HP J HI IHtnll IK! JflllffilM inHHB Ufiii mm L l iButiJ Hi Si Hill I JnHglsfl iBBifiBH isin mmm JH m 11 1111 iHIHil 111 wBm imSm 1 HJi ffli in LIBRARY OF THE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN 510.84 no."77€>-78l cop. 2-* 1 he person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN 1 L161 — O-1096 ' UIUCDCS-R-76-780 yymw THE APPLICATION OF BURST PROCESSING TO DIGITAL FM RECEIVERS BY PAUL LAWRENCE MOHAN January 1976 DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN URBANA, ILLINOIS If. TH. Digitized by the Internet Archive in 2013 http://archive.org/details/applicationofbur780moha UIUCDCS-R-76-780 THE APPLICATION OF BURST PROCESSING TO DIGITAL FM RECEIVERS BY PAUL LAWRENCE MOHAN January 1976 Department of Computer Science University of Illinois Urbana, Illinois 61801 This work was supported in part by Contract No. N00014-75-C-0982 and was submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Science, at the University of Illinois. 1 1 1 ACKNOWLEDGMENTS The author wishes to express his appreciation to Professor W. J. Poppelbaum, Director of the Information Engineering Laboratory, for proposing this research and seeding numerous ideas throughout its pursuit. Also very greatly appreciated was the theoretical assistance and help provided by Professor Jane Liu. Thanks are finally given to the fellow members of the Hardware Research Group whose advice and friendship provided an environment that was a pleasure to work in. TV PREFACE In this thesis we shall investigate the application of Burst processing to the problem of tuning and demodulating FM signals using digital hardware. Such digital FM receivers are shown to be conceptu- ally sound and capable of worthwhile tradeoffs of performance and econ- omy. These results provide the basis for the implementation of a new class of digital FM receiver. The relative performance of the different configurations of the Burst receiver is discussed. TABLE OF CONTENTS Page 1. INTRODUCTION 1.1 Recent Trends 1 1.2 Scope of Work 2 2. THE DIGITAL FM TUNER 3 2.1 Basic FM Principles 3 2.2 Digital Filtering Methods 3 2.3 Frequency Translation 14 2.4 The Burst Concept 16 3. BURST FM DEMODULATORS 27 3.1 Burst Phase Locked Loops 27 3.2 Burst Slope Detectors 31 3.3 Burst Zero-Crossing Demodulators 33 3.4 Adjacent Signal Interference 34 3.5 Relative Performance of Burst Demodulators . . 36 4. CONCLUSION 41 LIST OF REFERENCES 43 Appendix 1 A BURST FM RECEIVER 44 2 PERFORMANCE EVALUATION OF THE BURST FM RECEIVER . . 50 LIST CF TABLES Table p aqe 1 Sideband Amplitude Factors 4 LIST OF FIGURES Figure Paqe 1. Direct Form of a Digital Filter 6 2. Cascade and Parallel Forms of a Digital Filter . . 8 3. General Bandpass Characteristics 11 4. Nonrecursive Filter Design Waveforms 12 5. Frequency Translation 15 6. Burst Representation 18 7. A Burst Encoder 19 8. The Block Sum Register 21 9. Nonrecursive Filter Realized with Burst Methods . . 23 10. iJonrecursive Filter Responses 24 11. Recursive Miter Realized with Burst Methods ... 26 12a. Basic Phase Locked Loop 27 12b. Burst Realization of a Phase Locked Loon .... 29 13. SI one Demodulator Implemented with Burst Hardware 3? 14. Zero Crossinq Demodulator 35 15. Adjacent Signal Interference 37 16. Block Diagram of Diqital FM Receiver utilizinq Burst Processing 45 Vll Page 17. Typical Signal Waveforms 46 18. BSR Realization using Open Collector Inverters . . 48 19. Typical Frequency Spectra of Signals 51 20. Baseband Reproduction by the Prototype Receiver . . 53 1. INTRODUCTION 1 .1 Recent Trends With the widespread use of digital electronics today, it is not surprising to find digital techniques being applied to areas which have been traditionally analog. Designs of radio receivers composed mainly of digital building blocks have appeared in much of the litera- ture over the past ten years. 1 " 3 The advent of fast Fourier transforms and other digital signal processing techniques have made the digital detection problem much easier to handle. Devices such as digital phase locked loops and digital filters have been successfully used in radio receivers for frequency discrimination and filtering. Due to the con- tinued decrease in the cost of digital hardware, one can design a digi- tal receiver with such a degree of redundancy that reliability can be greatly increased without prohibitive costs. It is also possible to reduce sensitivity to environmental changes in a digital receiver be- cause the binary nature of the data processed eliminates the need for stable amplifiers and gain control. Recently, a new method of digital processing termed Burst proces- sing was introduced by Prof. W. J. Poppelbaum. 5 In this system, the basic functional element is the Block Sum Register which permits one to obtain relatively accurate results from yery crude data samples through appropriate averaging. Manipulation of Burst strings (addition, multiplication, etc.) can be achieved through the use of arrays of shift registers and Block Sum Registers. Since the operations of multiplying and summing required in digital filtering become relatively cheap and simple operations in the Burst format, this method is particularly suited for use in digital receivers. 