Channel Allocation Policy for Distributed Wireless Network: Derivation and Analysis of Optimal Interference

Abstract

Distributed wireless networks with smart users (independent and rational) are becoming popular, and researchers are studying distributed equilibrium solutions like Nash Equilibrium (NE) to analyze and predict the convergence of such networks. Our goal is to drive the distributed wireless network to NE with high total throughput. Study of the distribution of network metrics at NE with high total throughput shows that communication links still have significant amount of interference. Adding an interference-received term with an optimal weight ( ${\alpha }_{\text{opt}}^{\ast }$ ) to the link’s payoff can push the distributed network to converge to NE with high total throughput. The channel allocation trend at NE with high total throughput is as follows: each of the $C-1$ links occupies its own channel, and the remaining $N-C+1$ links share the remaining one channel, where $N$ is the number of links and $C$ is the number of channels in the network. The links (transmitters and receivers) are randomly located and $C<N$ (limited resources). The transmitter of a link has a direct connection with the receiver of the link; hence, several links overlap. This leads to a dense network with considerable amount of interference especially for links sharing channels. A practical application of our work is when smart devices in a room, hall, or concert arena have a direct communication with other smart devices in the area using limited bandwidth. Using best response technique and definitions of NE, we derive and propose an approximate way to mathematically express ${\alpha }_{\text{opt}}^{\ast }$ (referred to as ${\widehat{\alpha }}_{\text{opt}}$ ) along with its probability density function (PDF) for a specific scenario. Then, a generic equation for ${\widehat{\alpha }}_{\text{opt}}$ is inferred for varying network sizes (links) and available resources (channels). Implementing such a policy enhances the total throughput of the distributed wireless network by up to 15%. In a more general setting, our distributed policy can achieve up to 75% of the maximum total throughput (benchmark value reached by centralized solution via exhaustive search) at a fraction of the time and computation resources.