This paper studies the performance of a coded convolutional spreading CDMA system with cyclic prefix (CS-CDMA/CP) combined with the zero correlation zone code generated from the M-sequence (M-ZCZ code) for downlink transmission over a multipath fast fading channel. In particular, we propose a new pilot-aided channel estimation scheme based on the shift property of the M-ZCZ code and show the robustness of the scheme against fast fading through comparison with the W-CDMA system empolying time-multiplexed pilot signals.