Perturbation Analysis for Spectrum Sharing in Cognitive Radio Networks

A primary ad-hoc network working in parallel with a secondary ad-hoc network is considered. The main challenge in operating cognitive ad-hoc networks is the lack of a centralized controller performing resource allocation for different users in the network. In this paper, a distributed power allocation scheme is considered for secondary users and its performance is analyzed when time average channel gains are substituted for instantaneous channel gains. In this way, it is not necessary to exchange instantaneous channel information; however, users' allocated power will be perturbed. It is of interest to analyze mathematically this perturbation and to show how it affects the network performance. In particular, an upper bound on perturbation of each user's allocated power, rate, and interference caused to a primary receivers by the secondary users is obtained. Then, it is shown that how this perturbation affects the transmission rate and the probability of interference constraint violation by the secondary users.