156 IkEE TRANSACTIONS O N BROADCASTING, VOL 36, N O 2, J U N E 1990

Prediction/Cancellation Techniques For Fading

Broadcasting Channels - Part 11: CPM Signals

Abstact - The purpose of this paper is to study and generalize the application of the fading prediction/can- cellation technique, which was introduced in a compan- ion paper [l], to mobile broadcasting transmission sys- tems employing Continuous Phase Modulation (CPM) signalling formats. Our motivation for this study is due to the well-known fact that for nonlinearly am- plified systems CPM signals offer significant spectral advantages over equivalent non-constant envelope (e.g. bandlimited PSK) signals. Similarly to [l], based on the Maximum Likelihood Ratio Test (MLRT), we de- rive an algorithm which results in a fading cancellation detector. Furthermore, we extend the previously pro- posed technique to include novel multisample per re- ceived symbol receivers which are particularly attrac- tive for CPM schemes. Although our methodology is general enough t o accomodate any CPM signalling for- mat, here we are dealing mainly with Minimum Shift Keying (MSK) type of signals. The reason behind this choice is that MSK offers both high spectral efficiency and good performance with minimal implementation complexity, thus being a very suitable signalling for- mat for mobile broadcasting system applications. Our analysis includes also various generalizations, such as processing in a continuous time fashion as well as re- duced complexity detectors. The obtained performance evaluation results indicate that for the same channel conditions as in [l], i.e., for a mixture of Additive White Gaussian Noise (AWGN) and multiplicative, nonselec- tive fading, even higher Bit Error Rate (BER) perfor- mance improvements as compared to those reported in [l] are possible. Furthermore, in applications where nonlinear amplification is being employed, constant en- velope signals offer higher spectral and power efficien- cies as compared t o equivalent non-constant envelope signals.

D. Makrakis is with the Department of Electrical Engineering, Univer- sity of Ottawa, Ottawa, Ontario, KIN 6N5, Canada and the Department of Communications, Communication Research Centre, 3701 Carling Avenue, P.O. Box 11490, Station H, Ottawa, Ontario, K2H 8S2, Canada.

P. T. Mathiopoulos is with the Department of Electrical Engineering, The University of British Columbia, 2356 Main Mall, Vancouver, B.C., V6T 1W5, Canada.

This work was supported in part by the Natural Sciences and Engi- neering Research Council (NSERC) of Canada under Grant OGPINO11.

1 INTRODUCTION

In a companion paper [l], a noise prediction/cancellation tech- nique for reducing the effects of multiplicative noise such as fading on the performance of mobile broadcasting transmission systems was introduced. The idea behind the proposed tech- nique is to take advantage of the strong correlation properties of the fading process for identifying the most probable transmitted sequence in the Maximum Likelihood Detection (MLD) sense. Based on that, a new algorithm was derived and various per- formance evaluation results for both bandlimited (raised-cosine filtered) and constant envelope (unfiltered) QPSK signals have been reported [l]. These results have indicated that, for rela- tively low complexity receivers, BER improvements of more than three orders of magnitude are achievable (for Eb/N, > 23 dB). At the same time, considerable reduction of the fading caused error floors have been observed. Among the various type of sig- nals examined in [l], raised-cosine filtered QPSK offer the high- est spectral efficiency. In this respect and since the transmission bandwidth is always limited, bandlimited QPSK (or PSK signals in general) are of practical interest.

It is well-known, however, that bandlimited PSK signals when nonlinearly amplified by a high power amplifier (HPA), operated in the power efficient saturation mode, suffer from spec- tral regrowth of the signal sidelobes a t the output of the HPA due to the nonlinear effects of the amplifier [2]. These nonlinear- ities are mainly due to AM/AM and AM/PM convertion of the power amplifier. The regrown sidelobes cause significant interef- erence into the adjacent channels and thus degrade the proba- bility of error performance. This situation is typical in mobile, satellite and mobile-satellite radio and broadcasting applications where the available power is limited [3]. In recent years, this re- quirement for reduced adjacent channel interference (ACI) has become increasingly strigent, especially since the recent market driven expansion of the interference-limited digital mobile, digi- tal cellular and digital broadcasting systems [3]-[7]. Perhaps the

most popular method to reduce the spectral sidelobes regrowth is the use of spectrally efficient, constant envelope signalling for- mats. A large class of constant amplitude modulation schemes are being referred to as Continuous Phase Modulation (CPM) schemes [8]. There is a great variety of CPM schemes which can be obtained by choosing different pulse shapes to modulate the carrier. However, some of the most popular CPM schemes in-

