Spectrum sensing using energy detectors with performance computation capabilities

Abstract

Abstract-We focus on the performance of the energy detector for cognitive radio applications. Our aim is to incorporate, into the energy detector, low-complexity algorithms that compute the performance of the detector itself. The main parameters of interest are the probability of detection and the required number of samples. Since the exact performance analysis involves complicated functions of two variables, such as the regularized lower incomplete Gamma function, we introduce new low-complexity approximations based on algebraic transformations of the onedimensional Gaussian Q-function. The numerical comparison of the proposed approximations with the exact analysis highlights the good accuracy of the low-complexity computation approach.

Performance of compressive sensing based energy detection

“…Clearly, Gaussian approximations are accurate at large sample size and therefore, can be inaccurate when either N or the compression ratio ρ is small. Here, we make use of the power transformation approach [13], [14]. Basically, the power transformation approach approximates a central chi-squared random variable with the rth power of a Gaussian variable with appropriate mean and variance.…”

“…Basically, the power transformation approach approximates a central chi-squared random variable with the rth power of a Gaussian variable with appropriate mean and variance. The statistical relations between chi-squared random variables and power-transformed Gaussian variables are well known in the statistical literature [17]- [19], but have been investigated only recently for CR applications [13], [14]. Specifically, F ρN (x) is approximated aŝ…”

“…which depends on the product M = ρN , rather than on ρ and N separately. We now make use of (14) to calculate an analytical expression for the the number of samplesN required for a desired performance (P F A , P D ). We assume that the primary signal power σ 2 s , the noise power σ 2 w , and the compression ratio ρ, are fixed.…”

“…In this paper, we extend the work in [12]- [14] by merging the approximation techniques proposed in [13], [14] with the CS framework presented in [12]. In particular, we propose novel analytical closed-form expressions for the probability of detection of the CS-based ED when the number of available measurements is too low 978-1-5386-3531-5/17/$31.00 c 2017 IEEE to apply the central limit theorem.…”

“…In particular, we propose novel analytical closed-form expressions for the probability of detection of the CS-based ED when the number of available measurements is too low 978-1-5386-3531-5/17/$31.00 c 2017 IEEE to apply the central limit theorem. To this aim, we exploit the power transformations with generic exponents proposed in [13], [14], which have been shown to be a good alternative for low-complexity devices. Specifically, we formulate a family of equations to evaluate the CS-based ED performance, to easily quantify the effect of the reduced number of samples, and to determine the minimum number of samples needed to achieve certain detection performance.…”