Quasi-Nash Equilibria for Non-Convex Distributed Power Allocation Games in Cognitive Radios

Abstract

In this paper, we consider a sensing-based spectrum sharing scenario in cognitive radio networks where the overall objective is to maximize the sum-rate of each cognitive radio user by optimizing jointly both the detection operation based on sensing and the power allocation, taking into account the influence of the sensing accuracy and the interference limitation to the primary users. The resulting optimization problem for each cognitive user is non-convex, thus leading to a non-convex game, which presents a new challenge when analyzing the equilibria of this game where each cognitive user represents a player. In order to deal with the non-convexity of the game, we use a new relaxed equilibria concept, namely, quasi-Nash equilibrium (QNE). A QNE is a solution of a variational inequality obtained under the first-order optimality conditions of the player's problems, while retaining the convex constraints in the variational inequality problem. In this work, we state the sufficient conditions for the existence of the QNE for the proposed game. Specifically, under the so-called linear independent constraint qualification, we prove that the achieved QNE coincides with the NE. Moreover, a distributed primal-dual interior point optimization algorithm that converges to a QNE of the proposed game is provided in the paper, which is shown from the simulations to yield a considerable performance improvement with respect to an alternating direction optimization algorithm and a deterministic game.

Distributed resource allocation with imperfect spectrum sensing information and channel uncertainty in cognitive femtocell networks

“…Due to the inherent hardware limitations and variable wireless environment, spectrum sensing errors are inevitable, causing interference to macrocell user equipments (MUEs) in cognitive femtocell networks [13]. Hence, owing to the imperfectness of the spectrum sensing, the traditional resource allocation algorithms might experience performance decrease.…”

“…Based on the aforementioned solutions, jointly considered subchannel allocation and power allocation are a proper way to solve resource allocation problems. The objectives of resource allocation mainly focus on interference management [9,10,12,13,[19][20][21][22], capacity enhancement [8,10,13,15,[20][21][22], power efficiency improvement [15,16,19], and fairness [10,12]. However, to the best of our knowledge, resource allocation for cognitive femtocell network jointly considering interference management, fairness, imperfect spectrum sensing, and interference uncertainty has not been studied in previous works.…”

“…Based on the above analysis, the chance-constrained programming problem in (13) can be transformed into a convex optimization problem. Thus, we can obtain optimal power allocation by solving the following convex optimization problem:…”

Friendly Jamming in a MIMO Wiretap Interference Network: A Nonconvex Game Approach

“…The concept of QNE has been recently used in [12] in sum-rate maximization in cognitive radio users. However, no effort has been made to improve the performance of achieved QNEs.…”

“…For all simulated algorithms, β = 5 (cf. (12)) and the termination criterion is set to when the normalized relative difference in each link's secrecy rate for two consecutive iterations is less than 10 −3 . For the QNE selection algorithms, we set their parameters as follows: The step size matrix (i.e., γ ) is set such that γ …”