1 .2 Scope of Work In our research we dealt with the problem of designing digital receivers for conventional frequency modulated carriers. That is, digi- tal receivers that are compatible with standard FM transmitters. All data processing in the receivers is to be implemented using Burst methods We note that the factors which dictate an efficient use of hardware in an analog system are different from those in the correspond- ing digital system. Hence, when designing a system to be implemented digitally, one should avoid simply taking each subsystem in a correspond- ing analog design and rebuild it with digital hardware. Several configurations of the digital Burst receiver must be examined to determine which may lead to a better solution. In Section 2, we briefly discuss the basic FM principles and outline those design considerations in the implementation of a digital FM tuner. The concept of Burst processing is also introduced and its applicability to these areas is demonstrated. Section 3 deals with the different configurations of digital FM demodulators which have been pro- posed using Burst techniques. Relative performances of the various systems are discussed. Finally, a particular implementation of the digi- tal Burst FM receiver is examined in detail to demonstrate the hardware realization of such a device. 2. THE DIGITAL FM TUNER 2.1 Basic FM Principles A frequency modulated signal in the absence of noise can be represented as V(t) = A Cos(w t+3Sinoj t) when the modulating signal is a sinusoidal waveform at frequency w . In the expression for V(t), co is the carrier frequency and 3 is the modulation index. The instantaneous frequency of the signal is f = to /2tt + b(oj /2tt) Cos co t = f + 3f cosw t. ^ cm' mcmm Let |f-f | = Af be the instantaneous frequency deviation. Then clearly, the maximum frequency deviation, Af is 3f . It is generally agreed M J max m J 3 that distortion due to bandlimiting an FM signal is tolerable so long as 98 percent of the total power is passed by the system. This condition allows us to restrict ourselves to relatively few of the many sidebands in the spectrum of a frequency modulated signal. Table 1 indicates the bandwidth required for a given value of the modulation index 3. It can be shown that for sinusoidal modulation the required bandwidth is B = 2(Af +f ) which is known as Carson's rule. If the modulating waveform max m 3 has a Gaussian amplitude distribution, such as that physically encountered in many signals, the bandwidth which will pass 98 percent of the signal power is found to be B = 4.6 Af . Here, Af is the variance of the rms rms spectral density of the baseband signal. 2.2 Digital Filtering Methods The bandwidth requirements previously discussed will determine the necessary bandwidth of the digital bandpass filter used in the tuner CO u CU Q. E 03 JD a» T3 •i — LO lo CO cn LO o o CM o o CTi ■St ca LO r— CT> O CT> «3- O ^t" O O CO o o CM CO cr> o co LO co ■=i- oo lo CM CM CTi oo CO •3- LO oo LO LO o LO CM oo ^1- oo lo o CO CM LO O CM a-> en CM CTv oo LO lo ■=1- oo .— r— O ro CM lo CT> CM 00 lo o LO CM oo o s- 1 CU o CM r— LO cr> r™ o LO o r^ LO S- cr> lo LO r~- *d- o CTl r^. CM 1 CM CQ CO X C •r- c o • • r— E -t-> 4- ra CM r— ^ X -a o 00 E -a c 4- ro O JD CU CU -a rs •i — i — i/> rt3 > +-> E C ra CU u > •( — • 1— 4- en "P" c ro CD •i — i_ 00 o 4- 4- O 00 -a t_ c cu ra JD -Q E CU zs -o c • r— 00 CU JC +-> 4-> c fd O o 4-> • ^ 4- i — •r— ra C 3 CD cr •r— cu CU CJ) -a c •i— •( — ^ +-> -o 03 c o ra *r- JD -o c -a •T— ai i_ CU •t— r^ :s JD o- ra CL) t— Di of the digital receiver. The transition width of the filter will be dictated by the desired selectivity of the tuner. There are a number of configurations of digital filters which may provide suitable results for digital FM tuning. The two major classes of filters to be consid- ered are the nonrecursive and recursive implementations. Each method has certain unique advantages which can be tailored to a specific appli- cation. Because a digital filter must deal with finite word lengths, quantization noise and roundoff error become major factors to be con- sidered also. Figure 1 shows the direct form of digital filter with transfer function a n + a n z~ + . . . a z" H(z) = k-5 U "— . 1 + b lZ - ] + . . . bz" m 1 m In a nonrecursive implementation, all of the b.'s in this expression are equal to zero and thus we see that at any time, the output sample is a linear function of the input samples. Filters of this type have transfer functions which contain only zeros. Generally, a nonrecursive digital filter produces a linear phase shift and because of the absence of poles has no stability problem. Quantization and roundoff problems are usu- ally negligible in these filter forms. However, the lack of poles in nonrecursive transfer functions represents an inefficient use of hard- ware when one attempts to obtain sharp cutoff responses which are more easily achieved with pole factors. In a recursive digital filter some of the b.'s of Fig. 1 are not equal to zero. The output sample at any time instant is a linear Q U a> i. cn combination of previous output samples as well as the present and past input samples. This class of filter has poles as well as zeros and is capable of realizing sharper cutoff with fewer delay stages than nonre- cursive designs. However without proper consideration of pole location, instability problems may arise. The phase shift of the recursive filter design is nonlinear. This factor could produce some undesirable effects when we attempt to frequency demodulate the filtered signal. If we require a filter with a steep transition between pass- band and stop band, it is found that because we now require a large value of m in the direct form implementation, the pole locations, if present, may become extremely sensitive functions of the coefficients b . This means that the b, must be produced with a high degree of ac- curacy resulting in an increase in required hardware. These problems can be circumvented by choosing either the cascade or the parallel forms illustrated in Fig. 2 (a, b). These realizations, composed of second order sections, yield transfer functions n 1 + a, Z" 1 + b. Z" 2 A n *—, *— *- k-n + c k z _l + d k z"^ and M a, z" 1 + b. k=l c k Z" 2 + d k Z _1 + 1 for cascade and parallel forms respectively. The cascade form is parti cularly suited for bandpass filters because it requires significantly fewer multipliers for zeros on the unit circle in the Z plane. II +J to 