Joint Precoder and Combiner Design for MMSE Distributed Beamforming with Per-Antenna Power Constraints

We consider minimum mean square error (MMSE) joint precoder and combiner design for single and multi carrier distributed beam forming systems with nonuniform perantenna transmit power constraints. We show that, similar to the maximum-gain problem, an iterative Gauss-Seidel algorithm can be used for minimizing MSE which alternately optimizes the transmitter and receiver coefficients. In a single carrier system the optimum transmit coefficients are obtained by a simple projection of the effective MISO channel. In the multicarrier case with a sum-MSE objective, the Gauss-Seidel approach is once again applicable, but the transmit coefficients must be found by solving a quadratically constrained quadratic problem for which we apply a dual gradient algorithm. A numerical example is presented which shows improvement of 0.7 dB in carrier signal-to-noise ratio (SNR) relative to a projected eigenvector method for a multicarrier DBF system with Rayleigh-faded multipath channels.