Interactive Flat & Frequency-Selective Simulators (multi-path model)

Flat & Frequency Selective Channels & BER Simulator

Fading Distribution Rayleigh (NLOS) Rician (LOS) Nakagami-m (m=2)

Signal Frequency: 1.0 MHz

Multipath Taps: 3

Path Delay ($\tau$): 2.0 μs

SNR (for Spectrum): 30 dB

Coh. BW
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Status
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Instantaneous Channel Response $|H(f)|$

Mathematical Foundation & Workflow

1. Signal Generation

The simulator generates a discrete-time signal $x[n]$. For the spectrum, it is a sinusoid; for BER, it is a random BPSK sequence $b \in \{+1, -1\}$.

2. Statistical Fading Distributions

Each multipath tap amplitude $h_p$ is modeled as a random variable:

- Rayleigh: R = sqrt(X² + Y²) / sqrt(2) [X,Y ~ Gaussian]
- Rician: R = sqrt((s + X)² + Y²) [s = LOS component]
- Nakagami-m: Generalized distribution using the sum of squared Gaussians.

3. Frequency Selective Channel Modeling

The channel is modeled as a Finite Impulse Response (FIR) filter. Frequency selectivity arises when the path delay $\tau$ is large relative to the symbol period. The response in frequency is:

H(f) = Σ h_p * exp(-j * 2π * f * p * τ)

Coherence Bandwidth is calculated as $B_c \approx 1/\tau$. If $B_c < \text{Signal Bandwidth}$, the fading is Frequency Selective (notches appear).

4. Spectral Estimation

The received signal $y[n] = x[n] * h[n] + w[n]$ is processed using a Fast Fourier Transform (FFT) to estimate the Power Spectral Density (PSD) in dB.

5. Performance Analysis (BER)

The simulator performs a Monte Carlo simulation. It calculates Bit Error Rate by comparing transmitted bits with detected bits across a range of signal-to-noise ratios (SNR).

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