Digital Signal Processing for Communication Systems 0792399323, 9781461378044, 9781461561194

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DIGITAL SIGNAL PROCESSING FOR COMMUNICATION SYSTEMS

DIGITAL SIGNAL PROCESSING FOR COMMUNICATION SYSTEMS

edited by

Tadeusz Wysocki Edith Cowan University and A ustralian Telecommunications Research Institute Hashem Razavi Curtin University o/Technology Bahram Honary Lancaster University

SPRINGER SCIENCE+BUSINESS MEDIA, LLC

Library of Congress Cataloging-in-Publication Data Digital signal processing for communication systems / edited by Tadeusz Wysocki, Hashem Razavi, Bahram Honary. p. cm. -- (Kluwer international series in engineering and computer science; SECS 403) Selected revised papers from the Fourth UK/Australian International Symposium on DSP for Communication Systems, held in Joondalup, Perth, Western Australia, Sept. 23-27, 1996. Includes bibliographical references and index. ISBN 0-7923-9932-3 (alk. paper) ISBN 978-1-4613-7804-4

DOI 10.1007/978-1-4615-6119-4

ISBN 978-1-4615-6119-4 (eBook)

1. Signal processing--Digital techniques. 2. Digital communications. I. Wysocki, Tadeusz. II. Razavi, Hashem. III. Honary, Bahram. IV. UK/Australian International Symposium on DSP for Communication Systems (4th: 1996: Perth, W.A.) V. Series. TK5102.9.D533 1997 621.3 82 ' 2--dc21 97 -15446 CIP Copyright © Springer Science+Business Media New York 1997 Originally published by Kluwer Academic Publishers 1997 Softcover reprint of the hardcover 1st edition 1997 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media New York 1997

Printed on acid-free paper.

CONTENTS

PREFACE ............................................................................................................... ix Part I 1.

MODULATION AND CODING Levinson-Durbin algorithms used for fast BCH decoding M. Schmidt, G. P. Fettweis............................................................ ................. 3

2.

On the MAP algorithm, iterative decoding and turbo codes L. Zhang ......................................................................................................... 9

3.

A turbo-coded, low-rate HF radio modem L. Zhang, W. Zhang, J. T. Ball, M. C. Gill .................................................. 19

4.

Evaluation of the undetected error probability interleaved block codes H. J. Zepemick ............................................................................................. 27

5.

Effective trellis decoding techniques for block codes L. E. Aguado Bayon, P. G. Farrell ............................................................... 37

6.

On header forward error control in ATM systems A. Rieke, H. J. Zepemick ............................................................................ 45

7.

An alternative multi stage sigma-delta modulator circuit suitable for pulse stuff'mg synchronizers S. S. Abeysekera ...................................................................... .................... 55

8.

Digital pulse interval modulation: Spectral behaviour D. E. Kaluarachchi, Z. Ghassemlooy ...................................... ............ ........ 65

9.

Block multidimensional MPSK modulation codes with unequal error protection C.S.C.M. de Jesus, J.Portugheis .................................................................. 73

10.

A frame synchronisation scheme for Turbo Codes W. Zhang, L. Zhang, J. Ball, M. Gill ........................................................... 81

vi Part II 11.

CHANNEL CHARACTERISATION AND SIGNAL DETECTION

Radio channel measurement using a novel hybrid simulation approach R. Weber ...................................................................................................... 93

12.

A study of VHF troposcatter communication channels in South Australia W. Zhang, J. A. Hackworth, W. R. Schoff .... ..... ....... ..... ..... ....... ..... ..... ...... 103

13.

Implementation of a digital frequency selective fading simulator X. F. Chen, K. S. Chung ............................................................................ 113

14.

Measurements of noise in the 2.3 - 2.5 GHz band T. Walker, T. Wysocki, 1. Hislop ................................................................ 121

15.

On the development of a real time wide band channel simulator for LEO satellite channels M. Tykesson, L. Sabel, R. Wozniak, T. Zierch, D. Tran, P. Koufalas .... ... 131

16.

Portable channel characterisation sounder M. Mossammaparast, N. Afifi, K. S. Chung ............................................. 141

17.

A flexible DSP-based system for propagation path characterisation M. Darnell, P. D. 1. Clark, A. Barlett & P. W. Piggin ................................ 147

18.

Non-stationary, narrowband Gaussian signal discrimination in time-frequency space G. Roberts, A. Zoubir, B. Boashash .......................................................... 159

19.

A new delay Root-Nyquist filter design method for signals corrupted by ACI L. P. Sabel, T. I. Laakso, V. Rose, A. Yardim, G. D. Cain ......................... 167

20.

Adaptive CFAR tests for detection of a signal in noise and deflection criterion N.A. Nechval ...... ..... ......... ............................................................. ..... ....... 177

21.

Adaptive signal equalisation for frequency discriminator output signal in a mobile channel B. Rohani, K. S. Chung ............................................................................. 187

22.

Combination of a Viterbi decoder with an adaptive neural equaliser over a Rician fading channel I. Soto, R. A. Carrasco ............................................................................... 195

vii

23.

Tracking behaviour of lattice filters for linear and quadratic FM signals M. H. Kahaei, A. Zoubir, B. Boashash, M. Deriche .................................. 207

Part In SYSTEM DESIGN AND IMPLEMENTATIONS 24.

Regularisation procedures for iterated recursive digital filters B. 1. Phillips, N. Burgess, K. V. Lever ....................................................... 217

25.

On a design of FIR digital filters with equiripple error function F.Wysocka-Schillak, T.Wysocki ................................................................ 225

26.

Establishment of wide sense digital filter for wind noise cancellation in a low frequency sound measurement S. Miyata, M. Ohta .................................................................................... 231

27.

A detailed analysis of phase locked loops used in clock jitter reduction S. S. Abeysekera, A. Cantoni ..................................................................... 243

28.

A novel synchronisation scheme for Spred Spectrum communications D. E. Gossink, S. Cook .............................................................................. 255

29.

Reed-Solomon code (255,247,4) decoder with TMS320C30 S. Le-Ngoc, Ying Ye .................................................................................. 263

30.

An optimised implementation of Reed-Solomon FEC on the PC M. 1. Riley, I. E. G. Richardson ............ ........ .......... ..................... .............. 271

31.

