Bandwidth-SINR Tradeoffs in Spatial Networks

This paper addresses the following question, which is of interest in the design of a multiuser decentralized network: given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W/N should the band be partitioned into to maximize the number of simultaneous transmissions in the network? Dividing the available spectrum reduces the number of users on each band and therefore decreases multiuser interference level, but also increases the SINR requirement for each transmission because the same information rate must be achieved over a smaller bandwidth. Exploring this tradeoff between bandwidth and SINR and determining the optimum value of N in terms of the system parameters is the focus of the paper. Using stochastic geometry, we analytically derive the optimal SINR threshold on this tradeoff curve and show that it is a function of only the path loss exponent. Furthermore, the optimal SINR point lies between the low-SINR (power-limited) and high-SINR (bandwidth-limited) regimes.