Near-field Physical Layer Security: Robust Beamforming under Location Uncertainty

In this paper, we study robust beamforming design for near-field physical-layer-security (PLS) systems, where a base station (BS) equipped with an extremely large-scale array (XL-array) serves multiple near-field legitimate users (Bobs) in the presence of multiple near-field eavesdroppers (Eves). Unlike existing works that mostly assume perfect channel state information (CSI) or location information of Eves, we consider a more practical and challenging scenario, where the locations of Bobs are perfectly known, while only imperfect location information of Eves is available at the BS. We first formulate a robust optimization problem to maximize the sum-rate of Bobs while guaranteeing a worst-case limit on the eavesdropping rate under location uncertainty. By transforming Cartesian position errors into the polar domain, we reveal an important near-field angular-error amplification effect: for the same location error, the closer the Eve, the larger the angle error, severely degrading the performance of conventional robust beamforming methods based on imperfect channel state information. To address this issue, we first establish the conditions for which the first-order Taylor approximation of the near-field channel steering vector under location uncertainty is largely accurate. Then, we propose a two-stage robust beamforming method, which first partitions the uncertainty region into multiple fan-shaped sub-regions, followed by the second stage to formulate and solve a refined linear-matrix-inequality (LMI)-based robust beamforming optimization problem. In addition, the proposed method is further extended to scenarios with multiple Bobs and multiple Eves. Finally, numerical results validate that the proposed method achieves a superior trade-off between rate performance and secrecy robustness, hence significantly outperforming existing benchmarks under Eve location uncertainty.

Codebook Design for Limited Feedback in Near-Field XL-MIMO Systems

In this paper, we study efficient codebook design for limited feedback in extremely large-scale multiple-input-multiple-output (XL-MIMO) frequency division duplexing (FDD) systems. It is worth noting that existing codebook designs for XL-MIMO, such as polar-domain codebook, have not well taken into account user (location) distribution in practice, thereby incurring excessive feedback overhead. To address this issue, we propose in this paper a novel and efficient feedback codebook tailored to user distribution. To this end, we first consider a typical scenario where users are uniformly distributed within a specific polar-region, based on which a sum-rate maximization problem is formulated to jointly optimize angle-range samples and bit allocation among angle/range feedback. This problem is challenging to solve due to the lack of a closed-form expression for the received power in terms of angle and range samples. By leveraging a Voronoi partitioning approach, we show that uniform angle sampling is optimal for received power maximization. For more challenging range sampling design, we obtain a tight lower-bound on the received power and show that geometric sampling, where the ratio between adjacent samples is constant, can maximize the lower bound and thus serves as a high-quality suboptimal solution. We then extend the proposed framework to accommodate more general non-uniform user distribution via an alternating sampling method. Furthermore, theoretical analysis reveals that as the array size increases, the optimal allocation of feedback bits increasingly favors range samples at the expense of angle samples. Finally, numerical results validate the superior rate performance and robustness of the proposed codebook design under various system setups, achieving significant gains over benchmark schemes, including the widely used polar-domain codebook.

Two-stage Multi-beam Training for Multiuser Millimeter-Wave Communications

In this letter, we study an efficient multi-beam training method for multiuser millimeter-wave communication systems. Unlike the conventional single-beam training method that relies on exhaustive search, multi-beam training design faces a key challenge in balancing the trade-off between beam training overhead and success beam-identification rate, exacerbated by severe inter-beam interference. To tackle this challenge, we propose a new two-stage multi-beam training method with two distinct multi-beam patterns to enable fast and accurate user angle identification. Specifically, in the first stage, the antenna array is divided into sparse subarrays to generate multiple beams (with high array gains), for identifying candidate user angles. In the second stage, the array is redivided into dense subarrays to generate flexibly steered wide beams, for which a cross-validation method is employed to effectively resolve the remaining angular ambiguity in the first stage. Last, numerical results demonstrate that the proposed method significantly improves the success beam-identification rate compared to existing multi-beam training methods, while retaining or even reducing the required beam training overhead.

