T Symbol-Aided Plus Decision-Directed Reception for PSK/TCM Modulation on Shadowed Mobile Satellite Fading Channels

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. IO. NO. 8. OCTOBER 1992 1289

Symbol-Aided Plus Decision-Directed Reception for PSK/TCM Modulation on Shadowed Mobile

Satellite Fading Channels

Garrick T. Irvine, Member, IEEE, and Peter J. McLane, Fellow, IEEE

Abstract-There is much interest in providing mobile com- munications services via satellite (MSAT) to low-density areas for trucking, law enforcement, and other customers. The land- satellite link encounters multipath fading and foliage attenua- tion, which can be modeled mathematically as the vector sum of a lognormally-distributed LOS and a Rayleigh-distributed scatter component. Severe carrier phase jitter is the dominant problem for a coherent PSK receiver in this environment. Up to now, all MSAT modem studies for this channel have used differentially coherent detection. Herein, coherent detection is considered. Conventional decision-directed phase tracking techniques do not provide sufficient performance and are, in particular, prone to false lock. A concept developed by Moher and Lodge [18] multiplexes known symbols with the data stream for the purpose of channel estimation. This concept is applied to the phase tracking problem; moreover, improved perfor- mance is realized by extracting phase information from the data-bearing symbols, which is new to this investigation. The resulting phase estimator has good performance that is free of false lock. This is only true for modem techniques that involve trellis coded modulation (TCM) for PSK modulation: for in- stance, PSK without TCM yielded no performance improve- ment relative to differential detection. A variation of the ML Viterbi algorithm that weights the metrics with an estimate of the fading amplitude is employed to further enhance perfor- mance. With compensation for the reduced information rate, the resulting system has a 5 dB fade margin at a BER of and is 3 dB better than trellis-coded differential PSK, with 1 dB due to amplitude assistance in the Viterbi algorithm. The degradation from perfect phase tracking is about 3 dB.

I. INTRODUCTION

HE mobile satellite (MSAT) program proposes to

T

serve mobile users with digital voice and data com- munications in isolated, low-density areas of Canada us- ing a geosynchronous satellite. The satellite channel is both power and bandwidth limited, due to low mobile an- tenna gain and limited transponder bandwidth allocation.

The channel bandwidth is usually assumed to be 5 kHz.

Most studies are aimed at 4800 b / s operation with a sym- bol rate of 2400 symbols/second.

The MSAT channel is distorted by multipath fading, Doppler frequency shift, and attenuation of the line-of-

Manuscript received August 26, 1991; revised June 30. 1992.

The authors are with the Department of Electrical Engineering, Queen's IEEE Log Number 9202834.

University, Kingston, Ont. K7L 3N6 Canada.

sight (LOS) from foliage. Rician and shadowed Rician processes are used to mathematically model the distortion on the channel, which is often referred to simply as fad- ing. This distortion is particularly severe in Canada, where the angle between the LOS and the horizon is 10-15".

The Rician process assumes a constant LOS, whereas in the shadowed Rician process the LOS is lognormally dis- tributed and is considered more appropriate for Canada i l l , P I .

Phase shift keying is the modulation that has been con- sidered in most studies: interleaving and trellis coding [3]

are key aspects of all studies to date. References [4] to [12] are a representative sampling, although there are at least thirty papers in the open literature on this subject.

When the practical realities of the channel have been con- sidered, differentially coherent detection has been the re- ception technique of choice. However, it is not clear at this time whether this technique can provide sufficient fade margin for the fading scenarios of interest. This is true with or without the shadowed models of [ 13, [2].

A coherent detection system for Rician fading channels was considered in [18]. The idea of reference symbol phase tracking was introduced where one of every K transmitted symbols was known at the receiver and was used for carrier recovery. Only systems with trellis-coded modulation were considered. The results presented herein extend the applicability of the reference symbol technique of [ 181 to the shadowed Rician models of [ I ] , [2]. In ad- dition, we show that performance can be further improved by combining decision-directed techniques [ 141 with the reference symbol method. The value of K in the reference symbol technique is chosen by applying the Nyquist sam- pling theorem to the fading spectrum [18]. Finally, our consideration is only for tracking the phase jitter due to fading. Phase offset and Doppler tracking can be handled using known techniques [13]-[16]. In this manner, our investigation is similar to [17], whose concepts are also applied in our studies. In the final analysis, we find that coherent detection provides a 3 dB gain in E b / N , over differential detection for shadowed Rician channels.

An outline of our paper is as follows. In Section 11, we state our system model. Section 111 contains a statement of our algorithm for coherent reception: the algorithm is meant for DSP modem implementation. Section IV con-

0733-8716/92$03.00 @ 1992 IEEE

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. VOL. IO. NO. 8. OCTOBER 1992

SYSTEM BLOCK DIAGRAM

1 : K KNOWN

SYMBOLS

CHANNEL

Fig. 1 . System block diagram with coding and interleaving

h/

^SCATTER

Fig. 2 . Mobile satellite fading channel.

tains our simulation results. Section V presents a consid- eration of the time delays in our algorithm, and the con- clusions can be found in Section VI.

lowed by a deinterleaver and a trellis decoder based on the Viterbi algorithm.

