Uncovering the Iceberg in the Sea: Fundamentals of Pulse Shaping and Modulation Design for Random ISAC Signals

Integrated Sensing and Communications (ISAC) is expected to play a pivotal role in future 6G networks. To maximize time-frequency resource utilization, 6G ISAC systems must exploit data payload signals, that are inherently random, for both communication and sensing tasks. This paper provides a comprehensive analysis of the sensing performance of such communication-centric ISAC signals, with a focus on modulation and pulse shaping design to reshape the statistical properties of their auto-correlation functions (ACFs), thereby improving the target ranging performance. We derive a closed-form expression for the expectation of the squared ACF of random ISAC signals, considering arbitrary modulation bases and constellation mappings within the Nyquist pulse shaping framework. The structure is metaphorically described as an ``iceberg hidden in the sea", where the ``iceberg'' represents the squared mean of the ACF of random ISAC signals, that is determined by the pulse shaping filter, and the ``sea level'' characterizes the corresponding variance, caused by the randomness of the data payload. Our analysis shows that, for QAM/PSK constellations with Nyquist pulse shaping, Orthogonal Frequency Division Multiplexing (OFDM) achieves the lowest ranging sidelobe level across all lags. Building on these insights, we propose a novel Nyquist pulse shaping design to enhance the sensing performance of random ISAC signals. Numerical results validate our theoretical findings, showing that the proposed pulse shaping significantly reduces ranging sidelobes compared to conventional root-raised cosine (RRC) pulse shaping, thereby improving the ranging performance.

Antenna Health-Aware Selective Beamforming for Hardware-Constrained DFRC Systems II

This study introduces an innovative beamforming design approach that incorporates the reliability of antenna array elements into the optimization process, termed "antenna health-aware selective beamforming". This method strategically focuses transmission power on more reliable antenna elements, thus enhancing system resilience and operational integrity. By integrating antenna health information and individual power constraints, our research leverages advanced optimization techniques such as the Group Proximal-Gradient Dual Ascent (GPGDA) to efficiently address nonconvex challenges in sparse array selection. Applying the proposed technique to a Dual-Functional Radar-Communication (DFRC) system, our findings highlight that increasing the sparsity promotion weight ($\rho_s$) generally boosts spectral efficiency and communication data rate, achieving perfect system reliability at higher $\rho_s$ values but also revealing a performance threshold beyond which further sparsity is detrimental. This underscores the importance of balanced sparsity in beamforming for optimizing performance, particularly in critical communication and defense applications where uninterrupted operation is crucial. Additionally, our analysis of the time complexity and power consumption associated with GPGDA underscores the need for optimizing computational resources in practical implementations.

ISAC Super-Resolution Receivers: The Effect of Different Dictionary Matrices

This paper presents an off-the-grid estimator for ISAC systems using lifted atomic norm minimization (LANM). The main challenge in the ISAC systems is the unknown nature of both transmitted signals and radar-communication channels. We use a known dictionary to encode transmit signals and show that LANM can localize radar targets and decode communication symbols when the number of observations is proportional to the system's degrees of freedom and the coherence of the dictionary matrix. We reformulate LANM using a dual method and solve it with semidefinite relaxation (SDR) for different dictionary matrices to reduce the number of observations required at the receiver. Simulations demonstrate that the proposed LANM accurately estimates communication data and target parameters under varying complexity by selecting different dictionary matrices.

