Robust beamforming designs for multiuser MISO downlink with per-antenna power constraints

Abstract

This paper studies the robust beamforming designs for a multiuser multiple-input single-output (MISO) downlink system. Different from the conventional sum-power constraint across all transmit antennas, we consider individual power constraints per antenna at the base station. Assuming that the channel uncertainty is bounded by a spherical region, we develop the optimal robust designs to maximize the minimum worst-case signal-to-interference-plus-noise ratio (SINR) among all users. Specifically, we show that the optimal max-min SINR beamformers can be obtained by solving a sequence of "dual" min-max power problems. Relying on the S-procedure and the linear matrix inequality representation for the cone of Lorentz-positive maps (LPMs), respectively, two designs, which are referred to as Robust-SP and Robust-LPM, are proposed to efficiently solve such min-max power problems. Building on either Robust-SP or Robust LPM, a bisection search algorithm is then developed to find the robust max-min SINR beamformers with guaranteed global optimality and geometrically fast convergence speed. Using the max-min SINR solutions as a cornerstone, we further put forth the optimal robust design for the worst-case weighted sum-rate (WSR) maximization. By formulating the worst-case WSR maximization problem into a monotonic program (MP), we develop a polyblock outer approximation algorithm to obtain the globally optimal solution. Numerical results are presented to demonstrate the merits of the proposed robust beamforming designs.

Robust Beamforming for Downlink 3D-MIMO Systems with l11-norm Bounded CSI Uncertainty

“…Perfect CSI shows the performance when the perfect CSI is used to design the optimal beamforming matrix [18]. Robust SDP is the algorithm proposed in [4], with the spherical uncertainty set (4). The simulations are averaged over N run = 100 runs, each of which is chosen so that the problem is feasible for the observed range of the constraints.…”

“…Note that when the uncertainty set H 1 k is replaced with the set H 2 k , the problem (6) can be recasted as the robust beamforming problem with spherical uncertainty, as proposed in [4]. It can be solved by semi-definite programming (SDP) with the aid of S-procedure [15].…”

“…There are various of CSI uncertainty models in literature. The most commonly used CSI uncertainty sets are spherical or ellipsoidal region [4]- [6], defined by l 2 -norm or Frobenius norm. Another kind of CSI uncertainty set is a hyperrectangular region representing quantization errors [7], defined by infinite norm for real and imaginary part of CSI errors independently.…”