Continuous Aperture Array (CAPA)-Based Wireless Communications: Capacity Characterization

The capacity limits of continuous-aperture array (CAPA)-based wireless communications are characterized. To this end, an analytically tractable transmission framework is established for both uplink and downlink CAPA systems. Based on this framework, closed-form expressions for the single-user channel capacity are derived. The results are further extended to a multiuser case by characterizing the capacity limits of a two-user channel and proposing the associated capacity-achieving decoding and encoding schemes. 1) For the uplink case, the sum-rate capacity and capacity region, as well as the capacity-achieving detectors, are derived. 2) For the downlink case, the uplink-downlink duality is established by deriving the uplink-to-downlink and downlink-to-uplink transformations under the same power constraint, based on which the optimal power allocation policy and the achieved sum-rate capacity and capacity region are characterized. To gain further insights, several case studies are presented by specializing the derived results into various array structures, including the planar CAPA, linear CAPA, and planar spatially discrete array (SPDA). Numerical results are provided to reveal that: i) the channel capacity achieved by CAPAs converges towards a finite upper bound as the aperture size increases; and ii) CAPAs offer significant capacity gains over the conventional SPDAs.