Joint timing and channel estimation for bandlimited long-code-based MC-DS-CDMA: A low-complexity near-optimal algorithm and the CRLB

Joint Timing and Channel Estimation (JTCE) for bandlimited long-code-aided Multi-Carrier Direct-Sequence Code Division Multiple Access (MC-DS-CDMA) systems is investigated. We establish the optimal multiuser timing and channel estimates for the uplink MC-DS-CDMA receiver by minimising a weighted least squares cost function with respect to K independent parameters, where K is the number of active users. A guided random search procedure known as Repeated Weighted Boosting Search (RWBS) is invoked for numerically solving this challenging multivariate optimisation problem, and thereby for producing near-optimal timing and channel estimates. The Cramer-Rao Lower Bound (CRLB) for the JTCE problem of interest is derived to benchmark the performance of the proposed RWBS based estimator. Quantitatively, for the scenario of K=10 users, E_b/N₀≥3 dB where E_b is the energy per bit and N₀ the single-sided noise power spectral density, and for a near-far ratio of 10 dB, the RWBS based estimator using an observation window of 20 symbols is shown to approach the CRLB at a complexity 10 orders of magnitude lower in comparison to its full maximum likelihood search based counterpart. The proposed algorithm does not require the transmission of known pilots, yet it is capable of handling time-variant channel states.