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Compressed sensing (CS) techniques demand significant storage and computational resources, when recovering high-dimensional sparse signals. Block CS (BCS), a special class of CS, addresses both the storage and complexity issues by partitioning the sparse recovery problem into several sub-problems. In this paper, we derive a Welch bound-based guarantee on the reconstruction error with BCS. Our guarantee reveals that the reconstruction quality with BCS monotonically reduces with an increasing number of partitions. To alleviate this performance loss, we propose a sparse recovery technique that exploits correlation across the partitions of the sparse signal. Our method outperforms BCS in the moderate SNR regime, for a modest increase in the storage and computational complexities.

This paper develops a channel estimation technique for millimeter wave (mmWave) communication systems. Our method exploits the sparse structure in mmWave channels for low training overhead and accounts for the phase errors in the channel measurements due to phase noise at the oscillator. Specifically, in IEEE 802.11ad/ay-based mmWave systems, the phase errors within a beam refinement protocol packet are almost the same, while the errors across different packets are substantially different. Consequently, standard sparsity-aware algorithms, which ignore phase errors, fail when channel measurements are acquired over multiple beam refinement protocol packets. We present a novel algorithm called partially coherent matching pursuit for sparse channel estimation under practical phase noise perturbations. Our method iteratively detects the support of sparse signal and employs alternating minimization to jointly estimate the signal and the phase errors. We numerically show that our algorithm can reconstruct the channel accurately at a lower complexity than the benchmarks.

Beam alignment is key in enabling millimeter wave and terahertz radios to achieve their capacity. Due to the use of large arrays in these systems, the common exhaustive beam scanning results in a substantial training overhead. Prior work has addressed this issue, by developing compressive sensing (CS)-based methods which exploit channel sparsity to achieve faster beam alignment. Unfortunately, standard CS techniques employ wide beams and suffer from a low signal-to-noise ratio (SNR) in the channel measurements. To solve this challenge, we develop an IEEE 802.11ad/ay compatible technique that takes an in-sector approach for CS. In our method, the angle domain channel is partitioned into several sectors, and the channel within the best sector is estimated for beam alignment. The essence of our framework lies in the construction of a low-resolution beam codebook to identify the best sector and in the design of the CS matrix for in-sector channel estimation. Our beam codebook illuminates distinct non-overlapping sectors and can be realized with low-resolution phased arrays. We show that the proposed codebook results in a higher received SNR than the state-of-the-art sector sweep codebooks. Furthermore, our optimized CS matrix achieves a better in-sector channel reconstruction than comparable benchmarks.

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.

Fast millimeter wave (mmWave) channel estimation techniques based on compressed sensing (CS) suffer from low signal-to-noise ratio (SNR) in the channel measurements, due to the use of wide beams. To address this problem, we develop an in-sector CS-based mmWave channel estimation technique that focuses energy on a sector in the angle domain. Specifically, we construct a new class of structured CS matrices to estimate the channel within the sector of interest. To this end, we first determine an optimal sampling pattern when the number of measurements is equal to the sector dimension and then use its subsampled version in the sub-Nyquist regime. Our approach results in low aliasing artifacts in the sector of interest and better channel estimates than benchmark algorithms.

Phased arrays in near-field communication allow the transmitter to focus wireless signals in a small region around the receiver. Proper focusing is achieved by carefully tuning the phase shifts and the polarization of the signals transmitted from the phased array. In this paper, we study the impact of polarization on near-field focusing and investigate the use of dynamic polarization control (DPC) phased arrays in this context. Our studies indicate that the optimal polarization configuration for near-field focusing varies spatially across the antenna array. Such a spatial variation motivates the need for DPC phased arrays which allow independent polarization control across different antennas. We show using simulations that DPC phased arrays in the near-field achieve a higher received signal-to-noise ratio than conventional switched- or dual-polarization phased arrays.

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 artificial phase noise (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.

Millimeter wave vehicular channels exhibit structure that can be exploited for beam alignment with fewer channel measurements compared to exhaustive beam search. With fixed layouts of roadside buildings and regular vehicular moving trajectory, the dominant path directions of channels will likely be among a subset of beam directions instead of distributing randomly over the whole beamspace. In this paper, we propose a deep learning-based technique to design a structured compressed sensing (CS) matrix that is well suited to the underlying channel distribution for mmWave vehicular beam alignment. The proposed approach leverages both sparsity and the particular spatial structure that appears in vehicular channels. We model the compressive channel acquisition by a two-dimensional (2D) convolutional layer followed by dropout. We design fully-connected layers to optimize channel acquisition and beam alignment. We incorporate the low-resolution phase shifter constraint during neural network training by using projected gradient descent for weight updates. Furthermore, we exploit channel spectral structure to optimize the power allocated for different subcarriers. Simulations indicate that our deep learning-based approach achieves better beam alignment than standard CS techniques which use random phase shift-based design. Numerical experiments also show that one single subcarrier is sufficient to provide necessary information for beam alignment.

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 a few circulant shifts of the transmit beamformer and apply two-dimensional partial Fourier compressed sensing technique. We optimize these circulant shifts to achieve minimum coherence in compressed sensing. 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.

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. For the special case of beamforming along the boresight of an array, this waveform is analogous to the frequency modulated continuous wave (FMCW) chirp signal in radar. InFocus mitigates beam misfocus and beam squint when applied to near field and far field systems. Simulation results indicate that InFocus enables massive wideband phased array-based radios to achieve higher data rates than comparable beamforming solutions.

