How is receiver sensitivity calculated?

Receiver sensitivity is the sum of three terms in dB: the thermal noise floor, the receiver noise figure, and the minimum required SNR. The formula is: Sensitivity (dBm) = minus 174 + 10 log10(B) + NF + SNR_min. The first term (minus 174 dBm/Hz) is the thermal noise density at 290 K, a physical constant. The second term converts from 1 Hz to the actual receiver bandwidth. The third term accounts for the receiver's added noise. The fourth term is the minimum SNR the demodulator needs to achieve the target BER. For an LTE receiver with 10 MHz bandwidth (70 dB), 5 dB noise figure, and 1 dB required SNR for QPSK at 10 percent BLER: sensitivity = minus 174 + 70 + 5 + 1 = minus 98 dBm. This matches the 3GPP reference sensitivity specification for Band 1.

What are the three ways to improve sensitivity?

First, reduce the noise figure. Replacing a 5 dB NF LNA with a 1 dB NF LNA improves sensitivity by 4 dB. This is the most common approach: tower-mounted amplifiers, cryogenic LNAs for radio astronomy, and noise-matched input networks. Second, reduce the bandwidth. A radar receiver processing a 1 microsecond pulse has 1 MHz bandwidth (minus 114 dBm noise floor). Processing gain from pulse integration or matched filtering effectively reduces the noise bandwidth, improving sensitivity without losing signal. Coherently integrating 100 pulses provides 20 dB of processing gain. Third, reduce the required SNR. Forward error correction codes trade bandwidth for SNR: a rate-1/2 turbo code can demodulate at minus 1 dB SNR (1 dB below the noise floor) by spreading redundancy across twice the bandwidth. LDPC codes in 5G NR achieve similar performance.

Why does sensitivity differ so much between applications?

The three terms in the sensitivity equation vary enormously. A GPS receiver uses 2 MHz bandwidth (minus 111 dBm floor), 2 dB NF, and minus 16 dB processing gain from the 1023-chip spreading code, giving minus 125 dBm sensitivity. A WiFi 6 receiver at MCS11 (1024QAM) needs 35 dB SNR and uses 80 MHz bandwidth (minus 95 dBm floor), giving minus 54 dBm sensitivity. A radar receiver with 10 kHz bandwidth, 3 dB NF, and 13 dB SNR for detection has minus 128 dBm single-pulse sensitivity, improving to minus 148 dBm with 100-pulse coherent integration. The 94 dB difference between WiFi and radar comes entirely from bandwidth (39 dB), required SNR (22 dB), noise figure (1 dB), and processing gain (32 dB).

System Design

Receiver Sensitivity

A GPS satellite transmits at 27 W from 20,200 km altitude. By the time the signal reaches Earth, free-space path loss has reduced it to −130 dBm. The GPS receiver must detect this signal buried 19 dB below the thermal noise floor (−111 dBm in 2 MHz BW). It accomplishes this with a 1023-chip spreading code that provides 30 dB of processing gain, effectively pulling the signal out from under the noise. Receiver sensitivity is not one number; it is the intersection of thermal noise floor, noise figure, and the minimum SNR the demodulator needs, modified by any processing gain the signal design provides. Every dB of improvement translates directly into range, coverage, or data rate.

Category: System Design

Formula: −174 + 10log(B) + NF + SNR_min

Range: −54 dBm (WiFi) to −148 dBm (radar)

Sensitivity Across Applications

System	BW	NF	SNR_req	Processing Gain	Sensitivity
GPS L1 C/A	2 MHz	2 dB	14 dB	−30 dB (spreading)	−128 dBm
Radar (single pulse)	10 kHz	3 dB	13 dB	0 dB	−118 dBm
Radar (100-pulse CI)	10 kHz	3 dB	13 dB	−20 dB	−138 dBm
LTE QPSK (10 MHz)	10 MHz	5 dB	1 dB	0 dB	−98 dBm
5G NR 64QAM (100 MHz)	100 MHz	7 dB	17 dB	0 dB	−70 dBm
WiFi 6 1024QAM (80 MHz)	80 MHz	6 dB	35 dB	0 dB	−54 dBm

Receiver sensitivity equation:
S (dBm) = −174 + 10·log₁₀(B) + NF + SNR_min − G_p
G_p = processing gain (spreading, integration, coding)

Worked example (LTE Band 1 QPSK):
S = −174 + 70 + 5 + 1 − 0 = −98 dBm
Matches 3GPP TS 36.104 reference sensitivity

1 dB NF improvement =
1 dB better sensitivity = 12% more range = 25% more area

Common Questions

Frequently Asked Questions

How is sensitivity calculated?

S = −174 + 10log(B) + NF + SNR_min. Thermal floor (−174) is physics. Bandwidth and NF are hardware. SNR_min is set by modulation and target BER. Each term is an independent lever for improvement.

Three ways to improve?

1) Lower NF (better LNA, TMA, cryogenics). 2) Reduce effective BW (matched filtering, pulse integration). 3) Reduce SNR_min (FEC coding, spreading). GPS uses all three: low NF + spreading gain + coding.

Why such large variation?

WiFi 1024QAM: −54 dBm (wide BW + high SNR). Radar with integration: −148 dBm (narrow BW + processing gain). 94 dB difference from: BW (39 dB) + SNR (22 dB) + NF (1 dB) + processing (32 dB).

Related Terms

← Radar Cross Section Return Loss →

System Design

Receiver Sensitivity Calculator

Enter bandwidth, noise figure, modulation type, and coding rate. Compute receiver sensitivity and compare against standard specifications for cellular, WiFi, satellite, and radar.

Compute Sensitivity