Impact of noise estimation on energy detection and eigenvalue based spectrum sensing algorithms

Abstract

In this paper, semi-blind class of spectrum sensing algorithms, Energy Detection (ED) and Roy's Largest Root Test (RLRT), are considered under a typical flat fading channel scenario. The knowledge of the noise variance is imperative for the optimum performance of ED and RLRT. Unfortunately, the variation and unpredictability of noise variance is unavoidable. An idea of auxiliary noise variance estimation is introduced in order to cope with the absence of prior knowledge of the noise variance, thus a hybrid approach of signal detection is set forth for each considered method. The detection performance of the methods are derived and expressed by closed form analytical expressions. The impact of noise estimation accuracy on the the performance of ED and RLRT is compared in terms of Receiver Operating Characteristic (ROC) curves and performance curves (Probability of Detection/Miss-detection as a function of SNR by fixing the false alarm probability). It is concluded that optimum performance of ED and RLRT can be achieved even with the use of estimated noise variance by using a large number of slots for variance estimation. Finally, it is also found out that the impairment due to noise uncertainty is reduced on RLRT w. r. t. ED.

Effect of Primary User Traffic on Largest Eigenvalue Based Spectrum Sensing Technique

“…RLRT is "semi-blind" as it requires the exact knowledge of noise variance and is considered to be asymptotically optimum test in this setting [17]. Other related tests have been proposed in the literature for example λ 1 against smallest eigenvalue [16], λ 1 against trace of covariance matrix [18].…”

“…Since sensing slots are independent from each other, we treat each covariance matrix in (15) [17,20].…”

“…The largest eigenvalue of R N (D 0 ) is negligible compared to the largest eigenvalue of R S (N − D 0 ) given a signal identifiability condition is met [6]. It is known that the fluctuation of the largest eigenvalue of a rank-1 spiked population matrix normalized by the noise variance are asymptotically Gaussian [17,19] if the signal identifiability condition is met otherwise its distribution is again a Tracy-Widom of order 2.…”

“…Since R SS | H1 is a standard spiked population covariance matrix of rank-1, the distribution of the largest eigenvalue normalized by the noise variance in a SS sensing slot under H 1 can be approximated as [17,19],…”

Linear system construction of multilateration based on error propagation estimation

“…And, those algorithms work effectively if the noise is estimated precisely [7]. However, in a harsh scenario, the noise estimation is almost impossible to be achieved because of the insufficiency on measurement noise caused by the robots mobility [8]. A new strategy of improving localization accuracy is needed to solve the problem.…”