98 5.3 Digital de-multiplexing and phase-shifting 85 Taking n=- as an example, y -,k (t) can be express as y ( t) = D (4, θ ) c e,1,1 y ( t) = D (4, θ ) c e,, y ( t) = D (4, θ ) c e,3,3 y ( t) = D (4, θ ) c e,4,4 j 0γ j 1γ j γ j 3γ (5.7) where γ is the digital phase shifter in radians. Applying the definition of D n in (5.17), we get D (4, φ) = c e n 4 j( k 1) π sin( φ ) n, k (5.8) k= 1 Let γ=ϖ*sin(ø), we get y ( t) = y ( t) + y ( t) + y ( t) + y ( t), sum,1,,3,4 = D (4, θ ) c e, k = 1 = D (4, θ ) D (4, φ) 4 j( k 1) π sin( φ ) (5.9) k Applying the same calculation to Fig (b), (c), (d), and (e) results in y ( t) = D (4, θ ) D (4, φ) 1, sum 1 1 y ( t) = D (4, θ ) D (4, φ) 0, sum 0 0 y ( t) = D (4, θ ) D (4, φ) 1, sum 1 1 y ( t) = D (4, θ ) D (4, φ), sum 1 (5.30) If we preserve all sidebands power (extend to infinite) and transfer them to the fundamental frequency (n=0) through de-multiplexing, the complete input carrier power is preserved. If the desired phase delay is applied to each path, at the fundamental tone (n=0), all folded frequency components are added in phase, and at other location (n 0), all folded frequency components are added out-of-phase. Hence, the complete input carrier power is preserved at the fundamental tone (n=0), and we can obtain the power at the fundamental tone by fist adding the in-phase signal and then take the square of the sum, as y ( t) + y ( t) + y ( t) + y ( t) + + y ( t) = 1 (5.31), sum 1, sum 0, sum 1, sum +, sum

99 86 Chapter 5. Multiplexing architecture, ideal behavior Substituting (5.30) to (5.31), we obtain D ( K, θ) D ( K, φ) + D ( K, θ ) D ( K, φ) + D ( K, θ) D ( K, φ) = n n n n n 1 n 1 fundamental term = = positive harmonic terms negative harmonic terms (5.3) Note that (5.3) means physically adding the converted signal (from other harmonics) with phase information at the fundamental frequency (n=0). Defining Py n (K,θ,Ø) as the power transferred to the fundamental frequency from the n-th pair of side frequency, we obtain Py0( K, θ, φ) = D0 ( K, θ ) D0 ( K, φ) n = 0 Pxn ( K, θ, φ) = Dn ( K, θ ) D n( K, φ) + D n( K, θ ) Dn ( K, φ) n 1 (5.33) Thus, (5.3) can also be written as n= 0 Py (,, ) 1 n K θ φ = (5.34) The normalized power sum of the first N pairs of harmonics is given by Ry ( K, θ, φ) = Py ( K, θ, φ) N N n= 0 n 0 0 N = D ( K, θ) D ( K, φ) + D ( K, θ) D ( k, φ) + D ( K, θ) D ( K, φ) n n n n n= 1 n= 1 N (5.35) Equation (5.35) shows the array pattern after de-multiplexing. Remember that in (5.5) and Fig. 5.7, Rx N (K,θ) shows the array pattern after multiplexing. In the next section, the array pattern after multiplexing and de-multiplexing are plotted as a function of space angle of incidence θ. 5.4 Array pattern Following the discussion from the previous section, Fig shows the array patterns Rx N (K,θ) and Ry N (K,θ,Ø) as a function of θ. Here, we take an example of four antenna elements (K=4); the normalized power sum of the 1 st pairs of sideband frequencies which are preserved after analog

100 5.4 Array pattern 87 band-pass filtering (N=1), as shown in Fig. 5.8(b); and a desired viewing angle of 10 (Ø=10 ). Note that Rx N is the beam pattern before de-multiplexing and digital combination, while Ry N is the beam pattern after it Normalized Array Gain [db] Rx 1 Ry θ, Angle of Incidence [degree] Fig. 5.11: Rx N, Ry N as a function of θ, when K=4, N=1, Ø=10 As in Fig. 5.8(b), Rx 1 results from a frequency filter with bandwidth larger than the 1 st sideband but smaller than the nd sideband. Energies stored in the 0 st and 1 st sidebands are preserved, which is the available signal power, and sideband signals above nd order are filtered out. After de-multiplexing and digital phase shifting (with Ø=10 ), we obtain Ry 1 which is the recovered pattern. It cannot exceed the pattern given by Rx 1. Ry 1 is peaked at 10 as expected. Fig. 5.1 shows the polar diagram of Rx N (K,θ) and Ry N (K,θ,Ø). It shows that the final array (in red line) pattern can only stay within the area defined by the array coarse-pattern (in dashed blue line).

101 88 Chapter 5. Multiplexing architecture, ideal behavior Rx 1 Ry 1 Fig. 5.1: Polar diagram of Rx N, Ry N, when K=4, N=1, Ø=10 Remember in Fig. 5.7, we explained that the array coarse-pattern looks differently for various N. If N increases, array coarse-pattern in space becomes less selective, meaning less spatial filtering effect. In Fig. 5.13, the array final-pattern is plotted for various N Ry N, Normalized Array Gain [db] N=0 N=1 N= θ, Angle of Incidence [degree] Fig. 5.13: Ry N as a function of θ with N=0, 1, 10, when K=4, Ø=10

102 5.5 Conclusion 89 Assuming K=4, and Ø=10, a plot of Ry N (N=0, 1, 10) as a function of θ is shown in Fig It is also the array final-pattern. The ideal pattern should peak at (10, 0dB). Compare these three lines, the blue line (N=0) is peaking at (0, -1.7dB), the green line (N=1) is peaking at (7.3, -0.85dB), and the red line (N=10) is peaking at (9.7, -0.1dB). It means that the larger the N, the closer the final-pattern to the ideal pattern. Hence there is a trade-off between array coarse-pattern and final-patter for different N When N is large, which means the analog band-pass filter has a wide bandwidth, array coarse-pattern is less selective, but the array final-pattern is more accurate. When N is small, which means the analog band-pass filter has a narrow bandwidth, array coarse-pattern is more selective, but the array final-pattern is less accurate. However, we know this angle offset before-hand, so a look-up table in digital domain can be implemented to compensate this angle offset, but the power loss due to narrow band filtering is not correctable in digital domain. 5.5 Conclusion In this chapter, we have discussed the multiplexing architecture from a mathematical point of view. We used various models to understand the properties of the system. Firstly, the properties of the analog combined signal were described and a similarity with traditional phase modulation theory was explained. Secondly, a new coefficient function D n is introduced to help understand the properties of the combined signal. Thirdly, we introduced a new concept: frequency to space filtering transformation. Next, by processing the signals in the digital domain, the final array pattern is achieved. Furthermore, the array pattern is compared with the traditional analog beam-forming array pattern and key system parameters are revealed.

