  The problems regarding spectrum sensing are studied by exploiting a priori
and a posteriori in information of the received noise variance. First, the
traditional Average Likelihood Ratio (ALR) and the General Likelihood Ratio
Test (GLRT) detectors are investigated under a Gamma distributed function as a
channel noise, for the first time, under the availability of a priori
statistical distribution about the noise variance. Then, two robust detectors
are proposed using the exiting excess bandwidth to deliver a posteriori
probability on the received noise variance uncertainty. The first proposed
detector that is based on traditional ALR employs marginal distribution of the
observation under available a priori and a posteriori of the received signal,
while the second proposed detector employs the Maximum a posteriori (MAP)
estimation of the inverse of the noise power under the same hypothesizes as the
first detector. In addition, analytical expressions for the performance of the
proposed detectors are obtained in terms of the false-alarm and detection
probabilities. The simulation results exhibit the superiority of the proposed
detectors over the traditional counterparts.
