This paper presents the bit-error rate (BER) performance of the RAKE receiver over a multipath Rayleigh fading channel. The closed-form BER in the downlink single-cell environment is obtained through the analysis of the imperfect channel estimation. We compute the BER as a function of energy-to-noise ratio per bit including the effect of multiple access interference and multipath interference, with channel and system parameters: number of diversity channels L = 1, 3, 6, 12; Doppler frequency shift with fD T = 0.008333, 0.0167, 0.025; residual carrier frequency offset Δ f = -600 600 Hz; averaging length of the channel estimator Np = 128-1536 chips. This analysis allows predicting the system's performance and helps to optimize the parameter setting for the channel estimation process. We show that even if the optimal system parameters are used, the BER performance results in a minimal 4dB degradation in comparison to the perfect channel estimation. Finally, the theoretical results are verified by using the Monte-Carlo computer simulations.