11. MODEL A. Transmission Model

The end-to-end data transmission model is shown in Fig. 1. On the transmitter side, we have a trellis encoder and a convolutional interleaver followed by a PSK mod- ulator. The trellis code is required to vastly improve link transmission performance and this requires the convolu- tional interleaver shown in Fig. 1 to break up the error bursts associated with deep fades on the mobile satellite

B. Fading Model

We shall assume that fading is frequency nonselective and is depicted in Fig. 2. The fading model, introduced by Loo [ I ] , uses a shadowed Rician process. Some au- thors have used a Rician process to model fading whereby the LOS is assumed constant and the scatter is Gaussian.

In phasor notation, we have

rei!? = c

+

vel! ₍₁₎

fading channel. Use of a convolutional interleaver, rather than a block interleaver, was justified in [12]. The chan- ne1 characteristic in Fig. 1 is multiplication by a fading function followed by additive white Gaussian noise. The fading model will be discussed shortly. Finally, the re-

where ve is complex Gaussian and c is a constant. Ran- dom variables are denoted in boldface. In Loo’s model, the LOS component of the Rician process is subjected to

a From (1), we have

ceive; is composed of a coherent PSK demodulator fol- r e @ = ^- p

+

veJP (2)

I'

GR V -2

IRVINE A N D McLANE: S A D D RECEPTION FOR PSKiTCM MODULATION

3rd Order Butterworth

F i l t e r

- ^*

1291

TABLE I

P A R A M E T E R S FOR THREE DEGREES O F SHADOWING Degree of Shadowing

Light Average Heavy

f f / 2 0.158 0 . 1 2 6 0.0631

!J 0 0.115 -0.115 - 3 . 9 1

A<>

0.115 0 . 1 6 1 0.806

VAR = do Mean = 0

r

Butterworth ^{3rd Order} F i l t e r

VAR = ai2 ^LOS

I

VAR = ru2

Channel

SCATTER

1

^Gain

Mean = 0

3rd Order Butterworth

F i l t e r

Fig. 3 . Shadowed Rician simulator.

where

That is, = e" where n is Gaussian with mean p, and variance do. For the shadowed Rician model, we use the parameters in Table I where a is the variance of the com- plex Gaussian multipath component in ( 1 ) .

Our performance assessment will be based on a dis- crete-time version of the transmission link in Fig. 1. As such, a digital computer simulation model is needed for the fading model in (2) and (3). This will be carried out as depicted by the block diagram in Fig. 3 . Gaussian ran- dom variables are generated using a standard technique.

These samples are filtered as a time series by three inde- pendent third-order Butterworth filters. The bandwidth of these filters is the Doppler frequency Bd, which is related to the user vehicle speed. We usually normalize the Doppler frequency by the symbol rate T - ' and consider the normalized Doppler frequency Bd T.

111. SYMBOL-AIDED PLUS DECISION-DIRECTED PHASE JITTER TRACKING

A. Introduction

In the first part of this section, we will discuss an in- novative technique to track the fading phase developed by

Moher and Lodge [18]. This technique, which will be re- ferred to as symbol-aided (SA) tracking, multiplexes known symbols with data symbols at the transmitter. The known symbols are used to identify the fading phase dy- namically at the receiver. Results given by [ 181 pertaining to the Rician channel have shown excellent results. The method is herein extended to the shadowed Rician chan- nel, where performance was found to be equally good.

The second half of the section will discuss an improve- ment to symbol-aided tracking called symbol-aided plus decision-directed (SADD) tracking. The SA technique makes use strictly of the known symbols and neglects the data-bearing symbols. Our method extracts additional fading phase information from the data-bearing symbols.

Implementation of the SADD algorithm results in mean squared error (MSE) improvements of the estimated phase and bit error rate (BER) gains of up to 1 dB. Coherent detection with both SA and SADD tracking provided BER performance superior to that of differential detection for uncoded PSK.

The big advantage of SA and SADD tracking is the elimination of false lock. Unlike decision-directed meth- ods, the new technique makes a reference phase sample available at the receiver to be smoothed that is never cor- rupted by a decision error. The penalty for both algo- rithms is that sending redundant known symbols reduces bandwidth efficiency and recovering the phase increases delay. However, a 20% increase in bandwidth will be shown to suffice for MSAT systems.

I ) Rectangular Tracking: An alternative to tracking the phase directly is to track the real and imaginary compo- nents of the fading phasor re '9. The phase estimate is then obtained by taking the arc-tangent of the two components.

Effectively, this corresponds to switching from a polar form to a rectangular form of tracking. The rectangular form was found to yield slightly improved performance over the polar form and was therefore selected to be used.

In the interest of a concise representation, hereafter a ref- erence to the estimated phase is equivalent to estimation of the in-phase and quadrature components of the fading process reJq. Moreover, the rectangular form is used ex- clusively for both the SA and SADD estimators. Another advantage of rectangular tracking is that an estimate of the fading amplitude, r, is easily calculated by taking the magnitude of the in-phase and quadrature components. In Section IV, an estimate of r is used as a weight in the Viterbi decoding algorithm for trellis decoding.

B.

Symbol-Aided (SA) Tracking

1) Description of the Algorithm: The SA method sends symbols, which are known at the receiver, multiplexed with data-bearing symbols. The information phases of known and data symbols will be referred to as

ek

^and

ed,

respectively. The known symbols are multiplexed in a constant ratio at uniform time intervals. As illustrated in Fig. 4, one known symbol is transmitted followed by K - 1 data symbols, corresponding to a ratio of 1 : K . In

.

II

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. VOL IO. NO. 8. OCTOBER 1992

D E W X

SYMBOLS ulx

...

...

...

...

...

K"

SYMBOLS

...

....

..

