The Cross Rate: Linear Processing for the Two User Broadcast Channel

A novel linear precoding technique for the two user broadcast channel is presented. The performance measure used is the cross rate, defined as the difference between the sum throughputs of the system and its transpose. We show that the cross rate optimization problem can be reformulated as an alternating optimization of the steering matrix and power allocation. We solve the power allocation problem in closed form and give an efficient algorithm to compute the steering matrix. The algorithm is iterative and consists of simple operations, only requiring a single eigen-decomposition of a certain matrix. Simulation results indicate a 10% achievable rate gain over the regularized zero forcing algorithm with similar complexity, over a wide range of signal to noise (SNR) values.