Serviceman wrote:I know this terms pretty well, but what I don't know, how it mathematically relate with RSSI, if at all.
Here you go.
Because the RSSI detector is a nonlinear detector, it changes the Signal to Noise Ratio (SNR) of the signal that goes into it. The key to the ASK sensitivity calculation is the SNRout vs SNRin curve of the RSSI detector.
Once we know the SNRout vs SNRin relationship, the steps to finding the ASK sensitivity for a given Noise Figure, IF Bandwidth, and Data Rate are given below.
1. Determine the Eb/No needed for a target BER (10-3 in this example) then calculate the SNR from the Eb/No by using
SNR = (Eb/No) * (R/BBW)
Where R is the data rate and BBW is the Data Filter bandwidth.
2. Reduce the SNR calculated from the previous step by the ratio in dB of the IF (pre-detection) BW to the Data Filter BW. For instance, a 600 kHz IF BW and 6 kHz Data Filter BW means a 20 dB reduction in the SNR. This is the SNR of the signal coming out of the RSSI detector before the Data Filter gets rid of the high frequency noise (assumed to occupy the IF BW). At sensitivity, this ratio is usually negative in dB.
3. Use the RSSI SNRout vs SNRin curve to find the SNR at the input to the RF or IF Amplifier and RSSI detector. You actually use the curve "backwards" to find SNRin given the SNRout you calculated in Step 2.
4. Use the SNR formula for the front end of a receiver to find the signal level at the receiver input. This is the sensitivity, S.
S = (SNRin) * (kTBIFFS)
Where kT is the noise spectral density at 290 K (-174 dBm/Hz) BIF is the IF (pre-detection) BW, and FS is the system (not just the front-end) noise figure of the receiver.
Because the RSSI detector is a logarithmic detector, the SNR input-output relationship can be expressed in a closed-form expression, albeit a messy one. An old paper published in the IEEE Transactions on Aerospace and Electronic Systems derived the expression and plotted the SNRout vs SNRin curve. The curve in the article is small and doesn