Radio Receiver Architectures and Analysis

Radio Receiver Architectures and Analysis Robert Wilson December 6, 01 Abstract This article discusses some common receiver architectures and analyzes some of the impairments that apply to each. 1

Contents 1 Introduction 3 Basic Receiver Functionality 3 3 Super-Heterodyne Receiver 3 3.1 RF Filtering............................ 4 3. Low Noise Amplifier....................... 5 3.3 Mixer and Local Oscillator.................... 5 3.3.1 Image Reject Mixers................... 6 3.4 IF Amplification and Filtering.................. 7 3.5 Quadrature Mixing and Second LO............... 7 4 Low IF Receiver 7 5 Direct Conversion Receiver 8 6 Noise Analysis 9 6.1 Local Oscillator Noise...................... 9 7 IQ Imbalance 9 8 Non-linearity Impairments 9 8.1 Second-order Non-linearity.................... 9 8. Third-order Non-linearity.................... 11 8..1 Intermodulation...................... 1 8.. Desensitization and Blocking............... 13 8..3 Cross-modulation..................... 14

1 Introduction The purpose of a radio receiver is to take the observed RF signal and convert it into baseband symbols understandable by the demodulator. The receiver as defined for the purposes of this article doesn t include the estimation or detection of the actual value of the symbols, or any error-correction, equalization or demodulation. Three basic architectures are considered. First, the super-heterodyne architecture is described, which includes a description of all the basic components of each of the considered architectures. Following that the Low IF (LIF) and Zero IF (ZIF) architectures are examined. Finally the different types of impairments that radio receivers must overcome are each analyzed in their own sections. In all cases it is assumed that the transmitted signal is quadrature modulated, so the I and Q channels each have to be received and distinguished. Basic Receiver Functionality Every receiver must perform this minimum set of functions: frequency shift the desired RF signal to baseband, exclude all unwanted signals, and separate the in-band (I) and quadrature (Q) channels. Different architectures accomplish these tasks in different ways, but the most common architectures have a number features in common: they first amplify the observed signal with a low-noise amplifier (LNA), they accomplish frequency shifting by mixing the incoming signal with a local-oscillator (LO), they eliminate the unwanted signals with some combination of filtering and cancelation, and they separate I and Q by mixing the incoming signal with one in-band and one quadrature LO. The basic components will be examined first in the context of the traditionally most popular receiver structure: the super-heterodyne. 3 Super-Heterodyne Receiver The defining characteristic of a super-heterodyne receiver is that the desired signal is shifted to an intermediate frequency (IF) for filtering and amplification before being shifted to baseband. Performing filtering and amplification at an intermediate frequency makes it less expensive in terms of power and 3

area to filter out the unwanted channels than if the same bandpass filtering was done at RF. Also, the IF filter can be fixed and the receiver tuned by adjusting the local oscillator (LO) frequency to shift different RF channels to the IF frequency. The other receiver architectures treated in this article (LIF and ZIF) can be seen as special cases of the super-heterodyne (although the ZIF receiver in particular has a somewhat different set of obstacles to non-zero IF receivers). The basic functional blocks of the super-heterodyne receiver are: RF filtering; low-noise amplifier (LNA); mixer and local-oscillator (LO); IF filtering and amplification; quadrature (I and Q) mixers and second-lo; baseband filtering and amplification; and analog-to-digital converter (ADC). 3.1 RF Filtering Filtering at RF might be applied before and after the LNA. A bandpass preselection filter is often used before the LNA, to limit the signal power entering the subsequent stages, block large out-of-band signals, and help reject the image signal (see 3.3 below). Because the insertion loss of a filter that comes before the LNA contributes directly to SNR degradation it can sometimes be preferable to perform additional filtering after the LNA (an image reject filter) in order to allow pre-lna insertion loss to be minimized. However, because some degree of pre-selection filtering is generally required the current trend is to try to achieve all image-reject filtering at that stage and in fact eliminate the post-lna filter. One of the major requirements of the RF filtering is the attenuate the image frequency. Achieving sufficient attenuation of the image requires a trade-off between the complexity of the filter and the choice of LO frequency. A bandpass filter can provide 10dB of attenuation per decade per pole, and the image frequency occurs at f i = f LO f d, so a lower LO frequency in general demands more aggressive filtering. Note also that a decade means 10 times the desired signal frequency, thus higher carrier frequencies require a higher order filter or greater LO - carrier separation to get the same attenuation of the image in db. A Surface Acoustic Wave (SAW) filter is often used for RF filtering, pre- or post-lna, because of its high selectivity. 4

