Energy Detection Sensitivity Comparison

In the area of broadband spectrum sensing, there are multiple methods used to detect energy. Two common methods are:

1. Energy detection in the time domain (matlab example)
2. Spectrogram (often defined by a time and frequency resolution [Fs/NFFT], overlap percentage, and number of noncoherent averages [NAVG])

When doing energy detection in the time domain, a polyphase channelizer is often used make smaller subchannels of a large chunk of spectrum.

Questions:

1. How do you compare the sensitivity (ie probability of detection) between the two methods?
2. Is it accurate to say that the difference between the detection SNRs would be: $$\Delta \text{SNR} = 10\log_{10}(\Delta f_1 / \Delta f_2) + 10\log_{10}\sqrt {N_{AVG}}$$ where $$\Delta f = 1/F_s$$ for option 1 and $$\Delta f = F_s/N_\text{FFT}$$ for option 2?
• 1. by modelling or simulating signals of different powers and deriving or measuring least reliable detection (you'll need to define a least probability of detection). – Marcus Müller Feb 26 '20 at 19:34
• 2. no, since that depends on your signal model. – Marcus Müller Feb 26 '20 at 19:35