INTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS

Int. J. Satell. Commun., 16, 8793 (1998)

PERFORMANCE OF DS/CDMA SYSTEMS WITH

DIFFERENTIAL M-ARY ORTHOGONAL MODULATION
AND RS-CODING FOR LEO SATELLITE
COMMUNICATIONS
a. c. iossifides and f.-n. pavlidou*
Telecommunications Division, Department of Electrical and Computer Engineering, School of Engineering,
Aristotle University of Thessaloniki, PO Box 1641, 54006 Thessaloniki, Greece

SUMMARY
This paper presents a coded modulation scheme based on M-ary orthogonal modulation by means of
WalshHadamard (WH) sequences, suitable for low-earth-orbit (LEO) direct sequence/code division
multiple access (DS/CDMA) satellite communication systems. Based on the IS-95 scheme, we consider
ReedSolomon (RS)-coded M-ary orthogonal modulation with error or erasures decoding, which presents
good performance enhancement with low complexity. LEO satellite links are characterized by large
Doppler frequency shifts caused by the difference in velocity between the satellite and the earth mobile
terminal, which make conventional non-coherent detection ineffective. In order to overcome the phase
shift variations during the symbol period, which result in orthogonality loss of the WH sequences, we
applied a differential encoding process to the spreading sequences or the WH chips prior to transmission.
A special diversity process suitable for the environment under consideration is also applied. Simulation
results show that the proposed diversity/coding/modulation scheme attains very good performance at
low transmitter/receiver complexity. 1998 John Wiley & Sons, Ltd.
key words:
modulation

differential encoding; DS/CDMA; LEO satellite communications; RS codes; M-ary orthogonal

1. INTRODUCTION
M-ary orthogonal modulation by means of WH
sequences is a well-established scheme for
DS/CDMA applications. It has been investigated in
several configurations for terrestrial cellular mobile,
either indoor or outdoor, and LEO satellite
communications.110
The
increased
spectral
efficiency that M-ary orthogonal modulation offers,
compared with conventional DS/CDMA systems,
has placed it among the most promising schemes
for future wireless communications. In conjunction
with proper modulation, effective channel coding is
very important for CDMA systems in order to achieve higher bandwidth efficiency and user capacity.
Lately, RS-coded M-ary orthogonal modulation with
error decoding has been proposed and found to
present good performance with low complexity
(bounded distance decoding).1,2 In this paper, erasure decoding is also considered resulting in further
performance enhancement without significant complexity increase, owing to a simple erasure criterion.
The special character of the LMS (land mobile
satellite) channel originates crucial problems in the

*Correspondence to: F. N. Pavildou, Telecommunications

Division, Department of Electrical and Computer Engineering,
School of Engineering, Aristotle University of Thessaloniki, PO.
Box 1641, 54006 Thessaloniki, Greece.
Email: niovivergina.eng.auth.gr

CCC 07372884/98/0200877$17.50
1998 John Wiley & Sons, Ltd.

application of M-ary orthogonal modulation. The

most important one is the large performance degradation that M-ary orthogonal modulation faces in
high-Doppler-shift environments such as the LMS
channel when envelope detection is applied. This is
due to the phase shift of the transmitted waveforms, which destroys orthogonality at the
receiver.10,11 Thus envelope detection without any
special device to remove the Doppler shift (which
takes values of the order of the symbol rate or even
higher) is applicable only for low Doppler shifts
(lower than 0.3 times the symbol rate). Instead of
using such a device and in order to keep the complexity and cost as low as possible, we have recently
applied two techniques based on chip-by-chip differential encoding. Chip-by-chip differential encoding
after spreading was first proposed in Reference 12.
In this paper the differential process is applied either
to the resulting wave-form after coding and spreading (DDS M-ary)13 or at the WH chip level (DMary).14 This allows effective non-coherent detection
when the Doppler shift is lower than the chip rate.
Thus the system performs almost independently of
the Doppler shift, but this is achieved at the expense
of the signal-to-noise-plus-interference ratio (SNIR)
increase that is required to attain the desired bit
error probability (BEP).
In high-Doppler-shift environments where the path
amplitude may vary during the symbol period, the
selection or combination of two or more diversity
Received December 1997
Revised 27 January 1998
Accepted 18 March 1998

