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Communications receiver design using digital processing
DIGITAL
SIGNAL
PRGCESJNG
2, 2-13 (19%‘)
Communications Receiver Design Using Digital Processing Kesh Bakhru Cubic Defense Systems, 9333 Balboa Avenue, San Diego, California
1. INTRODUCTION
A digital processing receiver performs most receiver functions using digital processing techniques. Examples of such functions are frequency translation, filtering, demodulation, automatic gain control, mode of operation, equalization of group delay distortion, and passband ripple. An initial step in defining the receiver bandwidth and signal level is performed in the analog domain. The information-bearing signal is then sampled and quantized at a suitable IF frequency. The remainder of the processing is performed digitally using digital signal processing (DSP) techniques. The digital approach takes advantage of the everincreasing capability of digital signal processing and the potential of miniaturization of all digital receivers using VHSIC technology. Other advantages of using DSP are that it increases the reliability and repeatability of demodulating and monitoring the received signals. The signal output from an analog receiver can vary from unit to unit, and even the same unit can vary with time, temperature, and calibration. Conventional analog receivers use RF stages, frequency synthesizers, IF amplifiers, and analog demodulators which not only pose internal RF interference problems but also do not lend themselves to low-cost production or reduction in size, weight, and cost. The objectives of the digital receiver design are to provide overall improved performance, reliability, maintainability, and reduced cost and weight and to be cost-effective. The architecture and design lend themselves to flexibility in providing enhanced functional capa1051.2004/92 $1.50 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
92123
bility through the sharing of software and hardware and can be expanded to integrate other functions in the receiver for future growth. The research and development necessary for the advanced digital receiver technology were performed at Cubic Defense Systems under various IR&D projects and the experience acquired is being applied to the design of various receivers, such as communications receivers in HF and VHF/UHF bands, a multichannel digital sonobuoy receiver for ASW application, Global Positioning System receivers, and range and instrumentation receivers. Study of the digital receiver design requires a substantial background in communications receiver design as well as in digital signal processing techniques. The study may be broken into the following steps: (1) selection of candidate receiver architectures; (2) preliminary analysis and performance assessment; (3) comparison and selection of the preferred approach; (4) distortion analysis of each receiver stage for the various modulations; and (5) analysis of the overall receiver performance. The application of DSP technology to the design of the digital receiver can be illustrated by following the design of the VHF/UHF communication receiver developed at Cubic Defense Systems. The specifications of this receiver are tabulated in Table 1. Minimization of signal distortion is one of the objectives of such a design, and Section 2 discusses the sources of distortion in analog and digital receivers. Section 3 describes four different receiver architectures and compares their performance, advantages, and limitations. Section 4 discusses various digital demodulation schemes, and finally, Section 5 summarizes these design steps.
TABLE VHF/UHF
Receiver
Frequency range Dynamic range Noise figure, max Programmable channels Selectable IF bandwidths Modulation Tuning resolution IF rejection Image rejection Intermodulation distortion Distortion Gain control Readout Receiver processor Controls I/O bus External
reference
architecture
oscillator
1 Specifications 20-500 MHz 72 dB 10 dB 100 Various to 4 MHz AM, FM, FSK, USB, LSB 10,100, and 1000 Hz 80 dB 80 dB Third order-110 dBm from two inputs at -20 dBm Minimum achievable Manual/automatic Digital Is-bit Front panel/external RS-232/422/485 MIL-STD-118/114 Yes
2. DISTORTION IN ANALOG VERSUS DIGITAL RECEIVERS (a) Analog Receivers A number of factors affect the desired performance of well-designed analog radio frequency receivers. Many of these factors are independent of the frequency of operation, whereas other performance limitations are frequency dependent. For example, internal receiver noise is not usually a performance limitation at VLF, LF, or MF but becomes a significant limitation at VHF and UHF. The inability to handle extremely strong interfering signals may become a performance limitation at any frequency and the inability to reject intermodulation products resulting from two such strong signals with a particular frequency spacing from each other and from a desired signal can be a problem at any frequency at which channel assignments are evenly spaced and transmitters are located in close proximity to one another. In general, the most pertinent performance limitations in the design of a receiver are Noise Figure, Input Selectivity, RF Amplifier Dynamic Range, Mixer Dynamic Range, Mixer Spurious Responses, Oscillator Sidebands, Oscillator Phase Noise, Filter Selectivity, Filter Dynamic Range, IF Amplifier Dynamic Range, Detector Linearity, Detector Dynamic Range, Automatic Gain Control Range, and Automatic Gain Control Attack and Decay Times. In considering these performance limitations, the various states of receivers may contribute to one or more of each of the parameters.
Analog RF receivers introduce various distortions into the received signals. Amplitude-modulated signals can suffer from distortions caused by imperfections in the amplitude detectors and imperfect filtering in the IF and baseband parts of the receiver. If signals are affected by fading, a property of the AGC circuit can introduce substantial and noncorrectable distortions. Frequency synthesis can add phase noise and envelope distortions in single and vestigial sideband systems. Different applications will experience one or another combination of distortions. Modulated FM signals, even with the advantages provided by wideband FM, nevertheless are affected by other substantial imperfections which cause distortion of the demodulated signals. One of the more important sources of distortions is filtering. The RF bandwidth of a typical FM signal is very wide. Because filtering must be performed to meet acceptable noise performance, part of the FM spectrum inevitably will be lost, which causes very specific distortion of the demodulated signals. Another source of distortion in FM receivers is the shape of the frequency response of the analog filters. Table 2 shows various sources of distortion in analog receivers. Discussions on how to minimize the distortion by proper design of conventional receivers can be found in the literature [1,2]. Provided that received signals are simply listened to, the above distortions can be compensated by human intelligence or ignored because of the limited sensitivity of our ears. However, when the signals are analyzed by digital means, which can be as accurate as TABLE Sources 1. Deterministic Amplitude
Nonlinear
2. Statistical Phase noise
Image
in Analog
Receivers
Bandpass filters, low-pass filters, narrowband amplifiers. Errors in local oscillator frequencies. Bandpass filters, low-pass filters, narrowband amplifiers. Causes nonlinear distortion of demodulated FM/PM signals. Amplifiers-Harmonic and/or intermodulation distortion, especially variable gain/AGC stages. MixersHarmonic and intermodulation distortion.
Frequency Phase/group delay
Thermal
of Distortion
2
noise noise
Jitter in local oscillator used for down conversion, especially if synthesized. Amplifier noise, primarily determined by first stages of amplification. Possible source in superhetrodyne designs. Controlled by appropriate system and filter design.
we desire, imperfections in the receiver become an obstacle. The objective of the design study is to provide a receiver design with absolutely minimal distortions or colorations of any signal amplitude, frequency, and phase.
(b) Digital
Receivers
Digital receivers have many attractive features which make them outperform analog counterparts. The following are some of the salient features of digital receivers: potential for less signal distortion; l automated processing; . flexibility, commonality, and sophisticated service functions can be built into the system, as these functions are software controllable; l reduced component size due to the VLSI technique, which in turn saves space, weight, and power consumptions; l reliability due to modularity and reduced external connections; . less susceptible to drifts due to component aging and changing ambient conditions; l cost-effective due to time-division multiplexing and time-sharing capabilities of digital networks. l
Table 3 lists the distortions in digital receivers grouped into deterministic and statistical sources. The deterministic sources arise from finite word lengths used to represent the filter coefficients. These effects can be analyzed using either closed-form ex-
TABLE 3 Sources of Distortion in Digital Receivers 1. Deterministic Amplitude
IIR/FIR filters, DFT. Controllable by proper design. Errors in clock and/or local oscillator. These sre hardware related and can be controlled by careful design. IIR filters needs equalizer. No such problem with FIR filters. Can cause distortion in demodulated FM signal. A/D conversion causes harmonic and intermod products; depends on number of bits of A/D converter. Approximation in demodulation algorithms like Arctan, Square Root, etc. Mismatch in I,Q channels with respect to Gain, Phase, primarily in direct conversion to baseband approach.
Frequency
Phase/group delay Nonlinear
2. Statistical Analog A/D conversion Round-off
noise
Receiver front-end-RF filter/amplifier noise Granular noise-decreases with increasing number of bits of A/D, aperture timing errors. Due to finite precision arithmetic. IIR filtersdepends on specific filter structure. FIR filters-controlled by proper design. DFT processor-same as in FIR filters.
DIGITAL OUTPUT
FIG.
1.
Block
diagram
of a direct
digitization
digital
receiver.
pressions or iterative computer solutions. Furthermore, these filter sensitivities also depend on the specific filter structure used in the implementation. In any case, the coefficient sensitivities can be minimized by proper design of these filters. Another deterministic source arises from harmonic distortions introduced by the A/D converter. Analytical results for estimating these distortions are available in the literature [3-61. The statistical sources of distortion come from A/D conversion and round-off errors due to finite precision used in the arithmetic operation. Analytical expressions for evaluating the amounts of distortions introduced by these sources are available [3-61, and, therefore, their effects can be minimized by proper design.
