Optimal Beamforming for Multi-Target Multi-User ISAC Exploiting Prior Information: How Many Sensing Beams Are Needed?

This paper studies a multi-target multi-user integrated sensing and communication (ISAC) system where a multi-antenna base station (BS) communicates with multiple single-antenna users in the downlink and senses the unknown and random angle information of multiple targets based on their reflected echo signals at the BS receiver as well as their prior probability information. We focus on a general beamforming structure with both communication beams and dedicated sensing beams, whose design is highly non-trivial as more sensing beams provide more flexibility in sensing, but introduce extra interference to communication. To resolve this trade-off, we first characterize the periodic posterior Cram\'er-Rao bound (PCRB) as a lower bound of the mean-cyclic error (MCE) in multi-target sensing. Then, we optimize the beamforming to minimize the maximum periodic PCRB among all targets to ensure fairness, subject to individual communication rate constraints at multiple users. Despite the non-convexity of this problem, we propose a general construction method for the optimal solution by leveraging semi-definite relaxation (SDR), and derive a general bound on the number of sensing beams needed. Moreover, we unveil specific structures of the optimal solution in various cases, where tighter bounds on the number of sensing beams needed are derived (e.g., no or at most one sensing beam is needed under stringent rate constraints or with homogeneous targets). Next, we study the beamforming optimization to minimize the sum periodic PCRB under user rate constraints. By applying SDR, we propose a general construction method for the optimal solution and its specific structures which yield lower computational complexities. We derive a general bound and various tighter bounds on the number of sensing beams needed. Numerical results validate our analysis and effectiveness of our proposed beamforming designs.

Intelligent Reflecting Surface Based Localization of Mixed Near-Field and Far-Field Targets

This paper considers an intelligent reflecting surface (IRS)-assisted bi-static localization architecture for the sixth-generation (6G) integrated sensing and communication (ISAC) network. The system consists of a transmit user, a receive base station (BS), an IRS, and multiple targets in either the far-field or near-field region of the IRS. In particular, we focus on the challenging scenario where the line-of-sight (LOS) paths between targets and the BS are blocked, such that the emitted orthogonal frequency division multiplexing (OFDM) signals from the user reach the BS merely via the user-target-IRS-BS path. Based on the signals received by the BS, our goal is to localize the targets by estimating their relative positions to the IRS, instead of to the BS. We show that subspace-based methods, such as the multiple signal classification (MUSIC) algorithm, can be applied onto the BS's received signals to estimate the relative states from the targets to the IRS. To this end, we create a virtual signal via combining user-target-IRS-BS channels over various time slots. By applying MUSIC on such a virtual signal, we are able to detect the far-field targets and the near-field targets, and estimate the angle-of-arrivals (AOAs) and/or ranges from the targets to the IRS. Furthermore, we theoretically verify that the proposed method can perfectly estimate the relative states from the targets to the IRS in the ideal case with infinite coherence blocks. Numerical results verify the effectiveness of our proposed IRS-assisted localization scheme. Our paper demonstrates the potential of employing passive anchors, i.e., IRSs, to improve the sensing coverage of the active anchors, i.e., BSs.

Joint Transmission and Compression Design for 6G Networked Sensing with Limited-Capacity Backhaul

This paper considers networked sensing in cellular network, where multiple base stations (BSs) first compress their received echo signals from multiple targets and then forward the quantized signals to the cloud via limited-capacity backhaul links, such that the cloud can leverage all useful echo signals to perform high-resolution localization. Under this setup, we manage to characterize the posterior Cramer-Rao Bound (PCRB) for localizing all the targets as a function of the transmit covariance matrix and the compression noise covariance matrix of each BS. Then, a PCRB minimization problem subject to the transmit power constraints and the backhaul capacity constraints is formulated to jointly design the BSs' transmission and compression strategies. We propose an efficient algorithm to solve this problem based on the alternating optimization technique. Specifically, it is shown that when either the transmit covariance matrices or the compression noise covariance matrices are fixed, the successive convex approximation technique can be leveraged to optimize the other type of covariance matrices locally. Numerical results are provided to verify the effectiveness of our proposed algorithm.

