PDF | Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics. Compressed Sensing: Theory and Applications. Gitta Kutyniok. March 12, Abstract. Compressed sensing is a novel research area, which was introduced. Compressed sensing: theory and applications / edited by Yonina C. Eldar, Gitta Kutyniok. p. cm. wm-greece.info
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PDF; Export citation. Contents 3 - Xampling: compressed sensing of analog signals. pp 4 - Sampling at the rate of innovation: theory and applications. Compressive Sensing - Adriana Schulz, Eduardo A. B. da Silva e. Luiz Velho together to share ideas about the theory and its applications . We were. and numerical implementation, but richness and relevance of applications and . compressive sensing itself, and the underlying theory builds on various.
This approach takes only a few measurements using a Toeplitz matrix, recovers the wideband signal from a few measurements using Bayesian compressive sensing via fast Laplace prior, and detects either the presence or absence of the primary user using an autocorrelation-based detection method. The results show that the proposed approach speeds up the sensing process by minimizing the number of samples while achieving the same performance as Nyquist-based sensing techniques regarding both the probabilities of detection and false alarm.
Keywords: cognitive radio, compressive sensing, wideband spectrum sensing, software defined radio, Bayesian compressive sensing, autocorrelation, probability of detection, probability of false alarm 1. Introduction The growing number of wireless devices, the increasing demand for higher data rates, and the current static allocation of the radio spectrum are the leading causes of the radio spectrum scarcity problem.
To address this issue and to enhance access to the radio spectrum, cognitive radio technology has been proposed as a viable solution. A cognitive radio system is a smart wireless communication system that can sense the radio spectrum, detect unused spectrum holes, and adjust dynamically its transmission parameters to access free frequency channels without causing any harmful interference to the licensed users or primary users [ 1 , 2 , 3 ].
In this regard, spectrum sensing plays a crucial role in the 3-process cognitive cycle by making cognitive radio systems aware of their radio environments. Over the last decade, several sensing techniques have been proposed to detect the primary user activities. Examples of these techniques include energy detection [ 4 ], cyclostationary detection [ 5 ], and matched filter detection [ 6 ].
Energy detection is a simple technique as it does not require prior knowledge about the primary user signal. However, it is sensitive to noise as it does not distinguish between samples coming from the signal and those coming from noise.
Cyclostationary-based detection is robust to noise and has high detection performance compared with energy detection. Matched filter-based detection requires some prior knowledge about the primary user signal as it compares the received samples to some saved pilots from this signal. This technique is not practical as this information about the signal is often unavailable. These techniques aim at detecting spectral opportunities over narrow frequency bands; however, cognitive radio systems aim to exploit spectral opportunities over broad frequency bands ranging from hundreds of megahertz to hundreds of gigahertz and consequently these sensing techniques cannot be applied directly to perform wideband spectrum sensing.
Wideband spectrum sensing is one of the challenges facing researchers to design next-generation communication systems because this process requires a high sampling rate, which results in a high processing time and energy consumption.
In conventional communication systems, this sensing is performed by an Analog-to-Digital Converter ADC working at the Nyquist rate leading to a high sampling rate and implementation complexity [ 7 ]. The implementation of Nyquist-based sensing techniques is thus impractical for wideband spectrum sensing because of the hardware limitations and the computational cost.
Several sensing approaches have been proposed to perform wideband spectrum sensing [ 8 , 9 , 10 , 11 ]. These approaches perform wideband spectrum sensing using the Nyquist rate. For instance, the authors of [ 8 , 9 , 10 , 11 ] performed spectrum measurements to find the spectrum usage pattern for broad frequency bands.
To overcome the limitations of the models proposed in [ 8 , 9 , 10 , 11 ], some recent innovative techniques have been proposed such as wavelet-based detection [ 12 , 13 , 14 ], multi-band joint detection [ 15 ], and filter-band-based sensing [ 16 , 17 , 18 ].
The wavelet-based detection approach is an edge-based detection that characterizes the edges of the occupied channels. Using this information wavelet-based detection techniques divide the wideband spectrum into several elementary building blocks, and then a wavelet transform is applied to detect irregularities in the structure of the spectrum, which carry valuable information about the occupied channels and their frequency locations.
These techniques introduce a significant latency. One way to reduce this latency is to jointly sense several bands. In multi-band joint detection, a secondary user simultaneously senses several sub-bands, and for each band, the energy of the received samples is calculated. Then, it sets optimal thresholds for all the sub-bands to maximize the likelihood of detection and minimize the likelihood of false alarm. Solving the optimization problem to find the optimal thresholds introduces a large latency instead of reducing it.
In filter bank-based detection, several band-pass filters are used. At the output of each filter, an energy detector is used to detect the activity of the primary user. Current research generally considers multi-bit quantization. For systems employing quantization with a sufficient number of bits, a sparse signal can be reliably recovered using various CS reconstruction algorithms.
Recently, many researchers have begun studying the one-bit quantization case for CS. As an extreme case of CS, one-bit CS preserves only the sign information of measurements, which reduces storage costs and hardware complexity. By treating one-bit measurements as sign constraints, it has been shown that sparse signals can be recovered using certain reconstruction algorithms with a high probability.
Based on the merits of one-bit CS, it has been widely applied to many fields, such as radar, source location, spectrum sensing, and wireless sensing network.
In this paper, the characteristics of one-bit CS and related works are reviewed. First, the framework of one-bit CS is introduced. Next, we summarize existing reconstruction algorithms. Additionally, some extensions and practical applications of one-bit CS are categorized and discussed.
Finally, our conclusions and the further research topics are summarized. Unable to display preview. Download preview PDF. Skip to main content. Advertisement Hide. A survey on one-bit compressed sensing: Review Article First Online: This is a preview of subscription content, log in to check access. Donoho D L.
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Sign In. Access provided by: Application of compressive sensing to sparse channel estimation Abstract: Compressive sensing is a topic that has recently gained much attention in the applied mathematics and signal processing communities.
It has been applied in various areas, such as imaging, radar, speech recognition, and data acquisition.