103 90 Chapter 5. Multiplexing architecture, ideal behavior

104 C h a p t e r 6 6 Multiplexing architecture, non-ideal behavior In this chapter, a few important non-idealities of a multiplexing phased-array architecture are discussed. Section 6.1 discusses the angle deviation from the expected viewing angle due to the finite analog filter bandwidth. Section 6. presents the influence of non-ideal switches on the array pattern. Section 6.3 discusses the noise performance in a sampling environment. Section 6.4 discusses the impact of adjacent channel interference. Section 6.5 presents simulation results of the multiplexing architecture. Section 6.6 shows the signal, noise and distortion power flow diagram of a multiplexing architecture, which is the realization of the generalized phased-array model presented in chapter 3.6, and section 6.7 concludes what has been discussed in this chapter. Non-idealities like timing jitter impact and isolation between switch paths are not discussed in this chapter. They are recommended for future works. 91

105 9 Chapter 6. Multiplexing architecture, non-ideal behavior 6.1 Angle deviation Due to limited filter bandwidth, the formed viewing angle after de-multiplexing and digital phase shifting (in Fig this is the θ value where the array pattern has its peak) is not the same as the expected viewing angle (desired signal angle of incidence). Assuming N (Ø) represents the angle deviation of the formed viewing angle from the expected viewing angle Ø, where N denotes the first N pairs of sideband frequencies which are preserved after analog band-pass filtering. Define θ peak,n as the formed viewing angle after digital beam-forming, we have ( φ) = φ θ (6.1) N peak, N For example in Fig. 5.13, the expected viewing angle is 10, hence (10 ) = = (10 ) = = 0.3 (6.) Fig. 6.1 plots the relation shown in (6.1), where angle deviations N versus the expected viewing angle Ø N=1 N= N=10 30 N [degree] Φ, Expected viewing angle [degree] Fig. 6.1: N (in degree) as a function of Ø with N=1,, 10, when K=4

106 6. Non-ideal switches 93 It shows that the higher the N (thus larger filter bandwidth), the smaller the angle deviation N, the closer the formed viewing angle is to the expected viewing angle. In case of infinite bandwidth (N= ), the formed viewing angle can follow exactly the expected viewing angle, which means that =0. For K=4, and a spatial viewing range of (-30, +30 ), the band-pass filter shown in Fig. 5.8(b) (N=1) will result in an angle deviation between (-0.7,.7 ). As mentioned in chapter 5.4, the angle deviation caused by choosing a small N can be compensated by implementing a look-up table in digital domain. And this table can be created based on Fig. 6.1, but the power loss due to narrow band filtering is not correctable in digital domain. 6. Non-ideal switches In reality, the switches need to be implemented by electronic circuits that do not perform ideally. Assuming α 1 being the switch loss when switch is on, and α being the finite channel isolation when switch is off, the on/off difference is a 1 -a. Considering the previous LNA stage can provide gain to compensate the switch loss, the absolute values of a 1 and a are not of interest, thus we assume a normalized condition, a 1 =0dB for the following analysis. The according non-ideal variation of D n (4,θ) in (5.18) can be expressed as (taking K=4 as an example) D (4, θ ) 4 α1 α j( k 1) π sin( θ ) + α e n = 0 4 k = 1 = sin e e n 0 nπ 4 k = 1 n ni nπ 4 α1 α nπ j 4 j ( k 1) π sin( θ ) n π fs ts, k (6.3) The index ni refers to non-ideal. In the digital domain, the switching behavior is ideal, so there is no loss and infinite channel isolation, which results in D ( 4, φ) = D (4, φ) (6.4) n Considering a non-ideal situation, we can re-write Rx N in (5.5) as (when K=4) ni n Rx (4, θ ) = D (4, θ ) N ni 0 ni N Dn (4, θ ) D n(4, θ ) ni ni n= (6.5)

107 94 Chapter 6. Multiplexing architecture, non-ideal behavior Similarly, we can re-write Ry N in (5.35) as (when K=4) Ry N (4, θ, φ) ni = N D (4, θ ) D (4, φ) + D (4, θ ) D (4, φ) + D (4, θ ) D (4, φ) 0 ni 0 n ni n n ni n n= 1 n= 1 N (6.6) Fig. 6. shows a plot of Rx N (4,θ) ni and Ry N (4,θ,Ø) ni as a function of θ for K=4, N=1and Ø=10, and assuming a switch loss of α 1 =0dB, and a finite channel isolation of α =5dB. As the switch are non-ideal, the array patterns are affected. Fig. 6.3 shows the polar diagram of Rx N (4,θ) ni and Ry N (4,θ,Ø) ni. Fig 6.4 shows the array patterns as a function of θ when N=0, 1, Normalized Array Gain [db] Rx 1 ni Ry 1 ni θ, Angle of Incidence [degree] Fig. 6.: Rx N ni, Ry N ni as a function of θ, when K=4, N=1, Ø=10

108 6. Non-ideal switches Rx 1 ni Ry 1 ni Fig. 6.3: Polar diagram of Rx N ni, Ry N ni when K=4, N=1, Ø= Ry N ni, Normalized Array Gain [db] N=0-80 N=1 N= θ, Angle of Incidence [degree] Fig. 6.4: Ry N ni as a function of θ with N=0, 1, 10, when K=4, Ø=10

109 96 Chapter 6. Multiplexing architecture, non-ideal behavior Fig. 6.5 shows the angle deviation as a function of Ø with N=1,, 10, when K=4, α 1 =0dB, α =5dB N=1 N= N=10 30 N ni [degree] Φ, Expected viewing angle [degree] Fig. 6.5: N ni (in degree) as a function of Ø with N=1,, 10, when K=4, α 1 =0dB, α =5dB Comparing this with Fig. 6.1, we see that for all N, the angle deviation has become larger. Even with high filter bandwidth, the actual viewing angle still cannot perfectly follow the expected viewing angle. For K=4, within the range of 30, 1_ni has a deviation range between (-0., 4.4 ). The angle deviation can be corrected in digital domain with a look-up table. However, the signal power loss hence also the modulated signal loss can give direct influence to BER. The requirement of the switch on/off difference can be discussed following the BER analysis. 6.3 Noise in a multiplexing system In a multiplexing system, not only the signal but also the noise is pulse modulated. Noise from other frequencies can be mixed into the frequency of interest, as shown in Fig. 6.6.