ISAC Super-Resolution Receiver via Lifted Atomic Norm Minimization

This paper introduces an off-the-grid estimator for integrated sensing and communication (ISAC) systems, utilizing lifted atomic norm minimization (LANM). The key challenge in this scenario is that neither the transmit signals nor the radar-and-communication channels are known. We prove that LANM can simultaneously achieve localization of radar targets and decoding of communication symbols, when the number of observations is proportional to the degrees of freedom in the ISAC systems. Despite the inherent ill-posed nature of the problem, we employ the lifting technique to initially encode the transmit signals. Then, we leverage the atomic norm to promote the structured low-rankness for the ISAC channel. We utilize a dual technique to transform the LANM into an infinite-dimensional search over the signal domain. Subsequently, we use semidefinite relaxation (SDR) to implement the dual problem. We extend our approach to practical scenarios where received signals are contaminated by additive white Gaussian noise (AWGN) and jamming signals. Furthermore, we derive the computational complexity of the proposed estimator and demonstrate that it is equivalent to the conventional pilot-aided ANM for estimating the channel parameters. Our simulation experiments demonstrate the ability of the proposed LANM approach to estimate both communication data and target parameters with a performance comparable to traditional radar-only super-resolution techniques.

Optimizing Fingerprint-Spectrum-Based Synchronization in Integrated Sensing and Communications

Asynchronous radio transceivers often lead to significant range and velocity ambiguity, posing challenges for precise positioning and velocity estimation in passive-sensing perceptive mobile networks (PMNs). To address this issue, carrier frequency offset (CFO) and time offset (TO) synchronization algorithms have been studied in the literature. However, their performance can be significantly affected by the specific choice of the utilized window functions. Hence, we set out to find superior window functions capable of improving the performance of CFO and TO estimation algorithms. We first derive a near-optimal window, and the theoretical synchronization mean square error (MSE) when utilizing this window. However, since this window is not practically achievable, we then develop a practical window selection criterion and test a special window generated by the super-resolution algorithm. Numerical simulation has verified our analysis.

Network-level ISAC: Performance Analysis and Optimal Antenna-to-BS Allocation

A cooperative architecture is proposed for integrated sensing and communication (ISAC) networks, incorporating coordinated multi-point (CoMP) transmission along with multi-static sensing. We investigate how the allocation of antennas-to-base stations (BSs) affects cooperative sensing and cooperative communication performance. More explicitly, we balance the benefits of geographically concentrated antennas, which enhance beamforming and coherent processing, against those of geographically distributed antennas, which improve diversity and reduce service distances. Regarding sensing performance, we investigate three localization methods: angle-of-arrival (AOA)-based, time-of-flight (TOF)-based, and a hybrid approach combining both AOA and TOF measurements, for critically appraising their effects on ISAC network performance. Our analysis shows that in networks having N ISAC nodes following a Poisson point process, the localization accuracy of TOF-based methods follow a \ln^2 N scaling law (explicitly, the Cram\'er-Rao lower bound (CRLB) reduces with \ln^2 N). The AOA-based methods follow a \ln N scaling law, while the hybrid methods scale as a\ln^2 N + b\ln N, where a and b represent parameters related to TOF and AOA measurements, respectively. The difference between these scaling laws arises from the distinct ways in which measurement results are converted into the target location. In terms of communication performance, we derive a tractable expression for the communication data rate, considering various cooperative region sizes and antenna-to-BS allocation strategy. It is proved that higher path loss exponents favor distributed antenna allocation to reduce access distances, while lower exponents favor centralized antenna allocation to maximize beamforming gain.

Windowing Optimization for Fingerprint-Spectrum-Based Passive Sensing in Perceptive Mobile Networks

Perceptive mobile networks (PMN) have been widely recognized as a pivotal pillar for the sixth generation (6G) mobile communication systems. However, the asynchronicity between transmitters and receivers results in velocity and range ambiguity, which seriously degrades the sensing performance. To mitigate the ambiguity, carrier frequency offset (CFO) and time offset (TO) synchronizations have been studied in the literature. However, their performance can be significantly affected by the specific choice of the window functions harnessed. Hence, we set out to find superior window functions capable of improving the performance of CFO and TO estimation algorithms. We firstly derive a near-optimal window, and the theoretical synchronization mean square error (MSE) when utilizing this window. However, since this window is not practically achievable, we then test a practical "window function" by utilizing the multiple signal classification (MUSIC) algorithm, which may lead to excellent synchronization performance.

