An iterative arrangement of channel estimator (12), a Kalman filter unit (14), and a soft demodulator (16) is provided for producing an estimate of complex gain of a CDMA communications channel carrying data and pilot channels, and demodulated data of the data channel. An initial channel estimate is produced by the estimator (12) using only the low-power pilot channel. This later is improved by the iterative process using the data channel. The complex gains is represented by a sum of sinusoidal signals with different frequencies and randomly variable amplitude and phase.