In general, it is clear that for a receiver to "see" a signal it has to be greater than the
noise floor. To actually detect the signal, however, it is often required to be at a power level greater than the noise floor by an amount that is dependent on the type of detection used as well as other factors. There are exceptions to this requirement but coverage of these cases is outside the scope of this article. This required difference in power levels of the signal and the noise floor is known as the
signal-to-noise ratio (SNR). To establish the minimum detectable signal (MDS) of a receiver we require several factors to be known. • Required signal-to-noise ratio (SNR) • Detection bandwidth (BW) • Temperature
T0 of the receiver system • Receiver noise figure (NF) To calculate the minimum detectable signal we first need to establish the noise floor in the receiver by the following equation: : \begin{align}\text{Noise floor}_\textrm{dBm} & = 10\ \log_{10}(k T_0\times \mathrm{BW} / 1\,\textrm{mW})\ \textrm{dBm} + \mathrm{NF} \\ & = 10\ \log_{10}(k T_0 \frac \textrm{Hz}\textrm{mW})\ \textrm{dBm} + \mathrm{NF} +10\ \log_{10}( \mathrm{BW} / 1\,\textrm{Hz})\ \textrm{dB} \end{align} Here, is the
Boltzmann constant and is the available
noise power density (the noise is thermal noise,
Johnson noise). As a numerical example: A receiver has a bandwidth of , a noise figure of 1.5
dB and the physical temperature of the system is . : \begin{align}\text{Noise floor}_\textrm{dBm} & = 10\ \log_{10}(1.38\times 10^{-23} \times 290 \times 10^3 )\ \textrm{dBm} + 1.5\ \textrm{dB} +10\ \log_{10}( 100\times10^6 )\ \textrm{dB} \\ & = -174\ \textrm{dBm} + 1.5\ \textrm{dB} +80\ \textrm{dB}\\ & = -92.5\ \textrm{dBm} \end{align} So for this receiver to even begin to "see" a signal it would need to be greater than . Confusion can arise because the level calculated above is also sometimes called the Minimum Discernable Signal (MDS). For the sake of clarity, we will refer to this as the noise floor of the receiver. The next step is to take into account the SNR required for the type of detection we are using. If we need the signal to be 10 times more powerful than the noise floor the required SNR would be . Calculating the actual minimum detectable signal is simply a case of adding the required SNR to the noise floor: : \text{MDS}_\text{dBm}= \text{Noise floor}_\textrm{dBm}+\text{SNR}_\textrm{dB} So for the example above this would mean that the minimum detectable signal is \text{MDS}_\textrm{dBm} = -92.5\,\text{dBm}+10\,\text{dB}=-82.5\,\text{dBm}. The equation above indicates several ways in which the minimum detectable signal of a receiver can be improved. If one assumes that the bandwidth and SNR are fixed however by the application, then one way of improving MDS is by lowering the receiver's physical temperature. This lowers the NF of the receiver by reducing the internal thermally produced noise. These types of receivers are referred to as
cryogenic receivers. == Definitions ==