Convergent Complex Quasi-Newton Proximal Methods for Gradient-Driven Denoisers in Compressed Sensing MRI Reconstruction

In compressed sensing (CS) MRI, model-based methods are pivotal to achieving accurate reconstruction. One of the main challenges in model-based methods is finding an effective prior to describe the statistical distribution of the target image. Plug-and-Play (PnP) and REgularization by Denoising (RED) are two general frameworks that use denoisers as the prior. While PnP/RED methods with convolutional neural networks (CNNs) based denoisers outperform classical hand-crafted priors in CS MRI, their convergence theory relies on assumptions that do not hold for practical CNNs. The recently developed gradient-driven denoisers offer a framework that bridges the gap between practical performance and theoretical guarantees. However, the numerical solvers for the associated minimization problem remain slow for CS MRI reconstruction. This paper proposes a complex quasi-Newton proximal method that achieves faster convergence than existing approaches. To address the complex domain in CS MRI, we propose a modified Hessian estimation method that guarantees Hermitian positive definiteness. Furthermore, we provide a rigorous convergence analysis of the proposed method for nonconvex settings. Numerical experiments on both Cartesian and non-Cartesian sampling trajectories demonstrate the effectiveness and efficiency of our approach.

On Adapting Randomized Nyström Preconditioners to Accelerate Variational Image Reconstruction

Model-based iterative reconstruction plays a key role in solving inverse problems. However, the associated minimization problems are generally large-scale, ill-posed, nonsmooth, and sometimes even nonconvex, which present challenges in designing efficient iterative solvers and often prevent their practical use. Preconditioning methods can significantly accelerate the convergence of iterative methods. In some applications, computing preconditioners on-the-fly is beneficial. Moreover, forward models in image reconstruction are typically represented as operators, and the corresponding explicit matrices are often unavailable, which brings additional challenges in designing preconditioners. Therefore, for practical use, computing and applying preconditioners should be computationally inexpensive. This paper adapts the randomized Nystr\"{o}m approximation to compute effective preconditioners that accelerate image reconstruction without requiring an explicit matrix for the forward model. We leverage modern GPU computational platforms to compute the preconditioner on-the-fly. Moreover, we propose efficient approaches for applying the preconditioner to problems with nonsmooth regularizers. Our numerical results on image deblurring, super-resolution with impulsive noise, and computed tomography reconstruction demonstrate the efficiency and effectiveness of the proposed preconditioner.

Sensor Selection via GFlowNets: A Deep Generative Modeling Framework to Navigate Combinatorial Complexity

The performance of sensor arrays in sensing and wireless communications improves with more elements, but this comes at the cost of increased energy consumption and hardware expense. This work addresses the challenge of selecting $k$ sensor elements from a set of $m$ to optimize a generic Quality-of-Service metric. Evaluating all $\binom{m}{k}$ possible sensor subsets is impractical, leading to prior solutions using convex relaxations, greedy algorithms, and supervised learning approaches. The current paper proposes a new framework that employs deep generative modeling, treating sensor selection as a deterministic Markov Decision Process where sensor subsets of size $k$ arise as terminal states. Generative Flow Networks (GFlowNets) are employed to model an action distribution conditioned on the state. Sampling actions from the aforementioned distribution ensures that the probability of arriving at a terminal state is proportional to the performance of the corresponding subset. Applied to a standard sensor selection scenario, the developed approach outperforms popular methods which are based on convex optimization and greedy algorithms. Finally, a multiobjective formulation of the proposed approach is adopted and applied on the sparse antenna array design for Integrated Sensing and Communication (ISAC) systems. The multiobjective variation is shown to perform well in managing the trade-off between radar and communication performance.

Time-Modulated Intelligent Reflecting Surface for Waveform Security

We consider an OFDM transmitter aided by an intelligent reflecting surface (IRS) and propose a novel approach to enhance waveform security by employing time modulation (TM) at the IRS side. By controlling the periodic TM pattern of the IRS elements, the system is designed to preserve communication information towards an authorized recipient and scramble the information towards all other directions. We introduce two modes of TM pattern control: the linear mode, in which we design common TM parameters for entire rows or columns of the IRS, and the planar mode, where we design TM parameters for each individual IRS unit. Due to the required fewer switches, the linear mode is easier to implement as compared to the planar mode. However, the linear model results in a beampattern that has sidelobes, over which the transmitted information is not sufficiently scrambled. We show that the sidelobes of the linear mode can be suppressed by exploiting the high diversity available in that mode.

Enhance Security of Time-Modulated Array-Enabled Directional Modulation by Introducing Symbol Ambiguity

In this paper, if the time-modulated array (TMA)-enabled directional modulation (DM) communication system can be cracked is investigated and the answer is YES! We first demonstrate that the scrambling data received at the eavesdropper can be defied by using grid search to successfully find the only and actual mixing matrix generated by TMA. Then, we propose introducing symbol ambiguity to TMA to defend the defying of grid search, and design two principles for the TMA mixing matrix, i.e., rank deficiency and non-uniqueness of the ON-OFF switching pattern, that can be used to construct the symbol ambiguity. Also, we present a feasible mechanism to implement these two principles. Our proposed principles and mechanism not only shed light on how to design a more secure TMA DM system theoretically in the future, but also have been validated to be effective by bit error rate measurements.

