Joint Optimization of Cooperative Spectrum Sensing and Resource Allocation in Multi-channel Cognitive Radio Sensor Networks

Abstract

Cooperative spectrum sensing (CSS) that utilizes multi-user diversity to mitigate channel instability and noise uncertainty is a promising technique in cognitive radio networks (CRNs). However, the spectrum-sensing parameters which affect the channel-access opportunities of secondary users (SUs) are conventionally regarded as static and treated independently from the resource-allocation strategies. In this paper, joint optimization of CSS, channel access and resource allocation is investigated in an overlay CRN in which each SU carries multi-channel spectrum sensing and transmits the detected energy to a fusion centre in the imperfect reporting channel. An access factor is introduced to describe the channel-access strategies in both cooperative and non-cooperative schemes. Based on the aggregate interference and the transmit power constraints, an optimization problem of multi-channel CSS is formulated to obtain the optimal transmit powers, allocation-access strategies, and sensing threshold of CR system for maximization of the opportunistic throughput. To solve the non-convex problems in both the single and multiple CR systems, the efficient iterative algorithms are developed by exploiting the hidden convexity of the optimization problems. Numerical results show that the performance of our approaches yields a significant enhancement compared with the equal channel-access and equal power-allocation strategy.

Appendix

1.1 Proof of Lemma 1

Part (a) can be easily shown by using $\rho _k =1$ and $p_k = P_\mathrm{tot}$, to maximize Problem P2. We note that this upper bound is not achievable but can be used to show the convergence of the algorithm to a fixed point.

Next, we prove part (b) by contradiction. We first assume $R(\varvec{p^{(j)} },\varvec{\rho ^{(j)} }) > R(\varvec{p^{(j)} },\varvec{\rho ^{(j+1)} })$. This means that in Step 3 of Algorithm 1, the objective function decreases. However, this is not possible since the subproblem is convex and $\varvec{\rho ^{(j+1)} }$ is a feasible point and cannot have a smaller objective function than $\varvec{\rho ^{(j)} }$. Thus, we have $R(\varvec{p^{(j)} },\varvec{\rho ^{(j)} }) \le R(\varvec{p^{(j)} },\varvec{\rho ^{(j+1)} })$. Using the same argument, it can also be shown that $R(\varvec{p^{(j)} },\varvec{\rho ^{(j+1)} }) \le R(\varvec{p^{(j+1)} },\varvec{\rho ^{(j+1)} })$. Consequently, the objective function is non-decreasing in j, i.e., $R(\varvec{p^{(j)} },\varvec{\rho ^{(j)} }) \le R(\varvec{p^{(j)} },\varvec{\rho ^{(j+1)} }) \le R(\varvec{p^{(j+1)} },\varvec{\rho ^{(j+1)} })$.

The third part (c) follows directly from part (a) and part (b), since any upper bounded, non-decreasing function converges to a fixed value.