0018-9316/90/0600-0l56$01.00 @ 1990 IEEE

157

The output of the premodulation filter, H T ( ~ ) , is given by: L

c(t) = CkhT(t - kT) (4) k = l

where h ~ ( t ) is the impulse response of H T ( ~ ) , T the duration of the symbol ck and L the number of the transmitted symbols. As previously mentioned, in this paper MSK-type of signalling will be considered, in which case:

clude Tamed Frequency Modulation (TFM) [9], Minimum Shift Keying (MSK) [lo], Generalized TFM [I l l , Gaussian MSK [12] and Duobinary Frequency Shift Keying [13]. All these schemes have advantages and disadvantages depending on the applica- tion in which they are being employed. In this paper, we will be dealing with MSK-type of signalling because it represents, among CPM schemes, a good trade-off between performance and implementation complexity.

The organization of this paper is as follows. After this intro- duction, in Section 2, we present and analyze the model of the system under consideration. In Section 3, we derive the various algorithms. In Section 4, we present different performance eval- uation results in terms of Bit Error Rate (BER) performance. Finally, the conclusions of this paper are presented in Section 5.

2 SYSTEM DESCRIPTION

The system under consideration is illustrated in block digram form in Fig. 1.l Its transmitter consists of a Convolutional Encoder (CE), a Signal Mapper (SM), a premodulation low pass filter with a transfer function H T ( ~ ) and an FM modulator. The k-th input to the CE is a sequence of p-bits given by:

- U; = [U;, U:, ..., U;]

b;f = [b:, b i , ..., b;f] .

(1)

(2)

while its output is the sequence g , where: -

As usual, u i (1 5 i 5 p ) are assumed to be independent and equiprobable random variables taking values from the alphabet {0,1}. For comparison purposes, we will consider the same type of CE which was used in [l, see Eq. (5)].

At the SM, the sequence E is transformed into a 2*-level symbol, ck, as follows:

4

ck = c2' - ' (2$ - 1). (3) i=l

Clearly, for the chosen code Ck takes values from the alphabet {fl, +3}.

1 f o r O s t 5 T h T ( t ) = { 0 elsewhere. (5)

The output of the FM modulator, z ( t ) can then be expressed as :

z(t) = Re{2bct+6(')l} (6) with w, the carrier radian frequency and #( t ) is given by:

where mh is the modulation index. For a practical (i.e. reduced complexity) maximum likelihood detector for CPM signals, mh

has to take rational values, i.e. mh = Z/n with 1, n integers which have no common factors [SI. Furthermore, the main spectral lobe of a CPM signal increases as mh increases [SI. Based on these constraints, it was decided to use mh = f. This value of the modulation index results in a relatively narrowband CPM signal and thus in a good overall spectral efficiency.

Using Eq. (4), # ( t ) can be expressed as:

Since the information carrying phase #( t ) is continuous and MSK-type of signalling is considered, the change of +( t ) dur- ing the symbol interval is linear. Furthermore, its slope de- pends upon the value of ck. At the receiver, however, the sig- nals coming through the in-phase and quadrature channels con- tain information for the mod(27r) value of #( t ) rather than for the # ( t ) itself. When ck is integer and mh is a rational num- ber the mod(27r) value of #(kT) ( l e integer) takes only val- ues which represent equally spaced points on the unit circle. For the system under consideration here (ck e {+l,+3} and

Figure 1: Block diagram of the overall transmission system.

'For convenience, we will follow similar notation as in [l].

