Analysis of the Sample Size Required for an Accurate Estimation of Primary Channel Activity Statistics under Imperfect Spectrum Sensing

Abstract

Primary channel activity statistics play an important role in improving the performance of Dynamic Spectrum Access (DSA) / Cognitive Radio (CR) systems. The statistical information of the idle/busy periods of a primary channel can be estimated based on the outcomes of spectrum sensing. Recent studies have shown that these statistics can be estimated accurately even under Imperfect Spectrum Sensing (ISS) scenarios. Those studies, however, have assumed no constraints on the required sample size of observations of the idle/busy periods in order to provide accurate estimation (i.e., large sample size was assumed to test the accuracy of these statistics estimation methods). In real-world scenario, DSA/CR systems are limited to the hardware design capabilities, which include limited memory capacity, energy consumption and computational capability. As a result, it is very important to find how many samples of the idle/busy periods are required to provide an acceptable level of accuracy for the estimated statistics. Therefore, this work analyses the impact of the sample size on the estimation of the primary channel statistics under ISS and it finds closed-form expressions for the required sample size of the idle/busy periods to achieve a targeted accuracy. In addition, the analytical results achieved in this work are validated by means of simulations and hardware experiments.