How does sensitivity determine range?

Through the link budget: P_rx = P_tx + G_tx - FSPL + G_rx. At maximum range: P_rx = Sensitivity. FSPL(dB) = 20*log10(4*pi*d/lambda). Solving for range: d = lambda/(4*pi) * 10^((P_tx + G_tx + G_rx - Sensitivity)/20). Example: 3.5 GHz 5G BS, P_tx=46 dBm, G_tx=25 dBi, G_rx=0 dBi, Sensitivity=-101 dBm. FSPL_max = 46+25+0-(-101) = 172 dB. d = 0.086/(4*pi) * 10^(172/20) = 0.086/(12.6) * 1.26e8 = 860 km (theoretical free space). Real range much less due to: building penetration (20-30 dB), rain (1-5 dB/km), fading margin (10-20 dB), terrain. Practical urban range: 0.5-2 km.

What is the difference between MDS and sensitivity?

MDS (Minimum Detectable Signal) is the input power level equal to the noise floor: MDS = kTB + NF = -174 + NF + 10*log10(BW). At MDS, SNR = 0 dB. No useful information can be extracted at MDS. Sensitivity includes the required SNR for the modulation scheme: Sensitivity = MDS + SNR_required. For QPSK at BER=10^-3: SNR_req approximately = 7 dB. For 64QAM at BER=10^-3: SNR_req approximately = 17 dB. For 256QAM at BER=10^-3: SNR_req approximately = 23 dB. So sensitivity is always higher (worse) than MDS by the amount of SNR needed. Example: MDS = -104 dBm, QPSK: sensitivity = -97 dBm, 256QAM: sensitivity = -81 dBm. Higher-order modulation requires a stronger signal.

How do you improve sensitivity?

Three factors in the formula: (1) Reduce NF: every dB of NF improvement gives 1 dB of sensitivity improvement. LNA NF is critical (Friis equation). A 0.5 dB NF LNA at the antenna input vs. a 2 dB NF: 1.5 dB sensitivity improvement. (2) Reduce bandwidth: halving BW improves sensitivity by 3 dB but halves data rate. Narrowband systems (IoT, LoRa at 125 kHz) achieve extreme sensitivity (-137 dBm). (3) Reduce required SNR: coding gain. Turbo codes, LDPC, polar codes provide 5-10 dB coding gain. Forward error correction allows operation at lower SNR. Spreading gain: CDMA, LoRa spread the signal over wider BW, providing processing gain of 10*log10(spreading_factor). LoRa SF12 at 125 kHz: 21 dB processing gain. Antenna gain: not in the sensitivity formula but improves effective sensitivity. A 10 dBi antenna provides 10 dB improvement in link budget.

Receiver Performance

Receiver Sensitivity

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Sensitivity = -174 + NF + 10log(BW) + SNR_req. NF=5 dB, BW=10 MHz, SNR=10 dB: Sensitivity = -89 dBm. Every dB of NF costs 1 dB. MDS = noise floor (SNR=0); sensitivity adds required SNR. QPSK: +7 dB. 256QAM: +23 dB. Determines range via link budget. Improve by: lower NF, narrower BW, coding gain.

Floor: -174 + NF + 10log(BW)

1 dB NF: = 1 dB sensitivity

Range: Link budget

Understanding Sensitivity

Receiver sensitivity is the single most important specification that determines communication range. It defines the weakest signal a receiver can successfully demodulate. The formula breaks down cleanly: the thermal noise floor (-174 dBm/Hz at 290K), plus the receiver's noise figure (how much noise the receiver adds), plus the signal bandwidth (wider = more noise), plus the minimum SNR the demodulator needs for the chosen modulation scheme.

Sensitivity Calculations

Receiver sensitivity:
S = −174 + NF + 10log(B) + SNR_req dBm

MDS (Minimum Discernible Signal):
MDS = kTB × F = −174 + NF + 10log(B)

Sensitivity improvement:
ΔS = −10log(N) for N averaged samples

Sensitivity by Standard

Standard	BW	NF (typ)	Sensitivity	Modulation
LTE Cat 4	10 MHz	5 dB	-99 dBm	QPSK
5G NR FR1	100 MHz	7 dB	-87 dBm	QPSK
Wi-Fi 6	20 MHz	6 dB	-82 dBm	BPSK 1/2
LoRa SF12	125 kHz	6 dB	-137 dBm	CSS SF12
GPS L1	2 MHz	2 dB	-130 dBm	BPSK + PG

Key Equations

Decibel conversion:
Power: dB = 10log(P₂/P₁)
Voltage: dB = 20log(V₂/V₁)

dBm to watts:
P(W) = 10^{(dBm−30)/10}
0 dBm = 1 mW, +30 dBm = 1 W

Wavelength:
λ = c/f = 300/f(MHz) meters

Comparison

Standard	BW	NF	SNR_req	Sensitivity
BLE	2 MHz	8 dB	12 dB	−91 dBm
LoRa SF12	125 kHz	6 dB	−20 dB	−137 dBm
LTE 10M	10 MHz	5 dB	−1 dB	−100 dBm
WiFi 6 20M	20 MHz	6 dB	25 dB	−70 dBm
5G mmW	100 MHz	8 dB	5 dB	−81 dBm

Common Questions

Frequently Asked Questions

Range determination?

Link budget: max range where P_rx = sensitivity. FSPL = 20log(4*pi*d/lambda). 3.5 GHz BS with 46 dBm + 25 dBi: 172 dB path loss budget. Practical urban range: 0.5-2 km after fading/penetration margins.

MDS vs sensitivity?

MDS = noise floor (SNR=0, can't demodulate). Sensitivity = MDS + SNR for modulation. QPSK: +7 dB. 64QAM: +17 dB. 256QAM: +23 dB. Higher-order mod = weaker sensitivity (needs stronger signal).

Improve it?

Lower NF: 1 dB NF = 1 dB sensitivity. Narrower BW: half BW = +3 dB but half data rate. Coding gain: LDPC/Turbo 5-10 dB. Spreading gain: LoRa SF12 = 21 dB. Antenna gain helps link budget.

Related Terms

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Receiver Solutions

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