Development and implementation of robust and spectrally efficient medium data rate modems Part 1: Architectures A. Guidi, G. Bolding, W. G. Cowley ......................................................... 279

32.

Development and implementation of robust and spectrally-efficient medium data rate modems Part 2: Synchronisation algorithms W. G. Cowley, A. M. Guidi, G. Bolding .................................................... 289

33.

Avoiding phase accumulator truncation in a direct digital frequency synthesizer R. Wozniak, L. Sabel..... ....... ............ ................. .......... ................. ............. 297

34.

High performance DSP implementation with FPGA S. Nooshabadi, J. Montiel-Nelson ............................................................. 307

viii 35.

A DSP based diversity modem for FDMA and TDMA mobile satellite applications

M.Rice, J.Wojtiuk ...................................................................................... 319

36.

Scare-state-transition Viterbi decoding of punctured convolutional codes for VLSI implementation

L.H.C. Lee, P.G. Farrell ...................... ....... ... .............. ... ........................ .... 327

INDEX ................................................................................................................... 335

PREFACE

This book contains selected and revised papers from the Fourth UK/Australian International Symposium on DSP for Communication Systems which was held at Joondalup Resort Hotel, Joondalup, Perth, Western Australia from 23rd to 27th of September 1996. The revisions have been done by the authors after the Symposium to include the latest results and address the main issues raised during the question time. The Symposium was planned by a group of academics and professionals from both Australia and the UK to examine the plans for the future and the progress that has already been made in the field of DSP and their application to communication systems. A major objective of the Symposium was to pursue the progression from communication and information theory through to the implementation, evaluation and performance enhancing of practical communication systems using DSP technology. This was achieved by bringing together researchers and developers from many different backgrounds to share their experience in this important field of technology. The papers are presented in the following format: •

Part I deals with various types of coding and modulation techniques with the first six papers describing different applications of Turbo-Codes, BCH codes and general block codes. The next three papers are devoted to pulse modulations and combined modulation and coding in order to improve the overall system performance, while the last one addresses the issue of frame synchronisation for TurboCodes.

•

Part II groups papers dealing with DSP applications in measurements performed for channel characterisation, papers where the use of DSP for design of effective channel simulators is described, and finally includes eight papers concerned with equalization and detection of various signal formats for different channels.

•

Part III groups together papers concerning several system design issues where digital signal processing is involved. It also contains papers reporting on the successful implementation of the system components using DSP technology or on the problems involved with implementation of some DSP algorithms.

x The editors are most grateful to all the authors for their contributions to the Symposium and their hard work in preparing and revising the papers presented in this volume. We wish to acknowledge here the financial and logistic support the Symposium received from the following institutions: •

Cooperative Research Centre for Broadband Telecommunications and Networking, Perth, Western Australia,

•

Edith Cowan University, Perth, Western Australia,

•

Curtin University of Technology, Perth, Western Australia,

•

Defence Science and Technology Organisation, Salisbury, South Australia,

•

Western Australian Chapter of IEEE Communications Society.

Special thanks are also directed to Mrs. Beata J. Wysocki and Dr. Hans-Jiirgen Zepernick for their vital support in the preparation of this volume.

Tadeusz Wysocki, Hashem Razavi

Part I

MODULATION AND CODING

1 LEVINSON-DURBIN ALGORITHM USED FOR FAST BCH DECODING Michael Schmidt and Gerhard P. Fettweis Dresden University of Technology Department of Electrical Engineering Communications Labomtory Endowed Chair for Mobile Communications Systems

1.

INTRODUCTION

BCH codes are a subclass of cyclic codes in which the generator polynomials of the codes have as roots 2t consecutive powers of an element O! of order n. Let c be a code word of the (n, k)-BCH code of length n with minimum distance of dmin = 2t + 1 = n - k + 1, hence, the capability of error correction is t. The vector e is the additive error vector of length n which produces the erroneous received word r = c + e. The conventional way to retrieve c from r is the following:

1. Evaluation of the Syndromes: i

= 0, 1, ... , 2t -

1.

The complexity of this step is 2t(n - 1), using the well-known RuffiniHorner method. 2. Determination of the Error-Locator Polynomial: Suppose I ~ t errors occurred at locations it, h, ... ,it- Then the polynomial I

A(x)

= II (1 -

XiX)

with

Xi

= ali

i=l

T. Wysocki et al. (eds.), Digital Signal Processing for Communication Systems © Springer Science+Business Media New York 1997

Michael Schmidt and Gerhard P. Fettweis

"I- o.

determines the error locations, i.e. A(a- j ) = 0 ¢:} ej Ao = 1, it can be shown that A(x) is the solution of

Sj

=-

I

L AiSj -

j

i,

= 1,1 + 1, ... ,2t -

1,

Assuming

(1)

i=1

where both I and Ai are the unknown components and 1 is minimal [2]. The philosophy of the Berlekamp-Massey algorithm is to synthesize a linear feed back shift register of minimum length 1, such that the sequence of syndromes can be generated. This requires approximately CI' = 4t 2 + 2tl + lOt + e (multiplicative) steps [5J. The Berlekamp-Massey algorithm is very elegant and can be implemented efficiently.

3. Determination of Error Values: The actual error values ei can be computed as follows: ei =

{_f,\:~i!)

:

o :

A(a-~) = 0

A(a-t)

"I- 0

where N{x) is the formal derivation of A(x). The error-evaluator polynomial r(x) is given by the relation

r(x)

= A(x)S(x)

mod x2t.

There are completely different ways of BCH decoding. In particular, for the decoding of Reed-Solomon codes the introduction of the Welch-Berlekamp key equations may be advantageous, since they do not involve the computation of syndromes. However, re-encoding is required then, which seems to be of the same computational load as the syndrome computation. The main problem of BCH decoding is often focused on the computation of A(x) (and/or r(x)), although the computational complexity of the syndromes is much higher. In this paper, a different algorithm for the evaluation of A(x) which is based on fast inversion techniques for Hankel matrices is introduced.

2.

FAST INVERSION OF SINGULAR SECTIONS

HANKEL

MATRICES

The concept behind the algorithm is straightforward. With v can be written as: So S1 Sv AvSv+l Sv-1 Av 1 [SV [

S~~,

::

S2~-2

1[ 1

~'--------Vy--------~' Zv(S)

L

=-

S2~-1

WITH

= 1, equation 1

1 .

