Exploring the Advantages of Sparse Arrays in Near-Field XL-MIMO Systems: Beam Analysis and EDoF Function

This paper investigates near-field extremely large-scale multiple-input multiple-output (XL-MIMO) systems with sparse uniform planar arrays (UPAs). Based on the Green’s function-based channel model, the paper derives closed-form expressions for the signal beam power when the distance coordinate or the angular coordinates varies with respective to the focused position. Based on that, closed-form expressions for the lobe length and the suppressing ratio are obtained, indicating that both the distance-focusing property and the grating lobe behavior can be enhanced as the focal distance decreases or the antenna spacing increases. Furthermore, the paper introduces a crucial constraint on system parameters, under which effective degrees-of-freedom (EDoF) of XL-MIMO systems with sparse UPAs can be precisely estimated. Then, the paper proposes an algorithm to obtain a closed-form expression, which can estimate EDoF with high accuracy and low computational complexity. The numerical results verifies the correctness of the main results of this paper.