CDF of the spectral-efficiency of a simple distributed channel assignment algorithm in spatially distributed wireless networks

The Cumulative-Distribution-Function (CDF) of the spectral efficiency of links in spatially distributed networks with orthogonal channels and a simple channel assignment algorithm is presented for constant link-lengths and nearest-neighbor links. Transmitters are randomly distributed on the plane with uniform probability, and receivers are either randomly distributed or at hexagonal lattice sites. This result includes random channel assignments as a special case. The CDF is used to find the spectral efficiency for a given, small outage probability which is used to optimize the number of channels to maximize the spectral efficiency. The optimum number of channels represents the best trade off between increasing Signal-to-Interference-Ratio (SIR) and reducing the communication bandwidth by channelization. For the system parameters presented here, a greater than three-fold increase in spectral efficiency is possible going from random channel selection to the best-faded-channel algorithm which requires just a marginal increase in complexity in duplex systems with reciprocity making it an attractive alternative to random channel assignments. Additionally, it is found that the hexagonal placement of receivers results in approximately twice the spectral efficiency compared to a random placement of receivers for the same receiver density and outage probability.