# Minimum detectable signal

Minimum detectable signal (MDS) in a radio receiver is the smallest signal power that can be received at its input, processed by its conversion chain and demodulated by the receiver, resulting in usable information at the demodulator output. The MDS is also known as the noise floor of the system. It is mathematically defined as the input signal power required to give some specified output SNR.

## Equation

$MDS = 10*log_{10}(kT/1mW) ~ dBm~ + ~(noise~figure,~dB)~+~ 10\log_{10}(bandwidth,~Hz)~$[1]

In this equation:

kT is the available noise power in a bandwidth B = 1Hz, expressed in dBm. T is the system temperature in kelvins and k is Boltzmann's constant (1.38×10−23 joules per kelvin = −228 dBW/(K·Hz)). If the system temperature and bandwidth is 290 K and 1 Hz, then the effective noise power available in 1 Hz bandwidth from a source is −174 dBm (174 dB below the one milliwatt level taken as reference). This is the system's noise floor at its input. Any signal of lower power may not be discerned from noise, except for specific situations.

1 Hz noise floor: calculating the noise power available in a one hertz bandwidth at a temperature of T = 290 K defines a figure from which all other values can be obtained (different bandwidths, temperatures). 1 Hz noise floor equates to a noise power of −174 dBm so a 1 kHz bandwidth would generate −174 + 10 log10(1 kHz) = −144dBm of noise power (the noise is thermal noise, Johnson noise).

## Definitions

### Noise figure and noise factor

Noise figure (NF) is noise factor (F) expressed in decibels. F is the ratio of the input signal-to-noise-ratio (SNRi) to the output signal-to-noise-ratio (SNRo). F quantifies how much the signal degrades with respect to the noise because of the presence of a noisy network. A noiseless amplifier has a noise factor F=1, so the noise figure for that amplifier is NF=0 dB: a noiseless amplifier does not degrade the signal to noise ratio as both signal and noise propagate through the network.

If the bandwidth in which the information signal is measured turns out not to be 1 Hz wide, then the term 10 log10(bandwidth) allows for the additional noise power present in the wider detection bandwidth.

### Signal-to-noise-ratio

Signal-to-noise-ratio (SNR) is the degree to which the input signal power is greater than the noise power within the bandwidth B of interest. In the case of some digital systems a 10 dB difference between the noise floor and the signal level might be necessary; this 10dB SNR allows a bit error rate (BER) to be better than some specified figure (e.g. 10−5 for some QPSK schemes). For voice signals the required SNR might be as low as 6 dB and for CW (Morse) it might extend, with a trained listener, down to 1 dB difference (tangential sensitivity). Usable in this context then means it conveys adequate information for decoding by a person or a machine with acceptable and defined levels of error.

## References

1. ^ Smith, Jack. Modern communication Circuits (2e). McGraw Hill, 1998, p. 82.