Sparse Array Enabled Near-Field Communications: Beam Pattern Analysis and Hybrid Beamforming Design

Extremely large-scale arrays (XL-arrays) have emerged as a promising technology to enable <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">near-field</i> communications for achieving enhanced spectrum efficiency and spatial resolution, by drastically increasing the number of antennas. However, this also inevitably incurs higher hardware and energy cost, which may not be affordable in future wireless systems. To address this issue, we propose in this paper two types of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sparse arrays</i> (SAs) for enabling near-field communications. Specifically, we first consider the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">linear sparse array</i> (LSA) and characterize its near-field beam pattern. It is shown that LSAs can achieve the near-field beam-focusing gain with lower hardware cost and energy consumption, while it introduces several undesired <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">grating-lobes</i>, which are focused on specific regions exhibiting comparable beam power with the main-lobe. An efficient hybrid beamforming design is then proposed for the LSA to deal with the potential strong inter-user interference (IUI). Next, we further consider another form of SA, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">extended coprime array</i> (ECA), which is composed of two LSA subarrays with different (coprime) inter-antenna spacing. By characterizing the ECA near-field beam pattern, we show that compared with the LSA of the same array sparsity, ECAs can greatly suppress the beam power of near-field grating-lobes thanks to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">offset</i> effect of the two subarrays, albeit generating more low-power grating-lobes. This thus motivates us to propose a customized two-phase hybrid beamforming design for ECAs. Finally, numerical results are presented to demonstrate the energy-efficiency gain of the proposed two SAs over dense uniform linear arrays.