Given a sample of N independent and identically distributed Rayleigh random variables x_i with parameter \sigma, .
\sigma = \hat{\sigma} \frac {\Gamma(N)\sqrt{N}} {\Gamma(N + \frac {1} {2})} = \hat{\sigma} \frac {4^N N!(N-1)!\sqrt{N}} {(2N)!\sqrt{\pi}}[REF] .