# tapped delay line model

TDL is a model for the channel of a wideband fading process.

The channel consists of \(M\) channel taps, spaced \(\Delta\) apart such that \(\Delta < \frac{1}{B}\) where B is the bandwidth.

Each tap is and independent random process following some statistical distribution.

The average power derived from the autocorrelation of \(A_c(\tau, 0)\), which is also known as the power delay profile.

The correlation of channel at time \(t\) for two frequencies is simply \(A_C(\Delta f)\) where \(C\) is the fourier transform of the channel \(c\). The autocorrelation of this \(C\) also gives us coherence time and coherence bandwidth, as well as doppler spread.