David83
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Hello all,
I would like to implement single carrier-frequency domain equalization (SC-FDE) in continuous time in MATLAB.
In particular, I have the following:
1- The channel is given by:
\[h(\tau)=\sum_{q=1}^Qh_q\delta(\tau-\tau_q)\]
2- The transmitted signal is given by:
\[s(t)=\Re\left\{e^{j2 f_c t\pi}\sum_{k=0}^{K-1}s_k\,g(t-kT_s)\right\}\]
where fc is the carrier frequency, sk are the transmitted symbols, and g(t) is a rectangular pulse which is one over the interval [0,Ts) where Ts is the sample time.
3- The baseband received signal is given by:
\[v(t)=\sum_{k=0}^{K-1}s_k\sum_{q=1}^Q\alpha_q g(t-kT_s-\tau_q)+w(t)\]
where w(t) is additive white Gaussian noise (AWGN) process of zero-mean and power spectral density (PSD) N0, and
\[\alpha_q=h_q\exp(j 2 f_c \tau_q \pi)\]
If we assume that the transmitted symbols are binary phase shift keying (BPSK) with the following parameters:
How can I obtain v(t) in MATLAB?
I appreciate your help.
Thanks
I would like to implement single carrier-frequency domain equalization (SC-FDE) in continuous time in MATLAB.
In particular, I have the following:
1- The channel is given by:
\[h(\tau)=\sum_{q=1}^Qh_q\delta(\tau-\tau_q)\]
2- The transmitted signal is given by:
\[s(t)=\Re\left\{e^{j2 f_c t\pi}\sum_{k=0}^{K-1}s_k\,g(t-kT_s)\right\}\]
where fc is the carrier frequency, sk are the transmitted symbols, and g(t) is a rectangular pulse which is one over the interval [0,Ts) where Ts is the sample time.
3- The baseband received signal is given by:
\[v(t)=\sum_{k=0}^{K-1}s_k\sum_{q=1}^Q\alpha_q g(t-kT_s-\tau_q)+w(t)\]
where w(t) is additive white Gaussian noise (AWGN) process of zero-mean and power spectral density (PSD) N0, and
\[\alpha_q=h_q\exp(j 2 f_c \tau_q \pi)\]
If we assume that the transmitted symbols are binary phase shift keying (BPSK) with the following parameters:
Code:
N=128; %Number of symbols
fc=12*10^3; %Carrier frequency
B=1000; % Bandwidth
Ts=1/(2*B);%Nyquist Sample Time
nsamp=10^3;%Oversampling factor
Ta=Ts/nsamp;%Sample time after oversampling
K=N*nsamp;%Number of symbols in sample time Ta
tau=[0 5 7 20].*10^-3;%Pathe delays
h=[1 0.8 0.7 0.5];%Fixed channel coefficients.How can I obtain v(t) in MATLAB?
I appreciate your help.
Thanks