  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 in order to
maximize the number of simultaneous links in the network? Dividing the
available spectrum results in two competing effects. On the positive side, a
larger N allows for more parallel, noninterfering communications to take place
in the same area. On the negative side, a larger N increases the SINR
requirement for each link because the same information rate must be achieved
over less bandwidth. Exploring this tradeoff and determining the optimum value
of N in terms of the system parameters is the focus of the paper. Using
stochastic geometry, the optimal SINR threshold - which directly corresponds to
the optimal spectral efficiency - is derived for both the low SNR
(power-limited) and high SNR (interference-limited) regimes. This leads to the
optimum choice of the number of frequency bands N in terms of the path loss
exponent, power and noise spectral density, desired rate, and total bandwidth.