(2)

5

Digital Signal Processing for Communication Systems

Assume I I [2]. Hence, there is a unique solution for the coefficients of A(x) and they can be obtained by inverting Zl(S), This was used by the Peterson-Gorenstein-Zierler BCH decoder [2]. They tested the nonsingularity of Zv(S), beginning from v = t and decrementing v. However, the computational complexity for general matrix inversion techniques is still O(v 3 ). This makes the method of Peterson, Gorenstein and Zierler not applicable for large l. Equation 2 looks familiar with problems arising from auto-regressive models [3]. Fast algorithms (Levinson-Durbin-type algorithms) with complexity O(v 2 ) are known, which exploit the Toeplitz structure and the positive definiteness of such matrices. Hankel matrices can be inverted with similar algorithms, since Hankel and Toeplitz matrices are simply related by column permutation. However, in the case of Hankel matrices, as given in 2, positive definiteness cannot be assumed and therefore such matrices may not be strongly regular. This means that some of the leading principal submatrices may be singular. Thus, the inversion technique must apply to Hankel matrices with singular principal sections. Such algorithms have been studied by Heinig and Rost [4] and also by Zarowski [6], who corrected several typographical errors in [4]. A short outline for Hankel matrices is given here. Let b

= [bo

b1

.. .

b2t

f

and H t (b) be the txt Hankel matrix

f

f

XV-l and ev-l = [0 0 ... 0 1 be vectors of Let Xv = [Xo Xl dimension v. In order to find the inverse of Ht(b), the fundamental solutions

(3) hv,

h v def = [ bv ... b2v - l ]T

are recursively computed, beginning from v two cases:

= 1 to t.

(4)

Heinig and Rost consider

The Regular Case: Suppose Hv(b) isnonsingular. Letcv=[bv ... b2v] [w~ -If. Then HvH (b) is nonsingular, if and only if Cv "I O. In this case the solutions for W vH and YvH are given by: YvH

=

c1v

[w~

_l]T

(5)

6

where flv

Michael Schmidt and Gerhard P. Fettweis

= .1.. [ b +1 ev V

The Singular Case: Here, Hv (b) is supposed to be nonsingular but Hv+1 (b) is singular, that is cv = O. First, one has to find the number m with

Then for n = m + v, Hn+ 1 (b) is nonsingular. The index m is characteristic for the singular gap between Hv (b) and Hn+1 (b). The solutions for w n+1 and Yn+1 can be obtained as follows. Let I~,n = [8i ,Hd with i = 0, ... , m - 1 and j = 0, ... , n - 1. Let u v = I~,v' Using the identity [4]

where h(b, {) = [b v . . . b2v - 2 {] and { is arbitrary, it can be shown that the solution of

H v (b)wvm+l -- h vm+1 ~f - [b v+m+ 1

.••

b ]T 2v+m

is given by the following recursion: w~+l

= uvw~ + PkYv + "IkWv

k

= 0,1, . .. ,m,

(8)

with Pk = b2v+k-h~w~, "Ik = e~_lw~ and w~ = WV' Having evaluated W~+l, the fundamental solution for H n+1(b), vector wn+1 is given by:

+" m

m+l Wn+l -_ 10n+l,v w v

Values 'Yi must satisfy:

o

n[I]

~ i=O

=[

[T 'Yi I n+l,v+l Wv m i

bn+V+1] bn+V+2 b2n+1

_l]T.

(9)

[[ bv . .. b2v - 1 ]w~+1 ] [ bV+1 . . . b2v ]w~+1

. .

[bn

bn+v-l ]w~+1

(10)

The solution for Yn+1 is obviously given by Yn+1 _- - 1 10n+l,v+l [T Wv

am

-1 ]T.

(11)

Digital Signal Processing for Communication Systems

3.

7

ERROR-LOCATOR POLYNOMIAL EVALUATION

= [So S1 ... Sut be the vector of syndromes of r(x), where S2t is arbitrary. Let wo, Yo be vectors of dimension 0 and let co = So. Apply recursions 5, ... ,11 to Wv and Yv for v = 0, ... , t - 1. Then, with I the first v such that c/ = 0 and m ~ t - I, the cOOT'dinates of w/ = [wo W1 . . . Wl-l t correspond to the coefficients of the error-locator polynomial A(x) = 1 + A1x + ... + A/x', that is Wi = A,- i for i = 0, ... , 1- 1.

LEMMA. Let S

PROOF: Comparing equation 2 with 4, it is straightforward to verify that the l-th fundamental solution WI corresponds already to the desired solution. Thus, explicit inversion of the Hankel matrix HI (S) is not necessary. However, I is not known. Ci = 0 implies that HI+! (S) is singular but there may be a number l = m + I > I such that Hi+! (S) is nonsingular. If m ~ t -I then no such l exists, since Hv(S) is singular for v > t. The computational complexity becomes apparent now. The v-th fundamental solution is upperbounded by O(v 2 ) steps. This is also true in the singular case, since all matrix-vector products are simple shift operations. With cl = 0, one has to compute m according to equation 7. If H,(S) has maximum rank already, the check m ~ t - I requires about l(t .,.. I) steps. Thus, the total amount of steps is upperbounded by O(lt).

4.

IMPLEMENTATION

The fact that the computational workload of error-locator polynomial is O(lt) only rather than O(t 2 ) as with the Berlekamp-Massey algorithm may have some significant advantages. First, BCH codes are mostly applied in the region of relative safety. Thus, the average number of errors 1 is much less than ~. The decoder may then operate at a throughput rate according to its average run-time. In order to avoid increased error rate, when the decoder occasionally cannot keep up with the channel, buffers and punts can be used [1]. The decreased number of fetch and store operations may also lead to a reduced power consumption, assuming an implementation on a Digital Signal Processor (DSP). The algorithms from [4] for such Hankel matrices has been designed for the field of complex numbers actually. However, due to several tests for equality to zero this may lead to serious numerical stability problems. Since BCH codes are usually defined in finite fields GF(q), there is no such stability problem at all.

