Spread-Spectrum Multiple-Access Performance of Orthogonal Codes: Linear Receivers

This paper analyzes a direct-sequence, spread-spectrum, multiple-access (SSMA) communication system which assigns a set of orthogonal sequences to each user. With all direct sequence SSMA systems, users share a channel by phase modulating their transmissions with signature sequences. However, the users of our system transmit bits of information/sequence. This contrasts classical SSMA schemes which use a pair of antipodal sequences and transmit 1 bit/sequence. In this paper, we assume that the channel noise is a combination of additive white Gaussian noise (AWGN) and multiple-access interference. We employ the optimum (single-user) demodulator for orthogonal signals in Gaussian noise. The multiple-user performance of this receiver is analyzed. We obtain approximations for the multiuser probability of error by using a Gaussian approximation for the multiple-access interference. We also obtain an upper bound on the exact probability by using characteristic functions. Our SSMA system is Well suited for application at the lower radio frequencies. Therefore, a companion paper describes a realistic model for low-frequency radio noise, modifies the receiver to include a zero-memory nonlinearity, and studies the performance of the nonlinear receiver.