Multi‐user hybrid analogue/digital beamforming for relatively large‐scale antenna systems

Abstract

Power consumption and costs of analogue front-end (AFE) chains are often not negligible for large-scale antenna array systems. A low-complexity hardware architecture is to use a number of AFE chains that are less than the number of antennas. Beamforming for this low-complexity hardware architecture involves both digital and analogue beamforming, which is termed hybrid analogue/digital beamforming. In this study, minimising the transmit power subject to signal-to-interferenceplus-noise ratio (SINR) constraints and maximising the minimal SINR under the constraint of the transmit power, are investigated, respectively, for hybrid analogue/digital beamforming. Properties on the feasibility and optimality of the two problems are derived. Numerical algorithms based on semi-definite positive relaxation are proposed in an attempt to solve the two optimisation problems. The performance of the proposed algorithms is evaluated under the Gaussian and 60 GHz channel models. It is shown that the performance of hybrid analogue/digital beamforming is highly related to the correlation of the channel coefficients of subcarriers. Additionally, for different extents of the users' spatial separability, some heuristics ways of designing analogue beamforming are shown to be able to approach to at least the local optimums under the 60 GHz channel model.

Optimal Hybrid Beamforming for Multiuser Massive MIMO Systems With Individual SINR Constraints

“…We consider four baselines for comparison. The first baseline is the hybrid beamformer obtained using the SDR-Alt algorithm in [4] for solving Problem P Ori . The other three baselines are three typical fully-digital beamformers (N = M ), i.e., the optimal solution W ⋆ D of Problem P FD (optimal fullydigital beamformer), fully-digital beamformer based on zeroforcing (ZF) and fully-digital beamformer based on maximumratio-transmission (MRT), which satisfy the SINR constraints in (2).…”

“…The other three baselines are three typical fully-digital beamformers (N = M ), i.e., the optimal solution W ⋆ D of Problem P FD (optimal fullydigital beamformer), fully-digital beamformer based on zeroforcing (ZF) and fully-digital beamformer based on maximumratio-transmission (MRT), which satisfy the SINR constraints in (2). In evaluating the two proposed algorithms and the SDR-Alt algorithm in [4], we use the same convergence criterion; we generate 30 random channels (same for all schemes), and show the mean and standard deviation (cf. vertical bar at each point) of the performance.…”

“…However, most previous works on multiuser hybrid beamforming design fail to consider individual SINR constraints. In [4], the authors consider a non-convex multiuser hybrid beamforming design problem with individual SINR constraints and propose a semidefinite relaxation-based alternating (SDR-Alt) algorithm to obtain a feasible solution. In particular, in each iteration, a digital beamforming design problem is solved by computing a semiclosed form solution, and an analog beamforming design problem is solved with complexity O(M 4.5 N 4.5 ) using standard techniques for semidefinite programming (SDP), where M denotes the number of antennas and N denotes the number of RF chains.…”

“…until convergence criterion is met; 8: µ := 2µ; 9: end while iterative alternating procedure for given µ has much lower computational complexity than the SDR-Alt algorithm [4]. Since S v X (i) S w 2 F + µ trace(P T X (i) ) is nonnegative and is monotonically non-increasing with i, the iterative alternating procedure for given µ converges to a limit point.…”

A Novel Hybrid Beamforming Algorithm With Unified Analog Beamforming by Subspace Construction Based on Partial CSI for Massive MIMO-OFDM Systems

“…2) Even if the whole frequency band is allocated for a single UE or a single group of UEs, challenges still exist to apply HB algorithms in [12]- [14], [16], [17], [20], [21] to the considered massive MIMO-OFDM systems. Specifically, full Channel State Information (CSI) is assumed at either each BS or each UE, which is challenging to be acquired with HB because the number of RF chains is much smaller than the number of antennas.…”