Analytical expressions for the probability of false-alarm and decision threshold of hadamard ratio detector in non-asymptotic scenarios

Hadamard ratio detector (HRD) has been used for spectrum sensing scenarios with uncalibrated receivers in cognitive radios. In this letter, the theoretical analysis for the probability of false-alarm and the decision threshold was carried out under the asymptotic conditions. Therefore, the obtained results were theoretically valid only when the number of receivers is small but the number of samples is very large. In this letter, we focus on the HRD in non-asymptotic scenarios with relatively small samples. A new analytical expression for the probability of false-alarm is first derived by using the cumulant generating function method. Based on this, a computationally efficient method for determining the decision threshold is also provided. Simulation results validate the theoretical analysis.