On the Performance of Energy Detection Using Bartlett's Estimate for Spectrum Sensing in Cognitive Radio Systems

Energy detection can be used for spectrum sensing in cognitive radios when no prior knowledge about the primary signals is available. The performance of this technique, however, is strongly influenced by the available decision estimate. This paper presents accurate performance analysis of energy detection when using Bartlett's estimate as a test statistic. Both independent and identically distributed Rayleigh and Rician fading channels are investigated for unknown signals with complex envelopes. The novel contribution here is threefold. First, the quadratic form representation of Bartlett's estimate is formulated. Then, starting from the characteristic function, the cumulative distribution function is derived for each type of channel and accurate expressions are developed for the probabilities of false alarm and missed detection. Finally, a performance comparison with the raw periodogram is presented. The accuracy of the proposed analysis is confirmed using Monte Carlo trials. The results provide valuable insight into the performance of Bartlett's based energy detection. It will be seen that the additional degrees of freedom associated with Bartlett's method empower it to offer excellent performance. When compared with the raw periodogram, Bartlett's consistently leads to lower probability of miss, but its probability of false alarm is only superior at relatively higher sensing thresholds.