3. Low Noise Amplifier The purpose of the LNA is to help achieve a high signal-to-noise ratio (SNR) in the receiver. The SNR directly impacts the achievable bit error rate (BER) as well as being important for a number of auxiliary functions such as timing detection and channel estimation. The SNR seen by downstream receiver blocks is the SNR at the antenna combined with the cumulative marginal contribution of all subsequent noise sources. By amplifying the input signal plus noise by a large factor close to the antenna the marginal contribution of the noise added by downstream blocks is minimized, greatly simplifying their design. The amplifier used for this purpose should itself be low-noise in order to minimize degradation of the SNR, hence the use of the low-noise amplifier or LNA. An important characteristic of the LNA is its third order nonlinearity, which, in the presence of unwanted signals, can introduce in-band distortion to the desired signal, or reduce the receiver sensitivity. See Section 8. for details on third-order non-linearity impairments. Any band-selectivity of the LNA is an advantage because it will aid in image rejection. 3.3 Mixer and Local Oscillator After amplification and filtering the signal is multiplied with the LO in the mixer. The LO frequency is tuned so that the desired signal is shifted to the intermediate frequency (f IF ). The LO frequencies and number of LO stages greatly influence the magnitude and type of impairments the receiver must overcome. A receiver will often be trying to detect a signal in a given frequency band that is surrounded by signals in nearby frequency bands intended for other receivers. To successfully detect the desired signal the receiver must prevent the unwanted signals from interfering in the down-conversion process. Of particular concern are unwanted signals that are close in frequency to the desired signal (because they are more difficult to isolate or filter out) and signals that lie at the so-called image frequency of the desired signal with respect to the LO. The image frequency is the same distance from the LO as the desired signal, but on the other side of the LO. Unwanted signals that are transmitted at the image frequency are problematic because mixing a signal with a sinusoidal LO is the convolution in the frequency domain of 5

the two-sided signal spectrum with delta functions at both the positive and negative LO frequencies: y(f) = (s d (λ) + s i (λ)) (δ(λ f + f LO ) + δ(λ f f LO )) dλ (1) where s d (f) is the desired signal and s i (f) is the interfering signal. If the desired signal is centered around frequency f d (also called the carrier frequency) which is less than the LO frequency f LO, and the interfering signal is centered around f i = f LO f d then for f = f IF = f LO f d y(f IF ) = (s d (λ) + s i (λ)) (δ(λ + f d ) + δ(λ + f d f LO )) dλ = s d ( f d ) + s d (f i ) + s i ( f d ) + s i (f i ). () Thus at the output of the mixer both the desired and the image-frequency signals are shifted to frequency f IF (known as the intermediate frequency). To prevent contamination of the desired signal by the image-frequency signal either the image must be filtered out before the mixer, or a more complex image-reject mixer structure must be used, which is discussed below. Note also that in the above analysis the negative frequency part of the desired signal spectrum is what gets translated to f if, due to the use of an LO frequency greater that the carrier frequency (so called high-side LO injection), with the result that the spectrum is reversed compared to the positive frequency spectrum. 3.3.1 Image Reject Mixers To aid in rejecting signals at the image frequency an image reject mixer structure can be used (these mixers don t generally achieve sufficient suppression of the image to eliminate the need for other image frequency filtering). There are two types of image reject mixers: the Hartely and the Weaver. 3.4 IF Amplification and Filtering After the mixer comes the channel select filter, which is a narrow filter around the intermediate frequency with a passband equal to the desired signal band- 6

