W-function solution to MBER based power allocation for MIMO eigenmode transmission

In multiple-input and multiple-output (MIMO) eigenmode transmission systems, problem of minimizing bit error rate (MBER) based optimal power allocation does not have a simple closed-form solution. There are two existing methods: general purpose methods, i.e. interior point methods, and Q-function Chernoff approximative power allocation method. The paper proposes a novel solution to the MBER based optimal power allocation. A closed-form solution is obtained by utilizing Lambert W-function, and the optimal power allocation can be obtained by optimal algorithm for the W-function. Numerical simulations show that, the proposed W-function power allocation can achieve better performances than Q-function Chernoff approximative power allocation method and equal power allocation method.