Dear Gianluca Gorni,
Thank you very much for your comments. Yes, you are right I found one issue , I forgot to close the square bracket, and corrected and type the equation as follows.
s = (m + 0.5)*(2*0.74)/(3*10^8);
R = 0.99981;
T = 1.9*10^-4;
L = 0.74;
c = 3*10^8;
tp = 50*10^-6;
td = 450*10^-6;
a = 0.00126;
Tau = 50*10^-9;
v = 30000;
vc = 3*10^8/2*0.74;
Plot[Sum[T^2 R^(2 m)* (UnitStep[tp - t + s]*a + UnitStep[t - s - tp] UnitStep[td - t + s] (1 - (1 - a) Exp[-((t - s - tp)/(2Tau))]) + UnitStep[ t - s - td] (a + (1 - a) Exp[-((t - s - td)/(2Tau))])) Abs[Exp[2 Pi*I*([v+ vc)*(t - s) + I*UnitStep[t - s - tp] UnitStep[td - t + s]*Pi]], {m, 0, 5000}], {t, 0, 0.0008}]