Group sequence detection for the asynchronous Gaussian code-division multiple-access channel

The problem of coherently detecting S out of K simultaneously transmitting users of an asynchronous Gaussian CDMA channel is considered under the constraint that the signal amplitudes of the interfering users are unknown. A maximum generalized likelihood detector (MGLD) that achieves optimum values of group near-far resistance (the worst-case asymptotic efficiency over the unknown signal amplitudes) is obtained. Unfortunately, the MGLD is practically unimplementable because, for M-ary signalling, it has a time complexity per symbol (TCS) of O(M^SN/SN), N being the packet length. A group sequence detector (GSD) is proposed as an alternative, and it consists of a bank of K matched filters for a front-end, followed by a cascade of a K-input S-output group decorrelating filter and a multiuser variant of the Viterbi algorithm with a TCS of O(M^S/S). The high SNR performance of the GSD is characterized through its asymptotic multiuser efficiency and the conditions under which the GSD closely tracks the performance of the MGLD are discussed. When S=1, the GSD reduces to the decorrelating detector with optimum near-far resistance, and when S=K, the GSD coincides with the maximum likelihood sequence detector with optimum asymptotic efficiency. A parallel bank of GSDs can also be used, one for detecting users in each group of a partition of all users to be detected, thereby providing the designer the flexibility of trading performance for reduced implementational complexity