8

Michael Schmidt and Gerhard P. Fettweis

The algorithm has been implemented in C++. The expected run-time dependency on I could be verified. Using a (255,223)-RS code over GF(2 8 ) and a very low t-rate, the algorithm outperformed the Berlekamp-Massey algorithm by factor 3 ... 5. Simulation results showed, that the occurrence of singular gaps is relative low. It was even more interesting to note that in the case of appearance of such singular gaps, the index m was almost always equal to 1. Thus, the additional computational workload is relative small, when singular gaps occur. However, the program structure in the singular case is more complicated and requires more program code than the Berlekamp-Massey algorithm.

5.

CONCLUSIONS

A Levinson-Durbin-type algorithm for the evaluation of the error-locator polynomial has been introduced. It was shown that this algorithm needs O{lt) steps only instead of O{t 2 ) steps using the traditional Berlekamp-Massey algorithm. This can be advantageous, when the average number of errors is relative small compared to the maximum number. The algorithm requires more program instructions than the Berlekamp-Massey algorithm. There are some interesting problems for future research, for instance improved binary BCH decoding, erasures and one-run GMD for soft-decision Reed-Solomon decoding.

REFERENCES [1]

E. Berlekampj Bounded Distance+l Soft Decision Reed-Solomon Decoding, Preprint, 1995, Oktober.

[2]

R.E. Blahutj Theory and Practice of Error Control Codes, Addison-Wesley, 1984.

[3]

S. Haykinj Adaptive Filter Theory, Prentice-Hall, 1991.

[4]

G. Heinig and K. Rostj Algebraic Methods for '1beplitz-like Matrices and Operators, Akademie-Verlag Berlin, 1984.

[5]

J. Hong and M. Vetterlij Simple Algorithms for BCH Decoding, IEEE Transactions on Communications, vo1.43, no.8, Aug. 1995, pp.2324-2333.

[6]

Ch. J. Zarowskij Shur Algorithms for Hermitian 'Ibeplitz, and Hankel Matrices with Singular Leading Principal Submatrices, IEEE Transactions on Signal Processing, vo1.39, no.11, Nov. 1991, pp.2464-2480.

2 ON THE MAP ALGORITHM, ITERATIVE DECODING AND TURBO CODES Lin Zhang

Communications Signal Processing Discipline, Bldg 27 TSAS Communications Division, Defence Science and Technology Organisation DSTO, POBox J500, Salisbury, South Australia 5 J08 Email: [email protected]

1.

INTRODUCTION

Traditional error-control coding research has been focusing. on the construction of good codes with large minimum Hamming distances and/or large minimum squared Euclidean distances. This approach is often guided by some kind of performance bound, which gives the asymptotic error performance of the code over certain communication channels. Since performance bounds are valid only at large signal-tonoise ratio (SNR), good codes that are maximum likelihood decodable and perform well at low SNR (close to the theoretical limit) have not been found. Although there have been some very powerful code constructions such as the concatenation of ReedSolomon codes and large memory convolutional codes that are predicted to give excellent error performance at low SNR, it is currently impractical to implement maximum likelihood soft decision decoders for such codes. The recent emergence of turbo codes [1] has opened a whole new way of looking at the problem of error control. A turbo code is constructed from a parallel concatenation of recursive systematic convolutional codes separated by interleaver(s). The astonishing error performance of turbo codes (0.7 dB from the theoretical limit as claimed in [1]) is mainly due to the large interleaver(s) and the iterative decoding method that approaches the performance of optimal maximum likelihood decoding. At the core of iterative decoding is the MAP algorithm. This paper will concentrate on the analysis and simple implementation of the MAP algorithm for turbo codes. The MAP algorithm was first introduced by Chang and Hancock [2] in 1966 as an efficient detection method to eliminate intersymbol interference in high speed digital communication channels. Independently, the algorithm was re-discovered by Bahl et al. [3] as a method of minimising the symbol error rate in the decoding of linear codes. As an unattractive alternative to the Viterbi algorithm which minimises the sequence error rate, the MAP algorithm did not receive much attention because it is T. Wysocki et al. (eds.), Digital Signal Processing for Communication Systems © Springer Science+Business Media New York 1997

Lin Zhang

10

computationally much more complex, and requires much more memory. Furthermore, the goal of minimising symbol error rate is asymptotically the same as that of minimising the sequence error rate at large SNR. Recent advances in electronic technology has allowed the soft-decision maximum likelihood decoding of powerful error correcting codes, giving the MAP algorithm the attention it deserves. The major application of the MAP algorithm and its simplified versions (for example, soft output Yiterbi algorithm - SOYA) has been in channel detection and decoding concatenated codes, in order to provide a soft measure of the channel output, such that the succeeding decoder can use soft decision decoding. In the original turbo coding paper [1], Berrou et al. introduced a modified Bahl et al. MAP algorithm for the turbo decoder. Unfortunately, the Berrou et al. algorithm is an excessively complicated algorithm which calculates probability constants such as the probability of the received sequence, and associates the input bits with the intermediate probability functions that are used in the enumeration of the soft output. Pietrobon and Barbulescu [4] simplified the Berrou et al. algorithm by avoiding calculating the probability constants in enumerating the intermediate probability functions. The use of trellis information further simplifies the realisation of the MAP algorithm. However, the Pietrobon and Barbulescu algorithm still has the input bits in the enumeration of the intermediate probability functions, therefore doubling the necessary computation and storage requirements. The implementation of the MAP algorithm that we propose in this paper avoids associating the input bits with the intermediate probability functions, and makes use of trellis information as proposed in [4].

2.

THE MAP ALGORITHM

Consider a simple transmission model with a rate 1/2, memory length u convolutional encoder, as depicted in Fig.l. We follow the notation that was used in [3]. At time t, the information bit ut is encoded by a (2,1, u) systematic convolutional encoder. The encoder output comprises ut and a parity check bit. They are BPSK modulated into Xt (xti' x tp ) where x,i and x tp correspond to ut and the parity check bit respectively. The encoding process can be illustrated by a trellis diagram with M distinct states where M 2u . They are indexed by the integer m, m 0,1, ... , M - 1. The state of the trellis at time t is denoted by S, and its output by Xt . The state transitions of the encoder are governed by the transition probabilities

=

=

p, (mlm')

=

= Pr{S, = mlS,_1 = m'}, 0 ~ mlm'< M,

(1)

and the output by the probabilities

q,(Xlm',m)= Pr{X,

= XIS,_I =m';S,

=m},O~m,m'< M,e{-I,+I}.

