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Register a new userXampling: Signal Acquisition and Processing in Union of Subspaces
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Added by
Moshe Mishali
Publication date
2009
fields
Informatics Engineering
and research's language is
English
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We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two. Analog compression that narrows down the input bandwidth prior to sampling with commercial devices. A nonlinear algorithm then detects the input subspace prior to conventional signal processing. A representative union model of spectrally-sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally-sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework.
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We consider the phase retrieval problem for signals that belong to a union of subspaces. We assume that amplitude measurements of the signal of length $n$ are observed after passing it through a random $m times n$ measurement matrix. We also assume that the signal belongs to the span of a single $d$-dimensional subspace out of $R$ subspaces, where $dll n$. We assume the knowledge of all possible subspaces, but the true subspace of the signal is unknown. We present an algorithm that jointly estimates the phase of the measurements and the subspace support of the signal. We discuss theoretical guarantees on the recovery of signals and present simulation results to demonstrate the empirical performance of our proposed algorithm. Our main result suggests that if properly initialized, then $O(d+log R)$ random measurements are sufficient for phase retrieval if the unknown signal belongs to the union of $R$ low-dimensional subspaces.
This paper presents a spectrum sharing technology enabling interference-free operation of a surveillance radar and communication transmissions over a common spectrum. A cognitive radio receiver senses the spectrum using low sampling and processing rates. The radar is a cognitive system that employs a Xampling-based receiver and transmits in several narrow bands. Our main contribution is the alliance of two previous ideas, CRo and cognitive radar (CRr), and their adaptation to solve the spectrum sharing problem.
The achievable information rates of optical communication networks have been widely increased over the past four decades with the introduction and development of optical amplifiers, coherent detection, advanced modulation formats, and digital signal processing techniques. These developments promoted the revolution of optical communication systems and the growth of Internet, towards the direction of high-capacity and long-distance transmissions. The performance of long-haul high-capacity optical fiber communication systems is significantly degraded by transmission impairments, such as chromatic dispersion, polarization mode dispersion, laser phase noise and Kerr fiber nonlinearities. With the entire capture of the amplitude and phase of the signals using coherent optical detection, the powerful compensation and effective mitigation of the transmission impairments can be implemented using the digital signal processing in electrical domain. This becomes one of the most promising techniques for next-generation optical communication networks to achieve a performance close to the Shannon capacity limit. This chapter will focus on the introduction and investigation of digital signal processing employed for channel impairments compensation based on the coherent detection of optical signals, to provide a roadmap for the design and implementation of realtime optical fiber communication systems.
The field of satellite communications is enjoying a renewed interest in the global telecom market, and very high throughput satellites (V/HTS), with their multiple spot-beams, are key for delivering the future rate demands. In this article, the state-of-the-art and open research challenges of signal processing techniques for V/HTS systems are presented for the first time, with focus on novel approaches for efficient interference mitigation. The main signal processing topics for the ground, satellite, and user segment are addressed. Also, the critical components for the integration of satellite and terrestrial networks are studied, such as cognitive satellite systems and satellite-terrestrial backhaul for caching. All the reviewed techniques are essential in empowering satellite systems to support the increasing demands of the upcoming generation of communication networks.
The focus of this paper is on detection theory for union of subspaces (UoS). To this end, generalized likelihood ratio tests (GLRTs) are presented for detection of signals conforming to the UoS model and detection of the corresponding active subspace. One of the main contributions of this paper is bounds on the performances of these GLRTs in terms of geometry of subspaces under various assumptions on the observation noise. The insights obtained through geometrical interpretation of the GLRTs are also validated through extensive numerical experiments on both synthetic and real-world data.
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