^1..::... ... .>::

I.. ...

Fig. 4. SA phase tracker.

order to avoid spectral harmonics at multiples of K I T caused by transmission of a constant known information phase,

e,,

a pseudorandom series (0,) which is known to the receiver can be sent. At the receiver, the demodu- lator outputs a complex phasor

z

corresponding to each received symbol. The received phasor is distorted by fad- ing and corrupted with AWGN, and is given by

= r e J ( O + q ) + N = r / e j @ + q + $ ) (4) where

8 = information phase

N

= complex AWGN phasor r 4 = fading amplitude and phase

r ' , $ = adjusted amplitude and phase due to noise After demodulation, the phasor

z

is demultiplexed into known and data phasors

{z,)

and { z d }

The known information phase,

ek,

is rotated off the known phasors as shown below

After rotation, the residual phase, whose output consists of the fading phase plus noise, is put through a filter to remove noise.

After the filter, we-have, in effect, smoothed samples of the fading phase rPk spaced K symbols apart. Subse- quently, the phases associated with the data phasors can be interpolated between successive pairs of smoothed samples which were derived from the known symbols. A block diagram of the SA tracker is shown in Fig. 4. Note that the process of filtering and interpolating incurs a de- lay in the output of the detected data. If the smoothing filter results in a delay of DF baud, then the total delay of the detected data will be KDF. A typical value for DF would be 2-4 symbols for an IIR (recursive) filter, and 5-10 symbols for a more stable FIR (nonrecursive) filter [17]. Another drawback is that bandwidth usage is ex- panded by a factor of K / K - 1 . The choice of K deter- mines the delay and bandwidth efficiency and is the topic of the next section.

2 ) Choosing the Multiplexer Ratio 1 ^: K: An obvious question to pose is what value of K is sufficient to achieve an acceptable level of tracking performance? Clearly, a lower value of K will increase bandwidth usage; however, it also decreases overall detection delay. We can utilize sampling theory to predict a plausible upper limit on K (the lower limit is K = 2). Suppose we have a normalized fading bandwidth of 0.05, and a symbol rate of 2400 sym- bols/second. Spectral analysis of the fading process out- put from the simulator shows that most of the power is contained within a bandwidth of 0.08. Therefore, in order to recover the fading we require a sampling rate that is more than twice the worst-case normalized fading rate of 0.08. Thus, K is an integer satisfying (8)

1

2(worst fading bandwidth) .

K I (7)

When the worst-case fading bandwidth is 0.08, the max- imum value of K is 6. We will see that decreasing K has the effect of decreasing phase MSE and BER.

3) Smoothing Filter Cutof: The filter bandwidth of the smoothing filter (see Fig. 4) is related to T,, the sampling rate (using known symbols) of the fading process where T, = KT. Increasing the rate of known symbols by de- creasing K will allow a reduction in the smoothing filter bandwidth. This will filter more noise from the phase es- timate, resulting in lower MSE. Fig. 5 illustrates this re- lationship by plotting rms phase MSE as a function of smoothing filter cutoff normalized to T, for various K . Note that the optimum cutoff increases with K as plotted in Fig. 6.

4) Interpolation of the Phase Estimate over Data Sym- bols: An issue not yet raised is that of interpolation of the phase estimates in between the known symbols. The es- timated phases for the data symbols which occupy the bauds between the known symbols are interpolated using a straight-line method. As described in Section 111-A-1, the known symbols are initially filtered at the receiver after the known data has been removed. These filtered samples of the phase form the end points through which a straight line is drawn, giving the related phase estimates for the data-bearing symbols in between.

C. Symbol-Aided Plus Decision-Directed Tracker 1) Description of SADD Algorithms: The SADD al- gorithm is an extension of the SA phase tracker described in Section 111-A. It consists of an initial estimator which corresponds exactly to the SA method, and a final esti- mator incorporating fading phase information extracted from the data symbols. A block diagram appears in Fig.

7. When estimating the fading phase 4 , the SA tracker makes use of only the known symbols and ignores the data-bearing symbols. The proposed tracker utilizes the data symbols in a role which is subordinate to that of the known symbols yet provides input into the final phase es- timate. The SA portion p f the SADD algprithm generates initial phase estimates ^+d and decisions e d . Note that the

IRVINE A N D McLANE: SADD RECEPTION FOR PSKITCM MODULATION

0.40 ~ 0 , 4 0

J W v, 3

,020 -

k

- K = Z K = 3 K = 4 K = 5 ...

. .

_-.

.

. . _ _ _

. .

I. ^.>

. . . .

^\

. .

'

. .

_{- _ _}

- - - _ _ _ . . . .._...._..-.i

... y

-0.20

0 00

0 GO 0 20 0 40

Normalized Fllter Cutoff R o t l o

Fig. 5 . Phase MSE versus filter cutoff for various K(SNR = 10 dB)

050

,

^{40 50}

K

Fig. 6 . Optimum filter cutoff frequencies.

...

K" ...

... ^I ... :

1

^LEGEND

I

_, ... :.

j eo++0+9-60q p < p *

d ?

-

^L

! $p>;*

... ...

Fig. 7 . SADD phase tracker.