110 6.3 Noise in a multiplexing system 97 Fig. 6.6: Noise folding when sampling Assuming the noise spectrum is flat, and the noise RMS voltage is V n,in, in a single channel, after mixing, the noise power in the frequency of interest can be separated into two parts: noise power from its own, Pnoise 0, and noise power contributed from the n-th pairs of side frequencies, Pnoise n. Noise can be treated as signal without phase information. Based on equation (5.11), assume normalized resistor of 1Ω, the noise power can be expressed as 1 Pnoise0 ( K ) = V n, in n = 0 K 1 nπ Pnoisen ( K ) = sin Vn, in n 1 nπ K (6.7) where n is the harmonic order number, and K is the number of antennas. Assuming a noise bandwidth BW noise, and a signal bandwidth BW S, and the noise to signal bandwidth ratio as R n BW BW noise = (6.8) S Note that f S =*BW S. Defining N r as the number of harmonic pairs that are contained within the noise bandwidth, we assume the number of harmonic pairs is an integer, instead of a decimal. One can write for N r with integer function, N r Rn = INT 4 (6.9)

111 98 Chapter 6. Multiplexing architecture, non-ideal behavior The combined noise power of K paths can be directly summed over all channels. Taking noise summed up until the N r -th side band r N r ( ) ( ) Pnsum K = K Pnoise K (6.10) The noise power gain Gnoise r (K) can be denoted as the summed noise power divided by the original noise power (within the signal bandwidth) n= 0 n Gnoise r ( K ) = Pnsum V r n, in ( K ) Nr 1 1 nπ = + K sin K n= 1 nπ K (6.11) Fig. 6.7 shows the relation between Gnoise r (K) and the bandwidth ratio R n, for K=4. It indicates that the smaller the ratio R n, the better the noise reduction after multiplexing. When noise and signal use the same frequency band, the noise reduction is 6dB, which results in the same effect as in the conventional beam-forming. Fig. 6.7: Relation of noise power gain Gnoise r (K) with bandwidth ratio R n, when K=4

112 6.4 Frequency mixing Frequency mixing In chapter 4, we have explained the trade-off between antenna number K, signal bandwidth BW, and channel sampling frequency f S through equation (4.4). For a single channel, according to the Nyquist theory, the condition for no loss of data information is f S >BW. However, this condition is only valid when no interference comes from the adjacent channel. When the adjacent channel interference present, the signal and the interferer are both expanded in frequency at the multiplexer s output, leading to an irrecoverable spectrum overlap, as shown in Fig Fig. 6.8: Effect of adjacent channel interferer. In order to prevent the spectrum overlap, the channel sampling frequency f S must be increased to make sure the spectrum expansion is not causing any overlap. As shown in Fig. 6.9, if f S >BW total, the interferer and signal spectrums are expended together, where BW total is the summed spectrum of signal, interferer, and the signal interferer frequency difference. Interferer Signal BW total f f S f Fig. 6.9: Signal and interferer spectrum expansion without overlap. For a K channel multiplexer, the switching frequency of the multiplexer f MUL needs to fulfill f MUL >K*BW total to make sure no overlap for each channel.

113 100 Chapter 6. Multiplexing architecture, non-ideal behavior 6.5 System simulations Fig shows the system simulation diagram for multiplexing architecture in Advanced Design System (ADS). The goal for this test is to verify the spatial to frequency mapping theory that delivered in chapter 5. In this test, the desired and interference signal comes from 30 and -30, respectively, and their carrier frequency is the same. The phase shifter in digital domain is programmed at 30 to receive the desired signal. To simplify the simulation complexity, the follow settings are applied: RF carrier frequency is 6GHz, and sampling frequency for each channel is 50MHz.

114 6.5 System simulations 101

115 10 Chapter 6. Multiplexing architecture, non-ideal behavior Fig. 6.10: Multiplexing architecture system simulation diagram in ADS. Fig shows the simulation result. Spectrum (a) is the combined spectrum of desired and interference signal and they are located in the same frequency. Spectrum (b) is the effect of multiplexing in a single path. Spectrum (c) shows the 4 paths combined signal spectrum. Major part of the 30 signal shifts 50MHz towards left, and major part of the -30 signal shifts 50MHz towards right. With different angle incidence, the spectrum pattern shows differently. Spectrum (d) is the effect of de-multiplexing in a single path and the phase compensation for 30 is also

116 6.6 Power flow diagram for a multiplexed architecture 103 added. Spectrum (e) shows the 4 paths combined signal spectrum after phase shifter. Due to the phase compensation, the desired 30 signal shifts back to the original location, and the interference -30 signal spreads to other harmonic frequencies. Spectrum (f) is the final desired signal spectrum after a digital band-pass filter. Fig. 6.11: Multiplexing architecture system simulation result in ADS. Spectrum (a)-(f) corresponding to point a-f in Fig. 6.8, respectively. 6.6 Power flow diagram for a multiplexed architecture In chapter 3, we have introduced a signal, noise and distortion power (mw) flow diagram for analog phased-array, digital phased-array, and general case phased-array structure, respectively. For the multiplexing phased-array structure, we can also design a power flow diagram as shown in Fig. 6.1.