3ANDlDATE RECEIVER ARCHITECTURES Four candidate receiver architectures are discussed from a system-level standpoint. They are: (i) receiver based on direct digitization of RF signal, (ii) constructive aliasing using the aliasing effect due to undersampling or sampling rate conversion in a constructive manner, (iii) direct conversion to baseband, and (iv) superheterodyne receiver. The proper choice from among these architectures is influenced by various factors, such as intended application, cost, size, and feasibility [9-l 11.
(i) Direct
Digitization
A block diagram of the direct digitization receiver is shown in Fig. 1. The received RF signal is first filtered to reject out-of-band noise. This filter also serves as an anti-aliasing filter. The filtered bandpass signal is then sampled and quantized to the required number of bits of accuracy. Further processing of this signal is done digitally. Since the RF bandwidth covers the range 20 to 500 MHz, the initial sampling rate should be in excess of a gigahertz. However, since the individual carriers have
TABLE Comparison
for an M = 100 Decimator
One-stage
Filter
ratios
M,
lengths
Computation Computational stage RR
N,
(MPS) savings design
over
Two-stage
Two-stage
IIR
IIR Decimation
4
IIR
TABLE
M2 = 10
M, = 50 M2 = 2
M, = 10 Mz = 5 M3 = 2
N, = 4 N2 = 14
N, = 4 N2= 14
Nl N,
2200
810
920
598
N, = 38 N2 = 38 N3 = 356 406
1.0 14
2.7 18
2.4 18
3.7 798
5.4 436
M, M,
= 14
M,
= 10
5
Onestage
Direct form
Twostage
TABLE Filter FIR
Threestage l
lengths
MPS Rate reduction (MW Total storage for filter coefficients
= 423 = 347
niques will be chosen on the basis of accuracy, stability, and implementation factors. A comparison between finite impulse response (FIR) and infinite impulse response (IIR) filters is shown in Table 6. As a further comparison between the two filter types, Fig. 2 from [6] shows the number of multiplications per second required by these two filters to meet the same specifications. Performance, advantages, and limitations of direct digitization. This receiver architecture has the theoretical potential for the least signal distortion of any of the receiver candidates. However, to cover the full bandwidth of 500 MHz, the receiver dynamic range will require an A/D converter at sampling rates of i GHz with 12-bit resolution (72-dB dynamic range). Unfortunately, at these sampling rates, it does not appear that the device technology will support a 12bit instantaneous dynamic range. Six- to eight-bit versions may be achievable in the near future. Alternatively, lower carrier frequency and narrower signal
Comparisons of Filter Characteristics for Several Multistage Implementations of a Low-Pass Filter with Specifications F = 1.0, fp = 0.00475, fs = 0.005, 6, = 0.001, 6, = 0.0001
Filter
FIR
= 20 = 5
= 100
much smaller bandwidths than the sampling rate, there is a great potential for sampling rate reduction and this in turn lowers the expected computing speed of the signal processors. If the sampling rate reduction is achieved in stages, significant savings can be achieved in computational tasks and memory. An example is presented in Tables 4 and 5. One advantage of using multiple stages is that the decimated signal is already in the proper form so that demodulation is a simple task. The demodulated signal can be D/A converted if an analog output is desired, or the digital audio output can be processed further. In designing a direct digitization receiver, one would consider the various signal distortions present in the system, as discussed in the previous section. A/D converters will be selected on the basis of speed requirements, future advancements in technology, hardware limitations, etc. Suitable filtering tech-
rates
Three-stage
one-
Storage
Decimation
Two-stage FIR
7,795
165
11.9
10 5 2 50 44 356 9.4
1
47.2
655
829
-
100
15,590
16,466
50 2 423 347
l
l
l
l l
7,795
8,233
385
225
6
Comparison
filters
IIR
Exact phase linearity can be achieved Excellent passband and stopband characteristics possible Generally requires longer filter lengths Unconditionally stable
l
No limit cycles Need smaller coefficient word lengths
l
l
l
l
l
filters
Only approximation is possible Excellent passband and stopband characteristics possible Requires smaller filter orders Stability problems exist due to finite coefficient word length Possibility of limit cycles Need larger coefficient word lengths
(ii)
L 6p= 0.025 &= 0.0031 wm=0.2n A~=(wswp)/2n M =5
sua ;i z g 40 3 a 5 93-
FIR
LINEAR
30 20
/
PHASE
TRANSORMED ,ELLIPTIC
b 0.005
OPTIMUM
Aliasing
According to the Nyquist theorem, a bandpass signal must be sampled at a rate that is at least twice the bandwidth of the signal, provided that the signal band falls within half the sampling frequency. This will ensure perfect reconstruction without destructive aliasing, as is shown in Fig. 3. However, it is possible to sample a bandpass signal below the Nyquist rate and yet recover the signal frequencies lying beyond half the sampling frequency without aliasing distortion. For constructive aliasing, all the frequencies, f, in the signal bandwidth satisfy nfJ2 < f =c(n + l)f,/2, where f, is the sampling rate and n is a nonnegative integer. This will significantly ease the burden on the A/D conversion speed and, therefore, lead to a viable approach to digital receiver implementation. The concept of constructive aliasing is illustrated in Fig. 3. Figure 3a shows the RF bandpass signal, Fig. 3b, the Fourier transform of the sampling function, and Fig. 3c, the spectrum of the sampled function. Figure 3e shows the spectrum of the desired band signal after band-pass filtering. Similarly, Fig. 4 shows the constructive aliasing for a low-pass signal. The architecture of the constructive aliasing receiver is shown in Fig. 5. It is identical to that of the
ELLIPTIC
k
Constructive
IIR
0.05 !lF
FIG. 2. Multiplication rate vs AF for various equiripple FIR and RR single-stage decimeters. AF, transition band relative to the sampling frequency; a,,, passband ripple; 6,, stopband ripple; M, decimation factor; We, stopband edge relative to half the sampling frequency; wp, passband edge relative to half the sampling frequency. Reprinted with permission from R. E. Crochiere and L. R. Rabiner, Multirate Digital Signal Processing, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1983.
bandwidths would be achievable with 12-bit sampling. The digital processing rates required may also be excessive for device technology of the near future.
+ B II r/ +--RF
BAN0
+
t (n+%)FS
b
(n+l)FB
+ B
FIG.
3.
Constructive
aliasing
for bandpass
signals.
B
FIG.
4.
Constructive
direct digitization receiver except for the A/D conversion followed by bandpass filtering. This technique requires an additional filtering operation compared to the previous case. However, the reduced sampling rate used in A/D conversion should more than offset the additional filtering task. The underlying consideration for the constructive aliasing and direct, digitization approach is the major impact of A/D device technology on the viability of receiver design. With regard to the sources of distortion and the choice of filtering type to be used, the same arguments hold here as for the direct digitization receiver. Performance,
advantages, and limitations
of the con-
aliasing
for low-pass
signals.
This approach holds the structive aliasing approach. promise of practical implementation and has the advantage over the other candidates of being a fully digital approach except for front-end filtering and amplification. This receiver, as with the direct digitization example, offers the theoretical potential for minimal distortion. The theoretical performance limits will be approachable as device technology improves. This candidate also offers greater growth potential to take advantage of new device technology. Another obvious advantage is that the only nonlinear element is the wideband front-end amplifier. Unfortunately, all of the gain to cover the dynamic range must take place in this amplifier. This would place an upper limit on the dynamic range achievable. (iii)
Direct
Down
Conversion
to Baseband
One can use the principle of quadrature modulation to convert a narrow bandpass signal into quadrature components. A narrow bandpass signal can be expressed as AUDIO
D/A
DEMO,,
“%2L
CONVERTER
+ DIGITAL
FIG.
5.
Block
diagram
of a constructive
aliasing
digital
receiver.
x(t) = a(t)cos w,t - b(t)sin
wJ,
(1)
where a(t) and b(t) are low-pass signals band-limited
to W Hz. These two signals also represent lope and phase of the carrier given by
the enve-
envelope = vc?(t) + b’(t)
The quadrature signals can be recovered by mixing the signal x(t) with quadrature carriers and low-pass filtering. We can then sample a(t) and b(t) at a 2W samples per second rate for digital processing. As the signal is already in the proper format, demodulation is a simple task. A block diagram of the receiver is shown in Fig. 6. A digital receiver for the Global Positioning System, utilizing down conversion to baseband, has been implemented at Cubic. A block diagram of this receiver is shown in Fig. 7. The mixed-down signal contains Doppler frequency residual and is filtered through a matched filter before it passes through the 4-bit A/D converters. At this point, the signal is digitized and all the remaining sensor circuitry is digital. Only a 4-bit A/D was used because the “signal” is buried in noise and has a small dynamic range. Doppler removal and C/A code correlation are performed in the digital correlator, which is driven both by the code and by Doppler digitally synthesized and controlled oscillators (DCOs). Final output to the I/O preprocessor from the correlator is four pairs of 16-bit
I- and Q-channel correlations spanning four C/A code half-chips in correlation space. In the receiver structure of Fig. 7 the crucial stage is the down conversion stage. Improper phase of the local oscillator will cause serious degradation in signal extraction. Since sampling takes place at baseband rate, the signal processing portion of the receiver offers no unusual challenges. Performance, advantages, and limitations of direct conversion to baseband. The direct baseband conversion and digital signal processing offer some architectural advantages over other approaches by simplifying some of the requirements for minimum A/D rates (this means one can use more bits), no mixer image, and simple frequency synthesizer. The negative feature is the requirement of maintaining accurate amplitude and phase quadrature between the baseband I and Q channels. Baseband down conversion is accomplished with double balanced mixers. In order to keep the intermodulation products down, good wideband mixers with high intercept points are essential (730 dB). For discrete I,Q channels, a well-matched pair of mixers and amplifiers is needed. A low-pass filter is always recommended to band-limit and improve the noise figure of the video amplifiers. Several generic approaches are possible for minimizing the effects of 1,Q amplitude and phase distortions which lead to spurious signals as shown in Fig. 8. To maintain signal
I VIDEO AMP AGC AID
AMP 8 AGC
DEMOD
’
Q
D/A
9
v
9
ANLAOG
FIG.
