Analog Network Coding in General SNR Regime

Abstract—The problem of maximum rate achievable with analog network coding for a unicast communication over a layered relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered with two conditions: (1) each relay node scales its received signal to the maximum extent possible subject to its transmit power constraint, (2) the relay nodes in specific subsets of the network operate in the high-SNR regime. We establish that the condition (1), in general, leads to suboptimal end-to-end rate. We also prove that the performance of analog network coding in a wide class of layered networks without needing condition (2). The key contribution of this work is a lemma that states that the globally optimal set of scaling factors, which maximize end-to-end rate, for the nodes in a layered relay network can be computed layer-by-layer. Specifically, the rate-optimal set of scaling factors for the nodes in a layer is the one that maximizes the sum-rate of the nodes in the next layer. This result allows us to analyze analog network coding performance in even those network scenarios that cannot be addressed using the existing approaches. We illustrate this by computing the maximum rate achievable with analog network coding in one particular layered network, in various communication scenarios. I