117 104 Chapter 6. Multiplexing architecture, non-ideal behavior IIP3 FE IIP3 tot 1 χ G FE 1 I ADC IIP3 ADC χ1 L I ou t I in SADC S out G FE N tot S in N tot, in N FE D tot 1 χ N FE 1 χ F FE F tot D FE F ADC N ADC D FE D ADC kt BW Fig. 6.1: Signal, noise and distortion power flow diagram of a multiplexing phased-array One can notice that except for parameters that has been explained previously, there are two extra parameters: χ 1 and χ. They indicate the flexibility of the beam-forming system. The final array pattern is formed in digital domain. Hence the suppression factor L is located in the right part of the plane. χ1 represents the array coarse-pattern interference suppression, as in Fig It is varying between no coarse-pattern (χ 1 =1), and final-pattern (χ 1 =1/L). χ represents the array noise suppression, as in Fig It is varying between no noise suppression (χ =1), and maximum noise suppression (χ =K). In brief, there are two types of power flow in Fig. 6.1, The flow of the interference signal, from I in suppressed to I ADC, thanks to the array coarse-pattern suppression. Then from I ADC again suppressed to I out due to the array final-pattern suppression. The flow of the desired signal, from S in increased to S ADC, due to the front-end gain, and then from S ADC to S out with a power gain of one.

118 6.7 Conclusion Conclusion In this chapter, we have discussed a few important non-idealities of a multiplexing phased-array architecture. To reduce the analog filter bandwidth, hence the ADC bandwidth, we have introduced an actual viewing angle to the expected viewing angle deviation. The smaller the band-pass filter bandwidth, the larger the angle deviation. This deviation can be compensated by creating a look-up table in the digital domain, but the power loss due to narrow band filtering is not correctable in digital domain. The channel isolation indicates the switching quality. If we don t have a infinite channel isolation, even with high filter bandwidth, the actual viewing angle still can not perfectly follow the expected viewing angle. The channel isolation indicates the switching quality. If the channel isolation is not infinite, even with infinite filter bandwidth, the actual viewing angle still can not perfectly follow the expected viewing angle. To achieve the best signal to noise ratio improvement, the incoming noise bandwidth to signal bandwidth ratio should be small. If the signal and noise bandwidth are the same, then for a four antenna array, the SNR improvement is 6dB, which is the same improvement as the conventional beam-forming. For suitable applications, the power flow diagram can be used as a guideline to specify the block parameters. The system simulation result shows that a multiplexing phased-array architecture can achieve spatial to frequency mapping, and it is a good alternative for conventional phased-array architectures. Moreover, the simulation also shows that multiple sources (desired signal) selection is possible with this architecture.

119 106 Chapter 6. Multiplexing architecture, non-ideal behavior

120 C h a p t e r 7 7 Designs for the 30GHz components In this chapter, the designs of the various components are reported, all for operation at 30GHz. The designs consist of LNA, multiplexer, mixer, clock generator, integrated delay line, and power amplifier. Section 7.1 explains the design requirements for the multiplexing phased-array architecture. Section 7. and 7.3 focus on LNA, multiplexer, and mixer design. Moreover, sub-system performance including these three components is reported. Section 7.4 is about the design of a clock generator which provides the switching signal. Section 7.5 discusses the delay line used to generate the front-end input phase difference in the integrated system in chapter 8. Section 7.6 describes the switching power amplifier design. Section 7.7 concludes this chapter. 7.1 Design requirements The time multiplexing phased-array receiver uses a clock controlled multiplexer to combine K paths into one. The combined path contains the signals from the various paths in different time 107

121 108 Chapter 7. Designs for the 30GHz components slots. After down-conversion, band-pass filtering, and digitization, the time multiplexed signal is de-multiplexed by the synchronous clock to recover the original K signals in the digital domain. Then, the signals are processed by beam-forming algorithms. As this system differs from a conventional receiver system, besides the front-end gain, noise, as well as non-linearity performance, there are a few more parameters which need to be considered carefully. The multiplexer essentially incorporates a switch for each path which loads the LNA and drives the mixer. To minimize the influence to the LNA and mixer when changing of the switch status, the input (S11) and output (S) matching of the multiplexer should be maintained regardless of the switch status. In order to retain all amplitude and phase information from each antenna element up to the digital domain without mixing between each channel, the forward (S1) and reverse (S1) isolation of the multiplexer in an OFF (shut off) status should be designed to eliminate signals from other paths. To recover the signal from each path correctly in the digital domain, the sampling rate for each path (f S ) must fulfill the Nyquist sampling theory: f S > BW, where BW is the single-sided bandwidth of the incoming modulated signal. As a result, the multiplexer sampling rate f MUL can be expressed as: f MUL = K f S >K BW, which means that the incoming signal bandwidth is limited by the multiplexer switching speed. The technology used for the design is the 0.5µm SiGe BiCMOS process developed by NXP semiconductors [69]. It provides HBT NPN transistors with f T /f max up to 130/140GHz, breakdown voltage of.0v, measured at VBE=0.65V, moderate CCB, Rpinch=3kΩ/sq, RE=.5Ωum, high transconductance, and competitive low power-performance. 7. LNA and Multiplexer 7..1 Circuit design Design LNA using SiGe technology has been widely studied [70-74]. The differential LNA (as shown in Fig. 7.1) consists of a inductively degenerated cascade Q1-Q and Q3-Q4, driving load inductors LC1-LC. The cascaded LNA is necessary to reduce the miller effect and feedback caused by C mu, in order to increase the power gain. Inductors LB1-LB and LE1-LE are selected together with the emitter width of Q1-Q in order to realize noise and impedance matching simultaneously.

122 7. LNA and Multiplexer 109 Emitter degeneration inductors LE1 and LE are used to to obtain Γ in =Γ* opt, so that Γ in and are Γ opt conjugated matched. The high impedance of the current source generates a virtual ground for them. Scaling the input transistor Q1-Q (0.4um 9.1um) brings the real part of the optimum source impedance for minimum noise figure close to 50Ω at 30GHz. The biasing voltage of Q1 and Q are.v on the transistor base, in order to balance the output voltage swing and the remaining voltage headroom for the current source. Gyration of the emitter impedance of LE1-LE in series with the base resistance of Q1-Q sets the real part of the input impedance to 50Ω thereby matching Re[Zin] in the desired operation range. The inductor LB1-LB connected in series with the base is made series resonant with the input loop to set the imaginary part of the input impedance. Inductors LC1-LC are selected as matching components to tune the LNA output and the following multiplexer input at 30GHz. Fig. 7.1: Simplified schematic of a 30GHz LNA The circuit implementation of the multiplexer is shown in Fig. 7.. It consists of parallel identical switches 1-4, with shared output load inductors LC3 & LC4. The switch uses current steering technique to minimize switching time. A differential common-emitter stage, formed by transistor pair Q5-Q6, translates voltage into current. The switching function is achieved by transistors Q7-Q10, where transistor pair Q8-Q9 provide the core amplification element of the switch. When control voltage CO1 is high, Q8 & Q9 are biased in forward active region, and Q7 & Q10 are in cut-off region, thus allowing the signal to pass from port 1 to 5. When CO1 is low, the bias current is steered toward transistors Q7 & Q10, which connects port 1 directly to the supply.

