An optimal signal design for band-limited asynchronous DS-CDMA communications

An optimal signal design for band-limited, asynchronous, direct-sequence code-division multiple-access (DS-CDMA) communications with aperiodic random spreading sequences and the conventional matched filter receiver is considered in an additive white Gaussian noise (AWGN) channel, With bandwidth defined in the strict sense, two optimization problems are solved under finite bandwidth and zero interchip interference constraints. First, a chip waveform optimization is performed given the system bandwidth, the data symbol transmission rate, and the processing gain. A technique to characterize a band-limited chip waveform with a finite number of parameters is developed, and it is used to derive optimum chip waveforms which minimize the effect of multiple-access interference (MAI) for any energy and delay profile of users. Next, a joint optimization of the processing gain and the chip waveform is performed, given the system bandwidth and the data symbol transmission rate. A sufficient condition for a system to have lower average probability of bit error for any energy profile is found, and it is used to derive some design strategies. It is shown that the flat spectrum pulse with the processing gain leading to zero excess bandwidth results in the minimum average probability of bit error. Design examples and numerical results are also provided.