Covering the fundamental mathematical underpinnings together with key principles and applications, this book provides a comprehensive guide to the theory and practice of sampling from an engineering perspective. Beginning with traditional ideas such as uniform sampling in shift-invariant spaces and working through to the more recent fields of compressed sensing and sub-Nyquist sampling, the key concepts are addressed in a unified and coherent way. Emphasis is given to applications in signal processing and communications, as well as hardware considerations, throughout. With 200 worked examples and over 200 end-of-chapter problems, this is an ideal course textbook for senior undergraduate and graduate students. It is also an invaluable reference or self-study guide for engineers and students across industry and academia.

Sampling Theory: Beyond Bandlimited Systems

Increased amounts of bandwidth are required to guarantee both high-quality/high-rate wireless services (4G and 5G) and reliable sensing capabilities, such as for automotive radar, air traffic control, earth geophysical monitoring, and security applications. Therefore, coexistence between radar and communication systems using overlapping bandwidths has come to be a primary investigation field in recent years. Various signal processing techniques, such as interference mitigation, precoding or spatial separation, and waveform design, allow both radar and communications to share the spectrum.

Radar and Communication Coexistence: An Overview: A Review of Recent Methods

We study compressive sensing in the spatial domain to achieve target localization, specifically direction of arrival (DOA), using multiple-input multiple-output (MIMO) radar. A sparse localization framework is proposed for a MIMO array in which transmit and receive elements are placed at random. This allows for a dramatic reduction in the number of elements needed, while still attaining performance comparable to that of a filled (Nyquist) array. By leveraging properties of structured random matrices, we develop a bound on the coherence of the resulting measurement matrix, and obtain conditions under which the measurement matrix satisfies the so-called isotropy property. The coherence and isotropy concepts are used to establish uniform and non-uniform recovery guarantees within the proposed spatial compressive sensing framework. In particular, we show that non-uniform recovery is guaranteed if the product of the number of transmit and receive elements, MN (which is also the number of degrees of freedom), scales with K(logG)2, where K is the number of targets and G is proportional to the array aperture and determines the angle resolution. In contrast with a filled virtual MIMO array where the product MN scales linearly with G, the logarithmic dependence on G in the proposed framework supports the high-resolution provided by the virtual array aperture while using a small number of MIMO radar elements. In the numerical results we show that, in the proposed framework, compressive sensing recovery algorithms are capable of better performance than classical methods, such as beamforming and MUSIC.

/pdf/spatial-compressive-sensing-for-mimo-radar-j9jhdmlbei.pdf

Spatial Compressive Sensing for MIMO Radar

Ieee transactions® on aerospace and electronic systems

We investigate the problem of a monostatic pulse-Doppler radar transceiver trying to detect targets sparsely populated in the radar's unambiguous time-frequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem but either do not address sample rate reduction, impose constraints on the radar transmitter, propose CS recovery methods with prohibitive dictionary size, or perform poorly in noisy conditions. Here, we describe a sub-Nyquist sampling and recovery approach called Doppler focusing, which addresses all of these problems: it performs low rate sampling and digital processing, imposes no restrictions on the transmitter, and uses a CS dictionary with size, which does not increase with increasing number of pulses P. Furthermore, in the presence of noise, Doppler focusing enjoys a signal-to-noise ratio (SNR) improvement, which scales linearly with P, obtaining good detection performance even at SNR as low as - 25 dB. The recovery is based on the Xampling framework, which allows reduction of the number of samples needed to accurately represent the signal, directly in the analog-to-digital conversion process. After sampling, the entire digital recovery process is performed on the low rate samples without having to return to the Nyquist rate. Finally, our approach can be implemented in hardware using a previously suggested Xampling radar prototype.

/pdf/sub-nyquist-radar-via-doppler-focusing-4c9aj33kcd.pdf

Sub-Nyquist Radar via Doppler Focusing

Traditional radar sensing typically employs matched filtering between the received signal and the shape of the transmitted pulse. Matched filtering (MF) is conventionally carried out digitally, after sampling the received analog signals. Here, principles from classic sampling theory are generally employed, requiring that the received signals be sampled at twice their baseband bandwidth. The resulting sampling rates necessary for correlation-based radar systems become quite high, as growing demands for target distinction capability and spatial resolution stretch the bandwidth of the transmitted pulse. The large amounts of sampled data also necessitate vast memory capacity. In addition, real-time data processing typically results in high power consumption. Recently, new approaches for radar sensing and estimation were introduced, based on the finite rate of innovation (FRI) and Xampling frameworks. Exploiting the parametric nature of radar signals, these techniques allow significant reduction in sampling rate, implying potential power savings, while maintaining the system's estimation capabilities at sufficiently high signal-to-noise ratios (SNRs). Here we present for the first time a design and implementation of an Xampling-based hardware prototype that allows sampling of radar signals at rates much lower than Nyquist. We demonstrate by real-time analog experiments that our system is able to maintain reasonable recovery capabilities, while sampling radar signals that require sampling at a rate of about 30 MHz at a total rate of 1 MHz.

Sub-Nyquist radar prototype: Hardware and algorithm

Traditional radar sensing typically involves matched filtering between the received signal and the shape of the transmitted pulse. Under the confinement of classic sampling theorem this requires that the received signals must first be sampled at twice the baseband bandwidth, in order to avoid aliasing. The growing demands for target distinction capability and spatial resolution imply significant growth in the bandwidth of the transmitted pulse. Thus, correlation based radar systems require high sampling rates, and with the large amounts of data sampled also necessitate vast memory capacity. In addition, real-time processing of the data typically results in high power consumption. Recently, new approaches for radar sensing and detection were introduced, based on the Finite Rate of Innovation and Xampling frameworks. These techniques allow significant reduction in sampling rate, implying potential power savings, while maintaining the system's detection capabilities at high enough SNR. Here we present for the first time a design and implementation of a Xampling-based hardware prototype that allows sampling of radar signals at rates much lower than Nyquist. We demostrate by real-time analog experiments that our system is able to maintain reasonable detection capabilities, while sampling radar signals that require sampling at a rate of about 30MHz at a total rate of 1Mhz.

A Sub-Nyquist Radar Prototype: Hardware and Algorithms

http://ieeexplore.ieee.org/iel7/6468888/6468889/06468976.pdf

Eliahu Baransky

Papers

Sub-Nyquist radar prototype: Hardware and algorithm

A Sub-Nyquist Radar Prototype: Hardware and Algorithms

A Hardware Prototype for Sub-Nyquist Radar Sensing