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

Previous work on multiuser synchronization assumed that either timing recovery or carrier phase recovery schemes were available. Therefore, a generalized joint linear timing and carrier-phase estimation scheme to effectively estimate both the received timings and carrier phases at the same time is of paramount interest. Based on the idea to linearly combine the sufficient statistics of timings and carrier phases, we introduce the generalized joint linear timing and carrier phase estimation scheme with commensurate complexity of the generalized linear timing estimator. To avoid the difficulty of the design by minimizing the mean-square error (MSE), a simple and novel design criterion for this generalized joint linear estimation is proposed. With a discrete timing assumption, we not only mathematically prove that the MSE of the proposed estimator converges to zero as noise vanishes for an arbitrary number of users, but also conduct simulations to verify it. On the other hand, for the general case with a continuous timing assumption, arguments and simulations are provided to confirm the effectiveness of our proposed estimator for an arbitrary number of users. We further show that such an efficient linear-complexity joint estimation scheme is effective in the near-far environment. Consequently, the nonpolynomial (NP) hard multiuser synchronization over additive white Gaussian noise (AWGN) channel is successfully solved.