On pilot-based multipath channel estimation for uplink CDMA systems

The paper considers a pilot-based channel estimation for uplink CDMA systems where each user transmits an individual pilot signal (sequence) for estimating its multipath channel parameters. To obtain reliable estimates, the channel estimator at a base station must effectively combat multiple access interference. This stands in clear contrast to the one-to-many channel where all users share one common pilot signal. Assuming a widely used radio channel model, we derive lower bounds on the maximum mean square error for two types of linear channel estimators, namely the inverse filter and the linear minimum mean-square error (MMSE) estimator. We show that the inverse filter attains the lower bound if and only if pilot sequences are periodically self-invertible sequences. Interestingly, the matched filter achieves the same lower bound if pilot sequences form a periodic complementary set. In case of the MMSE estimator, the lower bound is either met or not depending on some system parameters. In all the cases where the bound is tight, we provide methods for constructing optimal pilot sequences. Such sequences appear not to have been constructed previously. The paper gives insight into the performance limits under the worst-case conditions.