The signal processing community is currently witnessing the emergence of sensor array processing and direction-of-arrival (DoA) estimation in various modern applications, such as automotive radar, mobile user and millimeter wave indoor localization, and drone surveillance, as well as in new paradigms, such as joint sensing and communication in future wireless systems. This trend is further enhanced by technology leaps and the availability of powerful and affordable multiantenna hardware platforms. © 1991-2012 IEEE.

A class of computationally efficient DOA estimators under the Partial Relaxation (PR) framework has recently been proposed. Conceptually different from conventional DOA estimation methods in the literature, the estimators under the PR framework rely on the non-complete relaxation of the array manifold while performing a spectral-search in the field of view. This particular type of relaxation essentially implies a modified signal model with partial information loss due to the relaxation. The information loss and its impact on the DOA estimation performance have not yet been analytically quantified in the literature. In this paper, the information loss induced by the relaxation of the array manifold is investigated through the Cramér-Rao Bound (CRB). The closed-form expression of the CRB for DOA estimation under the PR model, on the one hand, provides insight on the information loss in the asymptotic region where the number of snapshots tends to infinity. On the other hand, the proposed CRB characterizes the lower bound for the DOA estimation performance of all PR estimators. We prove that, under the assumptions of Gaussian source signal and noise, the CRB of the PR signal model is lower-bounded by the conventional stochastic CRB. We also prove that the previously proposed Weighted Subspace Fitting estimator under the PR framework asymptotically achieves the CRB of the PR signal model. Furthermore, it is shown that the asymptotic mean-squared errors of all Weighted Subspace Fitting estimators under the PR framework for any positive definite weighting matrix are identical. © 1991-2012 IEEE.

This paper considers the uplink of a single-cell multi-user massive multiple-input multiple-output (MIMO) system. Each receiver antenna of the base station is assumed to be equipped with a pair of analog-to-digital converters (ADCs) to quantize the real and imaginary part of the received signal. We propose a novel Bussgang-based weighted zero-forcing (B-WZF) receiver, which distinguishes the clipping and granular distortion. Numerical results demonstrate that for sufficiently high SNR and users that do not experience deep large-scale fading, the B-WZF brings significant performance gain over existing linear receivers in the literature, when the training sequence length is higher than the number of users. © 2020 IEEE.

This paper considers the uplink of a single-cell multiuser massive multiple-input multiple-output system. Each receiver antenna of the base station (BS) is assumed to be equipped with a pair of analog-to-digital converters to quantize the real and imaginary part of the received signal. We propose a novel clipping-aware receiver (CA-MMSE), which performs minimum mean square error (MMSE) reconstruction only on the clipped received samples, while the granular samples are left unchanged after the quantization. On this basis, we present an iterative algorithm to implement the CA-MMSE receiver and derive a sufficient condition for its geometrical convergence to a fixed point. We show that as long as the number of BS antennas or the quantization resolution is sufficiently high, then, the performance of the CA-MMSE is as good as the optimal MMSE receiver which reconstructs all quantized received symbols. Additionally, we propose a novel Bussgang-based weighted zero-forcing (B-WZF) receiver which distinguishes the clipping and granular distortion and it is shown that as long as the received training symbols per antenna are correlated, the CA-MMSE brings significant improvements compared to conventional receivers in the literature while for users that do not experience deep large-scale fading the simpler B-WZF is near to the CA-MMSE for sufficiently high signal-to-noise ratio and quantization resolution. © 1972-2012 IEEE.

In this paper, the Cramer-Rao Bound for the Direction-of-Arrival parameter under the partial relaxation framework is derived. We introduce a non-redundant parameterization of the signal model corresponding to the partial relaxation framework, in which the array structure in part of the steering matrix is neglected while the rank of the relaxed steering matrix is maintained. We prove that the stochastic Cramer-Rao Bound for the Direction-of-Arrival parameter under the partial relaxation signal model is lower-bounded by that of the conventional stochastic Cramer-Rao Bound. Furthermore, we prove that the partial relaxation estimator for the Weighted Subspace Fitting criterion asymptotically achieves the conventional Cramer-Rao Bound in the case of uncorrelated source signals.

The so-called Partial Relaxation approach has recently been proposed to solve the Direction-of-Arrival estimation problem. In this paper, we extend the previous work by applying Covariance Fitting with a data model that includes the noise covariance. Instead of applying a single source approximation to multi-source estimation criteria, which is the case for MUSIC, the conventional beamformer, or the Capon beamformer, the Partial Relaxation approach accounts for the existence of multiple sources using a non-parametric modification of the signal model. In the Partial Relaxation framework, the structure of the desired direction is kept, whereas the sensor array manifold corresponding to the remaining signals is relaxed [1], [2]. This procedure allows to compute a closed-form solution for the relaxed signal part and to come up with a simple spectral search with a significantly reduced computational complexity. Unlike in the existing Partial Relaxed Covariance Fitting approach, in this paper we utilize more prior-knowledge on the structure of the covariance matrix by also considering the noise covariance. Simulation results show that, the proposed method outperforms the existing Partial Relaxed Covariance Fitting method, especially in difficult conditions with small sample size and low Signal-to-Noise Ratio. Its threshold performance is close to that of Deterministic Maximum Likelihood, but at significantly lower cost. © 2019 IEEE

In this paper, the partial relaxation approach is introduced and applied to the direction-of-arrival estimation problem using spectral search. Unlike existing spectral-based methods such as conventional beamformer, Capon beamformer, or MUSIC that can be considered as single source approximation of multisource estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the "interference" parameters. Thanks to this relaxation, the conventional multi-source optimization problem reduces to a simple spectral search. Following this principle, we propose estimators based on the deterministic maximum likelihood, weighted subspace fitting, and covariance fitting methods. To calculate the null-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that, irrespective of any specific structure of the sensor array, the performance of the proposed estimators is superior to the conventionalmethods, especially in the case of low signal-to-noise-ratio and low number of snapshots, while maintaining a computational cost that is comparable to MUSIC.