Alternating Optimization for MMSE Broadcast Precoding

We address the problem of jointly optimizing the pre coder and the receivers in a multi-user broadcast system for a linear and nonlinear transmitter under sum mean square error (MSE) minimization. By means of alternating optimization (AO), we find an iterative algorithm which always converges to the global optimum. In addition to an elegant initialization of the receivers' weights, we come up with expressions for the speed of convergence. Our algorithm is applicable to both single-antenna and multi-antenna receivers and can be combined with nonlinear Tomlinson-Harashima precoding (THP). For THP, the precoding order can easily be included in the AO. Moreover, we show that for sum MSE minimization the user-wise channels are not necessarily diagonalized and give some ideas how this fact can be exploited