How secure is the time-modulated array-enabled ofdm directional modulation?

Time-modulated arrays (TMA) transmitting orthogonal frequency division multiplexing (OFDM) waveforms achieve physical layer security by allowing the signal to reach the legitimate destination undistorted, while making the signal appear scrambled in all other directions. In this paper, we examine how secure the TMA OFDM system is, and show that it is possible for the eavesdropper to defy the scrambling. In particular, we show that, based on the scrambled signal, the eavesdropper can formulate a blind source separation problem and recover data symbols and TMA parameters via independent component analysis (ICA) techniques. We show how the scaling and permutation ambiguities arising in ICA can be resolved by exploiting the Toeplitz structure of the corresponding mixing matrix, and knowledge of data constellation, OFDM specifics, and the rules for choosing TMA parameters. We also introduce a novel TMA implementation to defend the scrambling against the eavesdropper.

A Secure Dual-Function Radar Communication System via Time-Modulated Arrays

Dual-function radar-communication (DFRC) systems offer high spectral, hardware and power efficiency, as such are prime candidates for 6G wireless systems. DFRC systems use the same waveform for simultaneously probing the surroundings and communicating with other equipment. By exposing the communication information to potential targets, DFRC systems are vulnerable to eavesdropping. In this work, we propose to mitigate the problem by leveraging directional modulation (DM) enabled by a time-modulated array (TMA) that transmits OFDM waveforms. DM can scramble the signal in all directions except the directions of the legitimate user. However, the signal reflected by the targets is also scrambled, thus complicating the extraction of target parameters. We propose a novel, low-complexity target estimation method that estimates the target parameters based on the scrambled received symbols. We also propose a novel method to refine the obtained target estimates at the cost of increased complexity. With the proposed refinement algorithm, the proposed DFRC system can securely communicate with users while having high-precision sensing functionality.

DFRC with Improved Communication-Sensing Trade-off via Private Subcarrier Permutations and Pairing with Antennas

Dual function radar communication (DFRC) systems can achieve significant improvements in spectrum efficiency, system complexity and energy efficiency, and are attracting a lot of attention for next generation wireless system design. This paper considers DFRC systems using MIMO radar with a sparse transmit array, transmitting OFDM waveforms, and assigning shared and private subcarriers to active transmit antennas. Subcarrier sharing allows antennas to modulate data symbols onto the same subcarriers and enables high communication rate, while the use of private subcarriers trades-off communication rate for sensing performance by enabling the formulation of a virtual array with larger aperture than the physical receive array. We propose to exploit the permutation of private subcarriers among the available subcarriers and the pairing between active antennas and private subcarriers to recover some of the communication rate loss. Exploiting the $1$-sparse property of private subcarriers, we also propose a low complexity algorithm to identify private subcarriers and detect the antenna-subcarrier pairing.

Phased Array With Improved Beamforming Capability via Use of Double Phase Shifters

The passive electronically scanned array (PESA) is widely used due to its simple structure and low cost. {Its antenna weights have unit modulus and thus, only the weights phases can be controlled. PESA has limited degrees of freedom for beampattern design, where only the direction of the main beam can be controlled.} In this paper we propose a novel way to improve the beamforming capability of PESA by endowing it with more degrees of freedom via the use of double phase shifters (DPS). By doing so, both the magnitude and the phase of the antenna weights can be controlled, allowing for more flexibility in beampattern design. We also take into account the physical resolution limitation of phase shifters, and propose a method to approximate a given complex beamformer using DPS. Simulation results indicate significant beamforming improvement even at low phase resolution.

Simultaneous Monitoring of Multiple People's Vital Sign Leveraging a Single Phased-MIMO Radar

Vital sign monitoring plays a critical role in tracking the physiological state of people and enabling various health-related applications (e.g., recommending a change of lifestyle, examining the risk of diseases). Traditional approaches rely on hospitalization or body-attached instruments, which are costly and intrusive. Therefore, researchers have been exploring contact-less vital sign monitoring with radio frequency signals in recent years. Early studies with continuous wave radars/WiFi devices work on detecting vital signs of a single individual, but it still remains challenging to simultaneously monitor vital signs of multiple subjects, especially those who locate in proximity. In this paper, we design and implement a time-division multiplexing (TDM) phased-MIMO radar sensing scheme for high-precision vital sign monitoring of multiple people. Our phased-MIMO radar can steer the mmWave beam towards different directions with a micro-second delay, which enables capturing the vital signs of multiple individuals at the same radial distance to the radar. Furthermore, we develop a TDM-MIMO technique to fully utilize all transmitting antenna (TX)-receiving antenna (RX) pairs, thereby significantly boosting the signal-to-noise ratio. Based on the designed TDM phased-MIMO radar, we develop a system to automatically localize multiple human subjects and estimate their vital signs. Extensive evaluations show that under two-subject scenarios, our system can achieve an error of less than 1 beat per minute (BPM) and 3 BPM for breathing rate (BR) and heartbeat rate (HR) estimations, respectively, at a subject-to-radar distance of $1.6~m$. The minimal subject-to-subject angle separation is $40{\deg}$, corresponding to a close distance of $0.5~m$ between two subjects, which outperforms the state-of-the-art.