Secrecy capacity of independent parallel channels

Security has been one of the most prominent problems surrounding wireless and mobile communications, in large part due to the broadcast nature of the wireless medium where eavesdropping can be easily accomplished. On the other hand, the wireless propagation environment also causes users to have varying channel qualities. From an information theoretic view, secret communication in presence of eavesdropper is still possible by exploiting these variations. In this paper, we extend the prior results on secrecy capacity to a system consisting of multiple independent parallel channels. We show that the secrecy capacity of the system is simply the summation of the secrecy capacities of the individual channels. We further derive the optimal power allocation strategy for a system with parallel AWGN channels subject to a total power constraint. The results can be extended to random fading channels with additive Gaussian noise. Secrecy capacity under various channel conditions and the benefit of the optimal power allocation strategy are evaluated numerically for an OFDM system as an example.