6.
Down
conversion
to baseband.
OUTPUT
DIGITAL
r OvrpvT ovrpv~
P PREAMPl FILTER
I
AMPS
I
I
FREQUENCY SYNTHESIZER
t
I
I
I
INT
I
1 M-232 PREPROCESSOR 66000 VME
FIG.
7.
GPS
receiver
block
diagram.
(1) (2) DCO,
distortions at less than -50 dB, the gain and phase must be maintained at less than 0.05 dB and 0.05”, respectively. Since down conversion with this level of amplitude and phase match is usually not achievable, techniques for correcting the mismatch distortions may be considered. The most common baseband video approaches use: (1) Time-multiplexed 1,Q with either single or parallel channels -Switching of I and Q functions -Time delaying of Q relative to I (2) Frequency-multipled 1,Q -Different frequency translations for I and Q (3) Pilot reference tones -Generate out-of-band pilot signals for characterization of I and Q.
(iv)
Superheterodyne
Receiver
The usual reason for choosing a superheterodyne design is that it permits the bulk of the signal process-
Digitally
synthesized
EXTERNAL SUBSYSTEM INTERFACE
and
controlled
oscillator.
ing to occur at a fixed “intermediate” frequency, ordinarily a frequency lower than the received signal frequency. In analog systems, this allows the design of superior signal filters and demodulation circuitry. In designing a receiver to the specifications given in Table 1, the current technology in A/D converters appears to be the critical factor. For readily available A/D converters, true 12-bit performance is limited to a data rate of approximately 50 MHz in all but experimental converters; a superhet configuration may be desirable because it brings the signal down to a frequency range that the A/D converter can effectively handle. The ensuing paragraphs illustrate the process of designing a receiver to the stated requirements, leading up to the block diagram of Fig. 9. The fundamental design choices are the selection of the number and center frequencies of the IF stages. The final IF must allow alias-free sampling by an A/D system assumed to be limited to 50 megasamples per second. By the Nyquist criterion, the frequency content must then be limited to 25 MHz. With a practical
.OOOl
I 0
-10
I
I
1
-20
-30
-40
SPURIOUS
FIG. 8. Baseband ous signal levels.
I
I
I
I
I
.50
-60
-70
-80
-90
SIGNAL
amplitude/phase
I 1 -100
LEVEL(dS)
errors
and equivalent
spuri-
anti-aliasing filter, the highest IF band would be from 10 to 20 MHz, centered at 15 MHz. If this were the only IF, the image of the IF in the mixing process would be only 30 MHz away, requiring a whole series of narrow preselection filters. Therefore, it appears that at least two IFS are required. A similar receiver design using three IF stages is discussed in reference
Pll* Modern practice for multiple conversion receivers tends to put the first IF higher than the highest frequency to be received. For this application, covering 20 to 500 MHz, we tentatively chose a first IF of 600 MHz. The local oscillator must therefore cover 620 through 1120 MHz, synthesized with a 1-kHz maximum step size. A reasonable choice for the first IF bandwidth is 20 MHz, since it allows the desired signal bandwidth of 10 MHz to occupy the middle half of the bandwidth (where the group delay distortion is minimal). On the other hand, it is narrow enough to reject the image of the second conversion. The next step is to check for undesired mixer spuri-
K
ous products (commonly called “birdies”) in the frequency conversions. Analysis of the up conversion depends on the preselection scheme, which is discussed below. Analysis verifies that the 600-MHz choice is satisfactory. A long-proven computer program, for analyzing mixer birdies, revealed some mixer spurious problems with the second IF choice of 15 MHz, but a higher frequency of 30-40 MHz is satisfactory. This frequency range is too high, however, for a 50-MHz sampling rate to meet the Nyquist criterion. Since the signal bandwidth is less than 25 MHz, the constructive aliasing concept discussed earlier is applicable, provided that the entire signal spectrum is contained between integer multiples of half the sampling rate, or 25 MHz. The second IF is therefore chosen as 37.5 MHz, with a nominal bandwidth of 12 MHz and a maximum bandwidth on the filter skirts of 24 MHz. The birdie analysis of this frequency plan shows no significant spurious products (order 20 or less) appearing in the second IF passband. With dual conversion and the IF frequencies established, the overall block diagram is as shown in Fig. 9. The input passes first through one of a bank of preselection filters and a preamplifier. If the specification required an extremely low noise figure, the preamplifier would have to come first at the expense of greater susceptibility to preamplifier-caused intermodulation. At the specified noise figure of 10 dB, a preamp noise figure of 4-5 dB and a preselector loss of 2-3 dB will suffice. Both figures should be reasonably easy to achieve. A detailed design would, of course, also account for the noise figures of subsequent stages adjusted by the gain which precedes each. The preamplifier is followed by a gain-controlled amplifier, the first mixer, the first IF filter, and another gain-controlled amplifier. Depending on whether noise figure or intermodulation characteristics are to be optimized for stronger signals, one or the other of the two indicated gain-controlled stages could have a fixed gain. Next, the signal passes through the second mixer and the second IF filter. Finally, it is applied to
PRESELECTOR I
lo = 37.5 MHz BW=12MHr
f, = 600 MHz BW = 20 MHz
TRACWtfOLD AMP 6 AID CONV.
-
,
0 GAIN CONTROL
GAIN CONTROL
620-l
L.O. 120 MHz
FIG.
L.O. 562.5 MHz
9.
Superheterodyne
receiver.
CLOCK 50 MHZ
-
TO DIGITAL SIGNAL PROCESSOR
a sample-hold or track-hold amplifier for input to the A/D converter. The digitized samples are fed to a digital signal processor which performs the final bandpass filtering and demodulation. The purpose of input selectivity is fourfold. First, it suppresses signals at the image frequency of the first conversion. Next, it suppresses signals at the first IF from entering the receiver, and it reduces the amount of LO signal that the receiver emits. Finally, it suppresses interfering signals outside the frequency band of current interest which could intermodulate in the amplifier or mixer stages to create spurious signals within the band of interest. For the purposes of image rejection, LO rejection, and IF rejection, a low-pass filter cutting off between 500 and 600 MHz would suffice. A high-pass filter cutting off below 20 MHz would also be desirable. However, it is desirable to divide the input frequency range into segments of one-half octave each. This approach controls second-order intermodulation products, since any two frequencies within the segment will have a sum frequency above the segment and a difference frequency below the segment. The segments must overlap, of course, to allow for modulation about any carrier frequency. Table 7 shows how the input frequency range may be covered in 10 preselection frequency segments of approximately one-half octave each. This plan assumes that the full signal bandwidth of 10 MHz is not required below 75 MHz. The plan would be modified if full bandwidth down to the minimum frequency is a real requirement. Current practice would utilize PIN diode switches to select among the several preselection filters. However, if suppression of intermodulation beyond that available from this approach is desired, mechanical relays may be substituted. A preliminary mixer birdie search was performed using each of these frequency segments as the input to TABLE
7
Preselection Frequency Segments Frequency Segment 1 2 3 4 5 6 7 8 9 10
range
(MHz)
Minimum
Maximum
18 26 36 50 70 95 133 180 255 350
30 41 55 75 105 143 195 270 370 510
the first mixer. The output passband was from 590 to 610 MHz. The analysis showed no significant spurious mixer products of order five or lower except for one particular class. Those spurious products are all direct harmonics of the input frequency falling within the IF bandwidth. This situation can hardly be avoided in a receiver in which the input frequency range exceeds an octave and the IF is above the highest input frequency. It is controlled by the design of the preselector, first amplifiers, and first mixer for the greatest possible linearity, and by automatic gain control (AGC) to keep the desired signal within the linear range of these stages. The block diagram of Fig. 9 takes for granted that suitable local oscillator sources are available. Modern, general-purpose receivers generally use step-tuned frequency synthesizers for LOS, and it is critically important that the synthesizer have spectral purity sufficient to not contaminate the signals with sidebands or phase noise. The phase-lock synthesizers common in such receivers may not suffice for this application, and more expensive techniques usually associated with VHF and UHF laboratory synthesizers may be required. Advantages and limitations of the superhet approach. The principal advantage of the superhet approach to the design of a low-distortion digital receiver is that it avoids placing extreme demands on the analog-to-digital conversion equipment. The 50MHz 12-bit A/D converters required for a 72-dB dynamic range are close to production. By the time lGHz 12-bit converters are in production, 50-MHz converters will be achieving 16-bit accuracies, permitting a 96-dB instantaneous dynamic range in such a receiver. A second advantage is that by limiting the sample rate to slightly more than the minimum required to represent the modulated signal, the digital signal processing requirements are kept reasonable. At the present state of the art in DSP hardware, a highly parallel, extensively pipelined architecture would be required to cope with a l-GHz sample rate. The size, cost, and power consumption could well be formidable. For the superhet design, the three main types of signal contamination are: (1) additive noise, primarily due to noise of the first amplifier stages; (2) the creation of frequency components not included in the original signal by intermodulation of frequency components of the desired and undesired signals in a stage exhibiting some degree of nonlinearity; and (3) the modification of the amplitude and phase of the various frequency components of the signal by linear processes in various receiver stages, but particularly the filters.
