Adaptive rate coding using convolutional codes for asynchronous code division multiple access communications over slowly fading channels

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Abstract

This paper presents a method of code rate adaptation using punctured convolutional codes for direct sequence spread spectrum communication systems over slowly fading channels. A blind channel estimation technique is used to estimate the nature of the multi-user channel at the detector (before the decoder). The path gains obtained from the channel estimation technique are used to adapt the code rates. Punctured codes derived from a specific rate 1/2 (M = 4) mother code are used to provide error protection corresponding to the actual channel state. The upper and lower bounds on the bit error probability and the upper bound on the error event probability are derived for hard-decision and soft-decision decoding over Rayleigh and Rician fading channels. The throughput gains obtained using the adaptive scheme and the performances of the punctured codes are studied.

Introduction

In a direct-sequence spread-spectrum system, the bandwidth of a signal is expanded several orders of magnitude by multiplying the data sequence by a higher rate chipping sequence. In a code division multiple access (CDMA) system, each user has a unique pseudo-random chipping sequence that allows multiple users to share the system bandwidth, thus increasing system capacity. The pseudo-random sequences are designed to have low or zero cross-correlation so that the multi-user interference is negligible if the transmitted signals are synchronized (S-CDMA system). However, in an asynchronous CDMA (A-CDMA) system, the transmitted signals are not synchronized and two consecutive symbols from each interferer may overlap a desired symbol, resulting in multi-user interference (MUI).

In order to combat MUI and to protect the data transmitted over a noisy and fading channel, an error correcting code is applied. An error correcting code improves data reliability at the cost of extra parity bits which require additional bandwidth. To provide an acceptable level of performance while minimizing bandwidth usage, the code rate can be adapted to the changing channel conditions [1].

In an adaptive rate coding system, the highest rate code that gives the desired probability of bit error is used. When channel conditions are good, a low number of redundant bits are sent, thus increasing throughput. Deteriorating channel conditions are detected by the receiver, which notifies the transmitter to use a lower rate code to provide additional error protection.

In order to adapt to the changing channel conditions, a method of estimating the channel quality must be implemented. Torlak and Xu [2] proposed a blind multi-user channel estimation algorithm using subspace methods to estimate the nature of the multi-user A-CDMA channel. They suggest a method for computing the received signal power with path gains. We use this method to compute the received signal power with path gains in this paper (provided the channel remains relatively constant between the time when the channel is estimated and the time when the data is transmitted). If the channel varies during this time period, then we use the characterizing of the channel variation proposed by Goeckel in [3]. Rayleigh and Rician fading channels are used for the multipath fading channels in our paper. The fading is assumed to be slow, and changes every bit period.

Applications such as speech and video data transmission do not allow for retransmissions. For such systems, the return channel is only used to transmit the channel state information from the receiver to the transmitter and not for requesting the retransmission of the data. By changing the code rates, adaptive error protection is achieved [1]. The system considered in this paper uses punctured convolutional codes to provide error protection. The main idea of using punctured codes is to use the highest rate code that gives the desired probability of bit error. When the channel conditions are good, it is desirable to send a lower number of redundant bits, thus increasing the throughput. Puncturing, being a systematic deletion of parity bits, yields a higher rate code than the mother code. When the channel conditions are bad, (or when the channel goes into deep fade), the mother code is often used for channel encoding to maintain a given level of performance.

In this paper, the rate of the code needed to achieve a given level of performance is determined by the receiver. Depending on the received SNR, the receiver chooses a particular rate for the channel code. The performance of each of the codes is assumed to be known before incorporating the change in the code rate at each received SNR. In other words, for adapting the code rates at different SNRs, the probability of bit error for different codes is computed, and the highest rate punctured code which produces the desired bit error rate is chosen. The feedback channel between the receiver and the transmitter is used to send information to the transmitter to change its code rate as differing values of the received SNR are detected.