123 110 Chapter 7. Designs for the 30GHz components Switch1 CO1 Q7 Q8 VCC Q9Q10 B VCC A 188pH 188pH LC3 LC4 Vout Port5 Port1 Q5 Q6 6mA CO Switch Port CO3 Switch3 Port3 CO4 Switch4 Port4 Q5-Q10: 6.0µm/0.4µm Fig. 7.: Simplified schematic of a 30GHz multiplexer This topology inherently implements an absorptive switch. At input ports 1-4, it is ensured that the total current flow through the input transistors is always constant. At output port 5, the total current flow through the load inductors is also constant. Hence, the source and load impedance of the low noise amplifier and mixer will remain constant regardless of the state of the switch.

124 7. LNA and Multiplexer 111 Fig. 7.3: Die photo of the 30GHz LNA and multiplexer Fig. 7.3 shows the integrated die photo of the 30GHz LNA and multiplexer. Note that RF input is not power matched to the multiplexer. It is reserved for isolation measurement between each switch. The die area is 0.9mm and the active circuit occupies 0.mm. 7.. Measurements Fig. 7.4 shows the measurement setup for the 30GHz LNA and multiplexer die demonstrated in Fig The performance of the LNA-multiplexer combination is measured with switches of which the ON and OFF value can be varied with power supply and 3.

125 11 Chapter 7. Designs for the 30GHz components Fig. 7.4: Measurement setup of the 30GHz LNA and multiplexer Fig. 7.5(a) and (b) show the S parameters of the circuit when the switch is in the ON/OFF state, respectively. S11 and S remain constant regardless of the switch status. The transmission, measured by S1 is 14.4dB in ON state and -9.3dB in OFF state, which gives 3dB of switch ON/OFF difference. Fig. 7.5(c) shows a comparison between simulated and measured noise figure. The minimum measured noise figure was 4.1dB at 30GHz. Fig. 7.5(d) is IIP3 measurement, and the input two tone frequencies are located at 9.950GHz and GHz, respectively. Hence the 3 rd order intermodulation products are located at 9.850GHz and GHz, respectively. The measured IIP3 of the LNA multiplexer combination is -10dBm.

126 7. LNA and Multiplexer 113 Fig. 7.5: LNA-multiplexer measurement (a) s-parameter when the switch is ON; (b) s-parameter when the switch is OFF; (c) noise figure; (d) IIP3 measurement The measured isolation from switch 1 to switch is 5.dB when switch 1 is ON, and 8.7dB when switch 1 is OFF. The power consumption is 44mA, in which the LNA consumes 9mA and the multiplexer consumes 35mA.

127 114 Chapter 7. Designs for the 30GHz components 7.3 LNA-multiplexer-mixer combination Circuit design The mixer design using SiGe technology has been presented extensively in the literatures [75-80]. The mixer design is a double-balanced Gilbert cell as shown in Fig It down-converts the RF signal at 30GHz to the IF frequency of 10GHz. Further down-conversion will be considered in a future design. The transconductance part of the mixer Q11-Q1 interfaces with the multiplexer output by inductors LC3 & LC4 in Fig. 7., and it is optimized to achieve the highest power gain and the lowest noise figure simultaneously. The bias current density and transistor size of the switching parts Q13-Q16 were chosen for the highest operating speed to maximize the conversion gain. The emitter degeneration resistors RE1-RE and the loading resistors RC1-RC are designed to trade-off the gain and the linearity performance of the mixer. The DC biasing for the input transistors Q11-Q1 is 1.7V, and the DC biasing for the output transistors Q13-Q16 is.7v. Fig. 7.6: Simplified schematic of a 30GHz mixer

128 7.3 LNA-multiplexer-mixer combination 115 Fig 7.7 shows the simplified schematic which combines the LNA, the multiplexer, the mixer and the inter-connections between them. Fig. 7.7: Simplified schematic of the 30GHz LNA, multiplexer, and mixer Fig. 7.8 shows the integrated die photo of the above combined schematic. The die area is 0.9mm and the active circuit occupies 0.mm. Fig. 7.8: Die photo of the 30GHz LNA, multiplexer, and mixer

129 116 Chapter 7. Designs for the 30GHz components 7.3. Measurements Fig. 7.9 shows the measurement setup for the 30GHz LNA, multiplexer and mixer of the die that is demonstrated in Fig The performance of the LNA-multiplexer-mixer combination is measured with controllable switches implemented by power supply and 3. Fig. 7.9: Measurement setup of the 30GHz LNA, multiplexer, and mixer The front-end measurement includes the LNA, the multiplexer, and the mixer with controllable switches. To evaluate the linearity of the front-end, the input third-order intercept point (IIP3) were measured. Fig. 7.10(a) shows the conversion gain of the front-end was measured with both ON/OFF switch situations as shown in. The RF frequency was swept from 1 to 39GHz with -33dBm input power. The measured maximum conversion gain is 18.9dB at 30GHz, and the switch ON/OFF difference is 3dB, corresponding with the isolation measurement result in the previous section. For the IIP3 measurement, two tones were applied to the RF input to generate IF signals at and GHz. The third order intermodulation (IM3) products appear at and GHz, respectively. The results are shown in Fig. 7.10(b). The measured IIP3 of the circuit is -dbm. For input signal power of -45dBm, it is sufficient to operate in a linear region.

