ANALYSIS AND SIMULATION OF DS-CDMA MOBILE SYSTEM IN NON- LINEAR, FREQUENCY SELECTIVE SLOW FADING CHANNEL

Saverio Cacopardi, Fabrizio Frescura, Gianluca Reali

Istituto di Elettronica, Facolta di Ingegneria, Universita di Perugia 06125 Perugia - Italy

Absthzct; This paper presents an analysis of the performances of a -tal mobile radio link based on DS-CDMA technique and the RAKE receiver. Tbe adopted signature sequences are complex and characterized by different correlation properties, that lead to different performances in terms of bit error rate and spectral efficiency. Moreover, a preliminary analysis of the performances under non-linear channel behaviour and different modulation schemes is provided.

I. INTRODUCTION

The signal received by a mobile user can be modelled as some distinct components associated to different propagation paths with time-variant path weights and propagation delay. Such channel behaviour causes a severe degradation in terms of Bit Error Rate @ER) of the digital mobile communication systems unless anti- multipath techniques are used. Thanks to the feature of the spread spectrum techniques

of both counteracting the effects of the multipath propagation and allowing a multi-user sharing of the spectral resource, this paper considers the performances of a Direct Sequence - Code Division Multiple Access (DS- CDMA) systems, designed for digital mobile radio communications, using a RAKE receiver.

The CDMA technique is based on 4-phase signature sequences; in particular, the use of the 4-phase sequences with near-optimum correlation properties allows a good exploitation of the bandwidth reserved to the service [1][2]. The adoption of such sequences induces an increasing up to 50% of the number of the simultaneous users with respect to the case in which other sequences obtained by binary ones are adopted.

The paper is organized as it follows. In section I1 there is a report of the transmission model and in section I11 a brief description of the spreading sequences. In section IV, the asymptotic performances and a preliminary investigation in non-linear environment by computer simulation are presented. Finally, the section V contains the conclusions.

11. TRANSMISSION MODEL

A block scheme of the transmission chain is reported in Fig. 1, where the complex envelope representation has been used.

The some stream is supposed to be a sequence of i.i.d. binary symbols b,? (by) E (0,l) V i). It is e n d e d by using a convolutional coder characterized by a coding rate of 1/2 and a constraint length IU=7. The coded symbols are mapped according to the QPSK or DQPSK signal spaces, and then are sent to a block-interleavex with KL+I rows and 20 columns, in order to randomize the errors occurring in bursts. The input to the spreader can be written as

where ~,E{i~2/2*j~z/2). by i the imaginary unit, and p , ( t ) is a rectangular pulse of duration Tb.

The modulated symbols are then spread by the kth signature sequence:

being M the signature sequence period, TC the chip duration and $)E {I ,-I J,-j}: so, if every symbol is spread by one period of the spmding sequence, the complex envelope of the transmitted signal can be written as

being P the transmitted power that, for the present estimation, can be considered representative of the average controlled power and N the number of users. The overall transmitted signal, composed by the signals

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transmitted by all the users spread by Mferent quasi- orthogonal codes, represents the input to the amplifier:

N

ei (t ) = n, ( t ) + qpdp (t - T~ ) ej+p = p( t )eac) (4) p=l

being 2, the relative time delays modulo Tb , $p the relative phase shifts modulo 2x and q the signal attenuation.

The amplifier is supposed to be affected by a non-linear behaviour described by the AM/AM characteristic A(.) and the W M characteristic P(J, thus the output of the amplifier can be written:

e , ( t ) = A(p(t))e(fks(P().

The amplifier can be thought to be representative of a satellite transponder or a gate-way central station for a cellular terrestrial coverage.

The transmission channel is supposed to be affected by multipath fading, thus the received signal can be written:

where L = LT, / T,] + 1 is the diversity order, T, is the total multipath spread 131 and g n ( t ) indicates the nth channel tap weight.

