  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.
