Six-Port Direct Conversion Receiver: Novel Calibration for Multi-Port Nonlinear Circuits

Transcription

1 153 IEICE TRANS ELECTRON, VOLE87 C, NO9 SEPTEMBER 004 PAPER Special Section on Wave Technologies for Wireless and Optical Communications Six-Port Direct Conversion Receiver: Novel Calibration for Multi-Port Nonlinear Circuits Atsushi HONDA a), Kei SAKAGUCHI, Jun-ichi TAKADA, and Kiyomichi ARAKI, Members SUMMARY An RF front-end using a six-port circuit is a promising technology for realization of a compact software defined radio (SDR) receiver Such a receiver, called a six-port direct conversion receiver (DCR), consists of analog circuit and digital signal processing components The six-port DCR itself outputs four different linear combinations of received and local signals The output powers are measured at each port, and the received signal is recovered by solving a set of linear equations This receiver can easily cover a wide frequency band unlike the conventional DCR since it does not require the precise orthogonality that the conventional one does In this paper, we propose a novel calibration method for a six-port system that includes nonlinear circuits such as diode detectors We demonstrated the demodulation performance of a six-port DCR by computer simulation and experiments at 19, 45, and 585 GHz key words: software defined radio, six-port direct conversion receiver, nonlinearity calibration 1 Introduction To realize the software defined radio (SDR) [1], a multiband/multi-mode receiver with small size and low power consumption is required For example, multi-mode wireless equipment requires a broadband RF front-end circuit that covers a range from several hundred MHz to several GHz Conventionally, heterodyne receivers have been widely employed The disadvantage of heterodyne receivers is its hardware complexity due to multiple local oscillators and IF filters Therefore, direct conversion receivers using I/Q demodulator have been developed due to their compactness The major drawback of I/Q demodulations is DC offset due to self-mixing This is because mixers are used Orthogonality between the I and Q channels is another problem, especially when the required bandwidth is very large, such as in the SDR We studied a six-port circuit as an alternative for the I/Q demodulator Figure 1 shows a direct conversion receiver (DCR) utilizing this circuit The six-port circuit contains some passive components such as 90 hybrids and power detectors [] The RF signal (RF) and local signal (LO) are inputs to the six-port circuit, and four outputs are detected by the power detectors The baseband Manuscript received January 3, 004 Manuscript revised April 13, 004 The authors are with the Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, Tokyo, Japan The author is with the Department of International Development Engineering, Tokyo Institute of Technology, Tokyo, Japan Presently, with the Fujitsu Laboratories Ltd a) ahonda@labsfujitsucom signal is recovered by processing these four power values with some system parameters using a digital signal processor (DSP) These system parameters have to be determined in advance at each frequency through some calibration procedures Since only the power values are measured, there is no need for orthogonality as in the I/Q demodulator Thus, this receiver is expected to operate over a wide frequency range [3] [5] It is considered that one of the problems to be solved for realization of the six-port DCR is nonlinearity of the power detectors The six-port DCR assumes square-law characteristics for power detection Although the power detectors do exhibit square-law characteristics when the input level is low, they cannot maintain them when the input level increases This causes nonlinear distortion in the demodulated signal Thus, we have to apply a new calibration method that includes characterization of the power detectors in the six-port DCR Some calibration methods for power detectors in six-port reflectometers have been reported [6], [7] But they need a power meter or some specific loads, so they are not suitable for communication equipment In this paper, a novel calibration method is proposed that can be performed on-site without using a power meter or any loads Instead of using such reference instruments, this method uses a reference signal fed