Fading Online Simulator (Rayleigh, Rician, Nakagami, and Doppler)

Fading Online Simulator

Channel Type Without Fading Rayleigh Rician Nakagami Rayleigh + Doppler
Multipaths
Nakagami m
SNR(dB)

Input Signal

Signal After Fading

Constellation Diagram

BER vs SNR

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Wireless Fading Channel Models

1. Rayleigh Fading

Used when there is no line-of-sight (NLOS) path.

Channel coefficient:

h = x + j*y

Where x, y ~ N(0, σ²)

Amplitude distribution:

f(r) = (r / σ²) * exp(-r² / (2*σ²))

Key property:

• Mean power: E[r²] = 2σ²
• In code: sqrt(x² + y²) / sqrt(2)

2. Rician Fading

Occurs when a line-of-sight (LOS) path exists.

Channel coefficient:

h = s + x + j*y

Where s = LOS component, x, y = scattered paths

Distribution:

f(r) = (r / σ²) * exp(-(r² + s²)/(2*σ²)) * I₀(r*s/σ²)

Key parameter:

• K = LOS Power / Scattered Power
• In code: s = sqrt(K / (K + 1))

3. Nakagami Fading

A generalized fading model.

Distribution:

f(r) = (2*m^m / (Γ(m) * Ω^m)) * r^(2*m - 1) * exp(-m*r² / Ω)

Parameter:

• m = fading severity
• Special cases:
  • m = 1 → Rayleigh
  • m > 1 → Rician-like
  • m < 1 → severe fading

4. Doppler Fading

Occurs when the transmitter or receiver is moving.

Channel varies with time:

h(t) = Σ (a_i * e^(j*(2π*f_d,i*t + φ_i)))

Where f_d,i = Doppler shift

Maximum Doppler shift:

f_d = v / λ

This makes the channel time-varying.