(2)

Digital Signal Processing for Communication Systems

JJ

For a given input sequence { ul, ... , Ut' ... , uN}, the encoding process starts in the initial state So =0, and produces an output sequence x,' = {XI> ... , XI> ... , Xt} ending in the terminal state St = 0, where 't' = N + U.

Figure 1 A Convolutional Coded Transmission System.

The input to the noisy channel is X ,r , and the channel output is the sequence ~' = {YI> ... , Yt, ... , Yt } where Yt = (Ytb Ytp)' X t and Yt are related by Yt =X t + nt where nt comprises two independent zero mean Gaussian variables. The transition probability of the Gaussian noise channel is given by _

Pr { Y,IX, } - Pr

{

} __1_

Y,plx,l' -

2nu

2

exp

[_ (Y,; - X,;)2 + (Y,p

2u

2

- x'P

r1

(3)

The objective of the MAP decoder is to decide, based on the received sequence Y,' and the trellis information, the best estimate". of the transmitted information bit Ut. Let Pr{ut = 01 ~' } and Pr{ut = 11 Y,' } be the a posteriori probabilities (APP) of

the transmitted information bit ut. A logarithm of likelihood ratio (LLR), denoted by A(ut), of the APP can be r1p.finf~r1l1s P r {u, = II Y, ' } A (u,) = log --i-;"""":,,,-....;......:~P r {u, = 0 I Y,' } (4) such that

u,

is given by

u, = {

10 if A(u, ) < 0

(5)

otherwise.

Examining the trellis diagram (Fig.2, for example), it is obvious that the APP of ut

= 1, Pr{ Ut = 11 Y,' }, is the sum of the APP of all the state transitions that are caused

by ut = 1, i.e., the solid lined branches in Fig.2. Similarly, Pr{ut = 01 Y,' } is the sum of the APP of the dashed branches. The APP of ut can be written as Pr{u, = 01 y.'} = Pr{u, = 11 Y;'} =

L Pr{S,./ =m';8, =ml y.'}

(m·.mleR!'

L Pr{S,./ = m' ;S, = mlY;'}

(m'.m)e8~

(6)

12

Lin Zhang

where B," is the set of transitions (SI_I = m' ) ~ (SI = m) that are caused by the input information bit Ut = 0, and B,' is the set of transitions (SI_I = m') ~ (SI= m) that are caused by the input information bit Ut = 1. m

0

2

19)

0/00

0100

~o

0/00

0/00

0/00

~

,

/10 /

~0/~1//

.-

0/01/ /

..

1/11

1/11

0/01/ /

1111

Figure 2 Trellis Diagram of a (2.1.1) Systematic Convolutional Code.

Let us define Aim',m) as the joint probability Pr{s,., = m' ;S, = m; y,'} . Since Y,' } and Pr{ Y,' } is a constant, the LLR in Eq.(4) can be expressed as

Pr{S,., = m' ;S, = ml y,'} = Pr{S,., = m';S, = m; y,'} / Pr{

A(m'm) A(u,) = log '" L.J(m',m)EB: ' '" L.J(m'.m)EBO; A(m'm) ,

(7)

The decoding problem has now been reduced to calculating the joint probabilities At(m',m). Let us define the intermediate probability functions

alm} = Pr{s, =m~}; fl,(m) = Pr{ Y,~/ls, = m};

y,(m',m) = Pr{S, =m;Y,IS'.1 =m'}. If we can calculate these intermediate probabilities, the joint probability At(m',m) can also be obtained from

A,(m) =a,_I(m').y,(m' ,m)./3,(m).

(8)

According to [3], u/(m) and pt(m) can be recursively obtained by M-I

a,(m) = Ia,(m').y,{m',m);

(9)

m'=O M-I

/3,(m) = I/3,+I(m')·y,Am',m)

(10)

m'=O

with boundary conditions

ao{O) = ],andau(m) = O,form;t: 0;

/3,{O) =I,and /3,{m) = 0, form;t: 0; The intermediate probability Yt(m',m) is actually the decoding metric for the MAP algorithm. It is given by

Digital Signal Processing for Communication Systems

r,(m',m} = LP,(mlm'}.q,(Xlm',m}.Pr{Y,1X, = X}

J3

(II)

where pt(mlm' ), qt(Xlm', m) and Pr{YtIXt } were defined by Eqs.(I), (2) and (3) respectively. By utilising the trellis information as in [4], we may summarise the implementation steps of the MAP algorithm as follows: STEP 1: Generate trellis: for each trellis state m =0,1, ... ,M-I and information input i E {O,l}, generate the previous state S;(m) and the next state S;(m), and the code words X;(m) and ~(m) associated with the state transitions. Store them in an array of size 8· M. STEP 2: Forward recursion: • Initialise ao(m), m = 0,1, ... , M-I: ao(O) = 1; and, ao(m) = 0, for m -j:. O. • For t = 1,2, ... , t and m = 0, 1, ... , M-I, calculate and store at70

For South Australia Ns =315 is a good approximation over a year [3]. For a fixed frequency and distance, the path loss is determined by the attenuation function F(9d, Ns)' which in turn is dominated by 9. With a given distance d the scatter angle can be calculated by 9 =dla + 9 1 + 92 where a is the effective earth radius, 9 1 and 92 are the two radio beam elevation angles at the two antennas respectively. Software is developed to find out the minimum scatter angle 9miD for a given elevation profile and antenna heights. For the minimum scatter angle 9miD path from Salisbury to Berri, the link budget and related parameters are listed in Table 1. For VHF, it would be more useful if we combine the antenna gains and the path loss together. The combined basic loss thus can be defined as L'b = Lb - GI - G2 where Gl and G2 are the gains of transmission and reception antennas respeCtIVely. There exists an optimal pair of elevation angles, 9 10pt and 92opt' that produce the lowest combined loss (5)

This is indeed the case.

