A CDMA communication system includes a signal processor which encodes voice and nonvoice signals into data at various rates, e.g. data rates of 8 kbps, 16 kbps, 32 kbps, or 64 kbps as I and Q signals. The signal processor selects a specific data rate depending upon the type of signal, or in response to a set data rate. When the signal is received and demodulated, the baseband signal is at the chip level. Both the I and Q components of the signal are despread using the conjugate of the pn sequence used during spreading, returning the signal to the symbol level. Carrier offset correction is performed at the symbol level. A lower overall processing speed is therefore required.