Performance Analysis of Physical Layer Security: From Far-Field to Near-Field

The secrecy performance in both near-field and far-field communications is analyzed using two fundamental metrics: the secrecy capacity under a power constraint and the minimum power requirement to achieve a specified secrecy rate target. 1) For the secrecy capacity, a closed-form expression is derived under a discrete-time memoryless setup. This expression is further analyzed under several far-field and near-field channel models, and the capacity scaling law is revealed by assuming an infinitely large transmit array and an infinitely high power. A novel concept of "depth of insecurity" is proposed to evaluate the secrecy performance achieved by near-field beamfocusing. It is demonstrated that increasing the number of transmit antennas reduces this depth and thus improves the secrecy performance. 2) Regarding the minimum required power, a closed-form expression is derived and analyzed within far-field and near-field scenarios. Asymptotic analyses are performed by setting the number of transmit antennas to infinity to unveil the power scaling law. Numerical results are provided to demonstrate that: i) compared to far-field communications, near-field communications expand the areas where secure transmission is feasible, specifically when the eavesdropper is located in the same direction as the intended receiver; ii) as the number of transmit antennas increases, neither the secrecy capacity nor the minimum required power scales or vanishes unboundedly, adhering to the principle of energy conservation.

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.

On the Impact of Reactive Region on the Near-Field Channel Gain

The near-field channel gain is analyzed by considering both radiating and reactive components of the electromagnetic field. Novel expressions are derived for the channel gains of spatially-discrete (SPD) and continuous-aperture (CAP) arrays, which are more accurate than conventional results that neglect the reactive region. To gain further insights, asymptotic analyses are carried out in the large aperture size, based on which the impact of the reactive region is discussed. It is proved that for both SPD and CAP arrays, the impact of the reactive region on near-field channel gain is negligible, even as the array aperture size approaches infinity.

Performance Analysis for Near-Field ISAC: A Holographic MIMO Design

A near-field holographic multiple-input multiple-output (MIMO) based integrated sensing and communications (ISAC) framework is proposed for both downlink and uplink scenarios, where spherical wave-based model is considered to capture the characteristics of the near field. The coupling effect introduced by the densely spaced antennas of the holographic MIMO are characterized by spatially correlated Rayleigh fading. Based on the proposed framework, by considering both instantaneous channel state information (CSI) and statistical CSI, closed-form expressions are derived for sensing rates (SRs), communication rates (CRs), and outage probabilities under different ISAC designs. Further insights are gained by examining high signal-to-noise ratio slopes and diversity orders. Specifically, 1) for the downlink case, a sensing-centric (S-C) design and a communications-centric (C-C) design are investigated based on different beamforming strategies, and a Pareto optimal design is proposed to characterize the attainable SR-CR region; and 2) for the uplink case, the S-C design and the C-C design are distinguished by the interference cancellation order of the communication signal and the sensing signal, and the rate region is obtained through a time-sharing strategy. Numerical results reveal that the proposed ISAC system achieves more extensive rate regions than the conventional frequency-division sensing and communications system, highlighting its superior performance.

On the Performance of Near-Field ISAC

The technical trends for the next-generation wireless network significantly extend the near-field region, necessitating a reevaluation for the performance of integrated sensing and communications (ISAC) to account for the effects introduced by the near field. In this paper, a near-field ISAC framework is proposed with a more accurate channel model than the three conventional models (TCMs): uniform plane wave, uniform spherical wave, and non-uniform spherical wave, in which the effective aperture of the antenna is considered. Based on the proposed model, sensing and communication (S&C) performance in both downlink and uplink scenarios are analyzed. For the downlink case, three distinct designs are studied: the communications-centric (C-C) design, the sensing-centric (S-C) design, and the Pareto optimal design. Regarding the uplink case, the C-C design, the S-C design and the time-sharing strategy are considered. Within each design, sensing rates (SRs) and communication rates (CRs) are derived. To gain further insights, high signal-to-noise ratio slopes and rate scaling laws concerning the number of antennas are also examined. Finally, the attainable SR-CR regions of the near-field ISAC are characterized. Numerical results reveal that 1) as the number of antennas grows, the SRs and CRs of the proposed model converges to constants, while those of the TCMs increase unboundedly; 2) ISAC achieves a more extensive rate region than the conventional frequency-division S&C in both downlink and uplink cases.