Digital Signal Processing for Communication Systems

107

Table 1: Geometry and basic patb loss calculation for the path with minimum scatter angle between Salisbury and BeTTi. Equivalent earth radius

a = (4/3) x 6,378,137km = 8,504182km

Great circle distance at MSL

d = 187.7 km

Frequency

f =79.9 MHz

Refractive index

Ns = 315

Angular length

8 0= d / a = 22.0715mrad = 1.265"

Salisbury

Berri

Ground level above MSL

20m

40m

Mast height

hi = 17 m

h2

Antena height above MSL

37m

57m

Radio horizon distance

d l = 10.12 km

d2 = 32.27 km

Radio horizon height above MSL

hu =260m

hl.2 = 60 m

Elevation above chord

sl =32.472 mrad = 1.861 0

S2 = 9.142

Elevation of the horizon

8,. = 21.437 mrad = 1.228"

Scatter angle

= 17 m

mrad =-

0.5240 8,. = -1.894 mrad = - 0.108"

8 ml.= 8 0+ 8,. + 0,.= ", +.\', = 41.615 mrad = 2.384"

Cross over point

distance = 41.712 km, elevation = 1033.71 m

Symmetry factor

m =0.2222

Equivalent distance

8" = 353.898 km

Attenuation function

F(9d) = F(7.81105) = 164.04 dB

Lb = 175.65 dB

Basic loss

Combined baSIc bIB: faglS 818mal'll

'80

nemas. 187.7km, 79.9 MHz

'75

"'"

] '70 '85

10)

0

0.5

1.5

.'

2.5 '1MIe-ofIangIe

3.5

4.5

indegrae8

Figure 2 Calculation results of combined basic loss 1.:(8, ,8,) .

Weimin Zhang, John A. Hackworth and Wayne R. Schoff

108

The combined basic loss L'b (8 I' 82) is calculated and plotted in Figure 2, corresponding to the Vagi antenna gain pattern obtained from simulation. The global minimum loss is found at 8 10pt = 820pt = 1.4° from a numerical search with 0.1 ° steps for 8 1 and 82 respectively. This optimum path is plotted in Figure 2 with solid lines. The path loss calculation is given in Table 2. Comparing the Lb of Table 2 and Table I we see approximately 10 dB difference. This means a potential 10 dB gain in the absence of ground reflection.

Table 2: Combined basic loss when antenna elevation Elevations of the horizon Scatter angle

(},= (},=

(J,= (J,= 24.435 mrad

1.4'

=1.4'

(} = (} 0+ (},+ (J ,= 70.9407 mrad = 4.0646'

Cross over point Symmetry factor Equivalent distance

distance = 94.132 km, elevation = 2859.39 m m=0.5015

Attenuation function

F( (Jd) = F( 13.3156) = 173.48 dB

(Ja = 603.29 km

Basic loss Antenna gains

Lb

= 185.09 dB

G, (1.4') = 11.26 dBi, Gz(1.4') = 11.26 dBi

Combined basic loss

L'b = 16257 dB

For the Vagi antennas used, the combined basic path loss L; does not change for better geographic conditions l , as long as the minimum antenna elevation angles satisfy 8 1m ::s; 1.4° and 82m ::S; 1.4°. This reveals an important fact on our VHF tropo trial, that is, the domination of the ground reflection at low antenna elevation angles. To increase the antenna gain at low angles (eg. < 1°) is an important topic. One way to do this is to increase the height of the mast where the antenna is mounted. This however, may increase the reception of man-made noise coming up from the ground nearby.

4.

MEASUREMENT RESULTS

Signal level and noise power spectral densities have been logged since October 1995. From the logging data, hourly, daily and monthly averages are calculated. Statistics of signal level and noise power density are extracted. In Figure 3 short term variation on 80 MHz and 150 MHz have been plotted. It is seen that the short term correlation between the two signals is small. In the following 1. Except for the case when an antenna is located on a down looking slope or the edge of a cliff where there is less ground reflection.

Digital Signal Processing for Communication Systems

109

only the 80 MHz results are presented. In Figure 4 the hourly averages in January 1996 are plotted (0 o'clock on vertical grid). The daily variation of signal level is clearly seen from Figure 5 (a). Usually the strongest signal happens during the early hours in the morning, and the weakest in the afternoon. The weather change may override this trend temporarily. On average, as our recording shows, the signal at 6 am is still over 6 dB stronger than at 4 pm, as shown in Figure 5 (a). The noise appears to have a daily variation as well, though smaller and following a different trend. In Figure 5 (b) the monthly average signal and noise levels are plotted. Note that for the last two months a wire antenna was used .

"

.

~\

-30

... -35

... ... ...

I

\~--; .,1

·25

Ii

'wt,

'-.8DMhz

·20 -

~

r

I

,

'"

0

'00

nm.(s)

''''

200

1,\11

t'

250

Figure 3 Short tenn signals at 80 MHz and 155 MHz received simultaneously. '0r-------------------------~~~

l;J

.... "

•• 7 ••

W~U~~"~D~W~~~~N253V3~

DalBofJanumy1996

Figure 4 Hourly average signal and noise levels recorded in January 1996.

-'6

-118,----------------------, -'48

·120 .'

\

i

\

iD

~

-22

-122

-12'

\

-'''' \

-152

\

o

2

4

6

8

ro

-

'A. .--

·'3

-'30

12 1. 16 18

~

n

~

C.._10

............ -.