Finding Defective Elements in Intelligent Reflecting Surface via Over-the-Air Measurements

Due to circuit failures, defective elements that cannot adaptively adjust the phase shifts of their impinging signals in a desired manner may exist on an intelligent reflecting surface (IRS). Traditional way to find these defective IRS elements requires a thorough diagnosis of all the circuits belonging to a huge number of IRS elements, which is practically challenging. In this paper, we will devise a novel approach under which a transmitter sends known pilot signals and a receiver localizes all the defective IRS elements just based on its over-the-air measurements reflected from the IRS. The key lies in the fact that the over-the-air measurements at the receiver side are functions of the set of defective IRS elements. Based on this observation, we propose a bisection based method to localize all the defective IRS elements. Specifically, at each time slot, we properly control the desired phase shifts of all the IRS elements such that half of the considered regime that is not useful to localize the defective elements can be found based on the received signals and removed. Via numerical results, it is shown that our proposed bisection method can exploit the over-the-air measurements to localize all the defective IRS elements quickly and accurately.

Optimal Transmit Signal Design for Multi-Target MIMO Sensing Exploiting Prior Information

In this paper, we study the transmit signal optimization in a multiple-input multiple-output (MIMO) radar system for sensing the angle information of multiple targets via their reflected echo signals. We consider a challenging and practical scenario where the angles to be sensed are unknown and random, while their probability information is known a priori for exploitation. First, we establish an analytical framework to quantify the multi-target sensing performance exploiting prior distribution information, by deriving the posterior Cram\'{e}r-Rao bound (PCRB) as a lower bound of the mean-squared error (MSE) matrix in sensing multiple unknown and random angles. Then, we formulate and study the transmit sample covariance matrix optimization problem to minimize the PCRB for the sum MSE in estimating all angles. By leveraging Lagrange duality theory, we analytically prove that the optimal transmit covariance matrix has a rank-one structure, despite the multiple angles to be sensed and the continuous feasible range of each angle. Moreover, we propose a sum-of-ratios iterative algorithm which can obtain the optimal solution to the PCRB-minimization problem with low complexity. Numerical results validate our results and the superiority of our proposed design over benchmark schemes.

Hybrid Beamforming Design for Integrated Sensing and Communication Exploiting Prior Information

In this paper, we investigate the hybrid beamforming design for a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, where a multi-antenna base station (BS) with hybrid analog-digital transmit antenna arrays sends dual-functional signals to communicate with a multi-antenna user and simultaneously sense the location information of a point target based on the reflected echo signals. Specifically, we aim to sense the target's unknown and random angle information by exploiting its prior distribution information, with posterior Cram\'{e}r-Rao bound (PCRB) employed as the sensing performance metric. First, we consider a sensing-only case and study the hybrid beamforming optimization to minimize the sensing PCRB. We analytically prove that hybrid beamforming can achieve the same performance as the optimized digital beamforming as long as the number of radio frequency (RF) chains is larger than 1. Then, we propose a convex relaxation based algorithm for the hybrid beamforming design with a single RF chain. Next, we study the hybrid beamforming optimization to minimize the PCRB subject to a communication rate target. Due to the intractability of the exact PCRB expression, we replace it with a tight upper bound. Although this problem is still non-convex and challenging to solve, we propose an alternating optimization (AO) algorithm for finding a high-quality suboptimal solution based on the feasible point pursuit successive convex approximation (FPP-SCA) method. Numerical results validate the effectiveness of our proposed hybrid beamforming design.

Leveraging A Variety of Anchors in Cellular Network for Ubiquitous Sensing

Integrated sensing and communication (ISAC) has recently attracted tremendous attention from both academia and industry, being envisioned as a key part of the standards for the sixth-generation (6G) cellular network. A key challenge of 6G-oriented ISAC lies in how to perform ubiquitous sensing based on the communication signals and devices. Previous works have made great progresses on studying the signal waveform design that leads to optimal communication-sensing performance tradeoff. In this article, we aim to focus on issues arising from the exploitation of the communication devices for sensing in 6G network. Particularly, we will discuss about how to leverage various nodes available in the cellular network as anchors to perform ubiquitous sensing. On one hand, the base stations (BSs) will be the most important anchors in the future 6G ISAC network, since they can generate/process radio signals with high range/angle resolutions, and their positions are precisely known. Correspondingly, we will first study the BS-based sensing technique. On the other hand, the BSs alone may not enable ubiquitous sensing, since they cannot cover all the places with strong line-of-sight (LOS) links. This motivates us to investigate the possibility of using other nodes that are with higher density in the network to act as the anchors. Along this line, we are interested in two types of new anchors - user equipments (UEs) and reconfigurable intelligent surfaces (RISs). This paper will shed light on the opportunities and challenges brought by UE-assisted sensing and RIS-assisted sensing. Our goal is to devise a novel 6G-oriented sensing architecture where BSs, UEs, and RISs can work together to provide ubiquitous sensing services.

