# Performance of compressive sensing based energy detection

Title | Performance of compressive sensing based energy detection |

Publication Type | Conference Paper |

Year of Publication | 2017 |

Authors | Lagunas, E., Rugini, L. |

Conference Name | 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC) |

Date Published | oct |

ISBN Number | 978-1-5386-3531-5 |

Keywords | central limit theorem, closed-form expressions, Cognitive radio, cognitive radio applications, composability, compressed sensing, compressive ratio, compressive sampling, compressive sensing, CS framework, Cyber-physical systems, decision variable, detected idle channels, Detectors, energy detection, Gaussian processes, low-complexity approximations, Mathematical model, one-dimensional Gaussian Q-function, privacy, probability, Probability density function, pubcrawl, radio spectrum management, Random variables, resilience, Resiliency, sample size low, sensing time, signal detection, Signal processing, signal-to-noise ratio, spectrum sensing, Stochastic processes, test statistic |

Abstract | This paper investigates closed-form expressions to evaluate the performance of the Compressive Sensing (CS) based Energy Detector (ED). The conventional way to approximate the probability density function of the ED test statistic invokes the central limit theorem and considers the decision variable as Gaussian. This approach, however, provides good approximation only if the number of samples is large enough. This is not usually the case in CS framework, where the goal is to keep the sample size low. Moreover, working with a reduced number of measurements is of practical interest for general spectrum sensing in cognitive radio applications, where the sensing time should be sufficiently short since any time spent for sensing cannot be used for data transmission on the detected idle channels. In this paper, we make use of low-complexity approximations based on algebraic transformations of the one-dimensional Gaussian Q-function. More precisely, this paper provides new closed-form expressions for accurate evaluation of the CS-based ED performance as a function of the compressive ratio and the Signal-to-Noise Ratio (SNR). Simulation results demonstrate the increased accuracy of the proposed equations compared to existing works. |

URL | https://ieeexplore.ieee.org/document/8292460/ |

DOI | 10.1109/PIMRC.2017.8292460 |

Citation Key | lagunas_performance_2017 |

- central limit theorem
- closed-form expressions
- cognitive radio
- cognitive radio applications
- composability
- compressed sensing
- compressive ratio
- compressive sampling
- compressive sensing
- CS framework
- cyber-physical systems
- decision variable
- detected idle channels
- Detectors
- energy detection
- Gaussian processes
- low-complexity approximations
- Mathematical model
- one-dimensional Gaussian Q-function
- privacy
- probability
- Probability density function
- pubcrawl
- radio spectrum management
- Random variables
- resilience
- Resiliency
- sample size low
- sensing time
- signal detection
- signal processing
- signal-to-noise ratio
- spectrum sensing
- Stochastic processes
- test statistic