from the transmitter of the system, as described in Fig We also implemented the six-port DCR and validated the proposed calibration method through experiments as well as computer simulation The rest of this paper is organized as follows Section describes the I/Q demodulation theory of six-port DCRs Section 3 describes six-port calibration theory using the Fourier integral method Section 4 describes a multi-port nonlinearity calibration method Section 5 describes our investigation of I/Q demodulation by computer simulation and by experiments using a fabricated six-port circuit Section 6 concludes our work Six-Port Direct Conversion Receiver Two signals a (t) (RF modulated signal) and a 1 (local unmodulated signal) are assumed as inputs to the circuit Without loss of generality, these two signals are described using complex equivalent baseband notations Output powers P h (t)(h = 3, 4, 5, 6) are detected at each of the power detector Assuming that a (t) is a narrowband signal, P h (t) is expressed by a linear combination of a 1 and a (t) with coef-

2 HONDA et al: SIX-PORT DIRECT CONVERSION RECEIVER 1533 Fig 1 Six-port direct conversion receiver Fig Transceiver configuration for calibration mode ficients A h and B h : P h (t) = A h a 1 + B h a (t) = a 1 A h + B h W(t), (1) where W(t) = a (t)/a 1 is the normalized complex amplitude of the received I/Q demodulated signal which is timevariant, and A h and B h are complex constants determined by S-parameters of the six-port circuit and reflection coefficients of power detectors We define the power ratio h P i (t) between P i (t) and P h (t)(h, i = 3, 4, 5, 6, h i) as hp i (t) = P i(t) P h (t) = 1 + k hk i i W(t) 1 + k h W(t), () where hk i = A i A h, k i = B i A i, k h = B h A h (3) The coefficients h K i, k i,andk h are defined as system parameters of the six-port circuit Among h P i (t) and h K i, there are only three independent quantities due to the following relationship gp i (t) = h P i (t) hp g (t) gk i = h K i (5) hk g Thus, in Eq (), three real values h K i (h is fixed; i = 3, 4, 5, 6, i h) and four complex values k h (h = 3, 4, 5, 6) are the only independent parameters These system parameters can be determined by the six-port calibration method described in Sect 3 When port #4 is taken as the reference, Eq () becomes 1 + k i W(t) 4P i (t) = 4 K i 1 + k 4 W(t), i = 3, 5, 6 (6) (4) Fig 3 Radical center of 3 circles in complex plane; each circle corresponds to 4 P i (t)(i = 3, 5, 6) in Eq (6) (a) The case of perfect measurement and calibration (b) The case of imperfect Equation (6) represents a circle in the complex plane with respect to the complex variable W(t) for each value of i = 3, 5, 6 From the radical center of the intersection of three circles, W(t) can be determined as shown in Fig 3(a) However, for imperfect cases, the radical center may not be unique In those cases, the 3 3 linear equation is solved with respect to W(t), W(t), and W (t) as in Eq (7) From Eq (7), we can obtain a unique estimate of W(t), as shown in Fig 3(b) As described before, W(t) = a (t)/a 1 is the ratio of complex amplitudes of RF and LO signals Therefore, W(t) is equivalent to the I/Q demodulated signal of a (t) 3 Multi-Port Calibration We employ the Fourier integral method [8], [9] to calibrate the system parameters, ie, three real numbers 4 K 3, 4 K 5,and 4K 6 and four complex numbers k 3, k 4, k 5,andk 6 Due to the frequency dependency of the six-port circuit, the system parameters should be calculated at each operating frequency band In the calibration mode the RF signal a is fed from the SDR transmitter, and is assumed ideal in this paper If the relative phase θ of a with respect to a 1 varies from 0 to π, then the power ratio in Eq () is expressed by hp i (θ) = P i(θ) P h (θ) = hk i 1 + k i W 0 e jθ 1 + k h W 0 e jθ (8) where W 0 = a /a 1 Expanding Eq (8) by using the Fourier series, we have hp i (θ) = n= n h C ie jnθ (9)

