Abstract :
[en] 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.
