The Joint Impact of Fading Severity, Rotation Angle, and Non-Gaussian Noise on Signal Space Diversity-Based Relaying Networks

This work focuses on the interplay between rotation angle, transmit power, fading severity, and noise impairment severity in signal space diversity-based three time-slot decode-and-forward two-way relaying networks. Specifically, we develop a joint design for rotation angle selection and transmit power allocation, while taking into account the performance impact of fading severities on the channels and noise impairment severities on the receivers. To model different severities of fading and noise impairment, Nakagami distribution and additive non-Gaussian noise are used respectively. The objective in doing so is to promote the reliable reception of end-sources, while satisfying individual and total power budgets as well as average error probability. To this end, we start by deriving average error probabilities of end-sources for non-uniform constellations, which capture all possible signal constellations produced by using various rotation angles. Next, we formulate the joint design problem in an optimization form. Unfortunately, the resulting formulation is a non-convex optimization. To find the solution, we resort to numerical optimization. The numerical results not only validate the derived error probability expressions, but also demonstrate the efficacy of the proposed framework and provide useful insights on the interaction between rotation angle, transmit power, fading severities of the channels, and noise impairment severities at the end-sources.