a. c. iossifides and f.-n. pavlidou

88

branches must be properly designed. In order to

overcome the high amplitude variability, we propose
a diversity scheme based on the maximum output
selection scheme, where the diversity branches are
scanned at a higher rate than the symbol rate. In
this way the averaging process of the amplitude
that is implicit in symbol-by-symbol discrimination
is avoided.
The performance prediction of the proposed systems is done via simulation. This was necessary
because theoretical evaluation is rather sophisticated
when the special characteristics of the LMS channel
are taken into account. Channel simulation was
based on a deterministic model, recently proposed
in Reference 15, properly adapted to include the
LMS channel characteristics.
2. SYSTEM MODEL
It is assumed that the system under consideration
operates in a single spot beam of a satellite. Interference from other spot beams or users communicating with other satellites is ignored for simplicity.
Power control is applied and is considered to be
perfect in the sense of completely removing the
large-scale slow fading.1618
2.1. Transmitter
The transmitter of the proposed RS-coded
DS/CDMA system is shown in Figure 1. Figure 1(a)
illustrates the conventional scheme without differential encoding, Figure 1(b) the DDS M-ary scheme
with differential encoding applied at the spreading
sequence (SS) chips and Figure 1(c) the DM-ary
scheme with differential encoding applied at the
WH chips. In all cases, b source information bits
of rate rb are grouped and mapped to one of the
M = 2b information symbols. The information symbols of rate rs = rb /log2M symbols per second enter
an (n,k) RS encoder operating in GF(M), with n
and k the block length and the number of information symbols each block contains respectively.
The output coded symbols of rate rsc = rs /rc, where
rc = k/n, are interleaved and then mapped to one of
the M WH orthogonal sequences.
When no differential encoding is applied, the WH
chips are oversampled by a factor L = N/M (integer)
and then multiplied with an N-length random spreading sequence. The resulting samples modulate a Tcenergy chip wave-form g(t). The equivalent lowpass
transmitted signal of the kth user is given by

N1

u (t) =
(k)
m

c g (t nTc )
(k)
n

(1)

n=0

Figure 1. Transmitter configurations of (a) conventional, (b) DDS

M-ary and (c) DM-ary schemes

where h(k)
i,m is the ith WH chip amplitude of the mth
is the nth
WH sequence of the kth user and a(k)
n
chip amplitude of the spreading sequence of the
kth user.
For the DM-ary scheme14 the WH chips are differentially encoded and then oversampled and spread,
i.e.
(k)
(k)
c(k)
n = n/Lan

(k)
where n/L
are the oversampled differentially encoded WH chips of the kth user with period TH
generated by
(k)
(k)
= (k)
i
i1hi,m

with
(k)
cn(k) = h(k)
n/L,man

(2)

(3)

(4)

When differential encoding is applied at the

performance of DS/CDMA systems for leo satellites

spreading sequence chip level (DDS M-ary),13 the
samples
(k)
n(k) = hn/L,m
an(k)

(5)

after oversampling and spreading are differentially

encoded at the SS chip rate and generate the
binary symbols
(k)
cn(k) = c(k)
n1n

(6)

In all three cases the total bandwidth expansion

factor introduced by the modulator and the encoder is

W
N
=
rb rclog2 M

(7)

where W is the single-sided occupied spectrum.

Assuming a constant bandwidth expansion factor,
several configurations may be derived by choosing
a symbol set size M and then adjusting rc and N
so that N/M is an integer. Extended or shortened
RS codes may arise,1,2 some of which are given in
Table 1 for = 128.
2.2. Channel Model
The channel model used is identical to the one
used in References 16 and 18, coming out with a
modification of the model described in Reference
19. The received amplitude may follow a Rice or a
Rayleigh distribution depending on the existence or
not of a line-of-sight (LOS) path. The lognormal
process describing the large-scale variations of the
local mean power in the non-line-of-sight (NLOS)
case was not included because of the perfect slow
power control procedure assumed that eliminates it.
Thus the mixed envelope probability distribution
function is given by

