The capacity of the ergodic miso channel with per-antenna power constraint and an application to the fading cognitive interference channel

Abstract

This paper characterizes the ergodic capacity of the fading multiple-input single-output (MISO) channel with per-antenna power constraints (PerPC) with perfect Channel State Information (CSI) at all terminals. This turns out to be the sum-capacity achieving strategy for the ergodic fading Gaussian overlay cognitive interference channel (EGCIFC) in the strong interference regime. The EGCIFC is a two-user time-varying interference channel in which a primary / licensed transmitter and a secondary / cognitive transmitter share the same spectrum and where the cognitive transmitter has non-causal knowledge of the primary user's message. The MISO and the EGCIFC results are verified numerically for the case of independent Rayleigh fading gains. Different achievable strategies, corresponding to different amount of CSI, are compared to show the performance of the derived PerPC optimal power allocation.