Direction of Arrival Estimation and Localization Exploiting Sparse and One-Bit Sampling

Doctoral thesis (2021)

Data acquisition is a necessary first step in digital signal processing applications such as radar, wireless communications and array processing. Traditionally, this process is performed by uniformly ... [more ▼]

Data acquisition is a necessary first step in digital signal processing applications such as radar, wireless communications and array processing. Traditionally, this process is performed by uniformly sampling signals at a frequency above the Nyquist rate and converting the resulting samples into digital numeric values through high-resolution amplitude quantization. While the traditional approach to data acquisition is straightforward and extremely well-proven, it may be either impractical or impossible in many modern applications due to the existing fundamental trade-off between sampling rate, amplitude quantization precision, implementation costs, and usage of physical resources, e.g. bandwidth and power consumption. Motivated by this fact, system designers have recently proposed exploiting sparse and few-bit quantized sampling instead of the traditional way of data acquisition in order to reduce implementation costs and usage of physical resources in such applications. However, before transition from the tradition data acquisition method to the sparsely sampled and few-bit quntized data acquisition approach, a study on the feasibility of retrieving information from sparsely sampled and few-bit quantized data is first required to be conducted. This study should specifically seek to find the answers to the following fundamental questions: 1-Is the problem of retrieving the information of interest from sparsely sampled and few-bit quantized data an identifiable problem? If so, what are the identifiability conditions? 2-Under the identifiability conditions: what are the fundamental performance bounds for the problem of retrieving the information of interest from sparsely sampled and few-bit quantized data? and how close are these performance bounds to those of retrieving the same information from the data acquired through the traditional approach? 3-Does there exist any computationally efficient algorithm for retrieving the information of interest from sparsely sampled and few-bit quantized data capable of achieving the corresponding performance bounds? My thesis focuses on finding the answers to the above fundamental questions for the problems of Direction of Arrival (DoA) estimation and localization, which are of the most important information retrieval problems in radar, wireless communication and array processing. Inthis regard, the first part of this thesis focuses on DoA estimation using Sparse Linear Arrays (SLAs). I consider this problem under three plausible scenarios from quantization perspective. Firstly, I assume that an SLA quantized the received signal to a large number of bits per samples such that the resulting quantization error can be neglected. Although the literature presents a variety of estimators under such circumstances, none of them are (asymptotically) statistically efficient. Motivated by this fact, I introduce a novel estimator for the DoA estimation from SLA data employing the Weighted Least Squares (WLS) method. I analytically show that the large sample performance of the proposed estimator coincides with the Cram\'{e}r-Rao Bound (CRB), thereby ensuring its asymptotic statistical efficiency. Next, I study the problem of DoA estimation from one-bit SLA measurements. The analytical performance of DoA estimation from one-bit SLA measurements has not yet been studied in the literature and performance analysis in the literature has be limited to simulations studies. Therefore, I study the performance limits of DoA estimation from one-bit SLA measurements through analyzing the identifiability conditions and the corresponding CRB. I also propose a new algorithm for estimating DoAs from one-bit quantized data. I investigate the analytical performance of the proposed method through deriving a closed-form expression for the covariance matrix of its asymptotic distribution and show that it outperforms the existing algorithms in the literature. Finally, the problem of DoA estimation from low-resolution multi-bit SLA measurements, e.g. $2$ or $4$ bit per sample, is studied. I develop a novel optimization-based framework for estimating DoAs from low-resolution multi-bit measurements. It is shown that increasing the sampling resolution to $2$ or $4$ bits per samples could significantly increase the DoA estimation performance compared to the one-bit sampling case while the power consumption and implementation costs are still much lower compared to the high-resolution sampling scenario. In the second part of the thesis, the problem of target localization is addressed. Firstly, I consider the problem of passive target localization from one-bit data in the context of Narrowband Internet-of-Things (NB-IoT). In the recently proposed narrowband IoT (NB-IoT) standard, which trades off bandwidth to gain wide area coverage, the location estimation is compounded by the low sampling rate receivers and limited-capacity links. I address both of these NB-IoT drawbacks by consider a limiting case where each node receiver employs one-bit analog-to-digital-converters and propose a novel low-complexity nodal delay estimation method. Then, to support the low-capacity links to the fusion center (FC), the range estimates obtained at individual sensors are converted to one-bit data. At the FC, I propose a novel algorithm for target localization with the aggregated one-bit range vector. My overall one-bit framework not only complements the low NB-IoT bandwidth but also supports the design goal of inexpensive NB-IoT location sensing. Secondly, in order to reduce bandwidth usage for performing high precision time of arrival-based localization, I developed a novel sparsity-aware target localization algorithm with application to automotive radars. The thesis concludes with summarizing the main research findings and some remarks on future directions and open problems. [less ▲]

DoA Estimation Using Low-Resolution Multi-BitSparse Array Measurements

in IEEE Signal Processing Letters (2021)

This letter studies the problem of Direction of Arrival (DoA) estimation from low-resolution few-bit quantized data collected by Sparse Linear Array (SLA). In such cases, contrary to the one-bit ... [more ▼]