·128

~~~~~~~~~~~

-'48

SignalS

·118

s·

·18

-132

.. -

NOlIe Powar Danlily No

-

~

_" Wire antenna ·154 'S: \ -156 ;: \

-'58

,

·'60 ,

-U52

-164

OcUJ!J New.95 0ec.95 Jan.96 "".98 Mar.9& Apr.98 May98

(a) Al""CI'8se daily '\1IMations. 10/95 ~ 3/96.

Figure 5 Signal and noise variations.

(b) Month1}' , ..riations

g

110

Weimin Zhang, John A. Hackworth and Wayne R. Schoff

0.05

0.05;,-----------,

0.04

0.04

0.04

0.04

0.03

0.03

0.03

0.03 01:

01:

0.02

0.02

No

~

I

0.02

0.0 0.01

0.01

0.01

0.01

0.00

0.00

\

\

o~~~~~~~~~~

0L-~~~~~~~~~

-180 -170 -160 -150 -140 -130 -120 -110 -100 -90 -80

-180 -170 -160 -150 -140·-130 -120 -110 -100 -90 -80

No (dBnWHzj. S(dBm)

No (dBnWHzj. B(dBm)

(b) 4 - 6/96, wire antenna.

(a) 10/95 - 3/96. Yagi antenna.

Figure 6 Histograms of signal S and noise power density No.

The logging results show that man-made noise is a serious problem in urban areas. Power line noise has been observed as the dominant noise source especially in hot weather. It is generated by the leakage and sparks at the insulators of open high voltage power lines near the receiver. Apart from the power line noise, there are other sources of man-made interference such as computer noise, industrial noise and other VHF transmitters in city areas. An experiment was conducted when shifting the receiver to a rural, electronic quiet area and the noise level observed was significantly lower. The histograms of the signal level and noise power density, both at the front end of the receiver, are plotted in Figure 6 (a) and (b). The median (50%) values, as well as other availability v =90% and 99% values are listed in Table 3. Also listed are the SNR values denoted as y from histograms of corresponding S' and N' at the same time. If we interpret the median signal level during the 10195 - 3/96 period using the Yagi antenna (-119.2 dBm) as the median annual level, the measured loss can be calculated (Figure 1) as L:"', = 46 - 2 - (-119.2) = 163.2 dB . Compared with the calculation in Table 2, the ditterence -U.6JdH IS consIdered as the climate correction factor

L:

V(de). Note for the wire reception antenna, the signal level is smaller but the noise level is even smaller. The SNR is about 6 dB higher, though this includes an unknown monthly variation. Table 3: Measured percentages of signal level S. noise power spectral density NO and signal to noise ratio y in Bn = 2650 Hz, as well as data rates supported, if required Eb /No = 14 dB. Time v %

99 90 50

October 1995 - March 1996 g No R" dB dBm/Hz bitsls -139.5 -160.1 5 -21.7 -130.8 -157.4 -13.3 18 -119.2 -1.0 -153.7 112 S dBm

bit!s

S dBm

1 5 84

-145.5 -133.5 -120.9

R

1 April - 20 Jun 1996 g No R" dB dBm/Hz bits/s -168.4 -17.7 8 -166.1 72 -5.7 -162.1 525 6.3

R

bit! s 2 28 450

Digital Signal Processing for Communication Systems

III

From the measurement results, the availability and channel capacity can be calculated. assuming known modem performance and requirement. If a modem requires ~req of Eb INo to produce a specified bit error probability Pb, the bit rate R related to the SNR value y measured in Bn is given by y =~reqRIBn with linear units. If using dB for y and ~req , the data rate as a function of availability v can be obtained as

(6) If we assume Sand N are uncorrelated, we may derive the data rate Ru from S and No. Since in linear units ~req =Eb INo =SINoRu ' we have (7)

As a conservative figure, let the Eb INo required by a modem ~req = 14 dB [6], the data rates Ru and R are calculated and listed in Table 3. From the discrepancies between Ru and R, it is seen that the signal and noise recorded are not uncorrelated. One reason, as observed, is that some weather conditions that result in strong signal levels also increase the noise from power lines. The results using the Yagi antenna are not very promising. Only a 75 bitsls chirp modem is supported over 50% of the time. When the wire antenna is used, as from the April to June 1996 data, a data rate of 450 bitsls can be supported for 50% of the time. A number of system parameters may be improved to increase the data rate or availability. For example, by finding an electro-magnetically quiet reception location, or using a more effective noise reduction by digital signal processing techniques, a 5 dB noise reduction may be achieved. A three wire antenna may be used in place of the single wire one with 4 dB improvement. Diversity reception usually gives over 3 dB gain. An improved modem performance, an increased transmission power, and geographic advantage will also give some improvement. In the north coast of Australia the refractive index Ns may increase to 350 and a 2.5 dB improvement is expected. The data from 155 MHz, though not logged over a long period, has shown a better SNR. If the combined effect of the above improvements can produce a 7.5 dB increase in SNR, then the median data rate would be R(50%) =2400 bitsls over a year.

5.

CONCLUSIONS

Troposphere channel sounding experiments have been conducted and the results show good agreement with a combined antenna and path loss calculation. Channel data rate with various availabilities are calculated according to the logging statistics. At the present time. the 40 W transmitter may support 450 bitsls with over 50% availability at 80 MHz. Ground reflection and external noise and man-made interference

112

Weimin Zhang, John A. Hackworth and Wayne R. Schoff

are believed to be two major obstacles. With diversity technique, improved antenna and modems, quiet and geographically favourable locations, as well as using a higher frequency, a higher and more useful data rate and/or availability may be achieved.

ACKNOWLEDGEMENT The authors would like to thank Mr Mark Preiss for his original contribution in the logging software and AUSLIG for using the topographic data in this paper.

REFERENCES [I]

[2] [3] [4] [5] [6]

L. Boithias and J. Battesti. "Propagation due to tropospheric inhomogeneities", lEE Proc., Part F, vol. 130, pp. 657-664, Dec. 1983. F. A. Gunther,"Tropospheric scatter communications, past, present and future", IEEE Spectrum, pp. 79-100. Sept. 1966. G. Roda, Troposcatter Radio Links. Artech House, 1988. J. B. Scholz, T. C. Giles, and M. C. Gill, "A unique, robust low-rate {HF} radio modem", in MILCOM'93, pp. 333-337, IEEE, Oct. 1993. E. A. Laport, "Long-wire antennas". in Antenna engineering handbook, Editor: H. Jasik, McGraw-Hili Book Company, New York. 1961. F. Edbauer, "Performance of interleaved trellis-coded differential {8-PSK} modulation over fading channels", IEEE J. Select. Areas Commun., pp. 1340-1356, Dec. 1989.