In the design illustrated with Fig. 9, the principal sources of additive noise are the preamplifier and the losses of the preselector filters. Spurious frequency generation will occur mainly in the preamp, the following gain-controlled amplifier, and the first mixer. The proposed preselection scheme will minimize intermodulation within the amplifiers, and the use of a first mixer with a high third-order intercept point will minimize it within the mixer. It will likely remain the most significant source of spurious frequency products, however. The second mixer could also be a significant source, but the frequency plan looks particularly good for avoiding that problem. The amplitude and phase (or, equivalently, group delay) distortions will be introduced primarily by the bandpass filters of the preselector, the first IF, and the second IF. These are the consequences of having this much analog circuitry out in front of the A/D conversion process. Fortunately, these distortions are introduced by linear processes and are therefore more amenable to corrective techniques in the subsequent digital signal processing.
4. DIGITAL DEMODULATION This section discusses the analysis of distortion in each of the modulation waveforms. Demodulation of AM (and AM/OOK) is achieved by extracting the envelope of the carrier, whereas FM demodulation is accomplished by extracting the phase of the carrier. Since these are performed digitally, there are errors appearing as distortion at the demodulator output. To understand this phenomenon, consider a bandpass signal in I-Q form, x(n) = u(n)cos(nw,)
- b(n)sin(nw,),
444 = 4(n) - d4n.- 11,
where the prime refers to differentiation. Note that (6), however, requires arctangent function evaluation. One could use the analytical expression for the derivative of the arctangent function to evaluate (6), i.e.,
4’(n) = [a(nW(n) - b(nkz’(n)ll[a2(n) + b2(n)1,(7) where u’(n) = u(n) - a(n -
1)
b’(n) = b(n) - b(n -
1).
0 a
I
-100 0
where a(n) and b(n) are low-pass quadrature components and w,, is the carrier frequency. The envelope r(n) and the phase 9(n) are given by (54
4(n) = arc tan(b(n)/a(n)).
(5b)
One would like to analyze the effects of the approximations used in the evaluation of (5a) and (5b) and compare them with the time versions of these operations. Phase demodulation is carried out by evaluating the arctangent function. Frequency modulation can be performed by simply differentiating 4(n) given in (5b) as
(8)
Equation (7) is useful from the point of view of realtime implementation. But it introduces third harmonic distortion that is much higher than is necessary. Computer simulation was performed to evaluate the effect of approximations to qS(n) in (5) and some of the results are shown in Fig. 10. Figure 10a shows that the third harmonic of a demodulated FM sinusoid is only about 30 dB down from the fundamental. This occurs when a full bandwidth FM signal is demodulated with the derivative algorithm. The example used a 4-kHz modulation with a 4-kHz deviation for a signal bandwidth of approximately 16 kHz. The
L
(4)
r(n) = \la20+
(6)
0 r.
I 6
I
I
I ._ lb
32
kliz
I
fmod
= 4 KHz Af= 4 kHz Sample Rate = 32
kHz
-100 0
6
16
24
FIG. 10. Comparison of third harmonic performance derivative method with true arc tangent. (a) Derivative (Q’I + Z’Q)/(P + @). (b) True arc tangent method.
32 kHz
of phase methodf =
sample range was 32 kHz. The derivative approximation improves considerably at lower modulation indices. Figure lob shows the spectrum of the same signal demodulated according to Eqs. (5b) and (6). The true arctangent function results in negligible distortions. Both simulations were carried out in high-precision floating-point arithmetic to show errors in the algorithms alone. The next step in analyzing a demodulation algorithm for a particular receiver is to simulate it in arithmetic of the same class as will be used in the digital signal processor. The FM demodulator, based on the algorithm for the derivative of the arctangent function as given by Eq. (7), was implemented using TMS 32OC25 microprocessor architecture [lo]. The differentiations are performed by FIR filters. Test results show a maximum total harmonic distortion of 3% in the band 8 to 20 kHz with ?75 kHz deviation and a phase linearity of +2’ from a straight line in the same band. The low-pass filter following the digital differentiator was implemented as a 1:2 up sampling FIR filter (two phases) and is based on a 40-tap FIR design (20 taps per phase) operating on a floating-point calculation. Another source of distortion to be considered in PM and FM is the amplitude and phase nonlinearity of the bandpass channel. These properties have long been studied [7,8], and computer programs that implement these methods are available. The analysis of digital modulation schemes such as frequency shift keying requires the determination of the average probability of error with respect to the signal-to-noise ratio at the detector input. The demodulation of frequency shift keyed (FSK) signals can be achieved either by frequency discrimination or by a pair of bandpass filters. Computer simulations of these two schemes were performed and we found that the digital bandpass filter pair matched to two tones of FSK demodulation performs, as expected, better than the frequency discrimination scheme.
5. SUMMARYAND CONCLUSIONS The design of a VHF/UHF receiver using digital signal processing techniques has been discussed with emphasis on developing a receiver architecture that will provide minimum distortion to the received signal in the receiving process. Device technology, espe-
cially the A/D converter, plays a crucial role in the selection of the preferred approach. A combination of the state-of-the-art analog and digital technology can provide the proper design of a low-distortion, broadband, and high dynamic range system for signal analysis.
REFERENCES 1. Panter, P. F. Modulation, Noise, and Spectral Analysis. McGraw-Hill, New York, 1965. 2. Wang, H. S. C. Distortion of FM signals caused by channel phase nonlinearity and amplitude fluctuation. IEEE Trans. Commun. Technol. COM-14,4 (Aug. 1966), 440-448. 3. Taylor, F. J. Digital Filter Design Handbook. Dekker, New York, 1983. 4. Rabiner, L. R., and Gold, B. Theory and Applications of Digital Signal Processing. Prentice-Hall, New York, 1975. 5. Oppenheim, Processing.
A. V., and Schafer, Prentice-Hall, New
R. W. Theory York, 1975.
of Digital
Signal
6. Crochiere, R. E., and Rabiner, L. R. Multirate Digital Signal Processing. Prentice-Hall, New York, 1983. 7. RADC/DCIT Report RADC-78-44, Interactive Digital Receiver Simulator. Mar. 1978. 8. RADC Report TR-80-169, All Digital Receiver Study. May 1980. 9. RADC Report TR-85-138, All Digital Receiver Feasibility Model and Test, 31 July 1985. 10. Bakhru, K., Multichannel digital sonobuoy receiver. In Proc. IEEE Military Communications Conference, 1990, pp. 61.6.161.6.6. 11. Connelly, B. L., and Kroeger, B. W. Design and performance of an analysis receiver. In Proc. IEEE Military Communications Conference 1990, pp. 61.4.1-61.4.4.
KESH BAKHRU received the B.S. degree with honors and the M.S. degree in physics from the Benaras Hindu University, Varanasi, India; the M.S. (EE) degree from Columbia University, New York; and the Ph.D. degree in electrical engineering from the Polytechnic Institute of Brooklyn, New York. From 1970 to 1972 he was an assistant professor in the Department of Electrical Engineering, Pratt Institute, New York. From 1972 to 1976 he was with the Department of Electrical and Computer Engineering at San Diego State University, California. Since 1976 he has been with Cubic Corporation, Cubic Defense Systems in San Diego, California, where he is currently a senior staff scientist leading the System Engineering Group. His interests are primarily in the analysis and design of communications systems using spread spectrum techniques, applications of high-speed digital signal processing, and adaptive systems. Dr. Bakhru is a fellow of the Institute of Electrical and Electronics Engineers and a member of the Communication Theory Technical Committee of the IEEE Communications Society. He has offered several seminar courses in secure communication, spread spectrum systems, coding, and modulation theory at the University of California, San Diego, and San Diego State University.
