A characterization of multiple access interference in generalized quadriphase spread-spectrum communications

A proposition that is useful for studying multiple-access interference (MAI) in generalized quadriphase spread-spectrum systems is established. The proposition provides the conditional density functions and the conditional cumulative distribution functions of random variables that characterize the MAI. It is shown that these characterizing random variables converge almost surely to the true MAI. The proposition provides a method to study the effect of the chip waveform on the performance of the system and provides a means for the design and analysis of spectrally efficient systems with continuous-phase or M-ary phase-shift-keyed modulation. The proposition allows the evaluation of the average error probability with arbitrary accuracy without making a Gaussian approximation for the MAI and is also useful for studying systems that send data in packets, where the delays of the interferers are often fixed for the duration of a packet. For illustration, the proposition is applied to computing the average error probability of generalized quadriphase direct-sequence spread-spectrum multiple-access communication systems with various chip waveforms and offset parameters corresponding to commonly used modulation schemes.