4- C\J cu CO > (O en •^ to a> Cu i- 0) > •r- S- 3 O - 3 CM n (. J2 *3" «/) 13 where h are the required coefficients of the filter impulse response. In Fig. 4b we have broken H(s) into two separate frequency responses which when convolved yield the desired H(s). Since convolution in the frequency domain is equivalent to multiplication in the time domain, the impulse response h(t) of the desired filter is found by multiplying the time responses of H(s), and H(s)„ and is shown in Fig. 4c. Since the digital filter must deal with finite number of terms, the sampled im- pulse response must be trancated by windowing (Fig. 4d) . There are many types of windows one might choose according to how well the actual response must match the desired one. Ultimately, the window whose Fourier transform has the smallest sidelobes will yield the closest match. The net result after windowing gives an N sample impulse response (Fig. 4e), which approximates the desired impulse response. These N values now will be the required coefficients for the nonrecursive fil- ter of N-l sample delays. The final approximation to the desired fre- quency response appears in Fig. 4f and is derived by convolving the fre- quency responses of Fig. 4a and the window response. It can be seen that by varying the values of the N coeffic- ients previously obtained, we can alter the filter impulse response and shift the center frequency of the bandpass response. It is also shown that by increasing the value of the sample delay time, T, we can also shift the center frequency of the passband. The preceding brief survey of digital filter design techniques reveals several properties associated with digital filter hardware in 14 general. First, we see that all three canonical forms, Direct, Cascade, and Parallel, are equivalent with regard to the amount of storage re- quired, that being N unit delays. Also apparent is that, aside from the special case of zeros on the unit circle, all three forms require the same number of arithmetic operations, 2N + 1 multiplications and 2N ad- ditions per sampling period. This gives us some idea as to the amount and type of digital hardware required. The sampling period, dictated by the input frequency and Nyquist's theorem, will determine the speed at which this hardware has to operate. Presently, the use of binary arithmetic and a high degree of parallel processing has made these filters realizable. However, as will be shown, the concept of Burst processing allows one to achieve these required operations but in a much simpler and more economical way. 2.3 Frequency Translation When discussing the various Burst FM demodulators, it will become apparent that sensitivity to changing input frequencies can be greatly increased by employing frequency translation. One method of accomplishing this is demonstrated by Fig. 5 which shows the spectrum resulting from sampling and holding an input sinusoid of frequency f . Part a shows the response of instantaneously sampling the input at a sample rate f < f . This response must be weighted by the aperture factor 1n x , part b, due to the finite hold time 1/f . The resulting spectrum, part c, shows how the input sinusoid has been frequency trans- lated to a much lower value, f . , with higher harmonics effectively ct 3 15 (a) 2f -f s c = f ct 1 — f s ! 2f ' 3 V f c f c 4f s- f c I 3f ' 5f s" f c — r 4f. Sina)T s /2 J s /2 (b) 1- ct r 2f. i 3f, (c) Fig. 5. Frequency Translation. 16 suppressed. Now, if we imagine that the input sinusoid is being shifted in frequency by ± N cycles, it is apparent that the frequency shift will be a much larger percentage of the unmodulated frequency in the trans- lated case than in the case where it remained untranslated (i.e., N/f . >> N/f ). Since it is the percentage change in input frequency that produces output changes in the Burst demodulators, it is seen why frequency translation does so well in increasing overall sensitivity. It also becomes apparent that by employing this technique we allow our- selves to operate the digital hardware of tuners, demodulators, etc., at much lower clock rates and to utilize standard medium speed logic families. When frequency translating an input FM signal, the bandwidth requirements discussed earlier must still be met if distortion is to be limited. This fact requires that the translated FM signal fall suffic- C * iently inside the curve so as to allow passage of important side- A bands. This requirement can be met by choosing an appropriate sample rate. 2.4 The Burst Concept The concept of Burst Processing arose from the need to develop an on-line pulse processor which combined the speed of weighted binary systems with the noise tolerance of stochastic schemes. 5 The basic idea of Burst techniques is to employ low precision arithmetic which is made arbitrarily accurate by appropriate averaging. This concept lead to the method whereby numbers are represented by some number of 1 's in a 17 block or group of blocks each consisting of 10 slots. Each block can be thought of as a 10 bit word where the word "bit" is not to imply con- ventional weighted binary ordering. Figure 6 illustrates these principles by first representing the normalized decimal value of .4 with an accuracy of 10 percent. Greater precision is obtained by using 10 blocks whose contents when averaged, yield a result good to 1 percent. It is in this manner that simple crude approximations can be made to yield suit- ably accurate results. For simplicity we will initially consider only single block representation of data, i.e., 10 "bits" per data sample. The digital encoding and decoding in the Burst domain is quite convenient. Burst encoding of analog data may be accomplished using the scheme of Fig. 7. Here, the analog data to be. sampled and encoded is constantly compared to a staircase waveform which resets