Clutter Suppression, Time-Frequency Synchronization, and Sensing Parameter Association in Asynchronous Perceptive Vehicular Networks

Significant challenges remain for realizing precise positioning and velocity estimation in perceptive vehicular networks (PVN) enabled by the emerging integrated sensing and communication technology. First, complicated wireless propagation environment generates undesired clutter, which degrades the vehicular sensing performance and increases the computational complexity. Second, in practical PVN, multiple types of parameters individually estimated are not well associated with specific vehicles, which may cause error propagation in multiple-vehicle positioning. Third, radio transceivers in a PVN are naturally asynchronous, which causes strong range and velocity ambiguity. To overcome these challenges, 1) we introduce a moving target indication based joint clutter suppression and sensing algorithm, and analyze its clutter-suppression performance and the Cramer-Rao lower bound of the paired range-velocity estimation upon using the proposed clutter suppression algorithm; 2) we design algorithms for associating individual direction-of-arrival estimates with the paired range-velocity estimates based on "domain transformation"; 3) we propose the first viable carrier frequency offset (CFO) and time offset (TO) estimation algorithm that supports passive vehicular sensing in non-line-of-sight environments. This algorithm treats the delay-Doppler spectrum of the signals reflected by static objects as an environment-specific "fingerprint spectrum", which is shown to exhibit a circular shift property upon changing the CFO and/or TO. Then, the CFO and TO are efficiently estimated by acquiring the number of circular shifts, and we also analyse the mean squared error performance of the proposed time-frequency synchronization algorithm. Simulation results demonstrate the performance advantages of our algorithms under diverse configurations, while corroborating the theoretical analysis.

Symbol-Level Precoding for Near-Field ISAC

The forthcoming 6G and beyond wireless networks are anticipated to introduce new groundbreaking applications, such as Integrated Sensing and Communications (ISAC), potentially leveraging much wider bandwidths at higher frequencies and using significantly larger antenna arrays at base stations. This puts the system operation in the radiative near-field regime of the BS antenna array, characterized by spherical rather than flat wavefronts. In this paper, we refer to such a system as near-field ISAC. Unlike the far-field regime, the near-field regime allows for precise focusing of transmission beams on specific areas, making it possible to simultaneously determine a target's direction and range from a single base station and resolve targets located in the same direction. This work designs the transmit symbol vector in near-field ISAC to maximize a weighted combination of sensing and communication performances subject to a total power constraint using symbol-level precoding (SLP). The formulated optimization problem is convex, and the solution is used to estimate the angle and range of the considered targets using the 2D MUSIC algorithm. The simulation results suggest that the SLP-based design outperforms the block-level-based counterpart. Moreover, the 2D MUSIC algorithm accurately estimates the targets' parameters.

Pulse Shaping for Random ISAC Signals: The Ambiguity Function Between Symbols Matters

Integrated sensing and communications (ISAC) has emerged as a pivotal enabling technology for next-generation wireless networks. Despite the distinct signal design requirements of sensing and communication (S&C) systems, shifting the symbol-wise pulse shaping (SWiPS) framework from communication-only systems to ISAC poses significant challenges in signal design and processing This paper addresses these challenges by examining the ambiguity function (AF) of the SWiPS ISAC signal and introducing a novel pulse shaping design for single-carrier ISAC transmission. We formulate optimization problems to minimize the average integrated sidelobe level (ISL) of the AF, as well as the weighted ISL (WISL) while satisfying inter-symbol interference (ISI), out-of-band emission (OOBE), and power constraints. Our contributions include establishing the relationship between the AFs of both the random data symbols and signaling pulses, analyzing the statistical characteristics of the AF, and developing algorithmic frameworks for pulse shaping optimization using successive convex approximation (SCA) and alternating direction method of multipliers (ADMM) approaches. Numerical results are provided to validate our theoretical analysis, which demonstrate significant performance improvements in the proposed SWiPS design compared to the root-raised cosine (RRC) pulse shaping for conventional communication systems.