Abstract
In this article, an efficient distributed and parallel algorithm is proposed to maximize the sum-rate and optimize the input distribution policy for the multi-user single input multiple output multiple access channel (MU-SIMO MAC) system with concurrent access within a cognitive radio (CR) network. The single input means that every user has a single antenna and multiple output means that base station(s) has multiple antennas. The main features are: (i) the power distribution for the users is updated by using variable scale factors which effectively and efficiently maximize the objective function at each iteration; (ii) distributed and parallel computation is employed to expedite convergence of the proposed distributed algorithm; and (iii) a novel water-filling with mixed constraints is investigated, and used as a fundamental block of the proposed algorithm. Due to sufficiently exploiting the structure of the proposed model, the proposed algorithm owns fast convergence. Numerical results verify that the proposed algorithm is effective and fast convergent. Using the proposed approach, for the simulated range, the required number of iterations for convergence is two and this number is not sensitive to the increase of the number of users. This feature is quite desirable for large scale systems with dense active users. In addition, it is also worth noting that the proposed algorithm is a monotonic feasible operator to the iteration. Thus, the stop criterion for computation could be easily set up.
Highlights
The radio spectrum is a precious resource that demands for efficient utilization as the currently licensed spectrum is severely underutilized [1]
As stated by the sufficient and necessary conditions of Lemmas 1 and 2, for any optimal solution to the problem in (3), there is a point sequence generated by Algorithm AWCR such that the point sequence converges to that optimal solution
To improve the performance of the algorithm and reduce the cost of the computation, the objective function in step (3) of the AWCR can be evaluated at the four points mentioned in Remark 3.3, by parallel computation to find the estimate of β∗ of (25)
Summary
The radio spectrum is a precious resource that demands for efficient utilization as the currently licensed spectrum is severely underutilized [1]. By exploiting the structure of the weighted sum-rate optimization problem, we propose an efficient iterative algorithm to compute the optimal input policy and to maximize the weighted sum-rate, via solving a generalized water-filling problem in each of the iterations. We propose a generalized weighted water-filling algorithm (GWWFA) to form a fundamental step (inner loop algorithm) for the target problem. The weighted sum-rate problem is decomposed into a series of generalized water-filling problems With this decomposition, a decoupled system with each equation of the decoupled system containing only a scalar variable is formed and solved. The optimal scale factor is obtained by maximizing the target objective value (i.e., the weighted sum-rate) in the scalar variable β to expedite convergence of the proposed algorithm. For any complex matrix, its superscripts † and T denote the conjugate transpose and the transpose of the matrix, respectively
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