Communicating with Extremely Large-Scale Array/Surface: Unified Modelling and Performance Analysis (2104.13162v1)

Abstract: Wireless communications with extremely large-scale array (XL-array) correspond to systems whose antenna sizes are so large that conventional modelling assumptions, such as uniform plane wave (UPW) impingement, are longer valid. This paper studies the mathematical modelling and performance analysis of XL-array communications. By deviating from the conventional modelling approach that treats the array elements as sizeless points, we explicitly model their physical area/aperture, which enables a unified modelling for the classical discrete antenna arrays and the emerging 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 SNR with the optimal single-user MRC/MRT beamforming is derived. The expression reveals that instead of scaling linearly with the antenna number M as in conventional UPW modelling, 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. Additionally, we have derived an alternative insightful expression for the optimal SNR in terms of the vertical and horizontal angular spans. Furthermore, we also show that our derived results include the far-field UPW modelling 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.

• The paper proposes a unified XL-array model that integrates variations in signal phase, amplitude, and projected aperture for accurate near and far-field analysis.
• It derives a closed-form SNR expression under optimum MRC/MRT beamforming, revealing diminishing returns with increased antenna counts.
• It introduces a new uniform-power distance criterion based on horizontal and vertical angular spans, essential for precise far-field approximations.

Unified Modelling and Performance Analysis of XL-Array Communications

This paper thoroughly investigates wireless communications using extremely large-scale antennas, termed XL-arrays, by presenting a unified mathematical model along with comprehensive performance analysis. XL-arrays are characterized by their substantial physical size, which necessitates deviations from conventional modeling assumptions such as uniform plane wave (UPW) impingement. The paper addresses the inadequacies of prevailing models by adopting a novel approach that incorporates physical dimensions and the projected aperture area of individual array elements. This methodology encompasses both traditional discrete antenna arrays and the emerging continuous surfaces, delivering a generic model that yields more accurate results in both near-field and far-field regions.

Key Contributions and Findings

1. Developing a Unified XL-Array Model: The paper introduces a comprehensive array/surface model which considers variations in signal phase, amplitude, and projected aperture across array elements. This model is applicable to both far-field UPW conditions and radiative near-field conditions and extends beyond sizeless point assumptions typically used in less extensive arrays.
2. Closed-Form SNR Expression: Utilizing this model, the paper derives a closed-form expression for signal-to-noise ratio (SNR) under optimum single-user maximum ratio combining/transmission (MRC/MRT) beamforming. Contrary to linear scaling anticipated in traditional UPW models, the paper reveals that SNR increases with antenna count but exhibits diminishing returns influenced by array properties like occupation ratio and physical array dimensions.
3. Implications of Signal Geometrical Angles: The paper articulates an alternative SNR representation via horizontal and vertical angular spans, defined by geometric angles formed between user location and array/surface. It demonstrates that these spans critically influence communication performance.
4. Far-field Approximation and New Distance Criterion: In examining far-field behavior, the paper identifies the necessity of a new distance criterion termed uniform-power distance (UPD). UPD accounts for amplitude/power variations across array elements, supplementing the classical Rayleigh distance which focuses solely on phase discrepancies.
5. Numerical Validation: Extensive numerical results showcase the necessity for proper modeling in XL-array communications. Comparisons between the proposed model and benchmarks underscore the inadequacies of existing UPW and spherical wave models, especially in scenarios involving substantial arrays and inclined signal paths.

Practical and Theoretical Implications

The paper's findings pave the way for enhanced spectral efficiency and spatial resolutions in future beyond 5G (B5G) and sixth-generation (6G) networks using XL-MIMO and related technologies. By providing refined modeling tools, solution developers can account for previously overlooked factors like angular spans and projected apertures. This can lead to more efficient configurations and improved system designs that consider fluctuations in signals due to large antenna sizes.

Moreover, the introduction of the UPD criterion could precipitate new standards for radio communication systems that distinguish between near and far-field scenarios differently based on user angles. With these insights, future studies could explore broader implications, including software and hardware adaptations necessary for harnessing these XL-array benefits.

Through meticulous analysis, this paper enriches our understanding of XL-array communications, urging a revamped approach to developing future wireless networks potentially dominated by large intelligent surfaces and comprehensive MIMO setups.