This paper addresses the following question, which is of interest in the design and deployment 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? In an interference-limited ad-hoc network, dividing the available spectrum results in two competing effects: on the positive side, it reduces the number of users on each band and therefore decreases the interference level which leads to an increased SINR, while on the negative side the SINR requirement for each transmission is increased 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 (which directly corresponds to the optimal spectral efficiency) 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. In order to operate at this optimal point, the number of frequency bands (i.e., the reuse factor) should be increased until the threshold SINR, which is an increasing function of the reuse factor, is equal to the optimal value.
The problem studied in this work is essentially the optimization of frequency reuse in uncoordinated spatial (ad hoc) networks, which is a well studied problem in the context of cellular networks (see for example @cite_1 and references therein). In both settings the tradeoff is between the bandwidth utilized per cell transmission, which is inversely proportional to the frequency reuse factor, and the achieved SINR per transmission. A key difference is that in cellular networks, regular frequency reuse patterns can be planned and implemented, whereas in an ad hoc network this is impossible and so the best that can be hoped for is uncoordinated frequency reuse. Another crucial difference is in terms of analytical tractability. Although there has been a tremendous amount of work on optimization of frequency reuse for cellular networks, these efforts do not, to the best of our knowledge, lend themselves to clean analytical results. On the contrary, in this work we are able to derive very simple analytical results in the random network setting that very cleanly show the dependence of the optimal reuse factor on system parameters such as path loss exponent and rate.
@cite_1
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