SIGNAL
PRGCESJNG
2, 2-13 (19%‘)
Communications Receiver Design Using Digital Processing Kesh Bakhru Cubic Defense Systems, 9333 Balboa Avenue, San Diego, California
1. INTRODUCTION
A digital processing receiver performs most receiver functions using digital processing techniques. Examples of such functions are frequency translation, filtering, demodulation, automatic gain control, mode of operation, equalization of group delay distortion, and passband ripple. An initial step in defining the receiver bandwidth and signal level is performed in the analog domain. The information-bearing signal is then sampled and quantized at a suitable IF frequency. The remainder of the processing is performed digitally using digital signal processing (DSP) techniques. The digital approach takes advantage of the everincreasing capability of digital signal processing and the potential of miniaturization of all digital receivers using VHSIC technology. Other advantages of using DSP are that it increases the reliability and repeatability of demodulating and monitoring the received signals. The signal output from an analog receiver can vary from unit to unit, and even the same unit can vary with time, temperature, and calibration. Conventional analog receivers use RF stages, frequency synthesizers, IF amplifiers, and analog demodulators which not only pose internal RF interference problems but also do not lend themselves to low-cost production or reduction in size, weight, and cost. The objectives of the digital receiver design are to provide overall improved performance, reliability, maintainability, and reduced cost and weight and to be cost-effective. The architecture and design lend themselves to flexibility in providing enhanced functional capa1051.2004/92 $1.50 Copyright 0 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.
92123
bility through the sharing of software and hardware and can be expanded to integrate other functions in the receiver for future growth. The research and development necessary for the advanced digital receiver technology were performed at Cubic Defense Systems under various IR&D projects and the experience acquired is being applied to the design of various receivers, such as communications receivers in HF and VHF/UHF bands, a multichannel digital sonobuoy receiver for ASW application, Global Positioning System receivers, and range and instrumentation receivers. Study of the digital receiver design requires a substantial background in communications receiver design as well as in digital signal processing techniques. The study may be broken into the following steps: (1) selection of candidate receiver architectures; (2) preliminary analysis and performance assessment; (3) comparison and selection of the preferred approach; (4) distortion analysis of each receiver stage for the various modulations; and (5) analysis of the overall receiver performance. The application of DSP technology to the design of the digital receiver can be illustrated by following the design of the VHF/UHF communication receiver developed at Cubic Defense Systems. The specifications of this receiver are tabulated in Table 1. Minimization of signal distortion is one of the objectives of such a design, and Section 2 discusses the sources of distortion in analog and digital receivers. Section 3 describes four different receiver architectures and compares their performance, advantages, and limitations. Section 4 discusses various digital demodulation schemes, and finally, Section 5 summarizes these design steps.
TABLE VHF/UHF
Receiver
Frequency range Dynamic range Noise figure, max Programmable channels Selectable IF bandwidths Modulation Tuning resolution IF rejection Image rejection Intermodulation distortion Distortion Gain control Readout Receiver processor Controls I/O bus External
reference
architecture
oscillator
1 Specifications 20-500 MHz 72 dB 10 dB 100 Various to 4 MHz AM, FM, FSK, USB, LSB 10,100, and 1000 Hz 80 dB 80 dB Third order-110 dBm from two inputs at -20 dBm Minimum achievable Manual/automatic Digital Is-bit Front panel/external RS-232/422/485 MIL-STD-118/114 Yes
2. DISTORTION IN ANALOG VERSUS DIGITAL RECEIVERS (a) Analog Receivers A number of factors affect the desired performance of well-designed analog radio frequency receivers. Many of these factors are independent of the frequency of operation, whereas other performance limitations are frequency dependent. For example, internal receiver noise is not usually a performance limitation at VLF, LF, or MF but becomes a significant limitation at VHF and UHF. The inability to handle extremely strong interfering signals may become a performance limitation at any frequency and the inability to reject intermodulation products resulting from two such strong signals with a particular frequency spacing from each other and from a desired signal can be a problem at any frequency at which channel assignments are evenly spaced and transmitters are located in close proximity to one another. In general, the most pertinent performance limitations in the design of a receiver are Noise Figure, Input Selectivity, RF Amplifier Dynamic Range, Mixer Dynamic Range, Mixer Spurious Responses, Oscillator Sidebands, Oscillator Phase Noise, Filter Selectivity, Filter Dynamic Range, IF Amplifier Dynamic Range, Detector Linearity, Detector Dynamic Range, Automatic Gain Control Range, and Automatic Gain Control Attack and Decay Times. In considering these performance limitations, the various states of receivers may contribute to one or more of each of the parameters.
Analog RF receivers introduce various distortions into the received signals. Amplitude-modulated signals can suffer from distortions caused by imperfections in the amplitude detectors and imperfect filtering in the IF and baseband parts of the receiver. If signals are affected by fading, a property of the AGC circuit can introduce substantial and noncorrectable distortions. Frequency synthesis can add phase noise and envelope distortions in single and vestigial sideband systems. Different applications will experience one or another combination of distortions. Modulated FM signals, even with the advantages provided by wideband FM, nevertheless are affected by other substantial imperfections which cause distortion of the demodulated signals. One of the more important sources of distortions is filtering. The RF bandwidth of a typical FM signal is very wide. Because filtering must be performed to meet acceptable noise performance, part of the FM spectrum inevitably will be lost, which causes very specific distortion of the demodulated signals. Another source of distortion in FM receivers is the shape of the frequency response of the analog filters. Table 2 shows various sources of distortion in analog receivers. Discussions on how to minimize the distortion by proper design of conventional receivers can be found in the literature [1,2]. Provided that received signals are simply listened to, the above distortions can be compensated by human intelligence or ignored because of the limited sensitivity of our ears. However, when the signals are analyzed by digital means, which can be as accurate as TABLE Sources 1. Deterministic Amplitude
Nonlinear
2. Statistical Phase noise
Image
in Analog
Receivers
Bandpass filters, low-pass filters, narrowband amplifiers. Errors in local oscillator frequencies. Bandpass filters, low-pass filters, narrowband amplifiers. Causes nonlinear distortion of demodulated FM/PM signals. Amplifiers-Harmonic and/or intermodulation distortion, especially variable gain/AGC stages. MixersHarmonic and intermodulation distortion.
Frequency Phase/group delay
Thermal
of Distortion
2
noise noise
Jitter in local oscillator used for down conversion, especially if synthesized. Amplifier noise, primarily determined by first stages of amplification. Possible source in superhetrodyne designs. Controlled by appropriate system and filter design.
we desire, imperfections in the receiver become an obstacle. The objective of the design study is to provide a receiver design with absolutely minimal distortions or colorations of any signal amplitude, frequency, and phase.
(b) Digital
Receivers
Digital receivers have many attractive features which make them outperform analog counterparts. The following are some of the salient features of digital receivers: potential for less signal distortion; l automated processing; . flexibility, commonality, and sophisticated service functions can be built into the system, as these functions are software controllable; l reduced component size due to the VLSI technique, which in turn saves space, weight, and power consumptions; l reliability due to modularity and reduced external connections; . less susceptible to drifts due to component aging and changing ambient conditions; l cost-effective due to time-division multiplexing and time-sharing capabilities of digital networks. l
Table 3 lists the distortions in digital receivers grouped into deterministic and statistical sources. The deterministic sources arise from finite word lengths used to represent the filter coefficients. These effects can be analyzed using either closed-form ex-
TABLE 3 Sources of Distortion in Digital Receivers 1. Deterministic Amplitude
IIR/FIR filters, DFT. Controllable by proper design. Errors in clock and/or local oscillator. These sre hardware related and can be controlled by careful design. IIR filters needs equalizer. No such problem with FIR filters. Can cause distortion in demodulated FM signal. A/D conversion causes harmonic and intermod products; depends on number of bits of A/D converter. Approximation in demodulation algorithms like Arctan, Square Root, etc. Mismatch in I,Q channels with respect to Gain, Phase, primarily in direct conversion to baseband approach.
Frequency
Phase/group delay Nonlinear
2. Statistical Analog A/D conversion Round-off
noise
Receiver front-end-RF filter/amplifier noise Granular noise-decreases with increasing number of bits of A/D, aperture timing errors. Due to finite precision arithmetic. IIR filtersdepends on specific filter structure. FIR filters-controlled by proper design. DFT processor-same as in FIR filters.
DIGITAL OUTPUT
FIG.
1.
Block
diagram
of a direct
digitization
digital
receiver.
pressions or iterative computer solutions. Furthermore, these filter sensitivities also depend on the specific filter structure used in the implementation. In any case, the coefficient sensitivities can be minimized by proper design of these filters. Another deterministic source arises from harmonic distortions introduced by the A/D converter. Analytical results for estimating these distortions are available in the literature [3-61. The statistical sources of distortion come from A/D conversion and round-off errors due to finite precision used in the arithmetic operation. Analytical expressions for evaluating the amounts of distortions introduced by these sources are available [3-61, and, therefore, their effects can be minimized by proper design.
