Coverage probability in wireless networks with determinantal scheduling

TL;DR

This paper introduces a novel scheduling algorithm for wireless networks using determinantal point processes, enabling analytical coverage probability analysis and potential for optimized, learnable scheduling strategies.

Contribution

It extends spatial Aloha by employing determinantal processes for scheduling, providing explicit analysis and optimization opportunities for network performance.

Findings

Coverage probabilities are analytically tractable using determinantal processes.

Scheduling parameters can be optimized through statistical learning techniques.

Determinantal processes facilitate efficient sampling algorithms for implementation.

Abstract

We propose a new class of algorithms for randomly scheduling network transmissions. The idea is to use (discrete) determinantal point processes (subsets) to randomly assign medium access to various {\em repulsive} subsets of potential transmitters. This approach can be seen as a natural extension of (spatial) Aloha, which schedules transmissions independently. Under a general path loss model and Rayleigh fading, we show that, similarly to Aloha, they are also subject to elegant analysis of the coverage probabilities and transmission attempts (also known as local delay). This is mainly due to the explicit, determinantal form of the conditional (Palm) distribution and closed-form expressions for the Laplace functional of determinantal processes. Interestingly, the derived performance characteristics of the network are amenable to various optimizations of the scheduling parameters, which are determinantal kernels, allowing the use of techniques developed for statistical learning with determinantal processes. Well-established sampling algorithms for determinantal processes can be used to cope with implementation issues, which is is beyond the scope of this paper, but it creates paths for further research.