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Assumed the transmission system with channel impulse response is determined by the matrices $H(\tau_l) \in C^{N_R \times N_T}$ ( $N_R$ and $N_T$ are numbers of received and transmit antennas)

By taking the Fourier Transform (FT) of the impulse response, we get the frequency response of the channel at subcarrier $n$.

\begin{equation} H(n)=\sum_{l=1}^{L} H(\tau_l) \cdot e^{i \cdot 2 \pi (f_c+\Delta f \cdot n)\tau_l}, \end{equation} where $f_c$ is the centre frequency, $\Delta f$ is the subcarrier bandwidth, $n$ is a subcarrier index, $n=1, \ldots N$.$t$ denote time, $\tau$ is delay. $\tau_l$ is the cluster delays.

How should I change the equation above if I need to check how the doppler delay is affected system?

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