Asymptotically near-optimal blind estimation of multipath CDMA channels

In this paper, correlation matching techniques are applied to estimate multipath code division multiple access (CDMA) channels. We arrange unknown multipath parameters for each of J active users in a vector. Then, the output correlation matrix is parameterized by J unknown rank one matrices, with each one formulated from the corresponding channel vector. This correlation matrix is further compared with its sample average. The resulting error can be first minimized to obtain unbiased estimates of J unknown rank one matrices in closed forms. Thus, our estimator for each channel vector is derived by singular value decomposition (SVD) on the associated rank one matrix within a scalar ambiguity. It turns out that the performance of our estimator can be improved by introducing an asymptotically optimal weighting matrix in our cost function. This weighting matrix can be estimated directly from data samples only with a small penalty on the asymptotic performance. The asymptotic covariance of our estimator is also derived and can be compared with the Cramer-Rao lower bound, both in closed forms. Simulation results show the applicability of the proposed methods and consistency with our theoretical analysis.