x
x2
f(x) = B 2exp 2

B=

Db
Dg + Db

fd C fd /rsc
is used for the presented results. The Rice process
was developed similarly by adding the LOS amplitude to the real part of the complex random process
mentioned above. In either case (Rice or Rayleigh)
the fading is assumed to be non-selective. Figure 2
presents a block diagram of the channel model.
2.3. Receiver Model
The receivers structure is shown in Figure 3.
They consist of two major parts: the detector and
the decoder. The conventional detector without differential encoding (Figure 3(a)) consists of a filter
matched to the chip wave-form, followed by a sampling device. Perfect clock recovery is assumed so

x
xA
x2 + A2
+ (1 B) 2exp
I0 2

22

Figure 2. Channel model

Table I. Some possible system configurations with = 128

M
(n,k)
N

16
(16,4)
128

16
(16,8)
256

(9)

where Dg and Db are the mean durations of the

good and the bad state of the channel respectively.
The specific values of Dg and Db used in the
simulations were 9 m and 70 m respectively and
they were selected from measurement results19 corresponding to a city environment with an elevation
angle of 13. In the simulations the two states were
driven by a two-state Markov chain. The Rayleigh
process was developed using a deterministic model
(described in Reference 15) that generates a complex random process whose components (real and
imaginary) are zero-mean independent Gaussian processes with variance 2 and autocorrelation function
r(t) = 2J0(2fdt), where J0() is the zeroth-order
Bessel function and fd is the maximum Doppler
frequency. For compactness and generalization the
normalized Doppler frequency shift

(8)

where 22 is the mean power of the diffuse component and A is the amplitude of the specular component. The Rice factor is R = A2 /22 and was taken
equal to 7 dB for the simulation. B is the time-share
shadowing parameter determining the state of the
channel, namely good for the LOS and bad for
the NLOS case, given by

89

32
32
64
64
(30,12) (30,24) (63,21) (63,42)
256
512
256
512

90

a. c. iossifides and f.-n. pavlidou

Figure 3. Detector configurations of (a) conventional, (b) DDS

M-ary and (c) DM-ary schemes

that interchip interference is eliminated. The complex-valued samples rn are multiplied with the
locally generated spreading sequence and then pass
through a bank of envelope correlators corresponding to the M orthogonal WH sequences. The M
outputs zm,m = 1, $, M, are the final decision variables. Figure 3(b) illustrates the DDS M-ary detector. The complex-valued samples rn are differentially
decoded and then despreading and correlation are
applied. For the DM-ary scheme (Figure 3(c)), differential decoding takes place after summation over
the L SS chips that produce the estimated differentially encoded WH chips i. The differentially
decoded WH chips, i.e. hi,m = i*
i1, are used as
input to the correlators.
In order to deal with high Doppler frequency shift
and remove its effects, the differential encoding
procedure should be performed in a time basis that
assures stability of the channel phase. This fact led12
to the use of SS chip-by-chip differential encoding.
As the spreading gain gets higher, the variability of

the channel during the SS chip duration is reduced.

The drawback is that splitting the differential
encoding/decoding process among more chips during the symbol interval results in higher non-coherent combining loss. This was evident in Reference
12. In order to have successful differential decoding
and remove the channel phase, we need a differential
encoding rate much higher than the Doppler frequency shift. The WH chip rate is almost always
lower than the SS chip rate and for the channel
under consideration is higher than the Doppler frequency shift. Thus, by moving the differential encoding process from the SS to the WH chips, the
differential combining loss is lowered, while effective channel phase removal is secured when large
M-ary orthogonal sets are used (e.g. M = 64). Therefore the DM-ary scheme is expected to perform
better than the DDS M-ary scheme for the Doppler
frequency shifts under consideration.
After deinterleaving, the M decision variables are
used for the decoding process. When only errors
decoding is applied, the maximum decision variable
is considered to correspond to the correct symbol,
so mapping to this symbol over GF(M) is applied.
(nk)
errors.
The decoder is capable of correcting
2
When both error and erasure decoding are applied,
an erasure criterion should be considered. A commonly used criterion decides that the detected symbol is an erasure if the mean, during a certain
period, channel amplitude is below a certain value.20
This technique can be applied only if an amplitude
estimator is used at the receiver. We used a simpler,
yet satisfying, rule for the erasure determination
without channel state information, as proposed in
References 13 and 14. The two greater decision
variables obtained by the detector, i.e. zm and zp,
with zm zp, are subtracted and the result is normalized with respect to the maximum, namely zm.
When the result is lower than a certain value, the
symbol is considered to be an erasure. Thus, if
(zm zp )/zm , where is a preset value, an erasure is flagged. The decoder is capable of correcting
s errors and erasures provided that 2s + n k.
2.4. Diversity Considerations
Diversity is a standard technique for enhancing
the performance of the system. The conventional
system, i.e. without differential encoding, has
presented high performance gain with the use of
maximum output selection diversity (MOSD)21 for
terrestrial communications.1,2 Moreover, MOSD is a
very attractive scheme because no channel amplitude
or SNIR information is necessary, thus keeping the
receiver complexity low.
The application of diversity to the system under
consideration must be done carefully to secure performance enhancement. For low Doppler frequency
shift the channel amplitude is almost constant
throughout the symbol duration, i.e. the Hadamard