Near-field Target Localization: Effect of Hardware Impairments

The prior works on near-field target localization have mostly assumed ideal hardware models and thus suffer from two limitations in practice. First, extremely large-scale arrays (XL-arrays) usually face a variety of hardware impairments (HIs) that may introduce unknown phase and/or amplitude errors. Second, the existing block coordinate descent (BCD)-based methods for joint estimation of the HI indicator, channel gain, angle, and range may induce considerable target localization error when the target is very close to the XL-array. To address these issues, we propose in this paper a new three-phase HI-aware near-field localization method, by efficiently detecting faulty antennas and estimating the positions of targets. Specifically, we first determine faulty antennas by using compressed sensing (CS) methods and improve detection accuracy based on coarse target localization. Then, a dedicated phase calibration method is designed to correct phase errors induced by detected faulty antennas. Subsequently, an efficient near-field localization method is devised to accurately estimate the positions of targets based on the full XL-array with phase calibration. Additionally, we resort to the misspecified Cramer-Rao bound (MCRB) to quantify the performance loss caused by HIs. Last, numerical results demonstrate that our proposed method significantly reduces the localization errors as compared to various benchmark schemes, especially for the case with a short target range and/or a high fault probability.

Position Optimization for Two-layer Movable Antenna Systems

Movable antenna (MA) is a promising technology for improving the performance of wireless communication systems by providing new degrees-of-freedom (DoFs) in antenna position optimization. However, existing works on MA systems have mostly considered element-wise single-layer MA (SL-MA) arrays, where all the MAs move within the given movable region, hence inevitably incurring high control complexity and hardware cost in practice. To address this issue, we propose in this letter a new two-layer MA array (TL-MA), where the positions of MAs are jointly determined by the large-scale movement of multiple subarrays and the small-scale fine-tuning of per-subarray MAs. In particular, an optimization problem is formulated to maximize the sum-rate of the TL-MA-aided communication system by jointly optimizing the subarray-positions, per-subarray (relative) MA positions, and receive beamforming. To solve this non-convex problem, we propose an alternating optimization (AO)-based particle swarm optimization (PSO) algorithm, which alternately optimizes the positions of subarrays and per-subarray MAs, given the optimal receive beamforming. Numerical results verify that the proposed TL-MA significantly reduces the sum-displacement of MA motors (i.e., the total moving distances of all motors) of element-wise SL-MA, while achieving comparable rate performance.

MA-enhanced Mixed Near-field and Far-field Covert Communications

In this paper, we propose to employ a modular-based movable extremely large-scale array (XL-array) at Alice for enhancing covert communication performance. Compared with existing work that mostly considered either far-field or near-field covert communications, we consider in this paper a more general and practical mixed-field scenario, where multiple Bobs are located in either the near-field or far-field of Alice, in the presence of multiple near-field Willies. Specifically, we first consider a two-Bob-one-Willie system and show that conventional fixed-position XL-arrays suffer degraded sum-rate performance due to the energy-spread effect in mixed-field systems, which, however, can be greatly improved by subarray movement. On the other hand, for transmission covertness, it is revealed that sufficient angle difference between far-field Bob and Willie as well as adequate range difference between near-field Bob and Willie are necessary for ensuring covertness in fixed-position XL-array systems, while this requirement can be relaxed in movable XL-array systems thanks to flexible channel correlation control between Bobs and Willie. Next, for general system setups, we formulate an optimization problem to maximize the achievable sum-rate under covertness constraint. To solve this non-convex optimization problem, we first decompose it into two subproblems, corresponding to an inner problem for beamforming optimization given positions of subarrays and an outer problem for subarray movement optimization. Although these two subproblems are still non-convex, we obtain their high-quality solutions by using the successive convex approximation technique and devising a customized differential evolution algorithm, respectively. Last, numerical results demonstrate the effectiveness of proposed movable XL-array in balancing sum-rate and covert communication requirements.

Rotatable Antenna Aided Mixed Near-Field and Far-Field Communications in the Upper Mid-Band: Interference Analysis and Joint Optimization

In this paper, we propose to leverage rotatable antennas (RAs) for improving the communication performance in mixed near-field and far-field communication systems by exploiting a new spatial degree-of-freedom (DoF) offered by antenna rotation to mitigate complex near-field interference and mixed-field interference. Specifically, we investigate a modular RA-enabled mixed-field downlink communication system, where a base station (BS) consisting of multiple RA subarrays communicates with multiple near-field users in the presence of several legacy far-field users. We formulate an optimization problem to maximize the sum-rate of the near-field users by jointly optimizing the power allocation and rotation angles of all subarrays at the BS. To gain useful insights into the effect of RAs on mixed-field communications, we first analyze a special case where all subarrays share the same rotation angle and obtain closed-form expressions for the rotation-aware normalized near-field interference and the rotation-aware normalized mixed-field interference using the Fresnel integrals. We then analytically reveal that array rotation effectively suppresses both interference types, thereby significantly enhancing mixed-field communication performance. For the general case involving subarray-wise rotation, we propose an efficient double-layer algorithm to obtain a high-quality solution, where the inner layer optimizes power allocation using the successive convex approximation (SCA) technique, while the outer layer determines the rotation angles of all subarrays via particle swarm optimization (PSO). Finally, numerical results highlight the significant performance gains achieved by RAs over conventional fixed-antenna systems and demonstrate the effectiveness of our developed joint design compared to benchmark schemes.

