Linear Multiuser Detectors for Synchronous Code-Division Multiple-Access Channels

In code-division multiple-access systems, simultaneous multiuser accessing of a common channel is made possible by assigning a signature waveform to each user. Knowledge of these waveforms enables the receiver to demodulate the data streams of each user, upon observation of the sum of the transmitted signals, perturbed by additive noise. Under the assumptions of symbol-synchronous transmissions and white Gaussian noise, we analyze the detection mechanism at the receiver, comparing different detectors by their bit error rate in the low background noise region, and by their worst-case behavior in a near-far environment where the received energies of the users are not necessarily similar. Optimum multiuser detection achieves important performance gains over conventional single-user detection at the expense of computational complexity that grows exponentially with the number of users. It is shown that in the synchronous case the performance achieved by linear multiuser detectors (whose complexity per demodulated bit is only linear in the number of users) is similar to that of optimum multiuser detection. Attention is focused on detectors whose linear memoryless transformation is a generalized inverse of the matrix of signature waveform crosscorrelations, and on the optimum linear detector. It is shown that the generalized inverse detectors exhibit the same degree of near-far resistance as the optimum multiuser detector; the optimum linear detector is obtained subsequently, along with sufficient conditions on the signal energies and crosscorrelations to ensure that its performance is equal to that of the optimum multiuser detector.