An Efficient Design Method for Vector Broadcast Systems with Common Information

We consider the problem of determining an optimal transmission scheme for broadcasting a common message over vector channels, given (perfect) channel knowledge at both the receive and transmit ends. We provide an efficient method for jointly designing a linear transmitter and and a set of linear receivers so as to minimize a weighted Mean Square Error (WMSE) of the data estimates. The computational efficiency follows from the convex formulations that we develop. These formulations enable utilization of highly efficient interior point methods. For diagonal channel matrices, which appear in multicarrier systems' that employ cyclic prefixing, we show that the optimal transmitter is obtained by subcarrier allocation and power loading. The set of minimum MSE transceivers for a vector broadcast system is parametrized by a unitary matrix degree of freedom. For the case of diagonal systems, we show how this unitary matrix can be chosen so that the symbol error rate is minimized (over the given set). This optimal unitary matrix ensures that for each receiver, the subcarrier signal-to-noise ratios (SNRs) are all the same. Simulations indicate that our designs can provide significantly improved performance over standard designs.