after ten clock periods. At each clock pulse either a 1 is entered in the Burst register if the staircase voltage V is less than the analog voltage, V. or a s a zero is entered if V c is greater than V, . In this way a new Burst S a sample is contained in the register after every ten clock periods. It is easily seen that the number of l's in the register is directly pro- portional to the quantized magnitude of the analog signal sample. The step size (A) of the staircase is determined by the maximum amplitude (V ) of the analog signal to be encountered. That is, A = V /10. It can be shown that the quantizer of Fig. 7 produces a mean square quanti- 2 zation noise of magnitude A /3. It should be noted that when using this encoding scheme, the sample points on the analog waveform are not neces- sarily equally spaced in time. Just where the sample is taken is a 18 3 U o 3 3 « GO > u o jQ O to t- 3 CJ o s ^ c o 4> a: 3 CO • C7) en o a> i— 3 (O r- < > 19 "I i l i i i r OmooS(om*iow Burst Value i- o •r- Ct x: — 0> ■M VI cc L 3 CO i— o ii ii > > V A i t > > / \ • • • A \ o C >• 1 on -» ^ • '■< ► O 3 O 01 o o c 10 i- 3 CO CT> i— a (/) o i- i~ •r- O) (O c IO CD o *♦- 20 function of the waveform being encoded. This property can be very use- ful in applications where somewhat random sample points are required. It becomes apparent that to insure valid sampling, the "slope" of the staircase, A/T , must be greater than the maximum slope encountered in the input waveform. This condition may not be met simply by sampling at the Nyquist rate. Decoding Burst encoded data is easily achieved by what will be termed a Block Sum Register (BSR). This is simply a ten bit shift register containing parallel outputs each of which drives a separate current source which is summed on the output bus. Figure 8 illustrates the BSR principle, again for the data value of .4. The role of the source voltage, V, can be seen as it determines the relative weight a particular Burst string will have. That is, doubling V will double the apparent "analog" value of the given decoded Burst. The term analog used here is implying an output level which is quantized to one of ten possible levels. It is because of this method of Burst decoding that one can achieve quite tolerable outputs even when the sampling rate is so low as to normally predict large distortion. This fortunate result is due to the effect obtained when sample point data is serially shifted into a BSR. As l's are shifted, the output increases in a stepwise manner eventually leveling off as the number of l's in the BSR remains temporarily constant. When the next encoded sample is shifted in, the BSR output will eventually be that of the new sample, but it will be approached in a stepwise manner. It is this linear interpolation be- tween samples that gives the BSR a unique property of averaging discon- tinuities and making course sampling appear better than expected. 21 3 3 > -— ^ i- CC 3 II 3 O +J ■•-> 01 00 3 cr- s- o. u «o— ^ 3 C L. -M > CO •— i 3 !—««—■ O O I/} > 3 a ■•-> 3 C T3 0> ■o O U 0J o 3 3 O -4-> CO > O-VW cr CO CD -o s u 0) ■•-> (/) cr- ce E 3 o o CO CO 3 O c o .a E >> 22 With these basic concepts of Burst techniques at hand, we may now proceed to apply them to the area of digital filters. It is evident that the necessary operations of delay, addition, and multiplication are readily achieved by the use of Block Sum Registers and appropriate source voltages to obtain the desired scale factors when required. Therefore, the design methods outlined in the preceding section remain unchanged and are simply realized using Burst hardware. This is demon- strated by the general nonrecursive bandpass filter depicted in Fig. 9 which is implemented using the basic Burst modules. 6 As discussed earlier, the coefficient of each delayed sample is determined by the impulse response of the desired frequency characteristics. The value applied as the source voltage to each delay unit, BSR, will incorporate the required coefficient as well as the particular window scaling used. The center frequency of the bandpass response can be adjusted by alter- ing the length of the delay time, T. This is easily achieved by simply tapping the desired output on the shift register delay lines. Intui- tively, it becomes apparent that if we adjust the delay time, T, to equal that of the desired carrier period, the BSR outputs will add con- structively yielding a maximum response for frequencies equal to 1/T ± n(l/T). Undesired frequency components will add destructively due to the random sample values obtained and will produce no net time varying com- ponent in the output. Some typical frequency responses are plotted in Fig. 10 for both rectangular and triangular windowing. The effect of window shape on the frequency response becomes evident when going from rectangular 23 r t CD 9 cr co CD cc i- a. 3 c CO >— • cr (/) m • • • • • • • • T3 O •^ l~ 0) • «/> o O ••" ^-» i- a; v O 3 a» |M VI x: Q CT CO GO o CD y 1- 3 CO ■o «3 a: i- > •r- (- 3 U cn 3 3 O 24 L. «J en r— c 3 •r- 1 «/» C o c cr i. > i. U c o cr> T3 25 to triangular windows doubles the bandwidth of the filter but greatly reduces sidelobes. The dependence of tuner selectivity on the window function as well as on the number of delay elements, N, thus becomes apparent. Filters of this type have been successfully implemented with bandpass center frequencies of hundreds of KHz and bandwidths of tens of KHz. A Burst filter of the recursive type is shown in Fig. 11. As before, the sample weights are determined by the BSR source voltages. The major difference with this design however is the presence of N-l ad- ditional BSR's which provide separately weighted samples which are fed back to the input of the filter. This produces the required pole fac- tors in the overall transfer characteristic. The stability of the recur- ive