Sum secrecy rate in multicarrier DF relay beamforming

In this paper, we study sum secrecy rate in multi-carrier decode-and-forward relay beamforming. We obtain the optimal source power and relay weights on each subcarrier which maximize the sum secrecy rate. For a given total power on a given subcarrier k, P^k₀, we reformulate the optimization problem by relaxing the rank-1 constraint on the complex positive semidefinite relay weight matrix, and solve using semidefinite programming. We analytically prove that the solution to the relaxed optimization problem is indeed rank 1. We show that the subcarrier secrecy rate, R_s(P^k₀), is a concave function in total power P^k₀ if R_s(P^k₀) > 0 for any P^k₀ > 0. Numerical results show that the sum secrecy rate with optimal power allocation across subcarriers is more than the sum secrecy rate with equal power allocation. We also propose a low complexity suboptimal power allocation scheme which outperforms equal power allocation scheme.