Coexistence in Wireless Decentralized Networks

We consider a wireless communication network with a fixed number of frequency sub-bands to be shared among several transmitter-receiver pairs. In traditional frequency division (FD) systems, the available sub-bands are partitioned into disjoint clusters (frequency bands) and assigned to different users (each user transmits only in its own band). If the number of users sharing the spectrum is random, this technique may lead to inefficient spectrum utilization (a considerable fraction of the bands may remain empty most of the time). In addition, this approach inherently requires either a central network controller for frequency allocation, or cognitive radios which sense and occupy the empty bands in a dynamic fashion. These shortcomings motivate us to look for a decentralized scheme (without using cognitive radios) which allows the users to coexist, while utilizing the spectrum efficiently. We consider a frequency hopping (FH) scheme (with i.i.d. Gaussian code-books) where each user transmits over a selection of sub-bands and hops to another selection (with the same cardinality) from transmission to transmission. Developing an upper bound on the differential entropy of a mixed Gaussian random vector and via entropy power inequality, we offer a lower bound on the achievable rate of each user in the proposed scheme. Thereafter, in a setup where the number of active users and all the channel gains are unknown to transmitters, we obtain the maximum transmission rate per user to ensure a specified outage probability at a given SNR level. We demonstrate that “outage capacity” can be considerably higher in FH than the case of FD for reasonable distributions on the number of active users which guarantees a higher spectral efficiency in FH. Index Terms Frequency Hopping, Spectrum Sharing, Decentralized Networks, Mixed Gaussian Interference, -Outage Capacity