Joint Frequency-Space Sparse Reconstruction for DOA Estimation under Coherent Sources and Amplitude-Phase Errors

In this letter, we propose a joint frequency-space sparse reconstruction method for direction-of-arrival (DOA) estimation, which effectively addresses the issues arising from the existence of coherent sources and array amplitude-phase errors. Specifically, by using an auxiliary source with known angles, we first construct the real steering vectors (RSVs) based on the spectral peaks of received signals in the frequency domain, which serve as a complete basis matrix for compensation for amplitude-phase errors. Then, we leverage the spectral sparsity of snapshot data in the frequency domain and the spatial sparsity of incident directions to perform the DOA estimation according to the sparse reconstruction method. The proposed method does not require iterative optimization, hence exhibiting low computational complexity. Numerical results demonstrate that the proposed DOA estimation method achieves higher estimation accuracy for coherent sources as compared to various benchmark schemes.

Secure Transmission for Cell-Free Symbiotic Radio Communications with Movable Antenna: Continuous and Discrete Positioning Designs

In this paper, we study a movable antenna (MA) empowered secure transmission scheme for reconfigurable intelligent surface (RIS) aided cell-free symbiotic radio (SR) system. Specifically, the MAs deployed at distributed access points (APs) work collaboratively with the RIS to establish high-quality propagation links for both primary and secondary transmissions, as well as suppressing the risk of eavesdropping on confidential primary information. We consider both continuous and discrete MA position cases and maximize the secrecy rate of primary transmission under the secondary transmission constraints, respectively. For the continuous position case, we propose a two-layer iterative optimization method based on differential evolution with one-in-one representation (DEO), to find a high-quality solution with relatively moderate computational complexity. For the discrete position case, we first extend the DEO based iterative framework by introducing the mapping and determination operations to handle the characteristic of discrete MA positions. To further reduce the computational complexity, we then design an alternating optimization (AO) iterative framework to solve all variables within a single layer. In particular, we develop an efficient strategy to derive the sub-optimal solution for the discrete MA positions, superseding the DEO-based method. Numerical results validate the effectiveness of the proposed MA empowered secure transmission scheme along with its optimization algorithms.

Frequency-switching Array Enhanced Physical-Layer Security in Terahertz Bands: A Movable Antenna Perspective

In this paper, we propose a new frequency-switching array (FSA) enhanced physical-layer security (PLS) system in terahertz bands, where the carrier frequency can be flexibly switched and small frequency offsets can be imposed on each antenna at Alice, so as to eliminate information wiretapping by undesired eavesdroppers. First, we analytically show that by flexibly controlling the carrier frequency parameters, FSAs can effectively form uniform/non-uniform sparse arrays, hence resembling movable antennas (MAs) in the control of inter-antenna spacing and providing additional degree-of-freedom (DoF) in the beam control. Although the proposed FSA experiences additional path-gain attenuation in the received signals, it can overcome several hardware and signal processing issues incurred by MAs, such as limited positioning accuracy, considerable response latency, and demanding hardware and energy cost. To shed useful insights, we first consider a secrecy-guaranteed problem with a null-steering constraint for which maximum ratio transmission (MRT) beamformer is considered at Alice and the frequency offsets are set as uniform frequency increment. Interestingly, it is shown that the proposed FSA can flexibly realize null-steering over Eve in both the angular domain (by tuning carrier frequency) and range domain (by controlling per-antenna frequency offset), thereby achieving improved PLS performance. Then, for the general case, we propose an efficient algorithm to solve the formulated non-convex problem by using the block coordinate descent (BCD) and projected gradient ascent (PGA) techniques. Finally, numerical results demonstrate the convergence of the proposed optimization algorithm and its superiority over fixed-position arrays (FPAs) in terms of secrecy-rate performance.