filter depends strongly on the coefficient accuracy and therefore on the value of the BSR source voltages which must be accurately con- troled. This requirement may prove unsuitable in some applications. Also, quantization and roundoff errors in recursive designs are constantly fed back through the system. If we are dealing with 10 slot BSR's, each sample has an accuracy of 10 percent, being rounded to the nearest higher level. It is for these reasons that nonrecursive filter designs ap- pear more suitable for single block digital filtering. This does not imply, however, that utilizing 10 block representation (1 percent ac- curacy) will not prove adequate for some applications requiring recur- sive designs. ( i < > > 1 1 1 » • • • • » • • 1/1 (U 4-> •^ en ct < >> ia i 1 a: CO a:* i i -Q a: CO CO oc< z cc CO CO et< 1 i i 1 1 I ' 1 > 4 • • CO CO z CO CO Burst Encoder ' I * 1 i 1 ' f 1 I 26 3 3 O o a> 3 CO ■o or 0) > 3 u ct en en O -M ■— 3 lo 3 CO CL O C L. i-i O I o u a> IVI u o -C I/) I CD O C I- .f- O) CO IVI CO O L. (J 1- 0) CD 0) m r~ CO •i- oc: 93 L -> -f- 3 t- Q. i~ ai 4-> 4-> i— 3 «/» D. CL J- E C 3 «C •— i CO CO a> a. CO A CO t to -§ 01 4-> c 01 o 4-» it) 3 Q a> a. o CO CO o> u o 33 slope maxima, say over ten slope values, which are periodically loaded into the output BSR to appear as the reconstructed baseband signal . It can be shown that in a system of this type, the sensitivity expressed as percentage change in input frequency producing a one bit change in the output is f./20 f x 10%. Due to the input quantiza- k max tion, analog values rounded up, the maximum error which may appear be- tween two adjacent Burst samples will be one bit and therefore a local slope maxima may be in error also by one bit. Since input signal samp- ling is asynchronous, the occurence of these errors will be of a random nature. To prevent spurious noise spikes from being interpreted as valid data, a delay register is placed in the system which requires that a given slope increase be repeated several times before altering the output to the new slope maximum. The degree of noise immunity can be increased by increasing the length of the delay register. When the FM carrier frequency can be considered constant over many cycles, the delay register will allow maximum slope determination sufficiently soon so not to introduce appreciable output distortion. As in the case of the Burst PLL, frequency translating the input to the slope detector will provied one with full scale sensitivity even when maximum frequency shifts about the carrier are less than 10 percent f . c 3.3 Burst Zero-Crossing Demodulators A third method of FM demodulation well suited to Burst proces- sing is simply that of counting the zero crossings of the input FM 34 signal. It is quite obvious that for a fixed count interval, the number of zero crossings which occurred is directly proportional to frequency. Figure 14 illustrates a basic zero-crossing demodulator using the Burst data format. From the figure we see that for each zero crossing, a 1 is loaded into a 10 bit shift register which is cleared periodically. Be- fore being cleared, the contents of this register are parallel loaded into a buffer register which feeds the output BSR which is clocked at a rate which is ten times that of the clear pulse. Therefore, the out- put BSR will contain the instantaneous frequency samples whose variations will be the desired baseband signal. With this configuration we find that for a clock frequency of f , the input signal must be of a frequency in the range .If. < f < f. to be detected. Again, expressing the system's sensitivity as percentage change in input frequency to produce a one bit output change, we find it to be (f./f ) x 10%. Ideally, for input frequencies which are inte- K max gral multiples of f. /10, the output BSR will yield respective values which are constant in time. If, however, this frequency condition is not met, the BSR contents will fluctuate by one bit such that the aver- age of the BSR output will correspond to the input frequency. In this manner, the crude ten level quantized output will yield values which, when averaged (by the ear), appear much more resolved than would be expected. 3.4 Adjacent Signal Interference At this point it may be instructive to examine the interference 35 -* «/t o CJ> o 1 c r-» o •r- o i~ CO O) «/t rvi o -o o E a «/> O u <_> o en 32 ~ 4-* i/) O- O C i~ •-t <_) I o E a> 36 produced when an undesired signal from some other broadcasting station is present together with a desired FM signal. This situation might arise if the transition width of the tuner response is excessively large. The simplified representation of Fig. 15 shows when the desired carrier, waveform A, is present at the demodulator together with an undesired carrier of different frequency, waveform B, the resultant waveform is both amplitude and phase modulated. We are concerned with the phase modulation which produces a frequency modulation of magnitude f« R A6 where f. R is the difference in frequency of the two waveforms A and B and AG is the maximum phase shift between the resultant and the desired waveforms. Thus, even before we decide to frequency modulate carrier A, the presence of an undesired signal has already introduced a frequency modulation which will be detected and may appear as audible noise in the demodulator output. 3.5 Relative Performance of Burst Demodulators In comparing the performance of different FM demodulators many factors come into play (input SNR. 3, etc.) which tend to limit the number of general statements which can be made regarding the overall performance of a given system. Thus, while we may assume that while be- low threshold the Burst PLL will provide a greater output SNR, this may not be the case for higher input SNR's. It is for these reasons that the comments to be made regarding relative performance will be kept gen- eral in nature pointing out the gross differences and major advantages to be obtained with a particular scheme. 