Received Signal in Continuous Time

Hello all,

I am trying to do this in MATLAB, and I appreciate any help: I have the transmitted signal in a communication system where single carrier modulation with frequency domain equalization, known as SC-FDE, is used, as (I will use the Latex syntax in writing the equations):

s(t)=\sum_{k=-N_g}^{N_d-1}d_k g(t-kT_s)

where N_g and N_d are the lengths of the cyclic prefix and data block in symbols, d_k are the transmitted symbols and g(t) is a rectangular pulse of duration T_s, where T_s is the symbol duration.

The channel impulse response is given by:

h(\tau;t)=\sum_{p=1}^{N_p}h_p\delta(t-\tau_p)

where N_p is the number of resolvable paths, and h_p and \tau_p are the channel gains and delays, respectively.

The received signal then can be written as:

r(t)=\sum_{k=-N_g}^{N_d-1}d_k\sum_{p=1}^{N_p}h_p g(t-kT_s-\tau_p)+w(t)

where w(t) is AWGN process.

I have done the above system in the discrete time, but now I want to have r(t) in MATLAB, i.e., in the continuous time. How can I do that?

Thanks in advance