3ANDlDATE RECEIVER ARCHITECTURES Four candidate receiver architectures are discussed from a system-level standpoint. They are: (i) receiver based on direct digitization of RF signal, (ii) constructive aliasing using the aliasing effect due to undersampling or sampling rate conversion in a constructive manner, (iii) direct conversion to baseband, and (iv) superheterodyne receiver. The proper choice from among these architectures is influenced by various factors, such as intended application, cost, size, and feasibility [9-l 11.
(i) Direct
Digitization
A block diagram of the direct digitization receiver is shown in Fig. 1. The received RF signal is first filtered to reject out-of-band noise. This filter also serves as an anti-aliasing filter. The filtered bandpass signal is then sampled and quantized to the required number of bits of accuracy. Further processing of this signal is done digitally. Since the RF bandwidth covers the range 20 to 500 MHz, the initial sampling rate should be in excess of a gigahertz. However, since the individual carriers have
TABLE Comparison
for an M = 100 Decimator
One-stage
Filter
ratios
M,
lengths
Computation Computational stage RR
N,
(MPS) savings design
over
Two-stage
Two-stage
IIR
IIR Decimation
4
IIR
TABLE
M2 = 10
M, = 50 M2 = 2
M, = 10 Mz = 5 M3 = 2
N, = 4 N2 = 14
N, = 4 N2= 14
Nl N,
2200
810
920
598
N, = 38 N2 = 38 N3 = 356 406
1.0 14
2.7 18
2.4 18
3.7 798
5.4 436
M, M,
= 14
M,
= 10
5
Onestage
Direct form
Twostage
TABLE Filter FIR
Threestage l
lengths
MPS Rate reduction (MW Total storage for filter coefficients
= 423 = 347
niques will be chosen on the basis of accuracy, stability, and implementation factors. A comparison between finite impulse response (FIR) and infinite impulse response (IIR) filters is shown in Table 6. As a further comparison between the two filter types, Fig. 2 from [6] shows the number of multiplications per second required by these two filters to meet the same specifications. Performance, advantages, and limitations of direct digitization. This receiver architecture has the theoretical potential for the least signal distortion of any of the receiver candidates. However, to cover the full bandwidth of 500 MHz, the receiver dynamic range will require an A/D converter at sampling rates of i GHz with 12-bit resolution (72-dB dynamic range). Unfortunately, at these sampling rates, it does not appear that the device technology will support a 12bit instantaneous dynamic range. Six- to eight-bit versions may be achievable in the near future. Alternatively, lower carrier frequency and narrower signal
Comparisons of Filter Characteristics for Several Multistage Implementations of a Low-Pass Filter with Specifications F = 1.0, fp = 0.00475, fs = 0.005, 6, = 0.001, 6, = 0.0001
Filter
FIR
= 20 = 5
= 100
much smaller bandwidths than the sampling rate, there is a great potential for sampling rate reduction and this in turn lowers the expected computing speed of the signal processors. If the sampling rate reduction is achieved in stages, significant savings can be achieved in computational tasks and memory. An example is presented in Tables 4 and 5. One advantage of using multiple stages is that the decimated signal is already in the proper form so that demodulation is a simple task. The demodulated signal can be D/A converted if an analog output is desired, or the digital audio output can be processed further. In designing a direct digitization receiver, one would consider the various signal distortions present in the system, as discussed in the previous section. A/D converters will be selected on the basis of speed requirements, future advancements in technology, hardware limitations, etc. Suitable filtering tech-
rates
Three-stage
one-
Storage
Decimation
Two-stage FIR
7,795
165
11.9
10 5 2 50 44 356 9.4
1
47.2
655
829
-
100
15,590
16,466
50 2 423 347
l
l
l
l l
7,795
8,233
385
225
6
Comparison
filters
IIR
Exact phase linearity can be achieved Excellent passband and stopband characteristics possible Generally requires longer filter lengths Unconditionally stable
l
No limit cycles Need smaller coefficient word lengths
l
l
l
l
l
filters
Only approximation is possible Excellent passband and stopband characteristics possible Requires smaller filter orders Stability problems exist due to finite coefficient word length Possibility of limit cycles Need larger coefficient word lengths
(ii)
L 6p= 0.025 &= 0.0031 wm=0.2n A~=(wswp)/2n M =5
sua ;i z g 40 3 a 5 93-
FIR
LINEAR
30 20
/
PHASE
TRANSORMED ,ELLIPTIC
b 0.005
OPTIMUM
Aliasing
According to the Nyquist theorem, a bandpass signal must be sampled at a rate that is at least twice the bandwidth of the signal, provided that the signal band falls within half the sampling frequency. This will ensure perfect reconstruction without destructive aliasing, as is shown in Fig. 3. However, it is possible to sample a bandpass signal below the Nyquist rate and yet recover the signal frequencies lying beyond half the sampling frequency without aliasing distortion. For constructive aliasing, all the frequencies, f, in the signal bandwidth satisfy nfJ2 < f =c(n + l)f,/2, where f, is the sampling rate and n is a nonnegative integer. This will significantly ease the burden on the A/D conversion speed and, therefore, lead to a viable approach to digital receiver implementation. The concept of constructive aliasing is illustrated in Fig. 3. Figure 3a shows the RF bandpass signal, Fig. 3b, the Fourier transform of the sampling function, and Fig. 3c, the spectrum of the sampled function. Figure 3e shows the spectrum of the desired band signal after band-pass filtering. Similarly, Fig. 4 shows the constructive aliasing for a low-pass signal. The architecture of the constructive aliasing receiver is shown in Fig. 5. It is identical to that of the
ELLIPTIC
k
Constructive
IIR
0.05 !lF
FIG. 2. Multiplication rate vs AF for various equiripple FIR and RR single-stage decimeters. AF, transition band relative to the sampling frequency; a,,, passband ripple; 6,, stopband ripple; M, decimation factor; We, stopband edge relative to half the sampling frequency; wp, passband edge relative to half the sampling frequency. Reprinted with permission from R. E. Crochiere and L. R. Rabiner, Multirate Digital Signal Processing, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1983.
bandwidths would be achievable with 12-bit sampling. The digital processing rates required may also be excessive for device technology of the near future.
+ B II r/ +--RF
BAN0
+
t (n+%)FS
b
(n+l)FB
+ B
FIG.
3.
Constructive
aliasing
for bandpass
signals.
B
FIG.
4.
Constructive
direct digitization receiver except for the A/D conversion followed by bandpass filtering. This technique requires an additional filtering operation compared to the previous case. However, the reduced sampling rate used in A/D conversion should more than offset the additional filtering task. The underlying consideration for the constructive aliasing and direct, digitization approach is the major impact of A/D device technology on the viability of receiver design. With regard to the sources of distortion and the choice of filtering type to be used, the same arguments hold here as for the direct digitization receiver. Performance,
advantages, and limitations
of the con-
aliasing
for low-pass
signals.
This approach holds the structive aliasing approach. promise of practical implementation and has the advantage over the other candidates of being a fully digital approach except for front-end filtering and amplification. This receiver, as with the direct digitization example, offers the theoretical potential for minimal distortion. The theoretical performance limits will be approachable as device technology improves. This candidate also offers greater growth potential to take advantage of new device technology. Another obvious advantage is that the only nonlinear element is the wideband front-end amplifier. Unfortunately, all of the gain to cover the dynamic range must take place in this amplifier. This would place an upper limit on the dynamic range achievable. (iii)
Direct
Down
Conversion
to Baseband
One can use the principle of quadrature modulation to convert a narrow bandpass signal into quadrature components. A narrow bandpass signal can be expressed as AUDIO
D/A
DEMO,,
“%2L
CONVERTER
+ DIGITAL
FIG.
5.
Block
diagram
of a constructive
aliasing
digital
receiver.
x(t) = a(t)cos w,t - b(t)sin
wJ,
(1)
where a(t) and b(t) are low-pass signals band-limited
to W Hz. These two signals also represent lope and phase of the carrier given by
the enve-
envelope = vc?(t) + b’(t)
The quadrature signals can be recovered by mixing the signal x(t) with quadrature carriers and low-pass filtering. We can then sample a(t) and b(t) at a 2W samples per second rate for digital processing. As the signal is already in the proper format, demodulation is a simple task. A block diagram of the receiver is shown in Fig. 6. A digital receiver for the Global Positioning System, utilizing down conversion to baseband, has been implemented at Cubic. A block diagram of this receiver is shown in Fig. 7. The mixed-down signal contains Doppler frequency residual and is filtered through a matched filter before it passes through the 4-bit A/D converters. At this point, the signal is digitized and all the remaining sensor circuitry is digital. Only a 4-bit A/D was used because the “signal” is buried in noise and has a small dynamic range. Doppler removal and C/A code correlation are performed in the digital correlator, which is driven both by the code and by Doppler digitally synthesized and controlled oscillators (DCOs). Final output to the I/O preprocessor from the correlator is four pairs of 16-bit
I- and Q-channel correlations spanning four C/A code half-chips in correlation space. In the receiver structure of Fig. 7 the crucial stage is the down conversion stage. Improper phase of the local oscillator will cause serious degradation in signal extraction. Since sampling takes place at baseband rate, the signal processing portion of the receiver offers no unusual challenges. Performance, advantages, and limitations of direct conversion to baseband. The direct baseband conversion and digital signal processing offer some architectural advantages over other approaches by simplifying some of the requirements for minimum A/D rates (this means one can use more bits), no mixer image, and simple frequency synthesizer. The negative feature is the requirement of maintaining accurate amplitude and phase quadrature between the baseband I and Q channels. Baseband down conversion is accomplished with double balanced mixers. In order to keep the intermodulation products down, good wideband mixers with high intercept points are essential (730 dB). For discrete I,Q channels, a well-matched pair of mixers and amplifiers is needed. A low-pass filter is always recommended to band-limit and improve the noise figure of the video amplifiers. Several generic approaches are possible for minimizing the effects of 1,Q amplitude and phase distortions which lead to spurious signals as shown in Fig. 8. To maintain signal
I VIDEO AMP AGC AID
AMP 8 AGC
DEMOD
’
Q
D/A
9
v
9
ANLAOG
FIG.