This letter studies the problem of Direction of Arrival (DoA) estimation from low-resolution few-bit quantized data collected by Sparse Linear Array (SLA). In such cases, contrary to the one-bit quantization case, the well known arcsine law cannot be employed to estimate the covaraince matrix of unquantized array data. Instead, we develop a novel optimization-based framework for retrieving the covaraince matrix of unquantized array data from low-resolution few-bit measurements. The MUSIC algorithm is then applied to an augmented version of the recovered covariance matrix to find the source DoAs. The simulation results show that increasing the sampling resolution to $2$ or $4$ bits per samples could significantly increase the DoA estimation performance compared to the one-bit sampling regime while the power consumption and implementation costs is still much lower in comparison to the high-resolution sampling implementations. [less ▲]

On the Asymptotic Performance of One-Bit Co-Array-Based Music

in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2021)

Co-array-based Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable attention in array processing thanks to its capability of providing enhanced degrees ... [more ▼]

Co-array-based Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable attention in array processing thanks to its capability of providing enhanced degrees of freedom for DoAs that can be resolved. Additionally, deployment of one-bit Analog-to-Digital Converters (ADCs) has become an important topic in array processing, as it offers both a low-cost and a low-complexity implementation. Although the problem of DoA estimation form one-bit SLA measurements has been studied in some prior works, its analytical performance has not yet been investigated and characterized. In this paper, to provide valuable insights into the performance of DoA estimation from one-bit SLA measurements, we derive an asymptotic closed-form expression for the performance of One-Bit Co-Array-Based MUSIC (OBCAB-MUSIC). Further, numerical simulations are provided to validate the asymptotic closed-form expression for the performance of OBCAB-MUSIC and to show an interesting use case of it in evaluating the resolution of OBCAB-MUSIC. [less ▲]

Localization Performance of 1-Bit Passive Radars in NB-IoT Applications

in IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) (2019, December 14)

Location-based services form an important use-case in emerging narrowband Internet-of-Things (NB-IoT) networks. Critical to this offering is an accurate estimation of the location without overlaying the ... [more ▼]

Location-based services form an important use-case in emerging narrowband Internet-of-Things (NB-IoT) networks. Critical to this offering is an accurate estimation of the location without overlaying the network with additional active sensors. The massive number of devices, low power requirement, and low bandwidths restrict the sampling rates of NB-IoT receivers. In this paper, we propose a novel low-complexity approach for NB-IoT target delay estimation in cases where one-bit analog-to-digital-converters (ADCs) are employed to sample the received radar signal instead of high-resolution ADCs. This problem has potential applications in the design of inexpensive NB-IoT radar and sensing devices. We formulate the target estimation as a multivariate fractional optimization problem and solve it via Lasserre's semi-definite program relaxation. Numerical experiments suggest feasibility of the proposed approach yielding high localization accuracy with a very low number of 1-bit samples. [less ▲]

An Asymptotically Efficient Weighted Least Squares Estimator for Co-Array-Based DoA Estimation

in IEEE Transactions on Signal Processing (2019)

Co-array-based Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable interest in array processing thanks to its capability of providing enhanced degrees ... [more ▼]

Co-array-based Direction of Arrival (DoA) estimation using Sparse Linear Arrays (SLAs) has recently gained considerable interest in array processing thanks to its capability of providing enhanced degrees of freedom. Although the literature presents a variety of estimators in this context, none of them are proven to be statistically efficient. This work introduces a novel estimator for the co-array-based DoA estimation employing the Weighted Least Squares (WLS) method. An analytical expression for the large sample performance of the proposed estimator is derived. Then, an optimal weighting is obtained so that the asymptotic performance of the proposed WLS estimator coincides with the Cram\'{e}r-Rao Bound (CRB), thereby ensuring asymptotic statistical efficiency of resulting WLS estimator. This implies that the proposed WLS estimator has a significantly better performance compared to existing methods. Numerical simulations are provided to validate the analytical derivations and corroborate the improved performance. [less ▲]

Designing (In) finite-alphabet Sequences via Shaping the Radar Ambiguity Function

in ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2019)

In this paper, a new framework for designing the radar transmit waveform is established through shaping the radar Ambiguity Function (AF). Specifically, the AF of the phase coded waveforms are analyzed ... [more ▼]

In this paper, a new framework for designing the radar transmit waveform is established through shaping the radar Ambiguity Function (AF). Specifically, the AF of the phase coded waveforms are analyzed and it is shown that a continuous/discrete phase sequence with the desired AF can be obtained by solving an optimization problem promoting equality between the AF of the transmit sequence and the desired AF. An iterative algorithm based on Coordinate Descent (CD) method is introduced to deal with the resulting non-convex optimization problem. Numerical results illustrate the proposed algorithm make it possible to design sequences with remarkably high tolerance towards Doppler frequency shifts, which is of interest to the future generations of automotive radar sensors. [less ▲]

A Statistically Efficient Estimator for Co-array Based DoA Estimation

in Asilomar Conference on Signals, Systems, and Computers (2018, October)