158

mh = i), d(ICT) = modzm[4(ICT)] takes values from the alpha- bet { O , : , 4, ..., ?}, i.e. it can take values only from these eight different phases .

as follows: At this point it is convenient to define the function F(t, 8,, e,,)

where < t /T > represents the largest integer smaller or equal to t /T . The above equation describes the phase change of +(t) and modz,[d(t)] in the interval (kT,HT + T ) when Ck+l is such that it generates a phase transition from 8, to Bm. Notice, that 0, and 8, can take only values from the alphabet (0, :, 4, ..., F}. Clearly then, the value of I&+l generating this transition is:

In the channel, the transmitted signal z ( t ) is corrupted by ad- ditive white Gaussian noise (AWGN) n(t) with one-sided power spectral density No and by multiplicative fading f (t). Similar to [l], it will be assumed also here, that the fading is nonselective and can have Rician or Rayleigh characteristics. Furthermore, the fading process will be modelled as a complex summation of two white Gaussian noise processes filtered by two identical brickwall filters of bandwidth BF. In view of the above, the received signal T(t ) can be written as:

T ( t ) = .(t)f(t) + n(t). (11)

As shown in Fig. 1, the receiver consists of a complex demod- ulator, a predetection low pass filter with a transfer function H R ( f ) , a sampler and the detection algorithm.’ H R ( f ) is as- sumed to be wide enough so that it does not further distort the signal z ( t ) f ( t ) . Thus the signal a t its output is given by the following expression:

y(t) = [yI(t) +jyQ(t)] = [fI(t) +jfQ(t)]24@) +nb(t) . (12)

In the above equation, [y’(t) ; yQ(t)] and [f’(t) ; f Q ( t ) ] repre- sent the [real ; imaginary] part of y(t) and f(t), respectively?

n b ( t ) is the low pass equivalent of the filtered AWGN process and since it has a relatively wide spectrum it is assumed that it maintains the white characteristics of n(t).

y(t) is sampled every T‘ seconds, with T‘ = T / M and M being an integer number greater or equal to one. In other words, every received symbol is sampled M times and thus the vector of the received samples, E, can be represented as:

where E is an M-element array, i.e.:

In the next section the new algorithm will be derived.

’As in [l], for mathematical convenience it will be assumed that we is known at the receiver. However, any phase changes due to fading will be compensated by the detection algorithm.

3The fading process f(t)> assumed to be the same as in [l, see Eqs. (11) and (12)]. Notice that f1 denotes the mean of f ‘ ( t ) .

3 DERIVATION ALGORITHM

OF THE

For the derivation of the algorithm, we will in principle follow the methodology which was described in Section 3 of [I]. In addition to that however, here various generalizations as well as asymptotic cases will also be presented and analyzed. Similar to [I], the effects of the two intereferences (i.e. fading and AWGN) will be analyzed separately.

In this respect, let us consider first that the only disturbance on the received signal is fading. In this case, the sampled version of Eq. (12) can be rewritten as:

Yk+i /M = ( f i + i / M + j f k + i / M Q ),$#-T+(i/M)Tl (15)

where yk+; /M = y [ k T + ( i / M ) T ] , fL+; /M = f ’ [ k T + ( i / M ) T ] and f$+ilM = fQ[ICT + ( i / M ) T ] with 1 5 i 5 M . Since

I e j4[kT+( i /M)Tl I= 1 (16)

the two fading terms of Eq. (15) can be expressed as:

f i + i / M = + ( i / M ) T l h d + i / M

+ sin{4[(kT + ( i / M ) T I ) Y f + i / M (17)

and

f f + i / M = cos{d[(ICT + ( i / M ) T l } y f + i / M

-sin{d[(kT + ( i / M ) T l } y f + i / M . (18)

yi+ilM and ykqtilM are the real (in-phase) and the imaginary (quadrature) part of y k + ; / M , respectively.

The quantity which will be maximized according to the Max- imum Likelihood Detection Test (MLDT) is the conditional prob- ability density function (pdf) ([Ys/@(7i)] where:

--

(19) - @ ( E ) = [d(l) , 4 ( 2 ) , ‘e., d(Q1 *

- @ ( E ) represents an array with elements the phase terms d ( i ) (1 5 i 5 L ) which is generated when si = [ay, a:, ..., a i ] is transmitted.