6.
Down
conversion
to baseband.
OUTPUT
DIGITAL
r OvrpvT ovrpv~
P PREAMPl FILTER
I
AMPS
I
I
FREQUENCY SYNTHESIZER
t
I
I
I
INT
I
1 M-232 PREPROCESSOR 66000 VME
FIG.
7.
GPS
receiver
block
diagram.
(1) (2) DCO,
distortions at less than -50 dB, the gain and phase must be maintained at less than 0.05 dB and 0.05”, respectively. Since down conversion with this level of amplitude and phase match is usually not achievable, techniques for correcting the mismatch distortions may be considered. The most common baseband video approaches use: (1) Time-multiplexed 1,Q with either single or parallel channels -Switching of I and Q functions -Time delaying of Q relative to I (2) Frequency-multipled 1,Q -Different frequency translations for I and Q (3) Pilot reference tones -Generate out-of-band pilot signals for characterization of I and Q.
(iv)
Superheterodyne
Receiver
The usual reason for choosing a superheterodyne design is that it permits the bulk of the signal process-
Digitally
synthesized
EXTERNAL SUBSYSTEM INTERFACE
and
controlled
oscillator.
ing to occur at a fixed “intermediate” frequency, ordinarily a frequency lower than the received signal frequency. In analog systems, this allows the design of superior signal filters and demodulation circuitry. In designing a receiver to the specifications given in Table 1, the current technology in A/D converters appears to be the critical factor. For readily available A/D converters, true 12-bit performance is limited to a data rate of approximately 50 MHz in all but experimental converters; a superhet configuration may be desirable because it brings the signal down to a frequency range that the A/D converter can effectively handle. The ensuing paragraphs illustrate the process of designing a receiver to the stated requirements, leading up to the block diagram of Fig. 9. The fundamental design choices are the selection of the number and center frequencies of the IF stages. The final IF must allow alias-free sampling by an A/D system assumed to be limited to 50 megasamples per second. By the Nyquist criterion, the frequency content must then be limited to 25 MHz. With a practical
.OOOl
I 0
-10
I
I
1
-20
-30
-40
SPURIOUS
FIG. 8. Baseband ous signal levels.
I
I
I
I
I
.50
-60
-70
-80
-90
SIGNAL
amplitude/phase
I 1 -100
LEVEL(dS)
errors
and equivalent
spuri-
anti-aliasing filter, the highest IF band would be from 10 to 20 MHz, centered at 15 MHz. If this were the only IF, the image of the IF in the mixing process would be only 30 MHz away, requiring a whole series of narrow preselection filters. Therefore, it appears that at least two IFS are required. A similar receiver design using three IF stages is discussed in reference
Pll* Modern practice for multiple conversion receivers tends to put the first IF higher than the highest frequency to be received. For this application, covering 20 to 500 MHz, we tentatively chose a first IF of 600 MHz. The local oscillator must therefore cover 620 through 1120 MHz, synthesized with a 1-kHz maximum step size. A reasonable choice for the first IF bandwidth is 20 MHz, since it allows the desired signal bandwidth of 10 MHz to occupy the middle half of the bandwidth (where the group delay distortion is minimal). On the other hand, it is narrow enough to reject the image of the second conversion. The next step is to check for undesired mixer spuri-
K
ous products (commonly called “birdies”) in the frequency conversions. Analysis of the up conversion depends on the preselection scheme, which is discussed below. Analysis verifies that the 600-MHz choice is satisfactory. A long-proven computer program, for analyzing mixer birdies, revealed some mixer spurious problems with the second IF choice of 15 MHz, but a higher frequency of 30-40 MHz is satisfactory. This frequency range is too high, however, for a 50-MHz sampling rate to meet the Nyquist criterion. Since the signal bandwidth is less than 25 MHz, the constructive aliasing concept discussed earlier is applicable, provided that the entire signal spectrum is contained between integer multiples of half the sampling rate, or 25 MHz. The second IF is therefore chosen as 37.5 MHz, with a nominal bandwidth of 12 MHz and a maximum bandwidth on the filter skirts of 24 MHz. The birdie analysis of this frequency plan shows no significant spurious products (order 20 or less) appearing in the second IF passband. With dual conversion and the IF frequencies established, the overall block diagram is as shown in Fig. 9. The input passes first through one of a bank of preselection filters and a preamplifier. If the specification required an extremely low noise figure, the preamplifier would have to come first at the expense of greater susceptibility to preamplifier-caused intermodulation. At the specified noise figure of 10 dB, a preamp noise figure of 4-5 dB and a preselector loss of 2-3 dB will suffice. Both figures should be reasonably easy to achieve. A detailed design would, of course, also account for the noise figures of subsequent stages adjusted by the gain which precedes each. The preamplifier is followed by a gain-controlled amplifier, the first mixer, the first IF filter, and another gain-controlled amplifier. Depending on whether noise figure or intermodulation characteristics are to be optimized for stronger signals, one or the other of the two indicated gain-controlled stages could have a fixed gain. Next, the signal passes through the second mixer and the second IF filter. Finally, it is applied to
PRESELECTOR I
lo = 37.5 MHz BW=12MHr
f, = 600 MHz BW = 20 MHz
TRACWtfOLD AMP 6 AID CONV.
-
,
0 GAIN CONTROL
GAIN CONTROL
620-l
L.O. 120 MHz
FIG.
L.O. 562.5 MHz
9.
Superheterodyne
receiver.
CLOCK 50 MHZ
-
TO DIGITAL SIGNAL PROCESSOR
a sample-hold or track-hold amplifier for input to the A/D converter. The digitized samples are fed to a digital signal processor which performs the final bandpass filtering and demodulation. The purpose of input selectivity is fourfold. First, it suppresses signals at the image frequency of the first conversion. Next, it suppresses signals at the first IF from entering the receiver, and it reduces the amount of LO signal that the receiver emits. Finally, it suppresses interfering signals outside the frequency band of current interest which could intermodulate in the amplifier or mixer stages to create spurious signals within the band of interest. For the purposes of image rejection, LO rejection, and IF rejection, a low-pass filter cutting off between 500 and 600 MHz would suffice. A high-pass filter cutting off below 20 MHz would also be desirable. However, it is desirable to divide the input frequency range into segments of one-half octave each. This approach controls second-order intermodulation products, since any two frequencies within the segment will have a sum frequency above the segment and a difference frequency below the segment. The segments must overlap, of course, to allow for modulation about any carrier frequency. Table 7 shows how the input frequency range may be covered in 10 preselection frequency segments of approximately one-half octave each. This plan assumes that the full signal bandwidth of 10 MHz is not required below 75 MHz. The plan would be modified if full bandwidth down to the minimum frequency is a real requirement. Current practice would utilize PIN diode switches to select among the several preselection filters. However, if suppression of intermodulation beyond that available from this approach is desired, mechanical relays may be substituted. A preliminary mixer birdie search was performed using each of these frequency segments as the input to TABLE
7
Preselection Frequency Segments Frequency Segment 1 2 3 4 5 6 7 8 9 10
range
(MHz)
Minimum
Maximum
18 26 36 50 70 95 133 180 255 350
30 41 55 75 105 143 195 270 370 510
the first mixer. The output passband was from 590 to 610 MHz. The analysis showed no significant spurious mixer products of order five or lower except for one particular class. Those spurious products are all direct harmonics of the input frequency falling within the IF bandwidth. This situation can hardly be avoided in a receiver in which the input frequency range exceeds an octave and the IF is above the highest input frequency. It is controlled by the design of the preselector, first amplifiers, and first mixer for the greatest possible linearity, and by automatic gain control (AGC) to keep the desired signal within the linear range of these stages. The block diagram of Fig. 9 takes for granted that suitable local oscillator sources are available. Modern, general-purpose receivers generally use step-tuned frequency synthesizers for LOS, and it is critically important that the synthesizer have spectral purity sufficient to not contaminate the signals with sidebands or phase noise. The phase-lock synthesizers common in such receivers may not suffice for this application, and more expensive techniques usually associated with VHF and UHF laboratory synthesizers may be required. Advantages and limitations of the superhet approach. The principal advantage of the superhet approach to the design of a low-distortion digital receiver is that it avoids placing extreme demands on the analog-to-digital conversion equipment. The 50MHz 12-bit A/D converters required for a 72-dB dynamic range are close to production. By the time lGHz 12-bit converters are in production, 50-MHz converters will be achieving 16-bit accuracies, permitting a 96-dB instantaneous dynamic range in such a receiver. A second advantage is that by limiting the sample rate to slightly more than the minimum required to represent the modulated signal, the digital signal processing requirements are kept reasonable. At the present state of the art in DSP hardware, a highly parallel, extensively pipelined architecture would be required to cope with a l-GHz sample rate. The size, cost, and power consumption could well be formidable. For the superhet design, the three main types of signal contamination are: (1) additive noise, primarily due to noise of the first amplifier stages; (2) the creation of frequency components not included in the original signal by intermodulation of frequency components of the desired and undesired signals in a stage exhibiting some degree of nonlinearity; and (3) the modification of the amplitude and phase of the various frequency components of the signal by linear processes in various receiver stages, but particularly the filters.
