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

The performance of multiplexing and diversity achieved by continuous aperture arrays (CAPAs) over fading channels is analyzed. Angular-domain fading models are derived for CAPA-based multiple-input single-output (MISO), single-input multiple-output (SIMO), and multiple-input multiple-output (MIMO) channels using the Fourier relationship between the spatial response and its angular-domain counterpart. Building on these models, angular-domain transmission frameworks are proposed to facilitate CAPA-based communications, under which the performance of multiplexing and diversity is analyzed. 1) For SIMO and MISO channels, closed-form expressions are derived for the average data rate (ADR) and outage probability (OP). Additionally, asymptotic analyses are performed in the high signal-to-noise ratio (SNR) regime to unveil the maximal multiplexing gain and maximal diversity gain. The diversity-multiplexing trade-off (DMT) is also characterized, along with the array gain within the DMT framework. 2) For MIMO channels, high-SNR approximations are derived for the ADR and OP, based on which the DMT and associated array gain are revealed. The performance of CAPAs is further compared with that of conventional spatially discrete arrays (SPDAs) to highlight the superiority of CAPAs. The analytical and numerical results demonstrate that: i) compared to SPDAs, CAPAs achieve a lower OP and higher ADR, resulting in better spectral efficiency; ii) CAPAs achieve the same DMT as SPDAs with half-wavelength antenna spacing while attaining a larger array gain; and iii) CAPAs achieve a better DMT than SPDAs with antenna spacing greater than half a wavelength.