{

6,)

represent early hard decisions, which consider {

4,)

only and do not attempt to take advantage of any coding that may exist. We define

/3

as an indicator of the confi- dence we have in Foth the phase estimates { ^{( j d }} and the initial decisions {

e,>,

^{given by (9)}

The initial decisions are provided by the SA tracker. As- suming that the initial decision is typically correct (i.e.,

1293

6,

= e d ) , then a typical

/3

can be represented with the tiagram in P i g . 8 . A large

1/31

represents inaccuracy in and/or 6 d , or a large noise contribution $. Whatever the caseAmay be, the larger

1/31

is, the less confidence we have in

e,+

Since decision errors cause poor tracking per- formance, it is prudent to simply abandon the additional phase information rather than tolerate the damage of a more probable decision error. We can therefore- set a threshold

/3*

such that, if

1/31 > /3*,

the decision e d and the corresponding phase sample will be rejected. In this case, the SA estimate of the fading phase is utilized.

However, if

13) < /3*,

then

6,

is used to obtain a phase sample to be input into a fine smoothing filter which is filter FIR 2 in Fig. 7 . Phase samples derived from data symbols are given by (9)

(9)

( e d

+

^{6 d}

+ $1

-

6,.

If

6,

is correct and indicated by

/3

to be a good deci- sion, then we have ^{( 6 d}

+

$) as an input to the fine filter over the corresponding data symbols. Of course, (&

+

$) is always available from the known symbols since the signal phase Q k is rotated off with absolute certainty. If

/3

indicateSAthat an initial decision is not good, then we sim- ply use 6 d as the input to the fine filter. The output of the second smoothing filter gives2an improved final estiiiiate (j of the fading phase. y h e n 4 is available, t$e data sym- bols are rotated by - 4 and a final decision 8 is made.

2) Choosing Conjidence Threshold

0":

In choosing

/3*,

an upper limit is a / M since + n / M defines the (:?cision boundary when M is the constellation size. From simu- lation trials, a value of

/3*

= n/2M was found to yield near-optimum results. To demonstrate some measure of the quality of the indicator

/3*,

we can derive the pfoha- biiity density function (pdf) of

/3

conditioned on

(e,

⁼

e,),

^and of

/3

conditioned on

(ed

t= 0,). The procedure for the acquisition of a pdf through simulation is dF- scribed in [21]. The probability density functions p ( / 3 ( e d

=

e,)

^{and p}

^(PI 6,

^#

e,)

are shown graphically in Fig.

9 for

M

= 4 and are normalized for coinparison. This graph identifies the expected percentage of bad decisions used and the percentage of good decisions abandoned for a given

/3*.

The evaluation of

/3

and the ensuing action taken can be interpreted as a discriminator, whereby good decisions are accepted as input into the final phase esti- mator and decisions of dubious quality are rejected.

3) Improvements of the SADD Algorithm: The poten- tial for improvement in phase MSE, and thus BER of the SADD algorithm over SA tracking, is realized from the reduction in bandwidth of the fine smoothing filter which has the effect of removing more noise from the pha, s e es- timate. The bandwidth of the second filter can be tight- ened because there are more samples of the fadin8 phase avai1able:o be filtered. The additional samples, ( 8 d

+

^{6 d}

+

^{$ - e d ) ,} are derived from the data phasors { z , } . Of course, the known phasors c o n t h e to provide samples free from decision errors

(4k +

$). For

M

= 4, the im- provement in MSE can be seen in Fig. 10 for the cases of K = 2 and 5 . Other values of K showed similar improve-

1

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t

J

0.00

, , 3 , , , \ ; v 1/,I1IIIOII- - _ III(III,1II1II)II

' L

_ -

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. IO, NO. 8. OCTOBER 1992

400 ) 4 00

+ ^I

Fig. 8. Confidence indicator.

...-.(I'

^P p e d # e , ) IP (- e, # er ) ,,,, .-

s

^{4" *0°}

I

, , ( , , , , ,

;\

, , ( , , , /zoo

...-- . . . . ~ ~ ...

~ . . ~ . . .

0.00 0 00

0 00 0.20 0.40 0 60 0.80

B ("s)

Fig. 9. Discriminator probability density functions

0 2 5

0 15 0 10 0 05

0.00 i ~ i 0 0 0

5 10 15 20 25 30

SNR (2Eb/No)

Fig. 10. Phase mean squared error (SA versus SADD).

ment. Fig. 1 lA shows the pdf of the phase estimation error estimation error &e has more density centered around

&,

= 0. Although some of the samples associated with the data symbols include decision errors, the improved filter- ing capability of the fine filter outweighs this adverse af- fect in a MSE sense for properly chosen /3*.

4) Disadvantages of the SADD Algorithm: There are two chief disadvantages of the SADD algorithm: one is that it adds delay, the second is that it adds complexity.

The additional delay results from the fine smoothing filter of the final estimator. Complexity is increased by approx- imately 25% because of the operation of the discrimina- tor. If both the first and second filters are of identical or- der, then the additional delay amounts to a factor of 1 / ( K

+

^{1 ) .} Therefore, the added delay is relatively modest es- pecially when K is large. Although the increase in pro-

&e = r#)d - r#)d for SNR = 10 dB. Note that the SADD

! ,

1 ,

' \ -

SA K = 5

,'

' II - - - SADD [ K = 51

{

2 0 0 1

A

^12.00

cessing resources required by the discriminator does not significantly impair computer simulation, it may not be feasible on a signal processing chip which has limited ca- pacity. Basically, if the receiver design is relatively in- sensitive to minor increases in delay and complexity, then the disadvantages just described will have minor conse- quences.

