Pre-coder techniques disclosed herein are based on long-term statistical channel information for reducing channel feedback overhead and transmitter complexity. In an embodiment, a receiver includes two or more receive antennas spaced approximately λ/2 apart and a baseband processor. The baseband processor computes channel correlations for different combinations of transmit antennas and each receive antenna and averages the channel correlations over the different receive antennas to form a frequency-independent channel correlation matrix. The baseband processor also computes a scalar representing noise variance at the receive antennas and feeds back the frequency-independent channel correlation matrix and the scalar for use in performing transmitter pre-coding computations.