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Problem III) FSK signaling
A binary communication system uses the two FSK signals:
s1(t) = cos(2Ï€ft + 0)
s2(t) = cos(2πf2t + 0); 0 ≤ t ≤ Tp
The received signal is given by:
rt = st = cos(2Ï€ft + 0 + nt)
Implement the non-coherent correlation receiver first in the absence of noise. Since we do not know the phase of the incoming waveforms, we must test them with the signal alphabet and its quadrature phase version. The four cross-correlations in continuous time would be as follows:
ut = cos(2Ï€ft), vt = sin(2Ï€ft), ut = cos(2Ï€f2t), vt = sin(2Ï€f2t)
The correlation functions are given by:
ric(Tp) = ∫r(t)ut dt = ∫r(t)vt dt, i = 1, 2
In its digital implementation, choose the sampling frequency as fs = 5000/Tp and calculate the discrete correlation function:
ric(k) = ∑r(tn)ui(tn), k = 1, 2, ..., n
The decision variables D1, D2 are obtained at time k = 5000 by:
D1 = ric(k) + ric(k)
D2 = ric(k) - ric(k)
To decide between 0 and 1, test if D1 > D2.
Plot the four curves ric(k), ris(k), ric(k), ris(k) as a function of k when s1(t) = cos(2Ï€fit + 0) has been sent. These trajectories will show you how the correlator filters react as they are being filled in with the received signal.
Consider FSK reception under noise, where SNR is 7 dB. Plot D(k) and -D2(k) as a function of k for 1000 different realizations where logic 0 and logic 1 are chosen randomly. Comment on what you observe.