D. Coding

A rate 2 / 3 8-state convolutional encoder and mapping rule devised by Ungerboeck was used to encode the data stream. The block diagram, mapping rule, and trellis dia- gram which are described in more detail in [12], [21] are shown in Fig. 12(a)-(c). At the receiver, a maximum likelihood sequence estimator was employed to decode the incoming symbols using the Viterbi algorithm. For the Gaussian channel, this decoder is optimum; however, op- timum performance over fading channels requires weight- ing of the metrics and will be discussed shortly. A deci- sion depth of 18 symbols was used, which is consistent with that suggested in [12], [13]. Interleaving was used to make the burst-error fading channel appear more like a random error channel at the receiver, allowing the de- coder to operate more effectively. A convolutional inter- leaver was selected since it can be implemented with half the delay of an equivalent block interleaver [12]. An in- terleaving depth of 10 symbols was found to reduce the correlation of deinterleaved symbols to a negligible amount for a normalized fading bandwidth of 0.05.

The Viterbi algorithm is used as a sequence estimator to select the optimum, i.e., most likely, path through the trellis. The path metrics are updated according to the joint probability of the received sequence Z , conditioned on the coded sequence

X,

for the Gaussian channel

where

and

P K ( Z K I & ) (10)

Z K = (21, 229 2 3 , * * * 9 Z K )

x,

= (XI, x2, x3,

-

^{* 9} xK) .

On the fading channel, assuming perfect fading phase compensation, we have the following

IRVlNE AND McLANE: SADD RECEPTION FOR PSKITCM MODULATION

1295

C,'"

0426

1 537

4062

5173

2604

371 5

6240

7351

-

State

0 0 0

1 0 0

0 0 1

1 0 1

0 1 0

1 1 0

0 1 1

1 1 1

PRESENT NEXT

STATE STATE

(C)

Fig. 12. (a) Rate 2 / 3 8-state convolutional encoder. (b) Bit-to-symbol mapping rule and 8-PSK constellation. (c) Trellis diagram for the encoder of (a) and (b).

where

r, = fading amplitude x, = eJe1 - - modulation signal and

n, = complex AWGN.

A sequence 2, is decoded as correct if

K K

c ^-I&

^{- rlP,(2}

^> c

^{-/z, - r,f,I2,}

I = I I = I

for all PI # 2 , .

Equation (12) suggests that the branch metric for de- coding should be -

(zi

^- rifiI2 when the ri are known. In our case, we use fi (an estimate of ri). In order to imple- ment the ML sequence estimator described above, the Vi- terbi algorithm is altered so that the path metrics are up- dated using an estimate of the amplitude to weight the ( 3 ; ) . Recall from Section I11 that using a rectangular tracking method, an estimate of the fading amplitude ri is easily obtainable. Simulation results show that weighting using the estimate f i yields approximately 1 dB of gain over the conventional Viterbi algorithm which does not use weighting.

IV. BER ANALYSIS

This section will give the average probability of bit er- ror (BER) performance over the MSAT fading channel of SADD reception using 8PSK TCM, interleaving, and weighted Viterbi decoding, as illustrated in Fig. 1. It is shown through comparison that differential PSK using TCM, interleaving, and Viterbi decoding is inferior to the above. SADD and SA reception are also compared, whereby the former is found to yield an improvement in performance. Fade margins are calculated by comparison to the Gaussian channel, where fade margin is defined as the additional SNR required to attain the same BER as uncoded QPSK. Finally, the effect of a lower fading bandwidth is examined.

The fading model simulated was the light shadowed Rician process with a normalized fading bandwidth of 0.05, as described in Section 11. All coded results in this section use the rate 2 / 3 8-state 8PSK convolutional en- coder discussed earlier and will be referred to simply as coded hereafter. Convolutional interleaving with A = 10 symbols and weighted Viterbi decoding was used for fad- ing channel simulations, with the exception of the data for 8DPSK (taken from [12]) which used an interleaving depth of A = 8 symbols and conventional Viterbi decod- ing. Simulations for a normalized fading bandwidth of 0.025 were also performed to evaluate the effect on the various coding and modulation schemes of a lower vehi- cle speed.

In Fig. 13, the spread between perfectly coherent and differential 8PSK defines the maximum attainable im- provement of a realizable coherent receiver. Before dis- cussing the data associated with SA/SADD phase track- ing, two points are noteworthy. Whereas an amplitude estimate is readily available when using a rectangular phase tracker, it is not available when using differential detection and therefore would not be used. Moreover, the implementation of a weighting factor for the sequence es- timator is uncertain for DPSK. Secondly, since SA/SADD phase tracking requires excess bandwidth, the informa- tion rate is reduced. To compensate, the appropriate curves are shifted to the right by 10 log,, (5/4) = 1 dB and 10 log,, (2/1) = 3 dB for

K

= 5 and K = 2 , respec- tively. It is clear that even after this compensation, which is shown as a dashed line, coherent detection using

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-

^PERFECT

W X X S S A D D . K = 2 B S A D D . K = 5 COQ30SADD. K=2.

O W W SADD. K = 5 .

\ \

10 -'

10 - >

10 -'

7 00 1 2 0 0 1 7 0 0 2 2 00

SNR (2Eb/No)

Fig. 13. Coded 8-PSK comparing perfect coherence, differential detec- tion, and the effect of compensating for reduced information rate.

SA/SADD tracking yields a lower BER. The spread be- tween the coherent curves and the differential result wid- ens as the average probability of bit error decreases. This indicates that DPSK begins to encounter the error floor for the range of bit error rates on the graph, while there is no evidence of this effect from the data pertaining to coded coherent detection.

