A Parallel Low Complexity Zero-Forcing Beamformer Design for Multiuser MIMO Systems Via a Regularized Dual Decomposition Method

Abstract

Zero-forcing beamforming under per-antenna power constraint (PAPC) is considered in this paper and the objective is to maximize the minimum user information rate. A parallel low complexity zeroforcing beamformer design is proposed in this paper for MU-MIMO systems by introducing a regularized dual decomposition method. The idea of this method is to solve the problem via solving its dual problem.Since the dual objective is not differentiable, a Tikhonov regularization is introduced. The regularized problem can be solved by using a gradient-based method in a parallel manner. Moreover, the optimal solution of the Lagrangian is in a closed form. The smoothness properties of the regularized dual function are investigated. We also estimate the error bound between the optimal function value of the primal problem and that of the regularized dual problem. Corresponding convergence analysis and convergence rate of the proposed algorithm are established. Computational complexity analysis is carried out to compare the complexity of the proposed method with that of state-of-the-art interior point method.Simulation results are provided to show the effectiveness of the proposed method.

Revisiting the MIMO Capacity With Per-Antenna Power Constraint: Fixed-Point Iteration and Alternating Optimization

“…We will see shortly that in the second proposed iterative algorithm, Q n ≻ 0 for all iterations n, and thus Φ −1 n is well defined. Also, it is worth mentioning that the gradient of the objective in (23) with respect to Q is identical to that of the original objective in (15) when Q = Q n . This is essentially to ensure that the first order optimality conditions of the original problem are preserved even with the use of an upper bound.…”

“…subject to tr(S) ≤ P, tr(QP) ≤ P ; Q : diagonal (15) where P N i=1 P i . In the above formulation we define log |Q| = −∞ if Q is singular.…”

Energy-Efficient User Association with Open Loop Power Control for Uplink HCNs

“…Next, we will give the detailed discussions on how to solve the problem (20). As a general approach to solve the optimization problems, especially for large-scale problems [35], the dual decomposition method has been widely applied in resource allocation [36] and transceiver design [37] and routing [38]. By breaking the original problem up into smaller subproblems that can often be tackled in a distributed manner, an effective algorithm can be easily designed for distributed implement.…”

A low-complexity zero-forcing Beamformer design for multiuser MIMO systems via a dual gradient method

“…In [11], the constant step size rule is adopted, where the estimated Liptsiz constant t is chosen for the step size in each iteration. Here, we apply a backtracking line search to determine the step size t k in the kth iteration.…”

“…The computational complexity is only O M 3 N + N 2 in each iteration. In the literature, a constant number is chosen as the step size, and the Lipschitz constant is always chosen [11]. However, in this case the convergence is slow and sometimes it dos not even converge.…”