In the design illustrated with Fig. 9, the principal sources of additive noise are the preamplifier and the losses of the preselector filters. Spurious frequency generation will occur mainly in the preamp, the following gain-controlled amplifier, and the first mixer. The proposed preselection scheme will minimize intermodulation within the amplifiers, and the use of a first mixer with a high third-order intercept point will minimize it within the mixer. It will likely remain the most significant source of spurious frequency products, however. The second mixer could also be a significant source, but the frequency plan looks particularly good for avoiding that problem. The amplitude and phase (or, equivalently, group delay) distortions will be introduced primarily by the bandpass filters of the preselector, the first IF, and the second IF. These are the consequences of having this much analog circuitry out in front of the A/D conversion process. Fortunately, these distortions are introduced by linear processes and are therefore more amenable to corrective techniques in the subsequent digital signal processing.
4. DIGITAL DEMODULATION This section discusses the analysis of distortion in each of the modulation waveforms. Demodulation of AM (and AM/OOK) is achieved by extracting the envelope of the carrier, whereas FM demodulation is accomplished by extracting the phase of the carrier. Since these are performed digitally, there are errors appearing as distortion at the demodulator output. To understand this phenomenon, consider a bandpass signal in I-Q form, x(n) = u(n)cos(nw,)
- b(n)sin(nw,),
444 = 4(n) - d4n.- 11,
where the prime refers to differentiation. Note that (6), however, requires arctangent function evaluation. One could use the analytical expression for the derivative of the arctangent function to evaluate (6), i.e.,
4’(n) = [a(nW(n) - b(nkz’(n)ll[a2(n) + b2(n)1,(7) where u’(n) = u(n) - a(n -
1)
b’(n) = b(n) - b(n -
1).
0 a
I
-100 0
where a(n) and b(n) are low-pass quadrature components and w,, is the carrier frequency. The envelope r(n) and the phase 9(n) are given by (54
4(n) = arc tan(b(n)/a(n)).
(5b)
One would like to analyze the effects of the approximations used in the evaluation of (5a) and (5b) and compare them with the time versions of these operations. Phase demodulation is carried out by evaluating the arctangent function. Frequency modulation can be performed by simply differentiating 4(n) given in (5b) as
(8)
Equation (7) is useful from the point of view of realtime implementation. But it introduces third harmonic distortion that is much higher than is necessary. Computer simulation was performed to evaluate the effect of approximations to qS(n) in (5) and some of the results are shown in Fig. 10. Figure 10a shows that the third harmonic of a demodulated FM sinusoid is only about 30 dB down from the fundamental. This occurs when a full bandwidth FM signal is demodulated with the derivative algorithm. The example used a 4-kHz modulation with a 4-kHz deviation for a signal bandwidth of approximately 16 kHz. The
L
(4)
r(n) = \la20+
(6)
0 r.
I 6
I
I
I ._ lb
32
kliz
I
fmod
= 4 KHz Af= 4 kHz Sample Rate = 32
kHz
-100 0
6
16
24
FIG. 10. Comparison of third harmonic performance derivative method with true arc tangent. (a) Derivative (Q’I + Z’Q)/(P + @). (b) True arc tangent method.
32 kHz
of phase methodf =
sample range was 32 kHz. The derivative approximation improves considerably at lower modulation indices. Figure lob shows the spectrum of the same signal demodulated according to Eqs. (5b) and (6). The true arctangent function results in negligible distortions. Both simulations were carried out in high-precision floating-point arithmetic to show errors in the algorithms alone. The next step in analyzing a demodulation algorithm for a particular receiver is to simulate it in arithmetic of the same class as will be used in the digital signal processor. The FM demodulator, based on the algorithm for the derivative of the arctangent function as given by Eq. (7), was implemented using TMS 32OC25 microprocessor architecture [lo]. The differentiations are performed by FIR filters. Test results show a maximum total harmonic distortion of 3% in the band 8 to 20 kHz with ?75 kHz deviation and a phase linearity of +2’ from a straight line in the same band. The low-pass filter following the digital differentiator was implemented as a 1:2 up sampling FIR filter (two phases) and is based on a 40-tap FIR design (20 taps per phase) operating on a floating-point calculation. Another source of distortion to be considered in PM and FM is the amplitude and phase nonlinearity of the bandpass channel. These properties have long been studied [7,8], and computer programs that implement these methods are available. The analysis of digital modulation schemes such as frequency shift keying requires the determination of the average probability of error with respect to the signal-to-noise ratio at the detector input. The demodulation of frequency shift keyed (FSK) signals can be achieved either by frequency discrimination or by a pair of bandpass filters. Computer simulations of these two schemes were performed and we found that the digital bandpass filter pair matched to two tones of FSK demodulation performs, as expected, better than the frequency discrimination scheme.
5. SUMMARYAND CONCLUSIONS The design of a VHF/UHF receiver using digital signal processing techniques has been discussed with emphasis on developing a receiver architecture that will provide minimum distortion to the received signal in the receiving process. Device technology, espe-
cially the A/D converter, plays a crucial role in the selection of the preferred approach. A combination of the state-of-the-art analog and digital technology can provide the proper design of a low-distortion, broadband, and high dynamic range system for signal analysis.
REFERENCES 1. Panter, P. F. Modulation, Noise, and Spectral Analysis. McGraw-Hill, New York, 1965. 2. Wang, H. S. C. Distortion of FM signals caused by channel phase nonlinearity and amplitude fluctuation. IEEE Trans. Commun. Technol. COM-14,4 (Aug. 1966), 440-448. 3. Taylor, F. J. Digital Filter Design Handbook. Dekker, New York, 1983. 4. Rabiner, L. R., and Gold, B. Theory and Applications of Digital Signal Processing. Prentice-Hall, New York, 1975. 5. Oppenheim, Processing.
A. V., and Schafer, Prentice-Hall, New
R. W. Theory York, 1975.
of Digital
Signal
6. Crochiere, R. E., and Rabiner, L. R. Multirate Digital Signal Processing. Prentice-Hall, New York, 1983. 7. RADC/DCIT Report RADC-78-44, Interactive Digital Receiver Simulator. Mar. 1978. 8. RADC Report TR-80-169, All Digital Receiver Study. May 1980. 9. RADC Report TR-85-138, All Digital Receiver Feasibility Model and Test, 31 July 1985. 10. Bakhru, K., Multichannel digital sonobuoy receiver. In Proc. IEEE Military Communications Conference, 1990, pp. 61.6.161.6.6. 11. Connelly, B. L., and Kroeger, B. W. Design and performance of an analysis receiver. In Proc. IEEE Military Communications Conference 1990, pp. 61.4.1-61.4.4.
KESH BAKHRU received the B.S. degree with honors and the M.S. degree in physics from the Benaras Hindu University, Varanasi, India; the M.S. (EE) degree from Columbia University, New York; and the Ph.D. degree in electrical engineering from the Polytechnic Institute of Brooklyn, New York. From 1970 to 1972 he was an assistant professor in the Department of Electrical Engineering, Pratt Institute, New York. From 1972 to 1976 he was with the Department of Electrical and Computer Engineering at San Diego State University, California. Since 1976 he has been with Cubic Corporation, Cubic Defense Systems in San Diego, California, where he is currently a senior staff scientist leading the System Engineering Group. His interests are primarily in the analysis and design of communications systems using spread spectrum techniques, applications of high-speed digital signal processing, and adaptive systems. Dr. Bakhru is a fellow of the Institute of Electrical and Electronics Engineers and a member of the Communication Theory Technical Committee of the IEEE Communications Society. He has offered several seminar courses in secure communication, spread spectrum systems, coding, and modulation theory at the University of California, San Diego, and San Diego State University.