Diversity and Multiplexing for Continuous Aperture Array (CAPA)-Based Communications

TL;DR

This paper develops a fading model for continuous aperture arrays (CAPAs) and analyzes their diversity and multiplexing capabilities, showing they outperform traditional arrays in various channel conditions and configurations.

Contribution

It introduces a comprehensive fading model for CAPAs and provides analytical performance analysis, including outage probability, capacity, and diversity-multiplexing trade-offs, comparing with conventional arrays.

Findings

CAPAs achieve lower outage probability than SPDAs.

CAPAs attain higher ergodic channel capacity.

CAPAs outperform SPDAs in diversity-multiplexing trade-off, especially at larger antenna spacings.

Abstract

A general fading model for multipath channels between two non-parallel continuous-aperture arrays (CAPAs) is proposed. Building on this model, the performance of diversity and multiplexing achieved by CAPAs over fading channels is analyzed. i) For multiple-input single-output (MISO) and single-input multiple-output (SIMO) channels, Landau's eigenvalue theorem is applied to analyze the autocorrelation of the spatial response. Closed-form expressions are derived for the outage probability (OP) and ergodic channel capacity (ECC). Asymptotic analyses in the high signal-to-noise ratio (SNR) regime are conducted to reveal the maximal achievable diversity and multiplexing gains. The diversity-multiplexing trade-off (DMT) is characterized, along with the array gain within the DMT framework. ii) For multiple-input multiple-output (MIMO) channels, a wavenumber-domain-based transmission framework is proposed to leverage the spatial degrees of freedom offered by CAPAs. Asymptotic approximations for the OP and ECC are derived, and the DMT is explored. The performance of CAPAs is further compared with that of conventional spatially-discrete arrays (SPDAs). Analytical and numerical results demonstrate that: i) CAPAs achieve a lower OP and higher ECC than SPDAs; ii) CAPAs achieve the same DMT as SPDAs with antenna spacing no larger than half a wavelength while attaining a higher array gain; and iii) CAPAs outperform SPDAs with antenna spacing greater than half a wavelength in terms of DMT.