Noise uncertainty in cognitive radio sensing: Analytical modeling and detection performance

Methods for primary user detection in cognitive radio may be severely impaired by noise uncertainty (NU) and the associated SNR wall phenomenon. The ability to avoid the SNR wall is proposed herein by detailed statistical modeling of the noise process when NU is present. A Gaussian model for the inverse noise standard deviation is proposed, and good agreement with the more common lognormal distribution is demonstrated for low to moderate noise uncertainty. Closed-form pdfs for a single noise sample and the energy of multiple noise samples are derived, allowing an optimal Neyman-Pearson detector to be employed when NU is present, thus avoiding the SNR wall effect. Initial measurements are presented that explore energy detection at low SNR in a practical system, showing that the noise distribution can be easily calibrated (learned) using a switch and matched load in the receiver. Useful detection performance down to -16 dB with energy detection is demonstrated, and it is found that noise uncertainty is not significant for an instrument-grade low-noise amplifier (LNA) for sub-minute acquisition times.