Performance of punctured convolutional codes in asynchronous CDMA communications under perfect phase-tracking conditions

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Abstract

In this paper, the performance of punctured convolutional codes of short constraint lengths is discussed. The punctured codes are used to provide error protection to a particular user in an asynchronous code division multiple access (A-CDMA) system. Perfect channel estimation is assumed at the receiver. A slow fading Rician or Rayleigh channel is assumed. Maximum likelihood decoding through a Viterbi algorithm is used to decode the received symbols. Soft decision decoding for perfect phase tracking of the received signal is considered. Analytical bounds, which are useful in predicting the performance of the A-CDMA system are derived and plotted for the cases of infinite and finite channel memory. The upper bounds with Viterbi decoding are derived and plotted for the various punctured codes considered. The simulated results are found to agree very well with their upper bounds and predicted results.

Introduction

Multiple access schemes allow several users to simultaneously share a finite amount of radio spectrum. The sharing of spectrum is required to achieve high capacity by simultaneously allocating the available bandwidth to multiple users. This work is done without severe degradation of the system [1]. In a mobile cellular communication system, the users are the mobile transmitters in any particular cell of the system and the receiver resides in the base station of the particular cell [2].

In direct sequence spread spectrum systems, each user is assigned a unique code sequence or signature sequence which allows the user to spread the information signal across the assigned frequency band. The signals from the various users are separated at the receiver by correlation of the received signal with the signature sequence of the desired user [2]. The code sequences are designed to have very low cross-correlation between them. The crosstalk inherent in the demodulation of the signals received from multiple transmitters is thus minimized [2]. This multiple access technique is commonly referred to as code division multiple access (CDMA).

In CDMA systems, each user is assigned a distinct signature sequence, which the user employs to modulate and spread the information-bearing signal. The signature sequences also allow the receiver to demodulate the transmitted messages of multiple users of the channel, who transmit simultaneously and, generally, asynchronously [2]. In asynchronous CDMA (A-CDMA) systems, there are exactly two consecutive symbols from each interferer which may overlap a desired symbol [2].

Convolutional codes are employed in A-CDMA systems for correction of bit errors which occur in the transmission of the signal of a particular user. In a cellular communication system, there is a need to employ high-rate convolutional codes. The rate of a mother code is increased by the puncturing process. Punctured convolutional codes are employed in A-CDMA systems to provide error protection in accordance with the level of fading and noise attributed to the channel under consideration. Although the rate of the punctured code is higher than that of the mother code, the decoder of the punctured code operates with the low complexity of the mother code, assuming that there is a depuncturing mechanism before the decoding process for the punctured codes. Decoding is performed with the Viterbi algorithm.

In this paper, punctured codes given in [3] are used. The mother codes used are rate-1/2 codes of memory lengths 2, 3, 4, and 5. The modulation used is Binary Phase Shift Keying (BPSK). The A-CDMA channel consists of one desired user and several undesired users. The power levels of the interferers are chosen in such a way that they are not negligible when compared to the power of the desired user. In such cases, the ensemble of the received signals of the interferers and thermal noise can be considered to approach a Gaussian distribution, according to the central limit theorem [1].

The fading in the A-CDMA channel is assumed to be Rician or Rayleigh. If the fading is sufficiently slow, the phase shift can be estimated from the received signal without any error, thus assuming perfect phase tracking. In this case, coherent detection of the received signal can be achieved [2]. The received signal is processed by passing it through a correlation receiver which is designed to “filter” the signal of the desired user [1].

Cheng and Holtzmann in [4] show that matched filter receivers are robust for delay mismatch. The delay estimation errors always exists because of multiuser interference and thermal noise. Caffery and Stuber in [5] introduce a non-filtering algorithm to filter the time-delay estimation errors.

