Noise in Communication Systems

Noise is any unwanted signal that interferes with the desired signal in a communication system. It is the fundamental limiting factor in communication system performance, determining the minimum signal level that can be reliably detected and the maximum achievable data rate.

What is Noise?

Noise is defined as any unwanted electrical energy that enters the communication system and degrades the quality of the desired signal. Unlike distortion (which is deterministic and potentially reversible), noise is random and sets an irreducible lower bound on system error performance.

Classification of Noise

Internal Noise Sources

1. Thermal Noise (Johnson-Nyquist Noise)

Generated by random motion of electrons in conductors due to temperature.

Noise Power: P_n = kTB (Watts)

Where:

• k = Boltzmann's constant = 1.38 × 10⁻²³ J/K
• T = absolute temperature in Kelvin
• B = bandwidth in Hz

Noise Voltage (across resistor R): V_n = √(4kTBR) (Volts RMS)

Properties:

• White noise (flat power spectral density)
• Gaussian amplitude distribution
• Present in all resistive components
• Independent of current flow
• PSD: S_n(f) = kT W/Hz (one-sided)

Example: At room temperature (T = 290K), bandwidth 1 MHz: P_n = 1.38×10⁻²³ × 290 × 10⁶ = 4 × 10⁻¹⁵ W = -114 dBm

2. Shot Noise

Caused by the discrete nature of electric current (individual electron arrivals).

Noise Current: i_n = √(2qI_dc·B) (Amperes RMS)

Where:

• q = electron charge = 1.6 × 10⁻¹⁹ C
• I_dc = DC bias current
• B = bandwidth

Occurs in: Diodes, transistors, photodetectors

3. Flicker Noise (1/f Noise)

Power spectral density varies inversely with frequency.

PSD: S(f) = K/f^α (where α ≈ 1)

• Dominant at low frequencies (below ~1 kHz)
• Caused by impurities and crystal defects
• Important in oscillators and baseband circuits
• Also called pink noise or excess noise

4. Transit Time Noise

Occurs when carrier transit time across a junction becomes comparable to the signal period. Significant at microwave frequencies.

External Noise Sources

Noise Characterization

Noise Figure (F)

Measures how much a device degrades the SNR:

F = SNR_input / SNR_output = (S_i/N_i) / (S_o/N_o)

In dB: NF = 10×log₁₀(F)

For ideal (noiseless) device: F = 1 (NF = 0 dB)

Noise Temperature (T_e)

Equivalent temperature of a resistor that would produce the same noise:

T_e = (F - 1) × T₀

Where T₀ = 290 K (reference temperature)

Cascaded Noise Figure (Friis Formula)

For multiple stages in series:

F_total = F₁ + (F₂-1)/G₁ + (F₃-1)/(G₁G₂) + ...

Where G_i = gain of stage i, F_i = noise figure of stage i.

Key Insight: The first stage dominates! A low-noise amplifier (LNA) at the input is critical.

White Gaussian Noise (WGN)

The most important noise model in communication theory:

Properties:

• Flat power spectral density: S_n(f) = N₀/2 for all f
• Gaussian probability distribution: p(n) = (1/√(2πσ²)) × exp(-n²/(2σ²))
• Zero mean: E[n(t)] = 0
• Uncorrelated samples: E[n(t₁)·n(t₂)] = (N₀/2)·δ(t₁-t₂)

Noise in Analog Systems

AM System SNR:

SNR_o = (m² × S)/(2 × N₀ × W) × (1/(1 + m²/2)) (for envelope detection)

FM System SNR:

SNR_o = (3/2) × β² × (β+1) × (S/(N₀W)) (above threshold)

FM improvement over AM: I_FM = 3β²(β+1)/2 (can be 20-30 dB for β=5)

Noise in Digital Systems

The probability of bit error in AWGN:

For BPSK: P_e = Q(√(2E_b/N₀))

For BFSK (coherent): P_e = Q(√(E_b/N₀))

For QPSK: P_e = Q(√(2E_b/N₀)) (same as BPSK per bit)

Where Q(x) = (1/√2π)∫(x to ∞) exp(-t²/2) dt

Solved Example

Problem: A receiver has three stages: LNA (Gain=20dB, NF=1.5dB), Mixer (Gain=-6dB, NF=8dB), IF Amplifier (Gain=40dB, NF=4dB). Calculate the overall noise figure.

Solution:

Convert to linear values:

• G₁ = 10^(20/10) = 100, F₁ = 10^(1.5/10) = 1.413
• G₂ = 10^(-6/10) = 0.25, F₂ = 10^(8/10) = 6.31
• G₃ = 10^(40/10) = 10000, F₃ = 10^(4/10) = 2.512

Friis formula: F_total = F₁ + (F₂-1)/G₁ + (F₃-1)/(G₁×G₂) F_total = 1.413 + (6.31-1)/100 + (2.512-1)/(100×0.25) F_total = 1.413 + 0.0531 + 0.0605 F_total = 1.527

NF_total = 10×log₁₀(1.527) = 1.84 dB

Note: The LNA dominates the overall noise figure (1.5 dB out of 1.84 dB total), confirming the importance of a low-noise first stage.

Noise Reduction Techniques

Interview Questions

Q1: Why is the noise figure of the first amplifier stage most critical?

From Friis formula, subsequent stages' noise contributions are divided by the gain of preceding stages. A high-gain, low-noise first stage (LNA) amplifies the signal before noise from later stages can significantly affect the SNR. If the first stage has gain G₁=100, the second stage's noise is reduced by factor 100.

Q2: What is the difference between noise figure and noise temperature?

Noise figure (F) is the ratio of input SNR to output SNR — it measures SNR degradation. Noise temperature (T_e) is the equivalent temperature of a source resistor producing the same noise power. They are related: T_e = (F-1)×T₀. Noise temperature is preferred for very low-noise systems (like satellite receivers) where NF values would be very close to 0 dB.

Q3: Why is AWGN used as the standard channel model?

AWGN is mathematically tractable (Gaussian distribution allows closed-form solutions), physically motivated (central limit theorem: sum of many independent noise sources is Gaussian), and represents the worst-case uncorrelated noise. It provides a baseline for comparing system performance — if a system works in AWGN, it provides a starting point for more complex channel models.

Q4: How does bandwidth affect noise power?

Noise power P_n = kTB is directly proportional to bandwidth. Doubling the bandwidth doubles the noise power (3 dB increase). This is why receivers use the narrowest bandwidth that can pass the desired signal — matched filtering optimizes SNR by minimizing noise bandwidth while passing all signal energy.