performance of DS/CDMA systems for leo satellites

sequence. Thus the selection of the diversity branch
to account for demodulation may take place at the
symbol level, i.e. between the final decision variables zm of each diversity branch. On the other hand,
high Doppler frequency shift leads to significant
variability of the channel amplitude in the symbol
duration (Figure 4). Selecting the maximum variable
zm between diversity branches is unreliable since the
channel peaks and troughs are averaged during the
calculation of zm. Therefore diversity branch scanning should take place at time intervals shorter
than the symbol duration to yield performance gain.
Regarding LEO satellite communications, where
Doppler shifts usually take values beyond the transmitted symbol rate, diversity at the chip level will
be more effective than conventional diversity at the
symbol level.
3. RESULTS AND DISCUSSION
Among the various configurations presented in
Table 1, the M = 64, N = 512, RS (63,42) scheme
was selected for comparing conventional, DM-ary
and DDS M-ary signalling schemes. Two reasons
led to this selection. The selected coded/modulation
configuration was found to present the best performance for terrestrial applications1,2 including both
Rayleigh and Rice fading environments. Insofar as
the LEO satellite model under consideration refers
to the same fading processes, it is expected that the
performance of the selected configuration will
remain the best among the other ones. Compatibility
with the IS-95 configuration for voice communications, which uses an M = 64 WH signal set, was
the second reason. Towards this fact, the SS chip
rate under consideration is 1.2288 kchips/s, while
the WH chip rate is 153.6 kchips/s. This choice
validates the non-selective nature of the channel,
which presents a coherence bandwidth of several
MHz.
In order to simplify the simulation process and
focus on the effect of the channel characteristics,
the multi-user interference inherent in DS/CDMA
systems was assumed to act as an additional source
of additive Gaussian noise. This assumption is valid
for long spreading sequences, such as the ones
under consideration, and a significant number of
simultaneous users. Therefore the BEP results to be
presented are given as a function of the SNIR.
Figures 58 present simulation results, in terms of
BEP versus SNIR for the two differentially encoded
proposed systems and the conventional system,

Figure 4. Normalized received signal amplitude with fd = 1.0

91

under a wide range of Doppler frequency shifts.

The Doppler shifts simulated were selected in a
wide range of the transmission symbol rate, i.e.
fd C fd /rsc = 0.025, 0.25, 0.5 and 1. Higher Doppler
shifts may also appear in the LEO satellite channel.
However, the results to be presented show that in
such a case and provided that the Doppler shift
remains well below the chip rate, the performance
will not change significantly. On the other hand,
this Doppler shift range was selected in order to
make clear the necessity of a modulation/coding
scheme resistant to high Doppler frequency shifts.
In all cases a block interleaver operating at the
symbol level with length 63 (equal to the coded
word length) and depth 40 was used.
Figure 5 presents BEP results of the three schemes
under consideration, i.e. the conventional and chipby-chip differentially encoded systems, over the
LMS channel with normalized Doppler shift
fd = 0.025. The conventional system outperforms
the differentially encoded systems in all three cases
of uncoded and coded with error or erasure decoding. The DM-ary configuration clearly performs better than the DDS M-ary one. A difference of the
order of 34 dB is evident between the two differentially encoded schemes. Erasure decoding offers an
extra gain of about 1 and 2 dB for the conventional
and differentially encoded systems respectively at a
BEP of 103.
Figure 6 shows simulation results for a normalized
Doppler shift of 0.25. The conventional systems
performance is degraded, but it still remains better
than that of the differentially encoded schemes for
low SNIR values. On the other hand, the DM-ary
and DDS M-ary systems performance is getting
better. This is due in part to the fact that the channel