13 IMPLEMENTATION OF A DIGITAL FREQUENCY SELECTIVE FADING SIMULATOR XiaoFang Chen and KahSeng Chung

Curtin University o/Technology Western Australia

1.

INTRODUCTION

In a mobile radio environment, the received signal is made up of a number of scattered waves caused by reflection and diffraction of the transmitted signal by surrounding objects. The resultant scattered waves cause the well-known multipath fading phenomenon, such that the envelope, phase and frequency components of the received signal vary randomly. In general, the envelope of the received signal has a Rayleigh distribution when the receiver is moved locally around a small distance, and the phase is uniformly distributed from 0 to 2TC. Also, a Doppler shift component is present when the receiver is in motion [I]. These fading effects on a received signal can be simulated by using a fading simulator, which allows the study of the performance of a mobile system in a controlled laboratory environment. Such use of a simulator is more flexible, controllable and repeatable than field measurements. For a narrow-band system, a non-frequency selective fading simulator is capable of simulating the multi path effects. However, when the transmitted signal bandwidth approaches or surpasses the coherence bandwidth of the mobile channel, a more complex frequency selective fading simulator will be required to simulate the frequency selective effects. In this paper, the design of a digital frequency selective fading simulator for a wide-band UHF mobile radio channel is described. This simulator is based on a Texas Instrument DSP microprocessor (TMS320C31). Typical parameters for this fading simulator include: Number of delay paths: 6 Relative delay resolution: IOns Doppler shift frequency: 0 - 200Hz Maximum incoming signal bandwidth: 20MHz. T. Wysocki et al. (eds.), Digital Signal Processing for Communication Systems © Springer Science+Business Media New York 1997

XiaoFang Chen and KahSeng Chung

114

Moreover, for the study of space diversity, this simulator can be arranged to provide two groups, each of 3 paths, of Rayleigh fading signals whose correlation coefficient can be adjusted between zero and one.

2.

SYSTEM DEVELOPMENT

As shown in Figure I, the non-frequency selective flat fading can be simulated by modulating the transmitted signal in quadrature with two shaped independent lowpass Gaussian noise sources. Assuming that the receiving antenna is a vertical monopole, the power spectral density function (PSD) of the Gaussian noise sources is given by

(1)

S(f) =

o

otherwise

whereld is the maximum Doppler shift frequency, andle is the carrier frequency. The resultant fading signal so(t) then has the same PSD as the noise sources [1]. The frequency selective fading signal can be obtained by combining several time delayed fading signals, where the time delays represent the individual signal paths. Figure 2 shows a frequency selective fading simulator with m time delays tj (i=1,2, ... m) and m Rayleigh faders.

Figure 1 Non-frequency selective fading simulator.

Now, with the availability of high speed semiconductor technology, it is possible to build a wide-band UHF frequency selective fading simulator based on digital techniques. This digital approach is more flexible and controllable than analog approach. The functional block diagram of the digital frequency selective fading simulator described in this paper is shown in Figure 3.

Digital Signal Processing for Communication Systems

XclU

3.11E.os 3AOE.os 2.eIlE.os 2.211E.os 2.71E.os 2,_.os

-

Moan(dBm

-35,01128l1li -84.eem123 -3528412873 -IlII,C5851128 -35.&1122$ -35,7C6C&102

228E-Oii -8U:z.W1I8 2.16E-Oii -«l,~

3.57E.o& -84,}.

= (s, b2)

exp{ -

~ (z; -

(22)

based on (15) is S)2 /

(2b 2 )}

(23)

If can be shown that

max L H (0)

and

=(27tb~) -n/2 exp{ -

n / 2}

(24)

max LH (0) =(27tbf) -n/2 exp{- n I 2} ,

(25)

see;; see)'

0

I

where n

s== LZi In

(26)

i=1

are the well-known maximum likelihood estimators of the unknown parameters under the hypotheses Ho and HI' respectively. A substitution of (24) and (25) into (21) yields LR = (b~)n/2 /(bf)n/2

(27)

Taking the (n/2)th root, this likelihood ratio is evidently equivalent to (28) where (29)

Now the likehood ratio in (28) is equivalent to

Y== u; l(nuJ

(30)

Digital Signal Processing for Communication Systems

/83

It is known that the two-dimensional statistic (ul' u2) is a sufficient statistic for the parameter = (s, b 2 ) . Thus, the problem has been reduced to consideration of the sufficient statistic (u I, u2)' It can be shown that under Ho, y is a b2- free statistic which has the property that its probability distribution is independent of the variance b2. This is given by the following theorem.

e

Theorem 2. (PDP of the Test Statistic y). Under HI' the test statistic y is subject to a noncentral beta-distribution with the probability density function II-I I ( . _ ( n - 1 ..!..) ] -1 """2 -I "2 -I -nq/2 !:!. . ..!... nqy) fH,(y,n,q)- [ B 2'2 (1-y) Y e IFI 2'2' 2 .O ]

0

IX (m) I'dm ,(24) 0

where the monotonically increasing function 1;o(a) =

~() (.)

J4(a-~ina)

is given by, .

(25)

Note that when a ~ 0, ~(] (a) ~ a,J2/3 . Suppose the energy of the signal is given by, Eo ' then we also get, (26) -00

-0)

From equations 24 and 26, therefore,

(]

h (t) I< ~(] oY (t) PJ21C0>(]E().

Periodic Signals and line Spectra: If the signal spectrum consists of discrete lines resulting from the Fourier series expansion of periodic signals, then, instead of the Schwarz' inequality it is necessary to use the Cauchy inequality in equation 23. Suppose now a function ~ 1 (.) is defined as, 1;1 (a) =

J2sin(~) ,

which is monotonically increasing in 0 ~ a quality from equation 22. 0)

~

(27)

21t , we can obtain the following ine-

(1

h (t)12~i;rqO)oy(t)P

JIX(0»1 -0)

()

2 dO)

(28)

252

Saman S. Abeysekera and Antonio Cantoni

If the signal power is given by Po i.e., co

T

o

(29)

P

equation 28 results in, Ie I (t) I < ~ I (Iro (} y (t) J21tP o· We can justify the approximation if the squared error is negligible with respect to the signal power, i.e. if, IrooY (t) I «11(21t).

7.2

Lemma 2

l&.m.!lli!.: Suppose x (t) is a continuous time signal that is band limited to ±ro (} , and y (t) is a time varying signal, then x (t + y (t) ) - x (t) can be approximated by the second term of the Taylor series expansion of x (t) , with an error bounded by Iy (t) 1~3 COOI;~qcooy(t)i>

JIX(co)1 dco 2

;

2a 2 8sina 4 + -3- + 4cosa - -a-

.(30)

-co o

The

function

~

(.)

is

monotonically

increasing

and

~2 (a) ~ a2 ./11]1,. Therefore, h (t) I :s; ~2