  This paper focuses on analytical studies of the primary user (PU) traffic
classification problem. Observing that the gamma distribution can represent
positively skewed data and exponential distribution (popular in communication
networks performance analysis literature) it is considered here as the PU
traffic descriptor. We investigate two PU traffic classifiers utilizing
perfectly measured PU activity (busy) and inactivity (idle) periods: (i)
maximum likelihood classifier (MLC) and (ii) multi-hypothesis sequential
probability ratio test classifier (MSPRTC). Then, relaxing the assumption on
perfect period measurement, we consider a PU traffic observation through
channel sampling. For a special case of negligible probability of PU state
change in between two samplings, we propose a minimum variance PU busy/idle
period length estimator. Later, relaxing the assumption of the complete
knowledge of the parameters of the PU period length distribution, we propose
two PU traffic classification schemes: (i) estimate-then-classify (ETC), and
(ii) average likelihood function (ALF) classifiers considering time domain
fluctuation of the PU traffic parameters. Numerical results show that both MLC
and MSPRTC are sensitive to the periods measurement errors when the distance
among distribution hypotheses is small, and to the distribution parameter
estimation errors when the distance among hypotheses is large. For PU traffic
parameters with a partial prior knowledge of the distribution, the ETC
outperforms ALF when the distance among hypotheses is small, while the opposite
holds when the distance is large.
