Parallel group detection for synchronous CDMA communication over frequency-selective Rayleigh fading channels

A group detector jointly detects a group of users, and a parallel group detection scheme is a bank of J independently operating group detectors, one for each group of a J group partition of the K transmitting users of a code-division multiple-access (CDMA) channel. In this paper, two group detectors are introduced for the frequency-selective Rayleigh fading (FSRF) CDMA channel. While the optimum multiuser detector has a time complexity per symbol (TCS) of O(M ^K/K) for M-ary signaling, each of the two group detectors has a TCS of O(M(|G|)/|G|) where |G| is the group size. Hence, there are parallel group detection schemes, based on each of the two group detectors, that satisfy a wide range of complexity constraints that result from the choice of partition. Each of the two group detectors is minimax optimal in the corresponding conditional group near-far resistance measure. Furthermore, a succinct indicator of the average BER over high SNR regions is defined via the asymptotic efficiency. A lower bound and an exact formula for the asymptotic efficiency are derived for the first and second group detectors, respectively. The group detection approach for the FSRF-CDMA channel generalizes previous approaches to the complexity-performance tradeoff problem. It yields the optimum detector when the group size is K. When the group size is equal to one, the first group detector results in a new optimum linear detector and the second reduces to a recently proposed suboptimum linear detector. All other nontrivial partitions yield new multiuser detectors whose performances are commensurate with their complexities