Optimal Beamforming for Secure Integrated Sensing and Communication Exploiting Target Location Distribution

In this paper, we study a secure integrated sensing and communication (ISAC) system where one multi-antenna base station (BS) simultaneously communicates with one single-antenna user and senses the location parameter of a target which serves as a potential eavesdropper via its reflected echo signals. In particular, we consider a challenging scenario where the target's location is unknown and random, while its distribution information is known a priori. First, we derive the posterior Cram\'er-Rao bound (PCRB) of the mean-squared error (MSE) in target location sensing, which has a complicated expression. To draw more insights, we derive a tight approximation of it in closed form, which indicates that the transmit beamforming should achieve a "probability-dependent power focusing" effect over possible target locations, with more power focused on highly-probable locations. Next, considering an artificial noise based beamforming structure, we formulate the transmit beamforming optimization problem to maximize the worst-case secrecy rate among all possible target (eavesdropper) locations, subject to a threshold on the sensing PCRB. The formulated problem is non-convex and difficult to solve. We show that the problem can be solved via a two-stage method, by first obtaining the optimal beamforming corresponding to any given threshold on the signal-to-interference-plus-noise ratio (SINR) at the eavesdropper, and then obtaining the optimal threshold via one-dimensional search. By applying the semi-definite relaxation (SDR) technique, we relax the first problem into a convex form and further prove that the relaxation is tight, based on which the optimal solution of the original beamforming optimization problem can be obtained with polynomial-time complexity. Then, we further propose two suboptimal solutions with lower complexity. Numerical results validate the effectiveness of our designs.

User-Assisted Networked Sensing in OFDM Cellular Network with Erroneous Anchor Position Information

In the sixth-generation (6G) integrated sensing and communication (ISAC) cellular network, base stations (BSs) can collaborate with each other to reap not only the cooperative communication gain, but also the networked sensing gain. In contrast to cooperative communication where both line-of-sight (LOS) paths and non-line-of-sight (NLOS) paths are useful, networked sensing mainly relies on the LOS paths. However, in practice, the number of BSs possessing LOS paths to a target can be small, leading to marginal networked sensing gain. Because the density of user equipments (UEs) is much larger than that of the BSs, this paper considers a UE-assisted networked sensing architecture, where a BS transmits communication signals in the downlink, while the UEs that receive the echo signals scattered by a target can cooperate with the BS to localize it. Under this scheme, however, the positions of the UEs are estimated by Global Positioning System (GPS) and subject to unknown errors. If some UEs with significantly erroneous position information are used as anchors, the localization performance can be severely degraded. Based on the outlier detection technique, this paper proposes an efficient method to select a subset of UEs with accurate position information as anchors for localizing the target. Numerical results show that our scheme can select good UEs as anchors with very high probability, indicating that networked sensing can be realized in practice with the aid of UEs.

MIMO Integrated Sensing and Communication Exploiting Prior Information

In this paper, we study a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system where one multi-antenna base station (BS) sends information to a user with multiple antennas in the downlink and simultaneously senses the location parameter of a target based on its reflected echo signals received back at the BS receive antennas. We focus on the case where the location parameter to be sensed is unknown and random, for which the prior distribution information is available for exploitation. First, we propose to adopt the posterior Cram\'er-Rao bound (PCRB) as the sensing performance metric with prior information, which quantifies a lower bound of the mean-squared error (MSE). Since the PCRB is in a complicated form, we derive a tight upper bound of it to draw more insights. Based on this, we analytically show that by exploiting the prior distribution information, the PCRB is always no larger than the CRB averaged over random location realizations without prior information exploitation. Next, we formulate the transmit covariance matrix optimization problem to minimize the sensing PCRB under a communication rate constraint. We obtain the optimal solution and derive useful properties on its rank. Then, by considering the derived PCRB upper bound as the objective function, we propose a low-complexity suboptimal solution in semi-closed form. Numerical results demonstrate the effectiveness of our proposed designs in MIMO ISAC exploiting prior information.