Unified Analysis of Low-SNR Energy Detection and Threshold Selection

For spectrum sensing in cognitive radio networks, the IEEE 802.22 standard requires the detection of primary signals with a signal-to-noise ratio (SNR) as low as -20 dB and receiver sensitivity as low as -116 dBm. Under such low-SNR levels, the performance of a conventional energy detector is analyzed in this paper. The analysis includes novel expressions for missed-detection probability and area under the receiver operating characteristic (ROC) curve. Thus, a unified framework covering fading channels, square-law diversity combining, and cooperative spectrum-sensing scenarios is developed. The detection threshold is optimized to minimize the total error rate subject to bounded false-alarm and missed-detection probabilities, which outperforms traditional detection threshold selection. Numerical results and Monte Carlo simulation results with the IEEE 802.22 sensing requirements are provided and discussed.