Millimeter wave (mmWave) communication is one viable solution to support Gbps sensor data sharing in vehicular networks. The use of large antenna arrays at mmWave and high mobility in vehicular communication make it challenging to design fast beam alignment solutions. In this paper, we propose a novel framework that learns the channel angle-of-departure (AoD) statistics at a base station (BS) and uses this information to efficiently acquire channel measurements. Our framework integrates online learning for compressive sensing (CS) codebook learning and the optimized codebook is used for CS-based beam alignment. We formulate a CS matrix optimization problem based on the AoD statistics available at the BS. Furthermore, based on the CS channel measurements, we develop techniques to update and learn such channel AoD statistics at the BS. We use the upper confidence bound (UCB) algorithm to learn the AoD statistics and the CS matrix. Numerical results show that the CS matrix in the proposed framework provides faster beam alignment than standard CS matrix designs. Simulation results indicate that the proposed beam training technique can reduce overhead by 80% compared to exhaustive beam search, and 70% compared to standard CS solutions that do not exploit any AoD statistics.

Two arrays form a periodic complementary pair if the sum of their periodic autocorrelations is a delta function. Finding such pairs, however, is challenging for large arrays whose entries are constrained to a small alphabet. One such alphabet is the quaternary set which contains the complex fourth roots of unity. In this paper, we propose a technique to construct periodic complementary pairs defined over the quaternary set using perfect quaternion arrays. We show how new pairs of quaternary sequences, matrices, and four-dimensional arrays that satisfy a periodic complementary property can be constructed with our method.

Millimeter wave channels exhibit structure that allows beam alignment with fewer channel measurements than exhaustive beam search. From a compressed sensing (CS) perspective, the received channel measurements are usually obtained by multiplying a CS matrix with a sparse representation of the channel matrix. Due to the constraints imposed by analog processing, designing CS matrices that efficiently exploit the channel structure is, however, challenging. In this paper, we propose an end-to-end deep learning technique to design a structured CS matrix that is well suited to the underlying channel distribution, leveraging both sparsity and the particular spatial structure that appears in vehicular channels. The channel measurements acquired with the designed CS matrix are then used to predict the best beam for link configuration. Simulation results for vehicular communication channels indicate that our deep learning-based approach achieves better beam alignment than standard CS techniques that use the random phase shift-based design.

Receivers with one-bit analog-to-digital converters (ADCs) are promising for high bandwidth millimeter wave (mmWave) systems as they consume less power than their full resolution counterparts. The extreme quantization in one-bit receivers and the use of large antenna arrays at mmWave make channel estimation challenging. In this paper, we develop channel estimation algorithms that exploit the low-rank property of mmWave channels. We also propose a novel training solution that results in a low complexity implementation of our algorithms. Simulation results indicate that the proposed methods achieve better channel reconstruction than compressed sensing-based techniques that exploit sparsity of mmWave channels.

Millimeter wave (mmWave) communication in typical wearable and data center settings is short range. As the distance between the transmitter and the receiver in short range scenarios can be comparable to the length of the antenna arrays, the common far field approximation for the channel may not be applicable. As a result, dictionaries that result in a sparse channel representation in the far field setting may not be appropriate for short distances. In this paper, we develop a novel framework to exploit the structure in short range mmWave channels. The proposed method splits the channel into several subchannels for which the far field approximation can be applied. Then, the structure within and across different subchannels is leveraged using message passing. We show how information about the antenna array geometry can be used to design message passing factors that incorporate structure across successive subchannels. Simulation results indicate that our framework can be used to achieve better beam alignment with fewer channel measurements when compared to standard compressed sensing-based techniques that do not exploit structure across subchannels.

Short range channels commonly arise in millimeter wave (mmWave) wearable settings, where the length of the antenna arrays can be comparable to the distance between the radios. Conventional mmWave MIMO channel estimation techniques based on the far field assumption may perform poorly in short range settings due to the large angular spread and, hence, high available rank. We propose a geometry-aided message passing algorithm that exploits structure in short range line-of-sight (LoS) channels for spatial sub-Nyquist channel estimation. Our approach parametrizes the channel using angle-of-arrivals (AoAs) that are locally defined for subarrays of an antenna array. Furthermore, it leverages the dependencies between the local AoAs using factors based on the array geometry. We show that the LoS MIMO channel can be reconstructed using the derived local AoA estimates and the known transceiver geometry. The proposed approach achieves a reasonable rate with greatly reduced pilot transmissions when compared to exhaustive beam search-based local AoA estimation.

Millimeter wave (mmWave) systems can enable high data rates if the link between the transmitting and receiving radios is configured properly. Fast configuration of mmWave links, however, is challenging due to the use of large antenna arrays and hardware constraints. For example, a large amount of training overhead is incurred by exhaustive search-based beam alignment in typical mmWave phased arrays. In this paper, we present a framework called FALP for Fast beam Alignment with Low-resolution Phase shifters. FALP uses an efficient set of antenna weight vectors to acquire channel measurements, and allows faster beam alignment when compared to exhaustive scan. The antenna weight vectors in FALP can be realized in ultra-low power phase shifters whose resolution can be as low as one-bit. From a compressed sensing (CS) perspective, the CS matrix designed in FALP satisfies the restricted isometry property and allows CS algorithms to exploit the fast Fourier transform. The proposed framework also establishes a new connection between channel acquisition in phased arrays and magnetic resonance imaging.