Estimation of Primary Channel Activity Statistics in Cognitive Radio Based on Periodic Spectrum Sensing Observations

Primary channel activity statistics (such as the minimum idle/busy periods of the channel, the moments or the underlying distributions) can be exploited by cognitive radio (CR) systems to adapt their operation and improve their performance. Such statistics can be directly estimated from periodic observations of the instantaneous idle/busy state of the primary channel (i.e., periodic spectrum sensing). However, the periodicity of such observations (i.e., the sensing period) imposes a fundamental limit on the time resolution in which idle/busy periods can be observed, and consequently on the accuracy of any subsequent estimated statistics. In this context, this paper provides a comprehensive analysis on the estimation of the primary activity statistics based on periodic channel state observations performed with a finite sensing period. In particular, this paper provides a comprehensive set of closed-form expressions for the estimated statistics as a function of the true primary activity statistics and the employed sensing period. These expressions can find a wide range of applications in the analysis, design, and simulation of CR systems. Moreover, several methods to minimize the estimation errors and improve the accuracy are proposed and validated with both simulations and hardware experiments.