Optimum Time Diversity and BCH Codes for DS SS-CDMA Cellular Mobile Channels

This paper presents the results of optimum diversity and coding of a cellular radio system using spread-spectrum code division multiple-access (SS-CDMA) and binary phase-shift-keying modulation (BPSK). The base-to-mobile link is considered with the mobile at the boundary between cells. Hence, the received signal is subject to Rayleigh or log-normal fading, as well as to interference from neighbouring cells.First, the probability of error for the fading-interference channel is approximated as a simple, closed-form expression, with one-parameter which signifies the degree of channel fading and interference. It is shown that the approximation is quite satisfactory for a wide range of channel fading and interference. Beside avoiding numerical integration, the use of such simplification offers more insight into the nature of the channel.The use of error-correcting codes to enable increasing the system capacity is then investigated. Since employment of either SS or forward-error correction (FEC) techniques results in bandwidth expansion for a communication system using a fixed alphabet size, there exists a trade-off between how much processing gain and how much coding gain the system should employ such that the bit-error rate is minimum. Two types of coding are analysed, viz. repetitive coding and binary BCH codes. For the repetitive code, Chernoff upper-bound is used to approximate the bit-error rate (BER) and the optimum diversity is then found by a simple minimisation.To find the optimum trade-off between code rate k/n and correction capability t of BCH (n,k,t) codes, the first term of the series representing the BER is used as an estimate of the probability of error. Such approximation is shown to yield a nearly exact estimate of the optimum coding parameters, which minimise the BER. Although exact analysis can be used, the present approach yields a general solution, and optimum design parameters can be related to channel conditions.The essence of the results is as follows: (i) fading and interference channel is approximated as a one parameter family; (ii) optimum diversity increases and processing gain decreases, almost linearly, with the increase of interference and fading severity; (iii) optimum BCH code rate is 0.3 over a wide range of fading and interference conditions, and (iv) optimising coding gain and processing gain can provide substantial increase in system capacity.