130 7.4 Clock generator 117 Fig. 7.10: LNA-multiplexer-mixer measurement (a) conversion gain with switch ON/OFF status (b) non-linearity IIP Clock generator Circuit design The timing clock generator converts the input clock into four non-overlapping pulses, the control signals CO1-CO4, each with 5% duty cycle. The timing circuit is driven by a sinusoidal input clock but its operation is digital, divided in two parts: a modulus 4 counter and additional logic to obtain the four outputs. Table 7.1 represents the operation states of the timing circuit. Q1 Q0 CO1 CO CO3 CO Table 7.1: Truth table operation of the timing circuit

131 118 Chapter 7. Designs for the 30GHz components The modulus 4 counter is implemented as a two bit counter. The counting is done in gray mode instead of binary. In this way, only one bit changes at the transition between states. This is important in high-frequency operation because it eliminates overlapping and glitches on CO1-CO4 that might occur when the outputs Q0 and Q1 have different switching speed. The circuit including the modulus 4 counters and additional logic is represented in Fig Fig. 7.11: Timing clock generator circuit The D-type flip-flops provide Q0 and Q1 outputs according to Table 7.1 (D1 = Q0 and D0 = Q1/). The outputs CO1-CO4 are obtained by combining the flip-flop outputs Q1 and Q0 using only NOR gates. ( ) ( ) ( ) ( ) CO1 = Q1/ Q0/ = Q1 + Q0 / CO = Q1/ Q0 = Q1 + Q0 / / CO3 = Q1 Q0 = Q1/ + Q0 / / CO4 = Q1 Q0/ = Q1/ + Q0 / (7.1) The flip-flop and NOR gates use differential emitter-coupled logic (ECL), to accommodate the differential control signals required to drive the four switching cells. The external clock input is also made differential. Fig. 7.1 shows the simulated waveforms of the outputs CO1-CO4 connected to the switching input of the switch cells.

132 7.4 Clock generator 119 CO4 [V] CO3 [V] CO [V] CO1 [V] clk[v] Time [ns] Fig. 7.1: Simulated timing clock generator waveforms The simulations were performed with a 4GHz input clock with differential 100Ω load. The peak to peak voltage swing on each output is larger than 600mV, which is adequate to drive the switch well into ON/OFF state. Fig. 7.13: Die photo of the timing clock generator

133 10 Chapter 7. Designs for the 30GHz components Fig shows the photograph of the timing clock generator. The clock input is at the left side while the other three sides are reserved for the three outputs CO1, CO3 and CO4. Output CO is internally matched to 100Ω (see Fig. 7.14) due to limited number of spaces for bond-pad placement. The outputs also include DC blocking capacitors for direct connection to the measurement setup. The die area is 0.8mm and the active circuit occupies 0.1mm 7.4. Measurements The output waveforms were measured with an Agilent MSO6104 oscilloscope. This oscilloscope has a bandwidth of 1GHz which limits the maximum measurement frequency, especially the rise time of the waveform (minimum of 0.35ns). Fig shows the measurement setup for the timing clock generator die shown in Fig Fig. 7.14: Measurement setup of the timing clock generator Fig shows the waveforms of the adjacent outputs CO3 and CO4 with an input clock of 600MHz. At the mean value of the waveforms (0mV) there is no overlapping. The rise time of the waveforms is close to 0.5ns which is mainly due to the oscilloscope. The operation range for this circuit is from 500MHz to 7GHz.

134 7.5 Input delay line 11 Fig. 7.15: Waveforms of the adjacent outputs CO3 and CO Input delay line Circuit design In order to test the phased-array performance, we need to generate phase shifted input signals for the four channels. Due to measurement equipment limitations, the input phase shifts need to be generated on chip. Assuming a fixed incoming signal angle of 8.5 9, and adjacent antenna distance d=λ/, according to (.30), the corresponding electrical phase shift is 6.6, and the corresponding time delay is.4p second. Fig 7.16 shows transmission line structures that can provide such a time delay. 9 The input angle is fixed to 8.5. The reason is firstly due to the limited probe number (system implementation in chapter 8) and chip area, and secondly, satellite communication requires viewing angle with in ±10.

135 1 Chapter 7. Designs for the 30GHz components Fig. 7.16: Transmission line structures for generating 6.6 electric phase shifting (a) 376um (b) 776um (c) 1176um (d) 1576um

136 7.5 Input delay line 13 The built-up of the transmission line is shown in Fig Fig. 7.17: Transmission line structure (a) layout view. (b) cross-section view

137 14 Chapter 7. Designs for the 30GHz components The distance between the transmission lines is 5um, and the single transmission line width is 5um. Table 7. shows the modeling parameters for the transmission lines shown in Fig l c r S Z 0 Loss t φ ph ff Ω Ω db ps (a) 376u (b) 776u (c) 1176u (d) 1576u Table 7.: Modeling parameters for the transmission lines Because we do not want to introduce extra phase difference besides the intended ones that were shown in Fig. 7.16, the distances from each transmission line-end to the LNA input need to be equal for all channels. Structures in Fig have the same length, and they are used in the system level layout to connect the transmission line-end to the LNA input with equal distance. Fig. 7.18: Transmission line structures for equal distance to LNA input (a) type 1 (b) type The distance between the transmission lines is 6um, and the single transmission line width is 5um. Table 7.3 shows the modeling parameters for the transmission lines shown in Fig

138 7.5 Input delay line 15 l c r S Z 0 Loss t φ ph ff Ω Ω db ps (a) type (b) type Table 7.3: Modeling parameters for the transmission lines Fig shows the test structure to monitor the accuracy of the modeling. All values are based on the simulated modeling parameters of the transmission line, 160pH 50Ω Input_1_4 376u LM1 Type 1576u 50fF CM1 (a) 169pH 50Ω Input 3 776u LM Type u 177fF CM (b) Fig. 7.19: Test structure for transmission line model (a) transmission line 376um, 1576um, and type 1. (b) transmission line 776um, 1176um, and type. The inductor pair LM1 and capacitor pair CM1 is designed to match input_1_4 to 100Ω (differentially). Similarly, the inductor pair LM and capacitor pair CM is designed to match input 3 to 100Ω (differentially). If the measurement agrees with this design, it means the transmission line model is correct. Fig. 7.0 shows the integrated die photo of the transmission line test structure.

139 16 Chapter 7. Designs for the 30GHz components Fig. 7.0: Die photo of the transmission line test structure 7.5. Measurements Fig 7.1 shows the simulated and measured S11 results of the transmission line test structure. The simulation result is built on the model listed in Table 7.. From this figure, we can see that the measured result is closely matched to the simulated one. For example, at 30GHz, the measured matching of 376um, 1576um, and type is -14dB, and the measured matching of 776um, 1176um, and type1 is -17dB. Both S11 are below -1dB, hence the simulation model shown in Table 7. is accurate.