The multipath effect is partially counteracted by the use of a RAKE receiver, whose architecture is reported in Fig. 2. Such receiver is designed to identify the desired message, by despreading the overall signal which is done by using the conjugate of the spreading sequence, and to collect the signal power from all the channel paths. The RAKE receiver output is sent to the deinterleaver and finally to a soft Viterbi decoder that carries out a maximum likelihood estimation of the transmitted bit.

III. SPREADING SEQUENCES

A 4-phase sequence can be obtained by using two binary sequences according to the following rule [4]:

(7) c, =-(l+j)qE 1 +-(l-j)qF, 1 2 2

where c, is a 4-phase symbol and 4; and 4 2 are binary symbols that, for this application, belong to Gold sequences. The Gold sequences have been constructed by using the preferred pair m-sequences generated by the polynomials:

4(x)=x7 + x 3 + 1 (8) 4(x )=x7 + x 6 + x 5 + x 3 + x 2 + x + l . (9)

Recently, two families of 4-phase sequences with near- optimum correlation properties have been introduced [1][2]; in the present application the so called family A has been selected.

Such family is characterized by the following properties:

it is asymptotically optimal with respect to the Welch lower bound on the maximum nontrivial correlation parameter C,, , defined by:

where

M-1

is the complex periodic correlation of the spreading signature sequences; its correlation performances exceed that of any other 4- phase family constructed by binary sequences of the same size: the sequences are easily obtained by means of modulo- 4 shift registers whose generating polynomials, reported in [2], are related to the linear recurrence

(12) s ( n ) + u,-,s(n - l)+. ..+ aos(n - r ) = 0 where a i {0,1,2,3} V i; s(n) is just the nth symbol of a sequence of the elements belonging to a finite field of order 4. For brevitys sake, the initial value of the registers and the selected polynomials for the simulation trials are not reported, but they can be found in [5]: the family size associated to every shift register is M + 2 , where M is the sequences period: a selective access to the network is thereby allowed to a large number of users.

IV. SYSTEM PERFORMANCES

ASYMPTOTIC PERFORMANCES This section is devoted to the examination of the

performances of the system under ideal conditions. The following hypotheses have been considered: -the channel tap weight estimation is noiseless: -the power amplifiers behaviour is linear: -the binary symbols are shaped like rectangular pulses; no smoothed transitions have been considered:

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-a perfect shaping of the transmitting (TX) and receiving (RX) filters has been assumed in order to eliminate the inter-symbol interference: -a perfect acquisition and tracking of the spreading sequence has been assumed.

Under the stated hypotheses, a comparison between two cases has been carried out, relative respectively to the adoption of near-optimal4-phase sequences and complex sequences generated by means of two binary Gold sequences. The comparison is based on the Bit Error Rate (BER) and the spectral efficiency whose values have been obtained by means of a simulation pgram in FORTRAN environment.

The Fig. 3 reports the BER versus the coefficient y, defined as [ 31 :

Y = L%{l&lZ} (13) No

Fig. 3 shows that the use of the near-optimal sequences allows an increase of about 50% of the simultaneous users with respect to the case of the Gold sequences adoption, or a marked decreasing of the BER when an equal number of users is considered.

b. SYSTEM PERFORMANCES IN A NON-LINEAR ENVIRONMENT

In this section some realistic assumptions have been made. In particular, the simulation trials have included the non-linear behaviour of the amplifier shown in Fig.1. Moreover, smoothed transitions between the logical binary levels have been included. Timedomain simulations have been carried out by using the TOPSIM simulator and the following simulation conditions have been considered: -spreading factor = 127: -number of samples per chip = 10; -roll-off factor of the TX and RX filters = 0.7; -the TX and RX filters designed by considering a constant spectral modelling of the transmitted symbols and an equal distribution of the raised cosine shaping in the transmitting and receiving sections [6]. -the sampling instants have been evaluated by considering the maximum opening of the eye pattern criterion: -the non-linear amplifier modelled like a satellite TWTA, having the characteristics included in the TOPSIM simulator package.

The principal aim of this section is to evaluate the degradation of the performances of the system when the power amplifier is pushed to saturation. Moreover, two different modulation techniques, QPSK and DQPSK, have been considered.