width, thereby attenuating all undesired signals. Automatic gain control is also usually performed at IF: because the input signal power to the receiver can vary dramatically over time, the receiver must typically detect the input power and adjust the internal gain in order to maintain a relatively constant level at the demodulator, ensuring that the useful range of the ADC is maximized, for example. 3.5 Quadrature Mixing and Second LO Historically, for analogue modulation schemes, the next stage in the receiver was the detector than would generate the desired baseband signal, e.g., an envelope detector or Foster-Seeley discriminator. For complex digital modulation the signal must be converted to the digital domain for detection, so the output of the intermediate frequency stage is mixed with in-band and quadrature versions of a second LO signal and low-pass filtered to create the I and Q signals at a low enough frequency (perhaps DC) to be sampled by an ADC. The low-frequency signals might go through additional gain stages before being sampled. Note that the signal could be shifted down to an alias frequency with respect to the ADC clock rate, rather than to Nyquist, effectively completing the down-conversion during the sampling process. 4 Low IF Receiver As the name suggests, the LIF receiver shifts the desired RF channel down to a lower intermediate frequency than the super-heterodyne (perhaps one or two channel bandwidths above DC), which enables the IF signals to be directly sampled by an ADC. Intermediate frequency processing that was previously performed with analog blocks can now be done digitally, which is generally more flexible and cheaper to implement. This architecture is not without its problems, however. In particular the use of a low IF makes the image frequency very close to the desired RF signal, and thus impossible to remove with RF filtering in practical terms. Using an image reject mixer is possible in some cases, but many systems require much more rejection than can be achieved through that approach alone. Often the preferred approach is to perform quadrature downconversion to a low IF and sample the I and Q signals separately using two ADCs. This maintains the distinction between the desired and image frequencies, and the image signal 7

can then be eliminated through filtering or image reject mixing in the digital domain. The cost of this approach is the additional hardware in the form of the second ADC, in addition to stringent dynamic range requirements on the ADCs because the sampled signal includes both wanted and unwanted signals. 5 Direct Conversion Receiver Also known as a Zero-IF or Homodyne receiver, the direct conversion receiver eliminates the IF stage and shifts the desired signal directly to DC. It may use a pre-selection filter like the superheterodyne does, and uses an LNA for good SNR. Unlike the super-heterodyne the image filter is not required because there is no image. Instead the output of the LNA is mixed with in-phase and quadrature LO signals with the same frequency as the desired signal, followed by low-pass filters, thereby creating the desired I and Q baseband signals directly, which then have the appropriate gain applied before being sampled by the ADCs. Although simpler in concept than the super-heterodyne receiver, and requiring less hardware, the direct-conversion receiver suffers from some impairments. In particular, because the desired signal is being sampled by the ADCs with no frequency offset, any DC offset in the receive chain cannot be eliminated through simple filtering. Ideally the DC offset can be detected and eliminated in the digital domain, however if it is not sufficiently controlled at the ADC input then it reduces the effective range of the ADC that can be used for the desired signal, increasing quantization noise or causing clipping. Unfortunately there are many ways that DC offsets can be created in a receiver chain: 1. Second order non-linearities in the mixer, or to a lesser extent in the LNA if the mixer has some feedthrough (see 8.1). LO-to-RF leakage: the LO signal can leak into the RF port of the mixer or LNA (or any other component before the mixer) and thereby mix with itself. 3. RF-to-LO leakage: the reverse case of the above where the RF signal leaks into the mixer LO port. In general some form of DC offset control is required in the analog domain 8