140 7.6 Power amplifier 17 Fig. 7.1: Transmission line test structure: simulation result of S11 from (a) input_1_4. (b) input 3. And measurement result of S11 from (c) input_1_4. (d) input Power amplifier As explained in chapter 1, although transmitter design is not the focus of this these, a switch controlled power amplifier is designed in this chapter for reference Circuit design Design power amplifier using SiGe technology has been widely studied [81-87]. The simplified schematic of a 30GHz class A power amplifier with switch controls, is shown in Fig. 7.. The input of the power amplifier connects to a 100Ω differential antenna, and the output matching

141 18 Chapter 7. Designs for the 30GHz components network is designed through a large-signal load-line match to achieve large output power and high power efficiency. Fig. 7.: Simplified schematic of the 30GHz power amplifier with switch controls. The PA switch control uses the same mechanism as used in the multiplexer design. When the control voltage Switch_on is higher than Switch_off, Q4 & Q5 are biased in forward active region, and Q3 & Q6 are in cut-off region, thus allowing the signal to pass Vin to Vout. When the control voltage Switch_on is lower than Switch_off, the bias current is steered toward transistors Q3 & Q6, which connects Vin directly to the supply. To achieve an optimal power gain performance, the emitter width of the bipolar transistor is chosen to be 0.7um and the DC current density is approximately 1mA per um-emitter-width. Together with the output matching resistor of 0Ω, in simulation, the power amplifier achieves an available gain of 16dB and maximum output power of +0dBm at 30GHz.

142 7.6 Power amplifier 19 Fig. 7.3: Die photo of the 30GHz power amplifier. Fig. 7.3 shows the die photo of the 30GHz PA. The die area is 0.75mm and the active circuit occupies 0.mm Measurements Fig. 7.4 shows the measurement setup for the 30GHz power amplifier. The performance of the PA is measured with switches that are controllable implemented by power supplies.

143 130 Chapter 7. Designs for the 30GHz components Fig. 7.4: Measurement setup of the 30GHz power amplifier. The measured spectrum with only DC biasing connected (without RF input signal) is shown in Fig The circuit is oscillating at frequency n*1.33ghz. It indicates that the PA bias loop is not stable. Fig. 7.5: Measured PA output spectrum.

144 7.6 Power amplifier Trouble shooting To find the root cause of the PA instability, we first analyze the PA output stage. A separate PA output stage was available on die. It consists of input bondpads with transmission lines, PA output stage, and output bondpads with transmission lines, as shown in Fig Fig. 7.6: Die photo of the power amplifier output stage verification circuit. With load, open, and short de-embedding structures of the bondpads with transmission lines, we were able to characterize the loading resistance of the PA active stage as shown in Fig 7.7. The result shows that the output resistance is 5Ω. It is not exact 0Ω as expected, but the impact of this difference is small.

145 13 Chapter 7. Designs for the 30GHz components S(1,1) freq (9.50GHz to 30.50GHz) S(1,1) freq (9.50GHz to 30.50GHz) Fig. 7.7: De-embedding PA output stage. Next, we checked the bias loop with momentum simulations in the following steps 10 : Transistor core cells are removed and pins are reserved for multilevel simulation Matrices of vias are merged for simulation to reduce meshes Circular shapes are replaced with rectangles to reduce meshes Resistors, MIM caps, and diodes are removed to reduce meshes Only necessary metal layers and VIAs are reserved for DC biasing, signal flow and ground plane. We made sure that removing other layers will not influence the circuit function. Removed elements are added to the schematic simulation The simplified layout for momentum simulation is shown in Fig The simulation schematic with Momentum cell and re-adding removed cells is shown in Fig Thanks to my colleague Yu Pei who helped to perform this simulation

146 7.6 Power amplifier Fig. 7.8: Simplified layout for full EM (electromagnetic) momentum simulation. Fig. 7.9: Simulation schematic with momentum cell and re-adding removed cells. 133

147 134 Chapter 7. Designs for the 30GHz components The small signal simulation results of the above schematic are shown in Fig Fig. 7.30: Small signal simulation results of the re-modeled PA (a) K factor (b) B1f factor The results show that through the displayed frequency segment, the K factor drops below 1 and the B1f factor drops below 0. It indicates that the PA is not unconditionally stable, and the reason is the non-optimized layout design by adding small base resistors (10Ω) to transistor Q1 to Q6 in Fig. 7., we can improve the PA stability as shown in Fig Fig. 7.31: Small signal simulation results of the re-modeled PA, adding small base resistors (a) K factor (b) B1f factor The results show that through the displayed frequency segment, the K factor stays above 1 and the B1f factor stays above 0. It indicates that the PA is unconditionally stable. In conclusion, for such a high power level circuit, only the EM simulation on the signal path is not sufficient. It is necessary to perform the EM simulation also including the biasing lines.

148 7.7 Conclusion Conclusion In this chapter, the various designs of 30GHz components have been discussed. It comprises the LNA, the multiplexer, the mixer, the clock generator, the integrated delay lines, and the power amplifier. The measurement of the PA shows unstable behavior, and the root cause was found to be the non-optimized layout design. Simulation result shows that by adding small base resistors to the PA transistors, the un-stable problem can be avoided. The components will be connected to construct a time multiplexed phased-array receiver system in chapter 8.

149 136 Chapter 7. Designs for the 30GHz components

150 C h a p t e r 8 8 System integration and verification After demonstrating the 30GHz components in the previous chapter, a fully integrated 30GHz time multiplexed phased-array receiver in SiGe technology is introduced in this chapter. Section 8.1 introduces a first integration of the system, in which only one channel is activated. Section 8. demonstrates an integrated system with four channels. The delay line explained from chapter 7.5 is used to generate fixed electronic phase shift of 6.6 which is equivalent to a spatially angle of 8.5. Section 8.3 makes conclusions for this chapter. 8.1 System with one channel The time multiplexed phased-array receiver system with one activated channel includes one LNA, the multiplexer, the mixer, and the clock generator. Note that the other three channels are internally terminated by 100Ω resistors. The measurement setup of the system is shown in Fig The die photo of the fabricated circuit is shown in Fig

151 138 Chapter 8. System integration and verification Fig. 8.1: Measurement setup of the system with one channel. Fig. 8.: Die photo of the system with one channel.