3 1534 IEICE TRANS ELECTRON, VOLE87 C, NO9 SEPTEMBER 004 k 4 4P 5 k 5 4K 5 k 44 P 5 k 54 K 5 k4 4 P 5 k 5 4 K 5 k 4 4P 6 k 6 4K 6 k 44 P 6 k 64 K 6 k4 4 P 6 k6 4 K 6 k 4 4P 3 k 3 4K 3 k 44 P 3 k 34 K 3 k4 4 P 3 k3 4 K 3 W W W = 4K 5 4 P 5 4K 6 4 P 6 4K 3 4 P 3 (7) where the n-th Fourier coefficient is given by π n h C i = 1 hp i (θ)e jnθ dθ (10) π 0 Note that convergence of Eq (10) requires the condition k h W 0 < 1 (11) By using these coefficients, we obtain the system parameters in the six-port circuit by h k h W 0 = C 3 i h 1 h C = C i i h C = (1) i hk i = 0 h C 1 k h W 0 i 1 + k i W 0 R(k i kh ) W 0 (13) Since W 0 has the same effect on all of k h (h = 3, 4, 5, 6), there is no need to eliminate it from Eq (1) in practice Conventional six-port reflectometers require a standard load and a sliding load to determine the initial phase value However, since the six-port DCR is an item of communication equipment, the phase standard does not have to be established at the calibration procedure Thus, we do not need reference instruments for the six-port DCR Since the SDR transmitter feeds the reference signal a to the six-port receiver as shown in Fig, the phase θ can be easily changed by a small frequency offset between a 1 and a as in [10] 4 Multi-Port Nonlinearity Calibration since the argument of Eq (14) is composed of two complex values x and y To reduce the parameters, we therefore considered the following measurement method Firstly, the phases of x and y are adjusted to be in-phase with each other Then the amplitude of y is varied to measure the nonlinear characteristic of the power detector These steps enable the nonlinearity of the power detectors to be characterized with respect to the single parameter y As mentioned in Sect 3, the RF signal a is from the transmitter as in Fig Therefore, the phase and amplitude of y can be changed easily by controlling a It is noted that the local signal a 1 is assumed to be constant during operation The actual procedure of nonlinear characterization is as follows Firstly, the phase θ of a is adjusted so that x and y are in-phase, and it is defined as θ 0 This is equivalent to finding θ that maximizes the output value P θ 0 = max[ P] (15) θ Then, the power of a, which is defined as P = a,is varied by fixing the phase θ = θ 0 and θ = θ 0 + π as illustrated in Fig 4 When P = 0, the output power P is just a function of the local signal, and it is defined as the reference value P ref WhenP is increased, the output power P deviates from P ref with nonlinearity When P = P max, the output power P approaches P max when θ = θ 0 and approaches P min when θ = θ 0 + π The P max is designed to keep the monotonicity of P, and the dynamic range of the The output of the diode detector including nonlinear characteristics can be modeled as P = α[ Aa 1 + Ba ] = α[ x + y ] (14) where α[ ] indicates a nonlinear function of the arguments, and x = Aa 1 and y = Ba are redefined for explanatory purposes The nonlinearity is assumed to be an arbitrary function, but a monotonically increasing one In Sects and 3, the ideal square law of Eq (14) is assumed But in practice, it is not necessarily true, as the level of input signal increases Therefore, nonlinear calibration is required as the data pre-processing Our proposed calibration method has two steps: nonlinearity characterization and linearization To characterize the power detector in the six-port circuit, the nonlinear response of the output signal should be measured with respect to the amplitude of input signal But it is not easy to control the amplitude of the input signal Fig 4 Nonlinearity calibration In the calibration procedure, we assumed the amplitude and phase of a can be exactly controlled It is a reasonable assumption, since generally the SDR transmitter has high-precision DACs and also the SDR transmitter and receiver share the same frequency standard as in Fig to keep relative phase accuracy

4 HONDA et al: SIX-PORT DIRECT CONVERSION RECEIVER 1535 Table 1 Look-up table for linearization P: measured data γ: intermediate parameter P max 1 P ref 0 P min 1 system is determined from this value and the noise floor For convenience the intermediate parameter γ is introduced as γ = P when θ = θ 0 (16) P max γ = P when θ = θ 0 + π (17) P max The nonlinearity of the power detector can be characterized by the single parameter γ Now, the nonlinear characterization has been accomplished The next step is linearization As illustrated in Fig 4, the nonlinear function is linearized as follows Fig 5 Configuration of fabricated six-port circuit P = ( P max P ref )γ + P ref (18) = Bγ + à (19) This can be done by constructing a look-up table (LUT) as shown in Table 1 As for the data pre-processing, γ corresponding to measured