Minimum detectable signal
A minimum detectable signal is a signal at the input of a system whose power produces a signal-to-noise ratio of m at the output. In practice, m is usually chosen to be greater than unity. In some literature, the name sensitivity is used for this concept.
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.
To calculate the minimum detectable signal we first need to establish the noise floor in the receiver by the following equation:
As a numerical example:
A receiver has a bandwidth of 100 MHz and noise figure of 1.5 dB and the physical temperature of the system is 290 kelvins.
So for this receiver to even begin to "see" a signal it would need to be greater than −92.5 dBm. 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 10 dB. To calculate the actual minimum detectable signal is simply a case of adding the required SNR in dB to the noise floor. So for the example above this would mean that the minimum detectable signal is:
MDS (dBm) = -92.5 + 10 = -82.5 (dBm)
MDS (dBm) = 10Log(kTo/1e-3) + NF + 10Log(BW) + SNR (dB)
In this equation:
kT0 is the available noise power in a bandwidth BW = 1 Hz at T0, expressed in dBm. T0 is the system temperature in kelvins, and k is Boltzmann's constant (1.38×10−23joules 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 a reference).
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