In this paper, we consider 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 active users is a random variable with a given probability mass function. Moreover, users are unaware of each other's codebooks and hence, no multiuser detection is possible. We propose a randomized Frequency Hopping (FH) scheme in which each transmitter randomly hops over a subset of u sub-bands from transmission to transmission. Assuming all users transmit Gaussian signals, the distribution of the noise plus interference is mixed Gaussian, which makes calculation of the mutual information between the transmitted and received signals of each user intractable. We derive lower and upper bounds on the mutual information of each user and demonstrate that, for large Signal-to-Noise Ratio (SNR) values, the two bounds coincide. This observation enables us to compute the sum multiplexing gain of the system and obtain the optimum hopping strategy for maximizing this quantity. We compare the performance of the FH system with that of the Frequency Division (FD) system in terms of the following performance measures: average sum multiplexing gain (η (1) ), average minimum multiplexing gain per user (η (2) ), minimum nonzero multiplexing gain per user (η (3) ) and service capability (η (4) ). We show that (depending on the probability mass function of the number of active users) the FH system can offer a significant improvement in terms of η (1) , η (2) and η (implying a more efficient usage of the spectrum). It is also shown that
In a pioneering work, REF offers a clean analysis of a decentralized network where all users follow a randomized hopping strategy to share the resources, while the number of active users is a random variable with a given distribution.
A model for randomized resource allocation in decentralized wireless networks
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Mathematics Computer Science