Joint linear timing and carrier phase estimation of DS-CDMA multiuser communications

Previous works on multiuser synchronization assumed that either timing recovery or carrier phase recovery scheme is available. Based on the ideas to linearly combine the sufficient statistics of timings and carrier phases, we introduce the generalized joint linear timing and carrier phase estimation scheme which is of commensurate complexity with the generalized linear timing estimator. To avoid the difficulties of the design by minimizing the mean square error, a simple and novel design criterion for this generalized joint linear timing and carrier phase estimation is proposed. With he discrete timing assumption, we not only mathematically prove that the mean square error of the proposed estimator converges to zero as the noise vanishes for an arbitrary number of users, but also numerically verify it. For the general case with continuous timing assumption, we also confirm the effectiveness of our proposed estimator for an arbitrary number of users. With this effective linear complexity joint timing and carrier phase estimate, the non-polynomial (NP) hard multiuser synchronization over AWGN channel is completely solved