37 QJ O c c en u in a- CD 00 + < 38 The first parameter which deserves comparison i>s that of sensi- tivity to input frequency changes. Initially assuming a high input SNR we find, following the input frequency conditions required of each de- modulator, that each system provides the same maximum sensitivity, i.e., 1 bit change in output for a 10 percent change in the input fre- quency. If all processing registers are increased to 100 slots (10 blocks), each demodulator is now sensitive to 1 percent changes in input frequency. With each demodulator sensitive to the same amount of fre- quency deviation, it would appear that the effects due to unwanted fre- quency changes produced by additive noise would also be the same in each system. This however is not true due to the manner in which input data is treated by the different demodulators. It is seen that in de- modulation via direct zero crossing counting we are vulnerable to any undesired frequency deviations because each zero crossing is entered into the system and considered valid information. This problem is sub- stantially reduced by the introduction of "inertia" through the delay registers incorporated into the slope and phase locked loop demodulators. With this addition, any short term (with respect to the modulating wave- form) frequency shifts are effectively ignored by the system. Thus we expect a greater output SNR with the demodulators utilizing this technique. We should next like to address the effects of local clock jit- ters on the performance of Burst demodulators. In the Burst slope de- modulator it is required to take samples at equally spaced intervals to produce a slope value proportional to the sample value. It is found 39 that, assuming a sinusoidal input, the Burst slope demodulator will tolerate in the worst case approximately a 12 percent change in the sampling (or clock) period before an error is produced in a particular Burst sample value and subsequently an error in the slope value deter- mination. In the demodulators utilizing input zero crossings, similar results can be obtained. Initially assuming that the input zero crossings and master clock act synchronously, we find that the Burst PLL and zero crossing demodulators require a 10 percent change in clock period to produce an error in the Burst frequency value. Having the clock and zero crossings act asynchronously simply means that exceeding the above clock period changes will produce an error in the average Burst fre- quency value. It is to be noted that in the slope and zero-crossing de- modulators 10 clock periods are required before a new Burst value is entered. Thus, any clock jitter equal to the limits specified earlier must be maintained for at least 10 clock periods before it will cause an error. Therefore, for these demodulators, the maximum clock jitter which can be tolerated will be substantially increased if we assume that the clock jitters occur randomly or that they persist for less than 10 clock periods at any one time. It is apparent that the demodulators which utilize input zero crossings are insensitive to any amplitude variations of the input sig- nal whereas the slope demodulators are highly dependent on input signal amplitudes. This would indicate that the slope demodulators would be most effective where signal environments are such that signal amplitude 40 variations are less than 10 percent of peak. Limiting the input signal would provide a solution to amplitude sensitivity, so long as doing so does not completely eliminate any slope information. One major advan- tage in using slope demodulators is their absence of any counters, which tends to explain their greater tolerance to variations in clock period. As an aside, it becomes clear that the Burst slope demodulators can be considered universal demodulators in that they can perform FM or AM de- modulation equally well, given that certain input signal conditions are met. With regard to which demodulator would perform best under given signal environments—it seems apparent that under ideal, no noise circumstances, the Burst zero-crossing demodulator would provide the most quality of output for the least amount of hardware. Given worst case signal conditions, the Burst PLL would outperform the others mainly due to its inherent frequency selectivity and noise tolerance but at the cost of increased processing hardware. However, even the Burst PLL can tolerate only so much noise before being driven out of lock and no longer providing a demodulated signal. The role of the Burst slope de- modulator is that of providing some of the noise tolerance of the PLL (noise due to frequency variations) without employing counting methods which may be undesirable in certain instances. 41 4. CONCLUSION We have seen how Burst processing can be applied to tuning and demodulating FM signals. It was found that nonrecursive digital filters were particularly suited to implementation with the basic Burst modules. Through the use of Block Sum Registers, the necessary operat- ions of summing and scaling required of these filters is achieved. The relative simplicity of these filters, i.e., the simple hardware employed in the Burst digital filters, gives them substantial economic advantages over conventional digital filter implementations. The area of Burst de- modulators proves to be equally encouraging with various demodulation schemes devised to meet different performance criteria. Aside from analog comparators and sample-hold modules (if employed), the Burst FM receivers employ totally digital processing delivering the low cost and reliability inherent in digital systems. It appears that in the near future a single BSR could become part of a CCD array containing many such devices, thus further reducing the cost and size of Burst systems. With such BSR arrays, 100 slot data representation becomes yery practical and allows a tenfold increase in accuracy, thus improving the performance of digital filters and demodulators realized with Burst hardware. It becomes apparent that the use of Burst processing in digital FM receivers is just in its infancy and further development will no doubt yield more ingenious methods of applying the Burst concept to digital receivers. In the appendixes to follow, we shall examine the first pro- totype of a digital FM receiver to employ Burst techniques which has been implemented with standard logic hardware. The results obtained are very 42 encouraging and show that with only 10 slot Burst representation, quite satisfactory results can be obtained. 