Signal Statistical Mechanics

We are interested in determining the physics bound for the detection of signals in modern digital radio frequency (RF) hardware. Classical signal theory (Kalman filters) requires that the signal-to-noise power ratio (SNR) >10, but this is not the physics bound. Instead, the physics bound is much more complicated. Because an important application is radar, we ask whether, in a time interval of 1 μs, a signal is present within the noise of the receiver baseband. For radar, this would be the pulse return reflection. For our analysis, we use the Keysight Technologies UXR_25 oscilloscope as the RF receiver that has an analogue-to-digital converter (ADC) chip of 256 billion samples per second. In 1 μs, then, 256 thousand voltage samples are taken. We want to determine if a signal is present using the 256 thousand voltage samples using random matrix theory (RMT). The answer for this particular ADC is that we can detect any signals with SNR >−20 dB, a thousand-fold increase from SNR > 10. This paper gives the physics bound of signal detection.