Communicating With Extremely Large-Scale Array/Surface: Unified Modeling and Performance Analysis

Wireless communications with extremely large-scale array (XL-array) correspond to systems whose antenna sizes are so large that conventional modeling assumptions, such as uniform plane wave (UPW) impingement, are no longer valid. This paper studies the mathematical modeling and performance analysis of XL-array communications. By deviating from the conventional modeling approach that treats the array elements as sizeless points, we explicitly model their physical area/aperture, which enables a unified modeling for the classical discrete antenna arrays and the emerging active continuous surfaces. As such, a generic array/surface model that accurately takes into account the variations of signal phase, amplitude and projected aperture across array elements is proposed. Based on the proposed model, a closed-form expression of the resulting signal-to-noise ratio (SNR) with the optimal single-user maximum ratio combining/transmission (MRC/MRT) beamforming is derived. The expression reveals that instead of scaling linearly with the antenna number
$M$
as in conventional UPW modeling, the SNR with the more generic model increases with
$M$
with diminishing return, which is governed by the collective properties of the array, such as the
array occupation ratio
and the physical sizes of the array along each dimension, while irrespective of the properties of the individual array element. In addition, we have derived an alternative insightful expression for the optimal SNR in terms of the
vertical
and
horizontal angular spans
, which are fully determined by the geometric angles formed by the array/surface and user location. Furthermore, we also show that our derived results include the far-field UPW modeling as a special case. One important finding during the study of far-field approximation is the necessity to introduce a new distance criterion to complement the classical Rayleigh distance, termed
uniform-power distance
(UPD), which concerns the signal amplitude/power variations across array elements, instead of phase variations as for Rayleigh distance. Extensive numerical results are provided to demonstrate the necessity of proper modeling for XL-array communications by comparing the proposed model with various benchmark models.