P is selected by using Table 1, and is substituted into Eq (18) to calculate the linearized value P Now, the linearization process has been accomplished It is noted that B and à in Eq (19) are functions of B and A in Eq (14) This means that if we take other values of B and Ã, we get different values for the linear system parameters in Eq (3) Therefore, if we perform the linear calibration after the nonlinear calibration, the setting of B and à has no effect on the demodulated signal W(t) 5 Computer Simulation and Experiments 51 Fabricated Six-Port Circuit Figure 5 shows a schematic diagram of the fabricated sixport circuit used in the simulation and experiments Four 90 hybrids, two matched loads, and four diode detectors are employed as in [8] Figure 6 shows its photograph Two signals, LO and RF, are inputs to the six-port circuit and denoted by the symbols a 1 and a (t) respectively Assuming ideal circuit elements, the theoretical values of the detected powers P h (h = 3, 4, 5, 6) can be expressed in terms of a 1 and a (t) as follows [] P 3 (t) = 1 ( a1 a (t) ) (0) P 4 (t) = 1 (a 1) (1) Fig 6 P 5 (t) = 1 P 6 (t) = 1 Photograph of fabricated six-port circuit ( ) 1 + j a 1 + ja (t) ( ) 1 + j a 1 + a (t) () (3) Equation (1), shows that a (t) is not included in P 4 (t), namely P 4 is constant Therefore, we used port #4 as the reference port From Eqs (0), (1), (), and (3), the theoretical system parameters 4 K 3, 4 K 5, 4 K 6, k 3, k 4, k 5,and k 6 of the fabricated six-port circuit can be calculated using Eq (3) as follows 4K 3 = 1, 4K 5 = 1, 4K 6 = 1 k 3 =, k 4 = 0, k 5 = 1 + j, k 6 = 1 j 5 Computer Simulation In this subsection, the validity of the linear and nonlinear calibrationproceduresdescribedinsects3and4isconfirmed by computer simulation The input-output characteristics of the power detector are assumed to be as shown in Fig 7 The power detector obeys the square-law until the input voltage becomes V, but has saturated characteristics thereafter The input signals conditions for a 1 and a are summarized in Table Firstly, the simulation result without nonlinear calibration is illustrated in Fig 8 This graph shows the constellation pattern of demodulated signal for 16QAM modulation

5 1536 IEICE TRANS ELECTRON, VOLE87 C, NO9 SEPTEMBER 004 Fig 7 Input-output characteristic of power detectors in computer simulation Fig 9 Constellation pattern of received signal with nonlinear calibration (simulated ( ) andtheory( )) Table Input signal conditions for calibration and demodulation a 1 a nonlinear calibration 4 e jθ 0( 36 < < 36) linear calibration 4 e jθ, (0 <θ<π) demodulation 4 16QAM, average a = 15 Fig 10 Experimental setup for the six-port DCR is shown in Fig 9 From this figure and Table 3, we could confirm the validity of the proposed nonlinear calibration method It is noted that the estimated system parameters in Table 3 with nonlinear calibration are scaled so that comparisons with theoretical values can be made easily Fig 8 Constellation pattren of received signal without nonlinear calibration (simulated ( ) andtheory( )) Table 3 Calculated system parameters with and without nonlinear calibration without nonlinear calibration with nonlinear calibration 4K K K k j j k j j k j j k j j We can see the obvious distortion in the demodulated symbols This is because of the erroneous estimation of system parameters as described in Table 3 As the next step, the proposed nonlinear calibration is employed The constellation pattern of demodulated signal 53 Experiments We experimentally investigated the six-port DCR at 19, 45, and 585 GHz The experimental setup is shown in Fig 10 The six-port circuit, four power detectors, and lowpass filters are composed of coaxial components as in Fig 6 Although the quadrature hybrids we employed can operate in a wide band from to 8 GHz, they were not tuned in each measured frequency band One of the two signal generators outputs an RF modulated signal such as 16QAM They are synchronized by the reference frequency Four output signals were sampled by the 4-channel digital oscilloscope All the computations were performed off-line using a personal computer (PC) For the experiments, the digital oscilloscope and PC were used in place of the ADCs and DSP in Fig 1 in this experiments As the first step, the nonlinear calibration was performed at each output port except port #4 Both LO and RF signals were set as CW, and the LO power was fixed