152 8.1 System with one channel 139 Fig. 8.3 shows the input matching for the system with one channel activated. At 30GHz, S11 is -30dB. Fig. 8.3: Input matching for the system with one channel activated. Fig. 8.4 shows the output spectrum of the mixer with a -38dBm RF signal input at 30GHz, -5dBm LO signal at 0GHz, and -10dBm clock signal at 4GHz (1GHz clock for each channel). The output behaves as a switched 10GHz tone with 1GHz sampling spacing and 5% duty-cycle, confirmed by the theory shown in Fig. 5.. Fig. 8.4: Measured one channel system output spectrum at IF, spectrum view (a) zoom in (b) zoom out. The output behaves as a switched 10GHz tone with 1GHz sampling spacing and 5% duty-cycle.

153 140 Chapter 8. System integration and verification Compared to a conventional receiver, the multiplexer with 5% duty cycle receives 1/4 of the input signal power, which gives another 1dB drop for the 0th order harmonic at 10GHz (this drop will be compensated in the digital domain by combining 4 paths together). Considering also the 3dB loss in each cable, 4.7dB loss in each balun-probe setting and the conversion gain of 18.9dB, the output power at 10GHz can be calculated as 38dBm 3dB 4.7dB dB 1dB 4.7dB 6 db = 49.5dBm (8.1) input power cableloss balunloss F E gain samplingloss balunloss cableloss( ) Resulting in -49.5dBm, which closely agrees to the value shown in marker 1 (Fig. 8.4(a)). 8. System with four channels With the successful design of the system with one channel and the demonstrated delay lines introduced in chapter 7.5, we can demonstrate the time multiplexed phased-array receiver system with four activated channels. The demonstrated system includes the delay lines, the LNA, the multiplexer, the mixer, and the clock generator.

154 8. System with four channels Demonstration with one input signal The system measurement includes the delay lines, the LNA, the multiplexer, the mixer, and the clock generator. The measurement setup is shown in Fig The delay line explained from chapter 7.5 is used to generate fixed electronic phase shift of 6.6 which is equivalent to a spatial angle of 8.5. Fig. 8.5: Measurement setup of system with four channels, incoming signal angle of 8.5.

155 14 Chapter 8. System integration and verification Fig. 8.6: Die photo of the system with four channels, incoming signal angle of 8.5. The die photo of the fabricated circuit is shown in Fig Note that the delay lines 376um, 776um, 1176um, and 1576um are used to make time delay, and the delay lines type 1 and type are used to connect the line-ends with the LNA input with equal line distance.

156 8. System with four channels 143 Fig. 8.7: Input matching for system with four channels, incoming signal angle of 8.5. Fig. 8.7 shows the input matching of the system with four channels, including the delay lines. At 30GHz, S11 is -1dB.

157 144 Chapter 8. System integration and verification Fig. 8.8: Four channels system output spectrums at IF, incoming signal angle of 8.5 (a) theoretical (b) simulated (c) measured, zoom in (d) measured, zoom out Fig. 8.8 shows the four channels system output spectrums at the mixer output with incoming signal angle of 8.5. Fig. 8.8(a) is the theoretical normalized spectrum assuming ideal block components. Fig. 8.8(b) is the simulated spectrum in Cadence with all blocks implemented in practice. Fig. 8.8(c) and (d) are the measured spectrums. The theoretical, simulated, and measured spectrums show good agreement with each other. This confirms the theory explained in chapter 5: the time multiplexed phased-array architecture can achieve spatial domain to frequency domain mapping. Moreover, with 8.5º spatial input, the major part of the energy is stored in the fundamental and ±1 harmonics. So in this case, an analog band-pass filter with a single sideband bandwidth larger than 1GHz can successfully receive this signal.

158 8. System with four channels Demonstration with two input signals With a little change in the delay lines connections, we can make the system demonstrate two signal inputs. One signal comes from a spatial angle of 8.5, and the other signal comes from a spatial angle of The measurement setup is shown in Fig The spatial angle of 8.5 is generated from the following way of connections: The 376um delay line is connected to the LNA 1 that opens at first. The 776um delay line is connected to the LNA that opens at second. The 1176um delay line is connected to the LNA 3 that opens at third. The 1576um delay line is connected to the LNA 4 that opens at fourth. The spatial angle of -8.5 is generated in the above way but with the opposite sequence: The 376um delay line is connected to the LNA 4 that opens at first. The 776um delay line is connected to the LNA 3 that opens at second. The 1176um delay line is connected to the LNA that opens at third. The 1576um delay line is connected to the LNA 1 that opens at fourth. So connecting the 376um and 1576um delay lines to LNA 1 and LNA 4 at the same time; and connecting 776um and 1176um delay lines to LNA and LNA 3 at the same time, we can generate two input signals from angle 8.5 and -8.5º.

159 146 Chapter 8. System integration and verification Fig. 8.9: Measurement setup of system with four channels, and two incoming signals, at angle of 8.5 and -8.5.

160 8. System with four channels 147 Fig. 8.10: Die photo of the system with four channels, and two incoming signals, at angle of 8.5 and The die photo of the fabricated circuit is shown in Fig Note that the delay lines 376um, 776um, 1176um, and 1576um are used to make time delay, and the delay lines type 1 and type are used to connect line ends with LNA input with equal distance.

161 148 Chapter 8. System integration and verification Fig. 8.11: Input matching for system with four channels, two incoming signals angle of 8.5 and Fig shows the input matching of the system with four channels, including the delay lines. At 30GHz, S11 is -0dB.

162 8.3 Conclusion 149 Fig. 8.1: Four channels system output spectrums at IF, two incoming signals angle of 8.5 and -8.5 (a) theoretical (b) simulated (c) measured, zoom in (d) measured, zoom out Fig. 8.1 shows the four channels system output spectrums at the mixer output with two incoming signals, at angle of 8.5 and Fig. 8.1(a) is the theoretical normalized spectrum assuming ideal block components. Fig. 8.1(b) is the simulated spectrum in Cadence with all blocks implemented in practice. Fig. 8.1(c) and (d) are the measured spectrums. Also, with 8.5º and -8.5º spatial inputs, the major part of the energy is stored in the fundamental and ±1 harmonics. We can not separate these two input signals by the coarse filtering, because they are symmetrical in space, and will give the same response. However, with final spatial filtering in the digital domain, they can be separated. The simulated and measured spectrums have un-equal +1 and -1 harmonic amplitude, while the ideal theoretical spectrum has equal +1 and -1 harmonics amplitude. This is due to the non-ideal delay lines and multiplexing switches. Comparing with Fig. 8.8, the frequency spectrum pattern has changed due to incoming signal differences. This confirms with the theory explained in chapter 5.