How do I calculate the sensitivity of a receiver in dBm given the noise figure and bandwidth?
Calculating Receiver Sensitivity
Sensitivity defines the minimum input signal level that produces acceptable output quality. The calculation starts from the thermal noise floor and adds the receiver's noise contribution and the minimum signal-to-noise ratio needed by the demodulator or detector.
The thermal noise power in the receiver bandwidth sets the fundamental floor. At 290 K, this is -174 dBm/Hz. The bandwidth term 10·log10(B) scales this to the actual receiver bandwidth. The noise figure adds the receiver's excess noise. The required SNR depends on the application: 10 dB for voice communications, 15 to 25 dB for high-order digital modulations, or 13 dB for radar detection at specified Pd and Pfa.
System designers use this calculation to flow requirements down to the component level. The sensitivity target determines the maximum allowable noise figure, which drives LNA selection and receiver architecture choices. Improving sensitivity by 3 dB (by reducing NF or bandwidth) extends communication range by 41% in free space.
Example: B = 25 kHz, NF = 5 dB, SNR = 12 dB
= -174 + 44 + 5 + 12 = -113 dBm
Frequently Asked Questions
Does antenna gain affect sensitivity?
Antenna gain increases received signal power but does not change the receiver sensitivity specification. However, it improves the system sensitivity (minimum detectable signal at the antenna input) by the antenna gain in dB.
What SNR is needed for BER = 10⁻⁶?
For BPSK: about 10.5 dB. For QPSK: about 10.5 dB. For 16-QAM: about 14.5 dB. For 64-QAM: about 18.5 dB. These are theoretical values; practical implementations require 1 to 3 dB additional margin.
How does coding gain improve sensitivity?
Forward error correction (FEC) provides coding gain that effectively reduces the required SNR. A rate-1/2 convolutional code provides approximately 5 dB coding gain, improving sensitivity by 5 dB without changing the receiver hardware.