6 HONDA et al: SIX-PORT DIRECT CONVERSION RECEIVER 1537 Table 5 Measurement conditions frequency 19, 45, and 585 GHz LO power 4dBm RF power (PEP) 8dBm( dbm) modulation scheme 16 QAM filtering raised cosine filter roll off factor 05 symbol rate 15 ksym/sec sampling 1Msamp/sec, 8 bit Relationship between γ and the deviation from reference volt- Fig 11 ages Table 4 System parameters in the experiments at each frequency 19 GHz 4 GHz 58 GHz 4K K K k j j j k j j j k j j j k j j j Fig 1 Constellation pattern of received signal at 19 GHz at 4 dbm The LO power value was determined to satisfy Eq (11) Firstly, the output voltages were measured when the RF signal was turned off, and they were treated as reference voltages Secondly, the phase of the RF signal was adjusted to maximize the outputs to find the in-phase conditions Thirdly, the amplitude of the RF signal was swept until dbm, which is the maximum value Then the deviations from the reference voltages were measured Figure 11 shows the results of measurement, which corresponds to the look-up table Finally, linearization was performed as shown in Sect 4 After nonlinear calibration, the linear calibration was performed The six-port system parameters including errors of the 90 hybrids were parameterized through the linear calibration The LO and RF signal power levels were 4 and 4 dbm respectively The frequency of a hadanoffset of 1 khz from a 1 Then, the output voltages were measured while the relative phase θ varied in the range of π, andthe system parameters 4 K 3, 4 K 5, 4 K 6, k 3, k 4, k 5,andk 6 were calculated according to the method described in Sect 3 The system parameters at each frequency are shown in Table 4 After the system parameters had been determined, the RF modulated signal was fed to the RF port The measurement conditions are shown in Table 5 The experimental results at 19, 45, and 585 GHz are shown in Figs 1, 13, and 14 respectively Figure 15 shows the constellation without nonlinear calibration at 585 GHz From these figures, we could validate the proposed method experimentally as well as in the simulation It is noted that the degradation in Fig 13 Constellation pattern of received signal at 45 GHz Fig 1, 13 and 14 is mainly due to the accuracy of the LUT in the nonlinear calibration It is analyzed as follows There are two factors of degradation, ie, quantization error and nonlinearity characterization error As for the quantization error, the effect of 8-bit ADC was evaluated in the simulation As a result it was found that the error due to 8-bit ADC is almost negligible It is because in the calculation of six-port system parameters the quantization error is smoothed as a result of Eq (10) Furthermore this error is decreased by increasing the number of sample points in the numerical integration of Eq (10) On the other hand, in the experiment, only 4 different values of a were used to characterize the nonlinearity of power detectors The small number of samples was due to the limitation of instruments And the LUT of Fig 11 was created by interpolating the 4

7 1538 IEICE TRANS ELECTRON, VOLE87 C, NO9 SEPTEMBER 004 Architecture for the purpose of the 4th generation mobile communication systems References Fig 14 Constellation pattern of received signal at 585 GHz Fig 15 Constellation pattern of received signal without nonlinear calibration at 585 GHz samples using MMSE approximation Therefore, it is the main reason of degradation of the demodulated signal By improving the nonlinear characterization, the demodulated results will also be improved 6 Conclusion The six-port direct conversion receiver is a promising technology for realization of the software defined radio receiver, since it can easily cover a wide frequency band In this paper, we proposed a novel calibration method for a six-port system that includes nonlinear circuits such as diode detectors If the signal from the SDR transmitter is used as a reference signal, the proposed method can be performed onsite without using any power meter or standard loads, which are required in the conventional method The validity of the proposed method was confirmed in experiments as well as in the computer simulation [1] J Mitrola, The software radio architecture, IEEE Commun