6 Noise Analysis Noise Figure, Noise temperature, antenna temperature, noise figure of passive elements 6.1 Local Oscillator Noise Reciprocal mixing: because mixing is a convolution operation in the frequency domain, a strong interferer close to the carrier frequency will shift LO phase noise into the signal bandwidth at IF. 7 IQ Imbalance Gain and phase imbalance results in a residual side-band on the other side of the carrier, which contributes to SNR. 8 Non-linearity Impairments The gain of an RF device can be described in general using the Taylor series polynomial v out = α 1 v in + α vin + α 3 vin 3 + α n vin. n (3) Of particular interest are the third- and second-order terms, as these terms can result in unwanted spectral artifacts that interfere with the desired signal, at RF, IF, or baseband. (Higher order terms can create problematic spectral artifacts also, but generally of much smaller magnitude.) Typically, the second order coefficient α is positive while the third order coefficient α 3 is negative. 8.1 Second-order Non-linearity The output of a device with a second-order non-linearity will contain components at the sum and difference of all input frequencies, including the n=4 9

difference of every frequency with itself (i.e. 0 Hz). V out = α 1 V in cos(ωt) + α V in cos (ωt) = α 1 V in cos(ωt) + α V in (1 + cos(ωt)) (4) It is the 0Hz, or DC, component of the output that is usually the most troublesome for a receiver, because the spectrum of the modulating signal often contains some power at DC, thus it can be difficult to remove interfering DC signal without distorting the desired signal. Second-order non-linearity is usually measured in terms of the device s second-order Intercept-Point, or IP, which is the point on the input-output power curve at which the output signal power at ω equals that at ω. The IP can be specified in terms of the input or output power (IIP or OIP respectively), but it is usually specified in terms of the input power. From (4) it can be shown that ( ) α P IIP = 10 log 1 10 (5) α where P = V in, and P OIP = 10 log 10 (α 1 ) α1 α When measuring IP in practice the second harmonic of an input tone will often be outside of the bandwidth of the device, thus it is common to measure IP using a two-tone input signal. (6) V out = α 1 (V a cos(ω a t) + V b cos(ω b t)) + α (V a cos(ω a t) + V b cos(ω b t)) = α 1 (V a cos(ω a t) + V b cos(ω b t)) + ( V + α a (1 + cos(ω at)) + V b (1 + cos(ω bt)) + ) + V a V b (cos ((ω a + ω b )t) + cos ((ω a ω b )t)) (7) Assuming V a = V b the two-tone (TT) IIP is found by setting P T T α1v a / = αv a 4 /, therefore PIIP T T = V ( ) a α = 10 log 1 10 10 α OIP = (8)

and P T T OIP = 10 log 10 (α 1 α 1 α ) (9) 8. Third-order Non-linearity A third-order non-linearity in a receiver component can result in a number of different impairments, depending on where in the receive chain it occurs, and on the presence or absence of power in particular frequency ranges in the received signal. Consider the output of a device with a third-order non-linearity excited by two input sinusoids at frequencies ω a and ω b respectively (the two signals could both be interfering signals, or one might be the desired signal, different scenarios will be examined later) V out = α 1 (V a cos(ω a t) + V b cos(ω b t)) + α 3 (V a cos(ω a t) + V b cos(ω b t)) 3 (10) with a little algebra it can be shown that [ V out = α 1 + α 3 4 + [ α 1 + α 3 4 ( ) ] 3V a + 6Vb V a cos(ω a t) ) ] V b cos(ω b t) ( 3V b + 6V a + 3 4 α 3V a V b cos ((ω a ω b )t) + 3 4 α 3V a V b cos ((ω b ω a )t) + high frequency terms. (11) The high frequency terms are specifically at 3ω a, 3ω b, ω a +ω b, and ω b +ω a. In general these terms are not as important as the other terms because if the input signals are within the band-select filter bandwidth, then the highfrequency outputs are far away from the desired band and will be easily filtered by later stages. However, in scenarios with a large tuning range relative to the carrier frequency a potential interferer at one third of the desired signal frequency might still be within the band-select filter s passband. Third-order distortion effects are usually categorized into three types: Desensitization and blocking; Cross-modulation; Intermodulation. 11