43 LIST OF REFERENCES 1. Brown, J. E., "Digital Phase and Frequency Sensitive Detector," Proc. IEEE, vol. 59, pp. 717-18, April 1971. 2. Gill, G. S. and Gupta, S. C, "First-Order Discrete Phase-Locked Loop with Applications to Demodulation of Angle-Modulated Carrier," IEEE Trans, on Commun., vol. COM-20, pp. 454-62, June 1972. 3. Hinteregger, H. F. and Counselman, C. C, "Digital Single-Sideband Mixer," Proc. IEEE, vol. 61, p. 478, April 1973. 4. Liu, J.W.S., Bracha, E. and Mohan, P. L., "Performance Evaluation of the Digital AM Receiver," Department of Computer Science Report No. 757, University of Illinois, Urbana, IL, April 1975. 5. Poppelbaum, W. J., "Appendix I to 'A Practicability Program in Stochastic Processing,'" Department of Computer Sicence, University of Illinois, Urbana, IL, March 1974. 6. Poppelbaum, W. J., "Application of Stochastic and Burst Processing to Communication and Computing Systems," Department of Com- puter Science, University of Illinois, Urbana, IL, July 1975 44 Appendix 1 A BURST FM RECEIVER A block diagram of the digital Burst FM receiver implemented to date is shown in Fig. 16. Two baseband modulation generators in conjunction with two FM signal generators are used to simulate two adja- cent FM stations at carrier frequencies of approximately 1.8 and 2.1 MHz respectively. These sinusoidal carriers are added and applied to a sample-hold circuit whose function is to translate the input signals to a lower frequency range. The translated signals are Burst encoded and applied to a digital filter which allows passage of one of the two signals according to the tapped length of the filter delay elements. The fil- tered signal is then reencoded into Burst by employing a second sample- hold circuit which permits sampling at equal time intervals. These Burst samples are fed into a Burst slope demodulator, the output of which is loaded into a BSR which drives an audio amplifier to deliver the baseband signal. Figure 17 shows some typical waveforms associated with various stages of the digital receiver. In the receiver, the 10 slot Burst format is used exclusively, mainly to reduce hardware requirements. The digital filter employed was of the nonrecursive type discussed earlier (fig. 9), and utilized rec- tangular windowing. The delay time of each delay element is adjustable from zero to 48 clock periods according to where the output taps are placed. With 10 clock periods per Burst sample, we see that we can ac- commodate a maximum of 4.8 samples in each filter delay element. A 45 o c o +J •«- O -M a; • <0 r— CO CO -^ t (0 s- ■M 0) CT>t— CO I. >> o U *-> c , X >— 1 i- r- o <« -M s: c «o «o -O 4- O) 01 CO C > 1-^ t—t i- «— o «o +-> 5: c «tj i_i_ cr. c. •t- a» CO c a> o i , i— ■ •— i tm -o o C -M -o •#- o cri E 5(8 o i- oi > Ol u Ol a: Li_ C7> cr co CD >o CO -M CO •r- Ol CT. o •r— o Q w. Q. »♦- O ■M oo E 1. a. ■»-» 8 CO II Hi" in + co r> CD i— I m ro m CJ 0> [*i CO i— I co (0 m fO rO Cft ID to 8 ■>- lf> O ■0^ -o- If) . o ->- IT) + ■AAAr— ||i u o ■•-» u Of o c en c + CO 00 CD 0> C 0) 49 upper limit on the clock rate of the whole receiver if we wish to avoid synchronizing Burst strings which must be stored when using higher clock rates. Having established a maximum clock rate, the sample-hold rate operating on the input signal to the receiver is 1/10 this value. As shown earlier, the sample-hold rate will determine the translated fre- quency the input signal is to acquire. Thus, by adjusting the base clock frequency, we can optimize the translated frequencies of the two input signals to yield the best overall response for a given set of filter delay lengths. It should be -made clear that in tuning different signals, it is not required to change the clock frequency but merely to alter the lengths of the filter delay registers. 50 Appendix 2 PERFORMANCE EVALUATION OF THE BURST FM RECEIVER In this section we will discuss some of the pertinent per- formance figures which can be derived given the preceding FM receiver design (see Reference 4 for a similar discussion concerning the digital AM receiver) . Of primary concern is the signal-to-quantization noise ratio. As stated earlier, 10 slot Bursts are used to represent all data. This form of representation can be thought of as a PCM version of coding in which data is quantized into one of ten levels. With this assumption, and using the encoder of Fig. 7, the signal-to-quantization noise ratio 2 2 is expressed as (V ) /A /3 = SNR n . For a properly scaled sinusoidal input we find: SNR Q = 37.5 A 2 /A 2 /3 = 20.5 db. By applying an input offset of A/2 to the encoder of Fig. 7, the mean 2 squared quantization noise can be reduced to A /12, thus slightly im- proving SNR„ to 26.5 db. It should be noted that e^ery time we increase the number of slots/ sample by a factor of 10, we add 20 db to SNR-. If we choose a base clock frequency, f. , of 4.75 MHz, the typi- cal frequency spectra of signals shown in Fig. 19 is observed. We see that both input signals are translated well within the — - — curve im- A posed by sample and holding. However, some attenuation of sidebands is introduced by the translation which will distort the output somewhat when large baseband amplitudes are encountered. The filter response 51 |U(f) 100K 100K Input I I ' 1 ' »- 1.8 2.1 f(MHz) |C(f) Translated Input Ji \ \ «* « . — * - 475 575 ■"i ■* 100 275 ■f s-h 750 950 f(KHz) |H(f) (dbfl Filter Response f(KHz) Fig. 19. Typical Frequency Spectra of Signals. 