In the first class of work on adaptive rate coding [1], an adaptive coding scheme for digital communication over time varying channels was proposed. A non-selective Rician fading channel modeled each state in the finite-state Markov model. In [4] the tradeoff between co-channel interference and coding was evaluated over a Rayleigh fading channel. This work determined the best compromise between the power of error correction due to coding and the strength of the self-induced system interference in terms of numerous criteria for speech and data transmission. The main goal in [3] was to employ the characterization of the effects of the channel variation to design adaptive signaling schemes that were effective for the time varying channel. The major point of interest in [5] was the measurement of signal-to-interference plus noise ratio (SINR). The Euclidean (ED) metric, associated with the decoded information sequence was used as a channel quality measure. The information theoretical performance, namely the channel capacity and the error exponent, of Rayleigh fading channels is evaluated in [6] using variable rate adaptive channel coding (VRACE) with constant transmitted power. Finally in [7], rate adaptation techniques for achieving higher data rates have been specified for all major cellular standards. Wideband CDMA and cdma2000 systems discussed in [7] achieve higher data rates through a combination of variable spreading and coding. Both these systems include options from the network to obtain different kinds of measurements from the mobile in the form of metrics. The specified metrics include pilot strength measurements, bit error rates and signal-to-interference plus noise ratio (SINR) measurements [7]. Incremental redundancy is transmitted until the receiver is successfully able to decode the data frame. The procedure involves matching the code rate to the channel SINR without requiring SINR estimation and feedback. In this paper, an adaptive rate coding scheme using convolutional codes is developed to combat MUI over a slowly fading channel.

In Section 2, we present the description and analysis of the mathematical model of the A-CDMA channel, the fading process on the multipath fading channel, and also briefly explain the Markov model implemented to simulate transmission over this channel. In Section 3, the overall picture of the rate adaptation scheme is depicted. Section 4 presents a method of deriving the path gains of user 0 using the blind channel estimation algorithm. The description of the punctured codes, and their theoretical upper and lower bounds are derived in Section 5. Section 6 provides a comparison of the simulated and theoretical results. Finally, Section 7 presents the conclusions.

Section snippets

Channel model

The model for A-CDMA multiple access interference is shown in Fig. 1(a), and the correlation receiver for user 0 is given in Fig. 1(b). The A-CDMA system shown is an uplink model, from the mobile users to the base station. Let there be U users in an A-CDMA multiple access interference system. Each user is subjected to multipath fading. The multipath fading channel is described by the level of fading, and the total number of multipaths, which are assumed to be random. Multiple users

System model

The adaptive rate coding scheme is illustrated in Fig. 2. Data is encoded by one of the punctured convolutional codes (rate 2/3, 3/4, 4/5, 3/5, 4/7, 4/6, and 5/7), all of which are obtained from a rate 1/2 (M = 4) mother code, where M stands for the number of memory elements in the encoder. The encoded data is interleaved to reduce burst errors and then modulated. The modulated data is sent over the A-CDMA channel (comprising a single user and (U  1) interferers). The received signal is

Channel estimation

Consider an A-CDMA multiple access interference system as shown in Fig. 1(a). The system is corrupted by two kinds of Gaussian noise. The first one corresponds to MUI and the second one is the thermal noise. We can redraw the block diagram of the A-CDMA model as shown in Fig. 3. Digital signal b0(t) (of user 0) is transmitted over a fading multipath channel h(t), after which the signal has a memory of L symbols. Thermal noise is generated at the receiver and it is modeled as an additive white

Brief description of the FEC procedure

The punctured codes used in this paper are of rates 2/3, 3/4, 4/5, 3/5, 4/7, 4/6, and 5/7. They are obtained from a rate 1/2 (M = 4) mother code. The perforation patterns are chosen in such a way that the resultant punctured code is non-catastrophic. The punctured codes used in this paper are non-catastrophic and have a large minimum free distance (dfree). The free distances, ad, and cd of these codes are derived in [11]. ad is the number of paths at a distance d from the transmitted path, and cd

Simulation results

Fig. 4 shows the throughput performance of the adaptive coding system when the Doppler speeds of the mobile are 10 mph , 60 mph, and 80 mph. These velocities correspond to Doppler frequencies fm = 14 Hz, fm = 80 Hz and fm = 107 Hz, when the carrier frequency is fc = 900 MHz. Since the channel is slowly fading, transition is possible only between adjacent states. Basically, when the channel transits itself into a deep fade, we need higher error protection. Hence, we choose the minimum of the code rates between

Conclusions

In this paper, a method of adaptive rate coding for A-CDMA systems is presented. Subspace methods for channel estimation can be used to estimate the nature of time-varying channels. The blind channel estimation algorithm for A-CDMA systems is modified for the case when there is a single user and multiple interferers. The appropriate expressions for estimated channel vectors are derived. If the delay between the time when the data is transmitted and the time when the channel is estimated is

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

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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.

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