On source coding, channel coding and spreading tradeoffs in a DS-CDMA system operating over frequency selective fading channels with narrowband interference

For a fixed total bandwidth expansion factor, we consider the problem of optimal bandwidth allocation among the source coder, the channel coder, and the spread-spectrum unit for a direct-sequence code-division multiple-access system operating over a frequency-selective fading channel with narrowband interference. Assuming a Gaussian source with the optimum scalar quantizer, and a binary convolutional code with soft-decision decoding, and further assuming that the self-interference is negligible, we obtain both a lower and an upper bound on the end-to-end average source distortion. The joint three-way constrained optimization of the source code rate, the channel code rate, and the spreading factor can be simplified into an unconstrained optimization problem over two variables. Upon fixing the channel code rate, we show that both upper and lower bound-based distortion functions are convex functions of the source code rate. Because an explicit solution for the optimum source code rate, i.e., one that minimizes the average distortion, is difficult to obtain, computer-based search techniques are employed. Numerical results are presented for the optimum source code rate and spreading factor, parameterized by the channel code rate and code constraint length. The optimal bandwidth allocation, in general, depends on the system and the channel conditions, such as the total number of active users, the average jammer-to-signal power ratio, and the number of resolved multipath components together with their power delay profile.