Coverage Analysis of Millimeter Wave Decode-and-Forward Networks With Best Relay Selection

In this paper, we investigate the coverage probability improvement of a millimeter wave network due to the deployment of spatially random decode-and-forward (DF) relays. The source and receiver are located at a fixed distance and all the relay nodes are distributed as a 2-D homogeneous Poisson point process (PPP). We first derive the spatial distribution of the set of decoding relays whose received signal-to-noise ratio (SNR) are above the minimum SNR threshold. This set is a 2-D inhomogeneous PPP. From this set, we select a relay that has minimum path loss to the receiver and derive the achievable coverage due to this selection. The analysis is developed using tools from stochastic geometry and is verified using Monte-Carlo simulation. The coverage probabilities of the direct link without relaying, a randomly chosen relay link, and the selected relay link are compared to show the significant performance gain when relay selection is used. We also analyze the effects of beam misalignment and different power allocations at the source and relay on coverage probability. In addition, rate coverage and spectral efficiency are compared for direct and selected relay links to show impressive performance gains with relaying.