Since f’(t) and f Q ( t ) are independent Gaussian processes, C[K/5(Ti)] can be expressed through a noise prediction method based on the theorem presented in [l], as follows:

1 ~[Ys/5(7i)] = I I E ~ T exp{-[d;yf + d2ykQ - 7 -

- _ -

2a&sk k -

P k m ( d i - m y : - m + d2-myk4_m - f1)]’/2‘$.;,k) m = l

exPc-rd:Y,Q - &Yf - k

P k , m ( & d f - m - dkQ-m~f-m)l’/2‘$,k} ( 2 0 ) m = l

where

d: = cos(F{kT’,#(< kT’/T > +1) ,4(< kT’/T >) ) I (21)

and

dkQ = sin[.F{kT’,d(< kT’/T > +l ) ,d (< kT’/T >)}I . (22 )

In Eq. (20), represents the ICth minimum mean square error resulting from the lcth order prediction, whereas Pk,m (1 5 IC 5 M L ; 0 6 m 5 IC) represent the prediction coefficients to be used with the fading process. Clearly, for this multisampling scheme, the maximum order of prediction is M L .

159 k

- Pk,m(d:-mY:=m + &my?-,) m= 1

k - -f'(1 - Pk,m)]' + - dfyf

m = l I - 1

- P+m(d:-mYf-m - @ - m ~ f - m ) ] ~ } . m= 1

(28 ) Similarly, it can be shown that maximization of ( [y(t) /m(~)] is approximately equal to minimizing the following quantity:

To further generalize the proposed detector, the asymptotic case where M -+ 03 will be also investigated. In other words, we will consider the case where the received signal y(t) is not sampled but is processed in a continuous manner. In practice, such an approach should be followed in applications where M is relatively large.

Let us first assume that for relatively slow fading channels the amount of fading during one symbol interval can be consid- ered constant, i.e.:

with 0 5 i 5 M - 1. Under this assuption and for M -+

03 the pdf of the received signal y(t) assuming that T(n) was transmitted is given by:

Furthermore,

where

and

In Eq. (25), pk,, represent the prediction coefficients of the fading process corresponding to the case where one sample per received symbol ( M = l ) is taken. The values of WL and Wf can be extracted by employing a bank of linear filters as is described in

In order to apply the algorithms described by Eqs. (20) and (25), in each step of the process, prediction coefficients of one or- der magintude higher than those used in the previous step have to be employed. One way of avoiding this high computational complexity, is to limit the order of prediction to a maximum

number of z [l]. By using this condition, it can be shown that maximization of ( [ Y s / 9 ( ~ ) ] is approximately equivalent to min- imizing BFJJ E 5(7i)] where:

181.

_ _

1 M L B F , D [ K i T ( S i ) ] = 1 {[d:yf + d?yf

P,z k=z+l I

Q Q - Pk+m(d:-mYf-m + dk-mYk-m)

m = l I

-JiCl- C ~ z , m ) I ' )

+ c -d [d:Y: + &Y,Q

m=l

" 1

k = l lp,k

-- where w = [W'; WQ] with wi = [W:, W,', ..., Wi] and = [WF,Wz, ..., Wf]. To account for the effects of the AWGN,

the linear combining approach will be followed [l]. When both interferences, i.e. fading and Gaussian noise, are present, the detection is based on minimizing the following quantity:

where i = D or C. In the above equation, = F, = 7, BG is the quantity minimized by a conventional Viterbi decoder and & ( K ; No) is a weighting factor which depends on both K and No. Using similar arguments as in [I], it can be concluded that for the Rayleigth fading channel 4 should be set equal to zero, i.e. &(-m;No) = 0. Furthermore, in the case where the only interference is fading, or in otherwords the AWGN can be considered negligible, c, should also be set equal to zero, i.e. cw(K;O) = 0. In the next section, various performance evaluation results will be presented and discussed.

4 PERFORMANCE EVALUATION RESULTS AND DISCUSSION

In order to evaluate the proposed algorithms in conjuction with MSK-type of signals, we have followed the computer simula- tion approach. The simulation methodology employed is based on Monte-Carlo error counting techniques and thus the perfor- mance measure is Bit Error Rate (BER) performance. In all sys- tems considered, fading was assumed to have Rician or Rayleigth characteristics.

