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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 givendistribution and the channel gains are quasi-static Rayleigh fading. Thetransmitters are assumed to be unaware of the number of active users in thenetwork as well as the channel gains and not capable of detecting the presenceof other users in a given frequency sub-band. Moreover, the users are unawareof each other's codebooks and hence, no multiuser detection is possible. Weconsider a randomized Frequency Hopping (FH) scheme in which each transmitterrandomly hops over a subset of the $u$ sub-bands from transmission totransmission. Developing a new upper bound on the differential entropy of amixed Gaussian random vector and using entropy power inequality, we offer aseries of lower bounds on the achievable rate of each user. Thereafter, weobtain lower bounds on the maximum transmission rate per user to ensure aspecified outage probability at a given Signal-to-Noise Ratio (SNR) level. Wedemonstrate that the so-called outage capacity can be considerably higher inthe FH scheme than in the Frequency Division (FD) scenario for reasonabledistributions on the number of active users. This guarantees a higher spectralefficiency in FH compared to FD.

Randomized vs. orthogonal spectrum allocation in decentralized networks: Outage Analysis