Mag, vol33, no5, pp6 38, May 1995 [] GF Engen, An improved circuit for implementing the six-port technique of microwave measurements, IEEE Trans Microw Theory Tech, volmtt-5, no1, pp , Dec 1977 [3] R Kohno, M Abe, N Sasho, S Haruyama, RM-Zaragoza, E Sousa, F Swarts, P Van Rooyen, Y Sanada, L Michael, H Amir- Alikhani, and V Brankovic, Universal platform for software defined radio, International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS 000), vol1, pp53 56, Nov 000 [4] M Abe, N Sasho, V Brankovic, and D Krupezevic, Direct conversion receiver MMIC based on six-port technology, European Conference on Wireless Technology 000, Paris, Oct 000 [5] J Li, RG Bosisio, and K Wu, Computer and measurement simulation of a new digital receiver operating directly at millimeter-wave frequencies, IEEE Trans Microw Theory Tech, vol43, no1, pp766 77, Dec 1995 [6] JR Juroshek and CA Hore, A dual six-port network analyzer using diode detectors, IEEE Trans Microw Theory Tech, volmtt- 3, no1, pp78 8, Jan 1984 [7] E Bergeault, B Huyart, G Geneves, and L Jallet, Characterization of diode detectors used in six-port reflectometers, IEEE Trans Instrum Meas, vol40, no6, pp , Dec 1991 [8] T Yakabe, Six-port based wave-correlator with application to beam direction finding, IEEE Trans Instrum Meas, vol50, no, pp , April 001 [9] T Yakabe, Precise calibration of 6-port circuit and its application to the microwave measurement, Doctoral Dissertation, Tohoku Univ, Jan 1996 [10] J Li, RG Bosisio, and K Wu, Dual-tone calibration of six-port junction and its application to the six-port direct digital millimetric receiver, IEEE Trans Microw Theory Tech, vol44, no1, pp93 99, Jan 1996 Atsushi Honda was born in Chiba, Japan, in 1977 He received the BE degree in electrical and electronic engineering from Tokyo Institute of Technology, Tokyo, in 003 He has joined Fujitsu Laboratories, Yokosuka, Japan, in 003 His current research interests are microwave circuits and antenna technologies for wireless communications Acknowledgement This work is partly supported by Telecommunication Advancement Organization of Japan (TAO) project entitled Research and Development of the Software Defined Radio

8 HONDA et al: SIX-PORT DIRECT CONVERSION RECEIVER 1539 Kei Sakaguchi was born in Osaka, Japan, on November 7, 1973 He received the BE degree in electrical and computer engineering from Nagoya Institute of Technology, Japan, in 1996, and the ME degree in information processing from Tokyo Institute of Technology, Japan, in 1998 From 000 he is a Research Associate at Tokyo Institute of Technology He received the Young Engineer Awards from IEICE Japan and IEEE AP-S Japan chapter in 001 and 00, respectively His current research interests are in mobile propagation measurement, MIMO communication systems, and software defined radio He is a member of IEEE Jun-ichi Takada was born in Tokyo, Japan, in 1964 He received the BE, ME, and DE degrees from Tokyo Institute of Technology, Japan, in 1987, 1989, and 199, respectively From 199 to 1994, he has been a Research Associate at Chiba University, Chiba, Japan From 1994, he has been an Associate Professor at Tokyo Institute of Technology, Tokyo, Japan His current interests are wireless propagation and channel modeling, array signal processing, and ultra-wideband radio He received the Excellent Paper Award and Young Engineer Award from IEICE, Japan, in 1993 and 1994, respectively He is a member of IEEE and ACES Kiyomichi Araki was born in 1949 He received a BE degree in Electrical Engineering from Saitama University in 1971, and ME and DE degrees in Physical Electronics from the Tokyo Institute of Technology in 1973 and 1978, respectively From 1973 to 1975, and from 1978 to 1985, he was a Research Associate at the Tokyo Institute of Technology; and from 1985 to 1995 he was an Associate Professor at Saitama University In and he was a visiting research scholar at the University of Texas, Austin, and the University of Illinois, Urbana, respectively Since 1995 he has been a Professor at the Tokyo Institute of Technology Dr Araki is a member of IEEE and the Information Processing Society of Japan His research interests include information security, coding theory, communication theory, circuit theory, electromagnetic field analysis and simulation, microwave circuit analysis, and design