For convenience, the obtained BER performance evaluation results are divided into two groups. The first one, includes schemes which employ receivers with single sample per received symbol ( M = l ) structures. The second one, presents the perfor- mances of schemes which employ the multisampling ( M > 1) approach. Based on the above division, Fig. 2 summarizes the BER performance for a MSK-type system which employs the al- gorithm given by Eq. (20) with M = l . For this receiver (Rx-A) the signal is filtered by a bank of linear filters prior to its pro- cessing by the decoder. The performance curves shown in Fig. 2

I

160

Bit Error Rate

10 O C

I Conventional Viterbi Decoder

I I

10 -44

Figure 2: Bit-Error-Rate (BER) performance of a convolutional encoded (rate i) MSK system with (shown as new detector) and without (shown as conventional) the proposed fading predic- tionlcancellation sequential algorithm. The employed receiver (Rx-A) operates on a single sample per received symbol (M=l) and consists of bank of linear filters.

are for a prediction order of z=4. In other words, the prediction process applied at time t=kT involves the samples taken during the previous four symbols. In Fig. 3, the performance of the receiver Rx-B, which employs the multisampling approach is il- lustrated. There are 4 uniformly spaced samples taken during each symbol period (M=4) and in order to apply the prediction process the algorithm uses the samples taken over the last four symbol intervals.

2 and 3, it can be seen that Rx-A has a slightly better performance than Rx-B for small &/No, i.e. when the major source of degradation is Gaussian noise. This is due to the fact that a receiver with a bank of matched filters provides optimal decoding for a signal which is corrupted by only AWGN [8]. On the other hand, for higher &/No, or equivalently when fading becomes the domi-

nant source of interference, the multisampling receiver (Rx-B) is more efficient in combating fading and thus it performs better as compared to Rx-A. Furthermore, the performance of Rx-B improves as the fading becomes faster.

As a final comment it should be noted that the penalty which has to be paid for the improved performance achieved by these receivers is complexity. As expected the complexity of these re- ceivers is higher, as compared to a conventional Viterbi receiver, due to the increased number of samples processed and/or the prediction/cancellation processes employed. Clearly the num- ber of required states is increased for larger number of sam-

Comparing the results of Figs.

Bit Error Rate

10 Conventional

I I I 3.0 9.0 15.0 2i.O

Rayleigh fading Ricianfndb - - - - -

Figure 3: Same as Fig. 2, but with the difference that here the receiver Rx-B takes 4 uniformly spaced samples per received symbol ( M = 4 ) over the previous 4 symbol intervals.

ples per received symbol (i.e. increased M ) and/or for predic- tion/cancellation processes which span over a large number of symbols (i.e. increased prediction order z). Nevertheless, with today’s fast advancement of the technology of digital signal pro- cessors (e.g. TMS-320 or DSP-56000), it is felt that impleme- natation of the proposed algorithms in software should not rep- resent a formidable task.

5 CONCLUSIONS

In this paper, the fading prediction/cancellation method intro- duced in [l] has been extended to include mobile broadcasting transmission systems employing CPM signals. In addition to that, a novel detector based on a multisampling receiver has been derived. Various generalizations such as processing in the continuous time domain and reduced complexity receivers have also been presented. BER performance evaluation results have indicated that the proposed receivers yield in substantial error floor reductions, which are even higher than those reported in [l]. At the same time, the spectral advantages of CPM signals over QPSK-type of signals can be maintained, thus leading to mobile broadcasting systems which achieve higher bandwidth and power efficiencies.

161

References

[l] D. Makrakis and P. T. Mathiopou- los,“Prediction/Cancellation techniques for fading channels - Part I: PSK signals,” IEEE Trans. on Broadcasting, this issue.

[2] K. Feher, Digital Communications: Satellite/Earth Station Engineering. Englewood Cliffs, NJ: Prentice-Hall, 1983.

[3] K. Hirade, “Mobile Communications,” in K. Feher (Edi- tor): Advanced Digital Communication Systems and Signal Processing Techniques. Englewood Cliffs, NJ: Prentice-Hall, 1987.

[4] W. C. Y. Lee, Mobile Communications Design Fundamen- tals. Indianapolis: Howard W. Sams, 1986.

[5] R. M. Nemerson, “Satellites, simulcasting form national paging system,” Mobile Radio Technology, pp. 22-30, Oct. 1987.

[6] J. Burgess, “Widening the scope of communication sys- tems,” Washington Post Business Magazine, April 11,1988.

[7] A. A. Reiter, “FOCUS on technology: National Satellite Pag- ing’s (NSP) Paging-Electronic Mail tie-in; Stock quotations over alpha,” Telocator, pp. 72-77, March 1988.

