Online Channel Impulse Response Simulator

 

Fundamental Theory of Channel Impulse Response

The fundamental theory behind the channel impulse response in wireless communication often involves complex exponential components such as:

\( h(t) = \sum_{i=1}^{L} a_i \cdot \delta(t - \tau_i) \cdot e^{j\theta_i} \)

Where:

• \( a_i \) is the amplitude of the \( i^{th} \) path
• \( \tau_i \) is the delay of the \( i^{th} \) path
• \( \theta_i \) is the phase shift (often due to Doppler effect, reflection, etc.)
• \( e^{j\theta_i} \) introduces a phase rotation (complex exponential)
• The convolution \( x(t) * h(t) \) gives the received signal

So, instead of representing the channel with only real-valued amplitudes, each path can be more accurately modeled using a complex gain:

\( h[n] = a_i \cdot e^{j\theta_i} \)

Channel Impulse Response Simulator

Input Signal (Unit Impulse x[n])

Multipath Delays (samples):

Path Amplitudes:

Path Phases (in degrees):

Channel Impulse Response (CIR)

Output Signal (Impulse Convolved with h[n]) — Real Part

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Further Reading

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