Abstract—We introduce a new approach to radar imaging based on the concept of compressive sensing (CS). In CS, a low-dimensional, nonadaptive, linear projection is used to acquire an efficient representation of a compressible signal directly using just a few measurements. The signal is then reconstructed by solving an inverse problem either through a linear program or a greedy pursuit. We demonstrate that CS has the potential to make two significant improvements to radar systems: (i) eliminating the need for the pulse compression matched filter at the receiver, and (ii) reducing the required receiver analog-todigital conversion bandwidth so that it need operate only at the radar reflectivity’s potentially low “information rate” rather than at its potentially high Nyquist rate. These ideas could enable the design of new, simplified radar systems, shifting the emphasis from expensive receiver hardware to smart signal recovery algorithms. I.

Realizing the great potential of impulse radio communications depends critically on the success of timing acquisition. To this end, optimum data-aided timing offset estimators are derived in this paper based on the maximum likelihood (ML) criterion. Specifically, generalized likelihood ratio tests (GLRTs) are employed to detect an ultra-wideband waveform propagating through dense multipath, as well as to estimate the associated timing and channel parameters in closed form. Capitalizing on the pulse repetition pattern, the GLRT boils down to an amplitude estimation problem, based on which closed-form timing acquisition estimates can be obtained without invoking any line search. The proposed algorithms only employ digital samples collected at a low symbol rate, thus reducing considerably the implementation complexity and acquisition time. Analytical acquisition performance bounds and corroborating simulations are also provided.

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The goal of this paper is to highlight the significance of the timing acquisition problem in ultra-wideband (UWB) communication systems and discuss efficient solutions to the problem. We discuss how the distinguishing features of UWB communication systems, such as their wide bandwidth and low transmission power constraints, are responsible for making the acquisition of UWB signals a difficult task. A survey of the current approaches to UWB signal acquisition is also given. In addition, we discuss some of the issues and challenges in UWB signal acquisition which may not have received sufficient attention in existing literature.

Abstract — Ultra-wideband (UWB) communications is envisaged to be deployed in indoor environments, where the noise distribution is decidedly non-Gaussian. A critical challenge for UWB is the synchronization of nanosecond-long pulses. In this paper, we propose a signal acquisition scheme that is robust to uncertainties in the noise distribution. Following Huber’s M-estimates for the Gaussian mixture noise model, the successive sampling-based robust acquisition system outperforms Gaussianoptimal maximum likelihood approach. We present performance evaluation based on the normalized mean-square error and the bit-error rate. I.

The sub-Nyquist estimation of line spectra is a classical problem in signal processing, but currently popular subspace-based techniques have few guarantees in the presence of noise and rely on a priori knowledge about system model order. Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error performance in the presence of noise and without advance knowledge of the model order. We propose an abstract theory of denoising with atomic norms and specialize this theory to provide a convex optimization problem for estimating the frequencies and phases of a mixture of complex exponentials with guaranteed bounds on the mean-squared error. We show that the associated convex optimization problem, called Atomic norm Soft Thresholding (AST), can be solved in polynomial time via semidefinite programming. For very large scale problems we provide an alternative, efficient algorithm, called Discretized Atomic norm Soft Thresholding (DAST), based on the Fast Fourier Transform that achieves nearly the same error rate as that guaranteed by the semidefinite programming approach. We compare both AST and DAST with Cadzow’s canonical alternating projection algorithm and demonstrate that AST outperforms DAST which outperforms Cadzow in terms of mean-square reconstruction error over a wide range of signal-to-noise ratios. For very large problems DAST is considerably faster than both AST and Cadzow. 1

Signal acquisition and reconstruction is at the heart of signal processing, and sampling theorems provide the bridge between the continuous and the discrete-time worlds. The most celebrated and widely used sampling theorem is often attributed to Shannon (and many others, from Whittaker to Kotel’nikov and Nyquist, to name a few) and gives a sufficient condition, namely bandlimitedness, for an exact sampling and interpolation formula. The sampling rate, at twice the maximum frequency present in the signal, is usually called the Nyquist rate. Bandlimitedness, however, is not necessary as is well known but only rarely taken advantage of [1]. In this broader, nonbandlimited view, the question is: when can we acquire a signal using a sampling kernel followed by uniform sampling and perfectly reconstruct it? The Shannon case is a particular example, where any signal from the subspace of bandlimited signals, denoted by BL, can be acquired through sampling and perfectly interpolated from the samples. Using the sinc kernel, or ideal low-pass filter, nonbandlimited signals will be projected onto

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