Accurate detection of moving targets via random sensor arrays and Kerdock codes

The detection and parameter estimation of moving targets is one of the most important tasks in radar. Arrays of randomly distributed antennas have been popular for this purpose for about half a century. Yet, surprisingly little rigorous mathematical theory exists for random arrays that addresses fundamental question such as how many targets can be recovered, at what resolution, at which noise level, and with which algorithm. In a different line of research in radar, mathematicians and engineers have invested significant effort into the design of radar transmission waveforms which satisfy various desirable properties. In this paper we bring these two seemingly unrelated areas together. Using tools from compressive sensing we derive a theoretical framework for the recovery of targets in the azimuth-range-Doppler domain via random antennas arrays. In one manifestation of our theory we use Kerdock codes as transmission waveforms and exploit some of their peculiar properties in our analysis. Our paper provides two main contributions: (i) We derive the first rigorous mathematical theory for the detection of moving targets using random sensor arrays. (ii) The transmitted waveforms satisfy a variety of properties that are very desirable and important from a practical viewpoint. Thus our approach does not just lead to useful theoretical insights, but is also of practical importance. Various extensions of our results are derived and numerical simulations confirming our theory are presented

Compressive Sensing Applied to MIMO Radar and Sparse Disjoint Scenes

The purpose of remote sensing is to acquire information about an object through the propagation of electromagnetic waves, specifically radio waves for radar systems. However, these systems are constrained by the costly Nyquist sampling rate required to guarantee efficient recovery of the signal. The recent advancements of compressive sensing offer a means of efficiently recovering such signals with fewer measurements. This thesis investigates the feasibility of employing techniques from compressive sensing in on-grid MIMO radar in order to identify targets and estimate their locations and velocities. We develop a mathematical framework to model this problem then devise numerical simulations to assess how various parameters, such as the choice of recovery algorithm, antenna positioning, signal to noise ratio, etc., impact performance. The experimental formulation of this project leads to further theoretical questions concerning the benefits of incorporating an underlying signal structure within the compressive sensing framework. We pursue these concerns for the case of sparse and disjoint vectors. Our computational and analytical treatments illustrate that knowledge of the simultaneity of these structures within a signal provides no benefit in reducing the minimal number of measurements needed to robustly recover such vectors from noninflating measurements, regardless of the reconstruction algorithm.Ph.D., Mathematics -- Drexel University, 201

The deep space network, volume 15

The DSN progress is reported in flight project support, TDA research and technology, network engineering, hardware and software implementation, and operations. Topics discussed include: DSN functions and facilities, planetary flight projects, tracking and ground-based navigation, communications, data processing, network control system, and deep space stations

Accurate detection of moving targets via random sensor arrays and Kerdock codes

The detection and parameter estimation of moving targets is one of the most important tasks in radar. Arrays of randomly distributed antennas have been popular for this purpose for about half a century. Yet, surprisingly little rigorous mathematical theory exists for random arrays that addresses fundamental question such as how many targets can be recovered, at what resolution, at which noise level, and with which algorithm. In a different line of research in radar, mathematicians and engineers have invested significant effort into the design of radar transmission waveforms which satisfy various desirable properties. In this paper we bring these two seemingly unrelated areas together. Using tools from compressive sensing we derive a theoretical framework for the recovery of targets in the azimuth-range-Doppler domain via random antennas arrays. In one manifestation of our theory we use Kerdock codes as transmission waveforms and exploit some of their peculiar properties in our analysis. Our paper provides two main contributions: (i) We derive the first rigorous mathematical theory for the detection of moving targets using random sensor arrays. (ii) The transmitted waveforms satisfy a variety of properties that are very desirable and important from a practical viewpoint. Thus our approach does not just lead to useful theoretical insights, but is also of practical importance. Various extensions of our results are derived and numerical simulations confirming our theory are presented