Spectrum sensing and SNR walls when primary user has multiple power levels

In this paper, we study the spectrum sensing problem when the primary user (PU) transmits over more than one power levels and when there exists noise uncertainty at the secondary user (SU) side. Energy detection is, again, proved to be the optimal for detecting the "on-off" status of PU and could also be used for recognizing the power levels of PU. We derive the closed-form decision region and compute the corresponding closed-form decision probability. Meanwhile, it is shown that when the signal-to-noise ratio (SNR) is lower than certain thresholds, both the detection and recognition of some power levels could suffer from SNR wall effects, i.e., detection or recognition fails no matter how long the sensing time is. Finally, simulation results are provided to cohobate the proposed studies.