Fig. 14 compares coded 8PSK and 8DPSK BER per- formance on the fading channel to uncoded QPSK on the Gaussian channel denoted as AWGN. QPSK was used be- cause it has the same information rate as coded 8PSK.

Recall that the dashed lines indicate a shift in the coherent curves compensating for bandwidth expansion of the SADD tracking algorithm. Coded, perfectly coherent 8PSK labeled PERFECT was plotted to identify optimum coherent detection on the fading channel. The above data was used to generate a table of fade margins as shown in Table 11. The rate 2 / 3 coding was also simulated for 8PSK on the Gaussian channel and is labeled as CODED AWGN. Fig. 15 shows the relative improvement in per- formance due to TCM, interleaving, and amplitude weighting.

Fig. 16 gives the simulation results for coded coherent detection comparing SA and SADD phase tracking using an interleaving depth of 10 symbols and a fading band- width of 0.05. The tracking algorithms also supply an es- timate of the fading amplitude which is used by the Vi- terbi decoder. Note that the BER curves have not been adjusted to reflect extra energy used by known symbols, since both SA and SADD trackers use the same propor- tion of known symbols. For a multiplexing ratio of K =

2, there is negligible separation; however, for K = 5 there is an improvement of 0.5 dB and for K = 8 there is up to 2 dB improvement at a BER = Larger K increases the spread in BER because the MSE of the SA phase es- timator increases, resulting from a reduction in phase in-

-

^{CODED AWGN}

1

- PERFECT

\ 0

10 00 1 5 0 0 20 00

10 - 5 00

SNR (2Tb/"o)

Fig. 14. Coded 8-PSK comparing BER results between the fading channel and Gaussian channel.

TABLE I1

FOR VARIOUS MODULATION A N D CODING OPTIONS

FADE MARGINS (BER =

~

Modulation Fading Interleaving Amplitude Fade*

(Tracking) BW Depth Weighting Margin

Coded 8PSK Coded 8PSK Coded 8PSK Coded 8PSK Coded 8DPSK

(Perfect) 0.05 10 Yes 2.0 dB

(SADD K = 2 ) 10 Yes 6.0 dB

(SADD K = 5) 10 Yes 5.2 dB

(SADD K = 8) 10 Yes 6 . 9 dB

(NIA) 8 no 8.2 dB

Coded 8PSK Coded 8PSK Coded 8PSK Coded 8DPSK

(SADD K = 2 ) 0.025 I O Yes 5.7 dB

(SADD K = 5 ) 10 Yes 5.0 dB

(SADD K = 8) 10 Yes 5.7 dB

W A ) 8 no 10.5 dB

*Compensated for a reduction in the information rate

formation available through the known symbols. There- fore, the phase information contained in the data symbols, and exploited by the SADD estimator, becomes more use- ful. Also, for larger K , both the SA and SADD techniques have improved bandwidth efficiency. For instance, with K = 8 the bandwidth expansion factor is only 1 4 % .

Fig. 17 shows the BER data when the channel was sim- ulated with a normalized fading bandwidth of 0.025. Re- call from Section I1 that this corresponds roughly to 50 kph for the MSAT channel that we are considering. Al- though the fading phase is changing slower, which makes it easier to track, the autocorrelation function has signif- icant magnitude over a longer time period. Therefore, in order to eliminate the correlation between adjacent signals

IRVINE AND McLANE: SADD RECEPTION FOR PSKiTCM MODULATION 1297

i

g

¹⁰ -’

“ 4

i

-

^{TCM, WEIGHTED, h = 1 0}

i

10

5 0 0 1000 1500 2000 30 00

SNR (2E;-,/Nof500

5 00 10 00 2000 2 5 0 0

SNR ’?%b/No) Fig. 15. Comparing the relative improvement of TCM, interleaving, and

amplitude-weighting using perfect phase coherence for all curves.

Fig. 17. Effect of lower fading bandwidth; (BW = 0.025).

V. TIME-DELAY ANALYSIS

The amount of delay caused by processing at the re- ceiver is primarily of concern to voice-related services.

Data services are more concerned with reliability of de- livery and can tolerate a larger delay. In contrast, the per-

110.’ ceptibility of voice communications degrades signifi-

cantly for delays of over 300 ms. Since transmission delay is fixed at 250 ms, only 50 ms is available for baseband processing. The delay of the Viterbi decoder is 18 sym- bols corresponding to the decision depth (14). The filter delay and interleaving delay are also given by (13)

I , l o - ’ G€€€OSADO, K = 2 - S A .

08BBE1SADD. K = 2 K=5

--SA. K = 5

-SADD.

-

^SA, K=8 ^K=8

310 -’

SYMBOL DELAY X(X - 1)

+

KDFI

+

D F ~

+

18 (symbols)

9 00 1 4 0 0 19 00”

SNR ( 2 E b / N o )

Fig. 16. Coded 8-PSK comparing SA tracking and SADD tracking

completely, the interleaver depth should increase accord- ingly. Since it is impractical to adjust interleaving depth during transmission, there will be some degradation when the fading bandwidth decreases due to increasing corre- lation between the symbols. There is gain, however, from better phase tracking in the case of coherent PSK, and a smaller rms differential phase jitter in the case of DPSK.

