Quasi-Orthogonal Beamforming in Near-Field Line-of-Sight MIMO Channel

Spatial multiplexing in far-field (FF) multiple-input multiple-output (MIMO) systems typically relies on the multipath provided by scatterers. Recent studies have revealed that near-field (NF) MIMO systems can exploit spatial multiplexing even in line-of-sight (LoS) propagation. Through singular value decomposition (SVD), an orthogonal basis consisting of the channel’s right singular vectors can be obtained to formulate a beamforming matrix. This matrix maps multiple data streams into orthogonal sub-channels, enabling spatial multiplexing. However, the SVD-based beamforming matrix, composed of entries with varying magnitudes and phases, generally requires a costly full digital array architecture. To achieve spatial multiplexing with low-complexity beamforming, this paper explores the channel’s structural characteristics of NF-LoS MIMO systems. Specifically, we consider a general point-to-point MIMO setup for a pair of uniform linear arrays (ULAs). We first investigate the ability of the transmitter (Tx) array to resolve paths to different Rx antennas under the NF spherical wave model. Based on the derived resolution, we explicitly formulate a quasi-orthogonal (QO) basis consisting of NF beamfocusing vectors, ensuring that the normalized magnitude of any two QO vectors remains sufficiently small to meet practical application requirements. By appropriately arranging these QO vectors into a beamforming matrix, we transform the spatial channel into a beamspace channel, where the beams serve as QO sub-channels. Furthermore, we utilize these QO beams or sub-channels for beamspace modulation (BM), where the Tx dynamically selects beams to deliver information via beam index modulation and via spatial multiplexing. Importantly, the beamformer designed for selecting QO beams, consisting of constant-magnitude entries, can be implemented using only analog phase shifters. Compared with the existing SVD based BM, the proposed scheme simplifies implementation in hybrid array architectures and achieves high spectrum efficiency with reduced computation complexity. We also show the feasibility of the proposed scheme in practical scenarios, including imperfect channel state information (CSI), finite-resolution phase shifters, mixed LoS and none-line-of-sight (NLoS) channels, and uniform planar arrays (UPAs).