  We consider minimum mean square error (MMSE) joint precoder and combiner
design for single and multi carrier distributed beamforming systems with
nonuniform per-antenna 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.