From the data in Fig. 17, it appears that the improve- ment realized by a coherent receiver from better phase tracking is more significant than the lower rms differential phase jitter, thus increasing the superiority of coherent detection. Another effect is that the phase tracker can op- erate with a larger multiplexing ratio K , with similar per- formance to lower K after adjusting for excess bandwidth usage.

symbol delay

TIME DELAY = (seconds) (1 3)

baud rate w - ,re

X = interleaving depth DF1, DF2 = filter delay

K = multiplexer ratio.

Table I11 compiles the delay for various interleaving and phase-tracking options. For a fixed information rate I, the baud rate is given by (14)

Baud Rate = -

[ K : 1 1

[

1 [symbol]

1

^{I [ x ]} (Hz). (14) 2[bits] second

The dominant source of delay is interleaving (up to 90 symbols for X = 10). DF1 and D F 2 correspond to the delay of the smoothing filters; typical values were 5 and 10 symbols, respectively, and are dependent on the type and order of the filter. D F 2 does not apply to SA tracking since

I

1298 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. VOL. IO. NO. 8, OCTOBER 1992

TABLE I11

DELAY FOR VARIOUS INTERLEAVING A N D PHASE TRACKING OPTIONS ^OF CODED 8PSK A N D 8DPSK

Information Interleave Multiplex Delay

Rate Depth Ratio

(b / s) h K Symbols ms

8PSK

4800 10 2 128 27

4800 10 5 143 48

4800 10 8 158 58

4800 8 5 109 36

4800 6 5 83 28

2400 10 5 143 95

It was found that reducing the multiplexing ratio ( K ) gave improved tracking and BER performance since more phase information is available to the tracker. However, after compensating for the reduction in energy assigned to data transmission, it was found that K = 5 gave opti- mum performance for a fading bandwidth of 0.05. Lower fading bandwidths could tolerate larger K . It is for larger K that SADD phase tracking shows a significant improve- ment over the SA technique.

REFERENCES

2400 10 2 128 53

2400 8 2 94 39 [ I ] C. Loo, “A statistical model for a land mobile satellite link,” in Links S.r the Future (ICC’84). Scirrrcr , Systems and Services for Communication, P. Dewilde and C . A . May, Eds. North-Holland:

[2] -, “Measurements and models of a mobile-satellite link with ap-

4800 8 NIA 74 31 plications,” in Proc. GLOEECOM’8.5, New Orleans, LA, December

2400 8 NIA 74 74 2-5, 1985.

[3] G. Ungerboeck, “Channel coding with multileveliphase signals,’’

IEEE Trans. Inform. Theory. vol. IT-28, pp. 56-66, Jan. 1982.

[4] D. Divsalar and M. K. Simon, “Trellis coded modulation for 4800 to 9600 b / s transmission over a fading satellite channel,” JPL Pub., vol. 86-8, Pasadena, CA, June 1, 1986; also, IEEE J . Selecr. Areas Commun.. vol. SAC-5. DD. 162-175, Feb. 1987.

8DPSK IEEEIElsevier Science. 1984.

it does not use a second smoothing filter. The information rate was set at 2400 b / s or 4800 b / s for all delay calcu- lations in the table. Using a lower value of K has the effect of reducing the time delay, but also reduces bandwidth efficiency. If minimum information rate requirements for acceptable voice quality are easily met within the allo- cated channel bandwidth, then processing delay would become more important, allowing a lower K . In contrast, with data transmission, time delay considerations are sub- ordinate to information rate and BER and are thus much less stringent.

VI. CONCLUSIONS

The symbol-aided (SA) synchronization concept devel- oped by Moher and Lodge [ 181 was applied to the MSAT channel modeled with a shadowed Rician process. Sim- ulation data demonstrated that it could track the severe phase jitter encountered on the fading channel free of the false lock which plagues conventional techniques. The al- gorithm multiplexes known symbols into the data stream, which establishes an absolute reference free of decision errors that is used to estimate the fading phase.

An improvement to the SA algorithm is proposed which extracts phase information from the data-bearing sym- bols. It was found that the new technique is more effective for larger K . The improved algorithm is referred to as symbol-aided plus decision-directed (SADD) phase esti- mation.

A system employing SADD phase estimation, trellis- coded modulation, interleaving, and amplitude weighting within the Viterbi decoder yielded the best BER perfor- mance on the shadowed MSAT channel considered in this paper. There was a 3-5 dB gain over coded DPSK after adjusting for the reduction of information rate. This low- ers the fade margin in an MSAT modem to 5 dB at a trans- mission rate of 4800 b / s . This fade margin approaches the requirement for the present specifications of MSAT systems.

[SI M. K. Simon and D. Diisalar, “Multiple trellis coded modulation (MTCM) performance on a fading mobile satellite channel,” in Proc.

1987 GLOEECOM, Tokyo, Japan, November 15-18, 1987, pp.

43.8.1-43.8.6.

[6] P. J. McLane, P. H . Wittke, P. K. -M. Ho, and C . Loo, “PSK and DPSK trellis codes for fast fading, shadowed mobile satellite com- munications channels,” lEEE Trans. Commun., vol. 36, pp, 1242- 1246, Nov. 1988.

[7] D. Divsalar and M. K. Simon, “The design of trellis coded MPSK for fading channels: Performance criteria,” IEEE Trans. Commun., vol. 36, pp. 1004-1012, Sept. 1988.

[SI -, “The design of trellis coded MPSK for fading channels: Set partitioning for optimum code design.” IEEE Trans. Commun., vol.

36, pp. 1013-1022, Sept. 1988.

