  We address a decentralized wireless communication network with a fixed number
$u$ of frequency sub-bands to be shared among $N$ transmitter-receiver pairs.
It is assumed that the number of users $N$ is a random variable with a given
distribution and the channel gains are quasi-static Rayleigh fading. The
transmitters are assumed to be unaware of the number of active users in the
network as well as the channel gains and not capable of detecting the presence
of other users in a given frequency sub-band. Moreover, the users are unaware
of each other's codebooks and hence, no multiuser detection is possible. We
consider a randomized Frequency Hopping (FH) scheme in which each transmitter
randomly hops over a subset of the $u$ sub-bands from transmission to
transmission. Developing a new upper bound on the differential entropy of a
mixed Gaussian random vector and using entropy power inequality, we offer a
series of lower bounds on the achievable rate of each user. Thereafter, we
obtain lower bounds on the maximum transmission rate per user to ensure a
specified outage probability at a given Signal-to-Noise Ratio (SNR) level. We
demonstrate that the so-called outage capacity can be considerably higher in
the FH scheme than in the Frequency Division (FD) scenario for reasonable
distributions on the number of active users. This guarantees a higher spectral
efficiency in FH compared to FD.