[8] C.-E. Sunberg, L‘Continuous phase modulation,” IEEE Communications Magazine, vol. 24, pp. 25-38, April 1986.

Dimitrios Makrakis (S ‘82, M ’90) received the Diploma from the Uni- versity of Patras, Patras, Greece, in 1982 and the M.A.Sc. degree from the University of Toronto, Toronto, Canada, in 1984, both in Electrical Engineer- ing.

From 1985 to September 1989 he worked at the Department of Electri- cal Engineering of the University of

Ottawa, first as Research Assistant and afterwards (since 1987) as Research Engineer in the a r e s of digital mobile and satellite com- munications as well as in computer networks. Presently, he is with the Communications Research Centre of the Canadian Government, Ottawa, where he is working in the fields of radio communications and propagation. He is also completing his Ph.D. in Electrical Engi- neering at the University of Ottawa. In 1982 he received the award of excellent achievements from the National Technical Chamber of Greece, and in 1985 he held a scholarship from the School of Grad- uate Studies of the University of Ottawa.

His research interests are in the areas of channel characteriza- tion for broadcasting communications (with emphasis in EHF and UHF) as well as digital communications, communication theory, de- tection/estimation and computer netwoks. His current work is di- rected mainly towards mobile and satellite communications. Mr. Makrakis is also a member of the Technical Chamber of Greece.

[9] F. de Jagger and C. B. Dekker, “Tamed frequency mod- ualtion, a novel method to achieve spectrum economy in digital transmission,” IEEE Trans. Comm., vol. COM-26, pp. 534-542, May 1978.

[ lo] S. Pasupathy, “Minimum shift keying: A spectrally efficient modulation,” IEEE Communications Magazine, vol. 17, pp. 17-22, July 1979.

[ll] K. S. Chung, “Generalized tamed frequency modulation and its application for mobile radio communication,” IEEE J. Select. Areas in Comm., vol. SAC-2, pp. 487-497, July 1984.

[12] K. Murota and K. Hirade, “GMSK modulation for digi- tal telephony,” IEEE Trans. on Comm., vol. COM-29, pp. 1044-1050, July 1981.

[13] G. S. Deshpande and P. H. Wittke, “Correlative encoded digital FM,” IEEE Trans. on Comm., vol. COM-29, pp. 156-162, Feb. 1981.

P. Takis Mathiopoulos (S ’79, M ’89) was born in Athens, Greece, on November 26, 1956. He received a Diploma from the University of Pa- tras, Patras, Greece, in 1979, a M.Eng. degree from Carleton University, Ot- tawa, Canada, in 1982 and a Ph.D. degree from the University of Ottawa, Ottawa, Canada, in 1989, all in Elec- trical Engineering.

From 1981-1983 he was with Raytheon Canada Limited, where he was involved in the analysis, design and evaluation of a new gen- eration of air-navigational equipments (DVOR and DME). He was also responsible for preparing and teaching courses for the operation and maintainance of both of these equipments. From 1983-1988 he was with the Department of Electrical Engineering at the University of Ottawa, where he served as a research engineer and twice as a ses- sional lecturer. During this time period and on several occasions he was also a Consultant to Raytheon Canada Limited and other com- panies including DIGCOM Inc. Since January 1, 1989 he has been an Assistant Professor of Electrical Engineering at the University of British Columbia, Vancouver, Canada, where he is also a faculty member of the Centre for Integrated Computer Systems Research (CICSR).

Dr. Mathiopoulos is a Consultant to several companies in the communication, broadcasting and air-navigational system areas. He has been also participating in various short courses. His research work has been in the general area of bandwidth and power efficient digital modulation techniques with current emphasis on digital cellu- lar, mobile satellite, land mobile and broadcasting applications. He has published numerous papers in this field.

Dr. Mathiopoulos is active within the IEEE Communication So- ciety and is a member of the Satellite and Space Communication, Radio and Communication Theory Technical Committees. He has organized and chaired technical sessions in conferences including ICC and GLOBECOM and is representing the Satellite and Space Com- munication Committee to SUPERCOM/ICC ’90. He is also a mem- ber of the Technical Chamber of Greece.

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