[9] C . Schlegel and D. J. Costello, J r . , “Bandwidth efficient coding for fading channels: Code construction and performance analysis,” IEEE J. Select. Areas Commun., vol. 7 , pp. 1356-1369, Dec. 1989.

[lo] M. K. Simon and D. Divsalar, “The performance of trellis coded multilevel DPSK on a fading mobile satellite channel,” IEEE Trans.

Vehic. Technol., vol. 36, pp. 78-91, May 1988.

1111 S . G. Wilson and Y . S . Leung, “Trellis coded phase modulation on Rayleigh channels,” in Proc. I987Inr. Conf. Commun., Seattle, WA, June 7-10, 1987, pp. 21.3.1-21.3.5.

[I21 A. C. M. Lee and P. J . McLane, “Convolutionally interleaved PSK and DPSK trellis codes for shadowed, fast fading mobile satellite communication channels,” IEEE Trans. Vehic. Technol., vol. 39, no. 1, Feb. 1990.

[ 131 F. Edbauer, “Performance of interleaved trellis-coded differential 8- PSK modulation over fading channels,” IEEE J . Select. Areas Com- mun., vol. 7 , pp. 1340-1347, Dec. 1989.

( 141 F. M. Gardner, “Demodulator reference recovery techniques suited for digital implementation,” Europ. Space Agency Rep., Contract # 6847/86iNIDG, May 1988.

[15] F. D . Natali, “Noise performance of a cross-product AFC with de- cision feedback of DPSK signals,” IEEE Trans. Commun., vol.

COM-34, pp. 303-307, Mar. 1986.

[ 161 P. J. McLane, “Two-stage Doppler phasor corrected TCMIDMPSK for shadowed mobile satellite channels.”

[I71 R. L. Cup0 and R. D . Gitlin, “Adaptive carrier recovery systems for digital data communication receivers,” IEEE J . Selecr. Areas Com- m u n . , vol. 7, pp. 1328-1340, Dec. 1989.

(181 M. L. Moher and J. H . Lodge, “TCMP-A modulation and coding strategy for fading channels,” IEEE J. Selecr. Areas ^Commun., vol.

7, pp. 1347-1355, Dec. 1989.

[I91 R. Haeb and H . Meyer, “A systematic approach to carrier recovery and detection of digitally phase modulated signals on fading chan- nels,” IEEE Trans. Commun., vol. 37, no. 8, pp. 748-754, July 1989.

I ’

IRVINE A N D McLANE: S A D D RECEPTION FOR PSKiTCM MODULATION 1299

[20] F. Stremler, Introduction fo Communicarion Systems, Sec. Ed. Don Mills, Ont., Canada: Addison-Wesley, 1982.

(211 G . T . ]Wine. “Symbol-aided plus decision-directed phase estimation for shadowed mobile satellite fading channels,” M.Sc. Thesis, De’pt.

Elect. Eng.. Queen’s Univ., Kingston, Ont.. Sept. 1990.

and 1966 and with the Defence Research Board of Canada in 1964. He joined the Department of Electrical Engineering, Queen’s University, Kingston, Ont., in 1969 as an Assistant Professor, and since 1978 has held the rank of Professor. His research interests are in signal processing for digital communication systems. Usually, this involves computer-aided analysis, but lately he has been involved in experimental work involving microurocessors and LSI-based imolementation. He has served as a con- Garrick T. Irvine (S386-M’90) received {he

B.Sc. and M.Sc. degrees in electrical engineering from Queen’s University, Kingston, Ont., Can- ada, in 1988 and 1990, respectively.

He joined Telesat Canada after graduation in 1990 and is currently with the Communication Systems Engineering Division. At Telesat, he has worked on the design and testing of radio and tel- evision carrier systems for satellite communica- tions. In particular, he has gained experience in digital audio systems, digital video systems, barid- edge carrier design and tesiing, and interference analysis.

Mr. lrvine is a member of the IEEE Communications Society.

sultant to the Canadian Department of Communication, the Canadian In- stitute of Guided Ground Transport, Canadian Astronautics Ltd. of Ottawa, Spar Aerospace of Toronto, and AT&T Bell Laboratories and Technology Group of Los Angeles, CA. During 1984-1985, he was on leave at AT&T Bell Laboratories, Holmdel, NJ. He held a Ford Foundation Fellowship at the University of Pennsylvania and a National Research Council of Canada Scholarship at the University of Toronto.

He has been active in the IEEE Communications Society. He is a mem- ber of the Communication Theory Committee and served as its Represen- tative on the Technical Program Committee of the 1978 International Con- ference on Communications. He is a former Associate Editor for the IEEE Communications Magazine and former Editor of the IEEE TRANSACTIONS O N COMMUNICATIONS. In addition, he was a coeditor of an issue of the IEEE JOURNAL O N SELECTED AREAS I N COMMUNICATIONS. He is also a member of

Kappa Nu, . the

and

Association of Professional Engineers is listed in American Men and Women

of Ontario in Science.

and Eta Peter J. McLane (S’68-M’69-SM’80-F’88) was

bom in Vancouver, B.C., Canada, on July 6, 1941. He received the B.A.Sc. degree from i:he University of British Columbia, Vancouver, in 1965, the M.S.E.E. degree from the University of Pennsylvania, Philadelphia, in 1966, and ithe Ph.D. degree from the University of Toronto, To- ronto, Ont., Canada, in 1969.

From 1966 to 1967, he was a Junior Research Officer with the National Research Council, Ot- tawa, Ont. He held summer positions there in 19165