Figure 5. BEP results of conventional, DDS M-ary and DM-ary

schemes for fd = 0.025

92

a. c. iossifides and f.-n. pavlidou

Figure 6. BEP results of conventional, DDS M-ary and DM-ary

schemes for fd = 0.25

Figure 8. BEP results of conventional, DDS M-ary and DM-ary

schemes for fd = 1

amplitude is averaged, as previously noted, for

higher Doppler shifts, thus reducing the effect of
deep fades. Additionally, higher Doppler shifts come
with faster channel amplitude fluctuations and thus
randomize detection errors. This results in a better
decoder performance under a fixed interleaving
depth.
Figures 7 and 8 present the simulation results for
fd = 0.5 and 1 respectively. The necessity of reducing the Doppler effect, either with a special device
or with differential encoding, is clear. The conventional systems performance is degraded rapidly with
Doppler increase and becomes unacceptable for
fd = 1. This is true for both coded and uncoded
cases. Even with erasure decoding, the conventional

systems performance is far worse than that of the

error decoding case of the differentially encoded
systems for BEPs of interest at fd = 0.5. On the
other hand, the 3 dB difference between the DMary and DDS M-ary systems remains almost
unchanged. This is expected to be continued for
higher Doppler shifts as well. The performance of
the differentially encoded schemes will improve until
the Doppler shift becomes so large that the phase
varies significantly during the chip interval. This will
be evident for the DM-ary scheme first of course.
Figure 9 presents simulation results of the DMary scheme with error and erasure decoding for
several normalized Doppler frequency shift values,
with MOSD of second order or without diversity.

Figure 7. BEP results of conventional, DDS M-ary and DM-ary

schemes for fd = 0.5

Figure 9. BEP results of DM-ary scheme with and without diversity

performance of DS/CDMA systems for leo satellites

Obviously, diversity enhances system performance
in all Doppler frequency shift cases. It should be
mentioned that diversity is more advantageous for
lower Doppler spread values. This is due to the fact
that with WH chip-based diversity the averaging
process implicit in the calculation of the final
decision variables is significantly removed, as more
than one channel branch is selected during the symbol duration. Therefore the system performs almost
identically for all Doppler frequency shifts. It must
be mentioned though that conventional MOSD with
a symbol time basis decision will yield better results
for low Doppler shifts. Square law combining at the
WH chip rate was also considered (omitted here for
the sake of space) and found to present slightly
worse performance than MOSD.

3.

4.

5.
6.

7.

8.

4. CONCLUSIONS
This work proposes a differential encoding technique
for DS/CDMA with M-ary orthogonal signalling
suitable for high-Doppler-spread environments such
as the LEO mobile satellite communication channel.
The differential encoding procedure is applied at the
WH chip level (DM-ary scheme) or at the spreading
sequence chip level (DDS M-ary scheme). At high
Doppler shifts the performance of the differentially
encoded schemes improves, while the conventional
systems performance is degraded rapidly. A 34 dB
gain of the DM-ary scheme over the DDS M-ary
scheme was evidenced in all cases. A diversity
technique based on the maximum output diversity
selection scheme and suitable for high-Doppler-shift
environments has also been proposed. The selection
between diversity branches is performed in a WH
chip time basis rather than in a symbol time basis,
leading to performance independent of the Doppler
shift. Moreover, RS encoding with erasure decoding
offers a 2 dB gain at least in all examined cases
without increasing receiver complexity, owing to a
simple erasure criterion presented. The channel
model used for the simulations corresponds to a
hostile city environment and further results should
be obtained for various channel models in order to
establish the effectiveness of the proposed scheme.
REFERENCES
1. A. C. Iossifides and F.-N. Pavlidou, Performance evaluation
of RS-coded DS/CDMA systems with orthogonal signaling
for microcellular radio communications, Proc. PIMRC 97,
Helsinki, September 1997, pp. 693697.
2. A. C. Iossifides and F.-N. Pavlidou, Capacity and throughput

9.