52 shown is that obtained when tuning the 1.8 MHz signal (100 KHz trans- lated). A similar tuner response is obtained when selecting the other signal. In the worst case, the filter provides approximately 12 db at- tenuation of the adjacent station, i.e., when the undesired station is partly passed by the folded filter response at 300 KHz. This amount of signal separation is sufficient to essentially eliminate audible effects of the adjacent FM signal. Considering the small amount of digi- tal hardware required to achieve these results, the quality of baseband reproduction is \/ery good. Demodulator performance proved to fulfill expectations. By choosing local slope maxima over 10 slope values, we are able to faith- fully reproduce baseband frequencies up to 20 KHz. If we choose a slope maxima over 50 slope values, upper limits on faithful audio repro- duction is 4 KHz (suitable for voice communications). Maximum slope er- rors are less likely to occur as the number of slope values compared is increased, thus reducing the noise introduced by the demodulator. Perceptive factors largely determine the ultimate performance rating of a given receiver. In this respect, the performance of the digital Burst FM receiver exceeds expectations, despite crude data quantization. This quality can be partly attributed to the integrating effect of the Block Sum Registers employed in the receiver. Figure 20, although possibly not as convincing as an audio recording, shows the baseband reproduction extracted from a tuned FM signal applied to the prototype receiver. 53 loriz. Scale : lms/div. Input Modulation Outout Fin. 20. Baseband Reproduction by the Prototype Receiver. SECURITY CLASSIFICATION OF THIS PAGE (Whan Data Bntarad) REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM 1 REPORT NUMBER UIUCDCS-R-76-780 2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER 4. TITLE (and Subtltlm) The Application of Burst Processing to Digital FM Receivers S. TYPE OF REPORT ft PERIOD COVERED Master's Thesis S. PERFORMING ORO. REPORT NUMBER UIUCDCS-R-76-780 7. AUTHORf*; Paul Lawrence Mohan • . CONTRACT OR GRANT NUMBERfaj N00011+-75C-0982 9 PERFORMING ORGANIZATION NAME AND ADDRESS Department of Computer Science University of Illinois at Urbana-Champaign Urbana, Illinois 6l801 tO. PROGRAM ELEMENT. PROJECT. TASK AREA ft WORK UNIT NUMBERS II CONTROLLING OFFICE NAME AND ADDRESS Office of Naval Research 219 South Dearborn Street Chicago, Illinois 6060U 12. REPORT DATE January 1976 IS. NUMBER OF PAGES 62 14. MONITORING AGENCY NAME ft ADDRESS*-*/ dlttarant /rooi Controlling Olllca) 18. SECURITY CLASS, (ol thlm tiport; ISa. DECLASSIFI CATION/ DOWN GRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of thl» Rtport) 17. DISTRIBUTION STATEMENT (of (ha abatract antatad In Block 20. It dlllaranl treat Raport) '8. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on ravaraa aid* II nacaaaary and Identity by block numbar) Burst Processing, Burst Phase Locked Loop, Burst Slope Detector, Block Sum Register, Digital Receiver 20. ABSTRACT (Continue on ravaraa alda If nacaaaary and Idantlty by block numbar) In this thesis we shall investigate the application of Burst processing to the problem of tuning and demodulating FM signals using digital hardware. Such digital FM receivers are shown to be conceptually sound and capable of worthwhile tradeoffs of performance and economy. These results provide the basis for the implementation of a new class of digital FM receiver. The relative performance of the different configurations of the Burst receiver is discussed. DD ,^73 1473 EDITION OF 1 NOV 6S IS OBSOLETE S/N 0102-014-660 1 | Release Unlimited SECURITY CLASSIFICATION OF THIS PAGE (Whan Data Inl«r«fj [3LI0GRAPHIC DATA 5EET 1. Report No. UIUCDCS-R-76-78O 3. Recipient's Accession N< i, !c mil Sunt it le The Application of Burst Processing to Digital FM Receivers 5. Report Date January 1976 1 nth or i Jr>aul Lawrence Mohan 8. Pcrf ormin-g Organization Kept No. UIUCDCS-R-76-786 i|,irniin,; Organization Name and Address Department of Computer Science University of Illinois at Urbana-Champaign Urbana, Illinois 6l801 10. Project Task/Work I nil N. 11. Contract '(itant No N0001U-75-C-0982 v'.'r.it. Organization Name and Address Office of Naval Research 219 South Dearborn Street Chicago, Illinois 60b04 13. Type of Report Si IVri.i Covered Master's Thesis 14. ny Notes In this thesis we shall investigate the application of Burst processing to the problem of tuning and demodulating FM signals using digital hardware. Such digital FM receivers are shown to be conceptually sound and capable of worthwhile tradeoffs of performance and economy. These results provide the basis for the implementation of a new class of digital FM receiver. The relative performance of the different configurations of the Burst receiver is discussed. K> ■ K or Js arid Document Analysis. 17a. Descriptors Burst Processing, Burst Phase Locked Loop, Burst Slope Detector, Block Sum Register, Digital Receiver li ntifiers Open-Ended Terms i ! I' ie Id /Group iiulity Statement RELEASE UNLIMITED 19. Security (lass (This Report ) UNCLASSIFIED 21. No. o! 1' ,,..•• 62 20. Security ( lass (Tins Page UNCLASSIFIED 22. Price USCOMM-DC 4'- :. «' UNIVERSITY OF ILLINOIS-UHBANA 510 84 IL6H no C002 no 776 781(1975 Theoretical limitations on the uie ot pa 3 0112 088402505 ran iiffi