Orthogonal matching pursuit (OMP) is a widely used greedy algorithm for sparse signal recovery in compressed sensing (CS). Prior work on OMP, however, has only provided reconstruction guarantees under the assumption that the columns of the CS matrix have equal norms, which is unrealistic in many practical CS applications due to hardware constraints. In this paper, we derive sparse recovery guarantees with OMP, when the CS matrix has unequal column norms. Finally, we show that CS matrices whose column norms are comparable achieve tight guarantees for the successful recovery of the support of a sparse signal and a low mean squared error in the estimate.

Millimeter wave (mmWave) technology can achieve high-speed communication due to the large available spectrum. Furthermore, the use of directional beams in mmWave system provides a natural defense against physical layer security attacks. In practice, however, the beams are imperfect due to mmWave hardware limitations such as the low-resolution of the phase shifters. These imperfections in the beam pattern introduce an energy leakage that can be exploited by an eavesdropper. To defend against such eavesdropping attacks, we propose a directional modulation-based defense technique where the transmitter applies random circulant shifts of a beamformer. We show that the use of random circulant shifts together with appropriate phase adjustment induces (APN) in the directions different from that of the target receiver. Our method corrupts the phase at the eavesdropper without affecting the communication link of the target receiver. We also experimentally verify the APN induced due to circulant shifts, using channel measurements from a 2-bit mmWave phased array testbed. Using simulations, we study the performance of the proposed defense technique against a greedy eavesdropping strategy in a vehicle-to-infrastructure scenario. The proposed technique achieves better defense than the antenna subset modulation, without compromising on the communication link with the target receiver.

Phased arrays, commonly used in IEEE 802.11ad and 5G radios, are capable of focusing radio frequency signals in a specific direction or a spatial region. Beamforming achieves such directional or spatial concentration of signals and enables phased array-based radios to achieve high data rates. Designing beams for millimeter wave and terahertz communication using massive phased arrays, however, is challenging due to hardware constraints and the wide bandwidth in these systems. For example, beams which are optimal at the center frequency may perform poor in wideband communication systems where the radio frequencies differ substantially from the center frequency. The poor performance in such systems is due to differences in the optimal beamformers corresponding to distinct radio frequencies within the wide bandwidth. Such a mismatch leads to a misfocus effect in near-field systems and the beam squint effect in far-field systems. In this paper, we investigate the misfocus effect and propose InFocus, a low complexity technique to construct beams that are well suited for massive wideband phased arrays. The beams are constructed using a carefully designed frequency modulated waveform in the spatial dimension. InFocus mitigates beam misfocus and beam squint when applied to near-field and far-field systems.

Millimeter-wave (mmWave) joint communication-radar (JCR) will enable high data rate communication and high-resolution radar sensing for applications such as autonomous driving. Prior JCR systems that are based on the mmWave communications hardware, however, suffer from a limited angular field-of-view and low estimation accuracy for radars due to the employed directional communication beam. In this paper, we propose an adaptive and fast combined waveform-beamforming design for the mmWave automotive JCR with a phased-array architecture that permits a trade-off between communication and radar performances. To rapidly estimate the mmWave automotive radar channel in the Doppler-angle domain with a wide field-of-view, our JCR design employs circulant shifts of the transmit beamformer to acquire radar channel measurements and uses two-dimensional compressed sensing (CS) in the space-time dimension. We optimize these circulant shifts to minimize the coherence of the CS matrix, under the space-time sampling constraints in our problem. We evaluate the JCR performance trade-offs using a normalized mean square error (MSE) metric for radar estimation and a distortion MSE metric for data communication, which is analogous to the distortion metric in the rate-distortion theory. Additionally, we develop a MSE-based weighted average optimization problem for the adaptive JCR combined waveform-beamforming design. Numerical results demonstrate that our proposed JCR design enables the estimation of short- and medium-range radar channels in the Doppler-angle domain with a low normalized MSE, at the expense of a small degradation in the communication distortion MSE.