10.
11.
12.

13.
14.

15.
16.

17.
18.
19.
20.
21.

93

of RS-coded DS/CDMA microcellular systems with M-ary

orthogonal signaling, Wireless Personal Commun., in press.
K. Pahlavan and M. Chase, Spread-spectrum multiple access
performance of orthogonal codes for indoor radio communications, IEEE Trans. Commun., COM-38(5), 574577
(1990).
M. Chase and K. Pahalavan, Performance of DS-CDMA
over measured indoor radio channels using random orthogonal codes, IEEE Trans. Vehic. Technol., VT-42(4), 617
621 (1993).
A. J. Viterbi, et al. Performance of power-controlled wideband terrestrial digital communication, IEEE Trans. Commun.,
COM-41(4), 559569 (1993).
L. F. Chang, et al. Comparison of two convolutional orthogonal coding techniques for CDMA radio communications
systems, IEEE Trans. Commun. COM-43(6), 20282037
(1995).
A. Jalali and P. Melemenstein, Effects of diversity, power
control, and bandwidth on the capacity of microcellular
CDMA systems, IEEE J Select. Areas Commun., SAC12(5), 952961 (1994).
M.-H. Fong, et al.,Concatenated orthogonal/PN spreading
sequences and their application to cellular DS-CDMA systems with integrated traffic, IEEE J. Select Areas Commun.,
SAC-14(3), 547558 (1996).
R. D. Gaudenzi, et al., A performance comparison of orthogonal code-division multiple access techniques for mobile
satellite communications, IEEE J. Select. Areas Commun,
SAC-13(2), 325332 (1995).
A. L. Kachelmyer and K. W. Forsythe, M-ary orthogonal
signaling in the presence of Doppler, IEEE Trans. Commun.,
COM-41(8), 11921200 (1993).
T. Wada, et al., A new M-ary/SSMA scheme applicable in
LEO satellite communications systems, Proc. GLOBECOM
96, London, November 1996, pp. 384389.
F. Giannetti, et al., Chip-level differential encoding/detection
of spread-spectrum signals for CDMA radio transmission
over fading channels, IEEE Trans. Commun., COM-45(4),
456463 (1997).
A. C. Iossifides and F.-N. Pavlidou, Performance evaluation
of RS-coded DS/CDMA with orthogonal signaling in land
mobile satellite systems, COST Action 252, TD(97)8, 1997.
A. C. Iossifides and F.-N. Pvalidou, Differentially encoded
M-ary orthogonal DS/CDMA with RS coding and diversity
for LEO satellite communications, COST Action 252,
TD(97)17, 1997.
M. A. Patzold, et al., A deterministic model for a shadowed
Rayleigh land mobile radio channel, Proc. PIMRC94, The
Hague, 1994, pp. 12021210.
B. R. Vojcic, et al., Performance of DS-CDMA with imperfect power control operating over a low earth orbiting satellite
link, IEEE J. Select. Areas Commun., SAC-12(4), 560
567 (1994).
B. R. Vojcic, et al., Total capacity in a shared CDMA
LEOS environment, IEEE J. Select. Areas Commun., SAC13(2), 232244 (1995).
A. M. Monk and L. B. Milstein, Open-loop power control
error in a land mobile satellite system, IEEE J. Select. Areas
Commun., SAC-13(2), 205213 (1995).
E. Lutz, et al., The land mobile satellite communication
channelrecording, statistics, and channel model, COST
Action 227, TD(93)045, 1993.
J. Hagenauer and E. Lutz, Forward error correction coding
for fading compensation in mobile satellite channels, IEEE
J. Select. Areas Commun., SAC-5(2), 215225 (1987).
G.-T. Chyi, et al., On the symbol error probability of
maximum-selection diversity reception schemes over a Rayleigh fading channel, IEEE Trans. Commun., COM-37(1),
7983 (1989).