This paper investigates the capabilities and effectiveness of backward localization centered on reconfigurable intelligent surfaces (RISs). In the backward sensing paradigm, the region of interest (RoI) is illuminated using a set of diverse radiation patterns. These patterns encode spatial information into a sequence of measurements, which are subsequently processed to reconstruct the RoI. We show that a single RIS can estimate the direction of arrival of incident waves by leveraging configurational diversity, and that the spatial diversity provided by multiple RISs further improves the accuracy of source localization and power estimation. The underlying structure of the sensing operator in the multi-snapshot measurement process is clarified. For single-RIS localization, the sensing operator is decomposed into a product of structured matrices, each corresponding to a specific physical process: wave propagation to and from the RIS, the relative phase offsets of elements with respect to the reference point, and the applied phase configuration of each element. A unified framework for identifying key performance indicators is established by analyzing the conditioning of the sensing operators. In the multi-RIS setting, we derive–via rank analysis–the governing law among the RoI size, the number of elements, and the number of measurements. Upper bounds on the relative error of the least squares reconstruction algorithm are derived. These bounds clarify how key performance indicators affect estimation error and provide valuable guidance for system-level optimization. Numerical experiments confirm that the trend of the relative error is consistent with the theoretical bounds. Finally, we develop a proof-of-concept prototype using universal software radio peripherals and employ a magnitude-only reconstruction algorithm tailored to the system. To the best of our knowledge, this represents the first experimental demonstration of its kind.

Accurate 3D localization is essential for realizing advanced sensing functionalities in next-generation Wi-Fi communication systems. This study investigates the potential of multistatic localization in Wi-Fi networks through the deployment of multiple cooperative antenna arrays. The collaborative gain offered by these arrays is twofold: (i) intra-array coherent gain at the wavelength scale among antenna elements, and (ii) inter-array cooperative gain across arrays. To evaluate the feasibility and performance of this approach, we develop WiCAL (Wi-Fi Collaborative Antenna Localization), a system built upon commercial Wi-Fi infrastructure equipped with uniform rectangular arrays (URAs). These arrays are driven by multiplexing embedded radio frequency (RF) chains available in standard access points or user devices, thereby eliminating the need for sophisticated, costly, and power-hungry multi-transceiver modules typically required in multiple-input and multiple-output (MIMO) systems. To address phase offsets introduced by RF chain multiplexing, we propose a three-stage, fine-grained phase alignment scheme to synchronize signals across antenna elements within each array. A bidirectional spatial smoothing MUSIC algorithm is employed to estimate angles of arrival (AoAs) and mitigate performance degradation caused by correlated interference. To further exploit inter-array cooperative gain, we elaborate on the synchronization mechanism among distributed URAs, which enables direct position determination by bypassing intermediate angle estimation. Once synchronized, the distributed URAs effectively form a virtual large-scale array, significantly enhancing spatial resolution and localization accuracy. WiCAL is validated using 3 × 4 URAs operating at the 5.2 GHz band. Experimental results demonstrate median AoA estimation errors of 1° in elevation and 1.5° in azimuth under intra-array coherent processing. For inter-array collaboration, the system achieves a median localization error of 15.6 cm using two URAs, outperforming state-of-the-art methods.

The reconfigurable intelligent surface (RIS) has garnered considerable attention due to its substantial potential in reconfiguring the electromagnetic environment. In RIS-aided communications, constrained ℓ2-norm maximization problems frequently arise due to the phase configuration requirements. This paper investigates a general discrete ℓp-norm maximization problem, with power aggregation through RIS as a specific example. We propose a mathematically concise iterative framework composed of alternating inner product maximizations, which is well-suited for addressing both ℓ1- and ℓ2-norm maximizations under either discrete or continuous uni-modular variable constraints. The iteration process is proven to be monotonically non-decreasing. Additionally, this framework exhibits a distinctive capability to mitigate performance degradation caused by discrete quantization in practical systems, which is applicable to any algorithm intended for the continuous solution. Furthermore, as an integral component of the alternating iterations framework, we present a divide-and-sort (DaS) method to tackle the discrete inner product maximization problem. In the realm of ℓ∞-norm maximization, the DaS method ensures the identification of the global optimum with polynomial search complexity. We validate the proposed methods’ effectiveness and superiority through numerical and prototype experiments. Finally, we demonstrate that the proposed framework can be extended and applied to a wide range of other engineering problems.