In order to alleviate the calculations amount and the simulation time that during the time-domain simulations

of spread spectrum systems could be extremely long, only 10 simultaneous users have been considered; nevertheless, the envelope variations are sufficient to appreciate the BER variations.

In Fig.4, the BER versus y is shown. Both QPSK and DQPSK have been considered for two values of the amplifier Input Back Off (IBO).

Note that only when the amplifier works in the linear region it is possible to distinguish the power associated to the various users. In fact, in saturation conditions, spectral intermodulation components are generated and it is hard to separate the useful received power from the nuisance intermodulation power. The figure must be read first by considering the system performances in an almost linear case (IBO = 6 dB), and then by increasing the transmitted power by 6 dB such as to push the amplifier to saturation. In other words, the values of y are related to the curves obtained by using an IBO equal to 6 dB, and the gap from the curve relative to an IBO equal to 0 dB must be regarded as a degradation of the performances when the power amplifier is pushed to saturation.

V. CONCLUSIONS

This paper shows an evaluation of the performances of the RAKE receiver based on 4-phase signature sequences. A first analysis has been carried out in ideal working conditions and good performances have been found in terms of spectral efficiency, induced by the adoption of the nearxiptimal4-phase sequences. Then, an analysis under realistic assumptions has been carried out; in particular a non-linear behaviour of the channel amplifier has been assumed. The time-domain simulation trials allow a comparison of the performance achievable by using the coherent or differential QPSK modulation schemes and show how the non-linear behaviour has a greater impact on the performance of differential QPSK than it does in the coherent case.

VI. REFERENCES

[l] P. Sole, "A Quatemary Cyclic Code and a Family of Quadriphase Sequences with Low Correlation Properties". Lecture Notes in Computer Science 388. Berlin: Springer, 193-201 (1989)

[2] S. Boztas, R. -mons, and P.V. Kumar, "4-phase sequences with near-optimum correlation properties", IEEE Transactions on Information Theory, vol. 38 , pp. 1101-1 113, May 1992.

[3] J. G. Proakis, "Digital Communications", McGraw- Hill, 1989.

[4] S. M. Krone and D. V. Sarwate, "Quadriphase Sequences for Spread-Spectrum Multiple-Access

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Communication", IEEE Transactions on Information to the 1994 International Zurich Seminar on Digital Theory, vol. IT-30, pp. 520-529, May 1984. Communications.

[5] S. Cacopardi, F. Frescura, and G. Reali, "Increased [6] M.C. Jerruchim, P. Balaban and K.S. Shanmugan, Capacity of DS-CDMA Mobile Systems in "Simulation of Communication Systems", Plenum Frequency-Selective Slow Fading Channel", accepted Press, 1992.

+ Binary Source Convolutional

KL=7, r a t e d 2

Symbol

Interleaver Encoder + Mapper

Fading Channel 4

2

Non-Linear 4 Amplifier * Otherusem+ e ThermalNoise

Fading Channel 4

Fig. 1. Baseband equivalent transmission model (double lines indicate complex quantities)

2

Non-Linear 4 Amplifier * Otherusem+ e ThermalNoise

U:) 4= adder and integrator

Fig. 2. Block scheme of the complex RAKE receiver (the double lines indicate complex quantities)

a

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Rake Symbol + SoftViterbi Deinterleaver Estimated Ets Receiver

1 .WE42

1 .WE43

BER

1 .WE44

1.00E-05

BER

1.00E-01

.OOE42

.OOE-03

.00E-04

.00E-05

1 1 1 1 1

10 15 20 25 30 35 40 7 WI

Fig. 3. BER versus y for 4-phase N.O. and 4-phase Gold sequences for diversity order L=2; the number in parenthesis indicate the users number.

1.00E-06

1.00E-07

1.00E-08

1.00E-09 10 11 12 13 14 15 16 17 8 9

y Wl

Fig.4. BER versus y for 4-phase N.0.sequence.s for L=2, N=10, QPSK and DQPSK modulation schemes and different values of the IBO.

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