Compressive sensing (CS) is key to reduce the overhead in estimating sparse high dimensional channels at millimeter wave or terahertz frequencies. The channel measurements in CS are usually perturbed by random phase errors, commonly modeled as a Wiener process, at the oscillators. CS algorithms that ignore such phase errors fail to accurately estimate the channel. In practice, the phase errors are similar within a batch of measurements acquired in a short burst and the errors vary significantly across different batches, resulting in partially coherent measurements. We develop a message passing-based channel estimation algorithm that exploits the sparse structure of the channel together with the Wiener statistics of the phase errors. To this end, we absorb the phase errors into the sparse channel, and introduce three hidden variables to model its support, magnitude, and phase. We derive the message flows between these variables while incorporating Wiener phase noise statistics. Finally, we use alternating optimization to decouple the sparse channel and the phase errors from the vector estimated with our message-passing technique. Using simulations, we show that the proposed algorithm achieves better channel reconstruction than comparable benchmarks.

Phase jitter at oscillators in high-frequency wireless systems perturbs the phase of the acquired channel measurements. As a result, standard sparse channel estimation algorithms that ignore phase errors fail. In this paper, we consider a frame structure in which channel measurements are acquired over two packets. Our model assumes that the phase errors are nearly constant over a packet and they change considerably across the packets, leading to partially coherent channel measurements. In this paper, we develop a message-passing-based technique that leverages the partially coherent structure in the measurements for sparse channel estimation robust to unknown phase offset across the packets. Simulation results show that our approach achieves a lower mean-squared error in the reconstructed channel than comparable benchmarks.

Channel estimation can lead to a substantial training overhead in millimeter wave (mmWave) and terahertz (THz) systems employing large arrays. Prior work has leveraged channel sparsity at these frequencies to reduce this overhead. Most of the sparsity-aware algorithms, however, assume perfect phase coherence in the channel measurements, which is disrupted due to phase noise. Due to the errors induced by phase noise, standard sparse channel estimation algorithms assuming perfect phase coherence can fail. In this paper, we consider a frame structure in which the channel measurements are acquired over multiple packets. Our model assumes that the phase errors remain constant within a packet and vary considerably across different packets, leading to partially coherent channel measurements. We develop a message passing-based technique for sparse channel estimation under such partially coherent phase errors and show that our approach achieves a lower channel reconstruction error than comparable benchmarks.

Beam acquisition is key in enabling millimeter wave and terahertz radios to achieve their capacity. Due to the use of large antenna 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 for faster beam acquisition. Unfortunately, most 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 and then used for beamforming. 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 a CS matrix optimized 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 and a higher achievable rate 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.