Optimum chip waveforms for DS/SSMA communications with random spreading sequences and a matched filter receiver

In this paper, we consider the transmitter optimization problem in direct-sequence spread-spectrum multiple-access (DS/SSMA) communications with random spreading sequences and a matched filter receiver. A chip waveform optimization is performed under strict-sense bandwidth and zero interchip interference (ICI) conditions. Optimum chip waveforms are found for the excess bandwidth 0⩽β⩽1, and are shown to achieve the minimum average bit error probability (BEP) for any distribution of the power and delay profiles of users. A simple efficiency measure is derived to assess how efficiently a chip waveform utilizes the excess bandwidth, and it is shown that the square-root raised cosine chip waveforms have only 50% efficiency. Numerical examples including BEP performance of the optimum chip waveforms are also provided