Chen and Wei in [6] discuss the performance of rate-1/2 convolutional codes with QPSK modulation in Rician fading channels under perfect fading amplitude measurements. Modestino and Mui in [7] analyze the performance of low-rate convolutional codes with BPSK modulation in Rician fading channels. This paper discusses the performance of punctured convolutional codes (high-rate codes) in A-CDMA systems under perfect phase tracking conditions in slow fading and time-varying channels. A phase locked loop is used to provide steady-state phase error, thus ensuring perfect phase tracking.

Section 2 describes the block diagram of the uncoded A-CDMA system. Sections 3 Performance of the uncoded A-CDMA system, 4 Performance of the coded A-CDMA system discuss the performance of uncoded and coded A-CDMA systems respectively. A subsection in Section 4 is devoted to discuss the predicted performance of the coded A-CDMA system in slow fading channels. Finally, Section 5 presents the conclusions.

Section snippets

Channel description

Fig. 1 shows the block diagram of the uncoded A-CDMA system. Let there be U users (one desired and (U  1) undesired) in the A-CDMA system. Each user is subjected to multipath fading which is considered to be Rician or Rayleigh. Since we are concerned only with the desired user, we consider the effect of the transmitted signals from the undesired users on user 0. The contribution of interferers tends to a Gaussian distribution if their powers are not negligible to that of user 0. The contribution

Performance of the uncoded A-CDMA system

In this section, the performance of an uncoded A-CDMA system is discussed. The A-CDMA system studied is non-interference limited and is assumed to have perfect power control. For slow fading channels, both the fading amplitude and the phase error are assumed to be independent of time [7]. In the discussion of the uncoded A-CDMA system, we will be assuming slow fading channels. The uncoded bit error rate as a function of a constant phase error ϕ and the fading amplitude A is given byPb(ϕ,A)=Qcosϕ

Performance of the coded A-CDMA system

The block diagram of the coded A-CDMA system is shown in Fig. 6. A rate-1/2 mother code is used to provide error protection to the information symbols of the desired user. In a process called puncturing, the coded bits from the mother code are deleted according to a perforation pattern. The output bits of the punctured code are interleaved and modulated. Baseband modulation is employed at the transmitter. The outputs of the modulator are transmitted waveforms which are corrupted with multiuser

Conclusions

In this paper, we considered the performance of coded A-CDMA systems in slow fading and time-varying channels. An extensive analysis is made to derive the upper bounds of coded BERs and predicted BERs of punctured codes. The simulated results are found to be in close agreement with their upper bounds for slow fading and time-varying channels for the cases of infinite and finite channel memory. The performance of a punctured code in slow fading channel conditions outperforms that in a

Vidhyacharan Bhaskar received the B.Sc. degree in Mathematics from D.G. Vaishnav College, Chennai, India in 1992, M.E. degree in Electrical & Communication Engineering from the Indian Institute of Science, Bangalore in 1997, and the M.S.E. and Ph.D. degrees in Electrical Engineering from the University of Alabama in Huntsville in 2000 and 2002 respectively. During 2002–2003, he was a post-doc fellow with the Communications research group at the University of Toronto. Since September 2003, he is

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Vidhyacharan Bhaskar received the B.Sc. degree in Mathematics from D.G. Vaishnav College, Chennai, India in 1992, M.E. degree in Electrical & Communication Engineering from the Indian Institute of Science, Bangalore in 1997, and the M.S.E. and Ph.D. degrees in Electrical Engineering from the University of Alabama in Huntsville in 2000 and 2002 respectively. During 2002–2003, he was a post-doc fellow with the Communications research group at the University of Toronto. Since September 2003, he is working as an Associate Professor in the Département Génie des systémes d’information et de Télécommunication at the Université de Technologie de Troyes, France. His research interests are in wireless communications, signal processing, error control coding and queuing theory.

Laurie L. Joiner received the B.S., M.S., and Ph.D. degrees in Electrical Engineering from Clemson University, Clemson, SC in 1992, 1994, and 1998 respectively. She is an Assistant Professor at the University of Alabama in Huntsville where she has taught since 1998. Her research interests include error control coding and modulation and coding tradeoffs.

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Member of Departement Genie des Systemes d’Information et de Telecommunication (GSIT).

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