Co-array-based Direction of Arrival (DoA) estimation using Sparse linear arrays (SLAs) has recently gained considerable interest in array processing due to the attractive capability of providing enhanced ... [more ▼]

Co-array-based Direction of Arrival (DoA) estimation using Sparse linear arrays (SLAs) has recently gained considerable interest in array processing due to the attractive capability of providing enhanced degrees of freedom. Although a variety of estimators have been suggested in the literature for co-array-based DoA estimation, none of them are statistically efficient. This work introduces a novel Weighted Least Squares (WLS) estimator for the co-array-based DoA estimation employing the covariance fitting method. Then, an optimal weighting is given so that the asymptotic performance of the proposed WLS estimator coincides with the Cram\'{e}r-Rao Bound (CRB), thereby ensuring statistical efficiency of resulting WLS estimator. This implies that the proposed WLS estimator has significantly better performance compared to existing methods in the literature. Numerical simulations are provided to corroborate the asymptotic statistical efficiency and the improved performance of the proposed estimator. [less ▲]

Eigenvalue-Based Multiple Antenna Spectrum Sensing: Higher Order Moments

in IEEE Transactions on Wireless Communications (2017), 16(2), 11681184

The problem of multiple antenna spectrum sensing in cognitive radio (CR) networks is studied in this paper. We propose two new invariant constant false-alarm rate eigenvalue-based (EVB) detectors, using ... [more ▼]

The problem of multiple antenna spectrum sensing in cognitive radio (CR) networks is studied in this paper. We propose two new invariant constant false-alarm rate eigenvalue-based (EVB) detectors, using the higher order moments of the sample covariance matrix eigenvalues, by exploiting the separating function estimation test framework. We find closed-form expressions for the false-alarm and detection probabilities of the proposed detectors by providing moment-based approximations of their statistical distributions. The accuracy of the obtained closed-form expressions is validated by Monte Carlo simulations. In addition, we compare the performance of the proposed detectors with that of their two counterparts, i.e., John’s and the arithmetic to geometric mean (AGM) detectors, in terms of the asymptotic relative efficiency. This comparison enables us to demonstrate the superiority of our proposed detectors over those detectors within the typical range of signalto-noise ratio in CR application. The comparative simulation results also illustrate the superiority of the proposed detectors over John’s and the AGM detectors as well as some other state-of-the-art EVB algorithms given in the literature. [less ▲]

Multiantenna GLR Detection of Rank-One Signals With Known Power Spectral Shape Under Spatially Uncorrelated Noise

in IEEE Transactions on Signal Processing (2016), 64(23), 6269-6283

We establish the generalized likelihood ratio (GLR) test for a Gaussian signal of known power spectral shape and unknown rank-one spatial signature in additive white Gaussian noise with an unknown ... [more ▼]

We establish the generalized likelihood ratio (GLR) test for a Gaussian signal of known power spectral shape and unknown rank-one spatial signature in additive white Gaussian noise with an unknown diagonal spatial correlation matrix. This is motivated by spectrum sensing problems in dynamic spectrum access, in which the temporal correlation of the primary signal can be assumed known up to a scaling, and where the noise is due to an uncalibrated receive array. For spatially independent identically distributed (i.i.d.) noise, the corresponding GLR test reduces to a scalar optimization problem, whereas the GLR detector in the general non-i.i.d. case yields a more involved expression, which can be computed via alternating optimization methods. Low signal-to-noise ratio (SNR) approximations to the detectors are given, together with an asymptotic analysis showing the influence on detection performance of the signal power spectrum and SNR distribution across antennas. Under spatial rank-P conditions, we show that the rank-one GLR detectors are consistent with a statistical criterion that maximizes the output energy of a beamformer operating on filtered data. Simulation results support our theoretical findings in that exploiting prior knowledge on the signal power spectrum can result in significant performance improvement. [less ▲]

SFET-Based Multiple Antenna Spectrum Sensing Using the Second Order Moments of Eigenvalues

in IEEE Global Communications Conference (GLOBECOM) (2015)

In this paper, we propose a new detector for multiantenna spectrum sensing in cognitive radios (CR) by exploiting the Separating Function Estimation Test (SFET) framework. Specifically, we consider a ... [more ▼]

In this paper, we propose a new detector for multiantenna spectrum sensing in cognitive radios (CR) by exploiting the Separating Function Estimation Test (SFET) framework. Specifically, we consider a blind scenario for multiantenna spectrum sensing in which both the channel gains and noise variance are assumed to be unknown. For such a scenario, we find an appropriate Separating Function (SF) whose Maximum Likelihood Estimate (MLE) leads us to a SFET-based detector which uses the second order moments of the eigenvalues of the Sample Covariance Matrix (SCM). We also find closed-form expressions for the detection and false-alarm probabilities of the proposed detector. The performance of the proposed detector asymptotically tends to that of the Uniformly Most Powerful Unbiased (UMPU) detector as the number of independent and identically distributed observations increases. In addition, simulation results show that the proposed detector outperforms the state-of-art eigenvalue- based detectors because of using the second order moments of the SCM eigenvalues. [less ▲]