Optimization of pilot symbol-assisted RAKE receivers for DS-CDMA systems

For optimizing pilot sequences for a general wideband direct-sequence (DS) code division multiple access (CDMA) system in a slow fading Rayleigh channel, we derive a design criterion by minimizing the mean square error (MSE) of the channel estimate. We analyze the effects of imperfect channel estimation (CE) on a CDMA system, based on the maximal ratio combining (MRC) RAKE receiver in both uniform power delay profile (UPDP) and non-uniform power delay profile (NPDP) channels. Published results on the effect of CE errors hold only for UPDP channels. We therefore use a characteristic function method to derive new closed-form expressions for the BER of RAKE receivers in NPDP channels. Constraining the energy per data frame to be constant, we optimize the length of the pilot symbols by minimizing the BER of the MRC receiver. We show an elegant result that the optimal number of pilot symbols is equal to the square root of the frame length for UPDP channels and for NPDP channels in the high SNR region.