Set the carrier frequency f_c = 8 Hz and the bit duration of T_b, = 1 s. For OQP

Question

Set the carrier frequency f_c = 8 Hz and the bit duration of T_b, = 1 s. For OQPSK, numerically evaluate and plot the power spectrum of using the Monte Carlo simulation. On the same figure, plot the theoretical power spectrum, repeat the same for MSK. Steps: Write down the expression for the transmitted waveform s(t) (Equation (3.3-23) and (3.3-20) for OQPSK and MSK, respectively). Generate samples of s Delta(t) = s(t - Delta) with the data sequences and the delay A randomly generated within [0.T_b]. Compute R_s Delta[tau], and then compute its Fourier transform. Set the frequency range to be [4, 12] Hz for presentation uniformity. The OQPSK signal can be written as s(t) = A [(Sigma n = -0 infinity^infinity I_2n g(t - 2nT) cos 2 pi f_c t + Sigma_n = - infinity^infinity I_2 n + 1 g (t - 2n T - T) sin 2 pi f_c t] and the modulated carrier signal is s(t) = A cos[2 pi f_c t + theta_n + 1/2 pi I_n (t - nT/T)] = A cos [2 pi (f_c + 1/4 I_n) t - 1/2 n pi I_n + _n] Equation 3.3-20 indicates that the binary CPFSK signal can be expressed as a sinusoid having one of t possible frequencies in the interval nT lessthanorequalto t lessthanorequalto (n+ 1)T. If

Explanation / Answer

Matlab code:

xa=8*randint(1,2*L)-1; % BPSK signal generation
%xb=2*randint(1,L)-1;
e_xa=xa(1:2:end-1);
o_xa=xa(2:2:end);
rc=rcosine(1,oversamp, 'sqrt');
e_filtered = rcosflt(e_xa,1,oversamp,'filter',rc)*sqrt(oversamp ); %filter
o_filtered = rcosflt(o_xa,1,oversamp,'filter',rc)*sqrt(oversamp ); %filter
x_deci_r=[e_filtered', zeros(1, ceil(oversamp/2))];
x_deci_i=[zeros(1, ceil(oversamp/2)) o_filtered'];

t = (0:length(x_deci_i)-1)/Fs;
tx_sig = sqrt(1/2)*x_deci_r .* cos(2*pi*fc*t) + sqrt(1/2)*x_deci_i .* sin(2*pi*fc*t);

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