8..1 Intermodulation The terms in (11) at frequencies ω a ω b and ω b ω a are called intermodulation distortion or IMD3 (the 3 indicating the distortion is due to a third-order non-linearity), i.e. the result of the modulation of the signal at ω a by the signal at ω b and vice versa. The inter-modulating signals might be the desired signal and an interferer, or two interferers that create products that fall in the desired signal s frequency band. A common measure of third-order distortion is the third-order intercept point, or IP3, defined as the point at which an IMD3 product has the same output power as the linear frequency term, assuming that the two inputs at ω a and ω b have the same amplitude, i.e. V a = V b. Using that assumption, the on-frequency term is given by V ωa = [ α 1 + 9 ] 4 α 3Va V a cos(ω a t) α 1 V a cos(ω a t) (1) assuming that α 1 >> 9 4 α 3V a. The IMD3 term is given by V ωa ω b = 3 4 α 3V 3 a cos ((ω a ω b )t) (13) Equating P ωa = V ω a / with P ωa ω b = V ω a ω b / gives the Input Intercept Point or IIP3 as P IIP 3 = V a = α 1 3 α 3 (14) and substituting V a = P IIP 3 into (1) or (13) gives the Output Intercept Point or OIP3 as P OIP 3 = V ω a = α3 1 3 α 3 (15) The Inter-Modulation Ratio (IMR) is the ratio of the power at the input signal frequency to the power at the IMD frequency 1

or in terms of the output values 16α IMR 3,dB = 10 log 1V a 10 9α3V a 6 = 10 log 10 16α 1 9α 3V 4 a = 10 log 10 4α 1 9α 3P a = 10 log 10 P IIP 3 P a = (P IIP 3,dB P a,db ) (16) IMR 3,dB = (P OIP 3,dB P ωa,db) (17) where x db = 10 log 10 (x). Now consider the case where the two inputs do not have equal power and P ωa ω b = α 1. P bp a P iip3 P ωb ω a = α 1. P b P a P iip3 (18) (19) with the result that with respect to ω a ω b IMR 3,dB = G db + P a,db + P b,db P iip3,db (0) where G db = α 1. Noting that P oip3,db = P iip3,db + G db (15), P ωa,db = P a,db + G db and P ωb,db = P b,db + G db we also have IMR 3,dB = P ωa,db + P ωb,db P oip3,db (1) 8.. Desensitization and Blocking In the case where the signal V a cos(ω a t) is the desired signal and V b cos(ω b t) is an interferer (or blocker) of much larger amplitude, the interferer can be considered to desensitize or ultimately block the desired signal. Consider the 13

output term at the desired signal frequency, neglecting the term 3α 4 3Va 3 on the basis that V b >> V a ( V ωa = α 1 + 3 ) α 3Vb V a cos(ω a t). () The effective gain of the desired frequency term is the linear gain plus some factor that depends on the third-order non-linearity and the interfering signal strength. Because α 3 is in general negative the interferer has the effect of reducing the effective gain at the desired signal frequency, increasing the minimum required strength of the desired signal for successful demodulation (i.e. desensitizing the receiver), and if the non-linearity and interfering signal strength are strong enough the gain can be reduced to zero, in which case the desired signal is blocked. 8..3 Cross-modulation Consider a scenario that is the same as Section 8.., except that the interfering signal is the amplitude modulated (AM) signal [1 + m cos(ω m t)] V b cos(ω b t). (3) Then at the output of the non-linearity the term at the desired signal frequency is ( V ωa = α 1 + 3 ]) α 3Vb [1 + m + m cos(ω mt) + m cos(ω m t) V a cos(ω a t). (4) Equation (4) shows that the at the output of the non-linearity the desired signal at ω a is amplitude modulated by a scaled version of the signal that modulates the interferer at ω b, hence the term cross-modulation. 14