My MATLAB code linked below implements ASK modulation of an M-ary signal, impresses it on a carrier, adds AWG noise of various SNRs. Then, for each SNR, demodulates the signal and calculates the Symbol Error Rate (SER). Finally, it plots two $10\log_{10}(E_{bav}/N_0)$ vs. SER graphs, as shown in the image. One of the graphs (red) is obtained from the the theoretically calculated SER from the equation, $$\text{SER} = \frac{2(M-1)}{M}Q\left( \sqrt{\frac{6 \log_2(M)E_{bav}}{(M^2-1)N_0}} \right)$$ $E_{bav}$ being the average energy per bit and $N_0/2$ being the variance of the added noise. Another graph (blue) is obtained by plotting the SER obtained from the code's demodulation scheme.

My questions are

  1. What's wrong with my code that the two graphs are way apart?
  2. Why even the theoretical curve does not give accurate values? (I checked it from a book)
  3. Is my calculation of $N_0$ (Line 41, 42) correct?
  4. Is my calculation of the basis function $\psi(t)$ (Line 35) and the expected cross correlator output (Line 36) correct? I calculated $E_g=T_s$ in these cases from $$ E_g = \int_0^{T_s}g_T^2(t) dt = \int_0^{T_s}dt=T_s$$ by assuming the arbitrary pulse $g_T(t)$ based on which the the modulated waveforms are created is given by $$g_T(t)= \begin{cases} 1 ~\text{for}~ 0 \le t \le T_s\\ 0 ~\text{otherwise}\end{cases}$$ Wrong assumption ?

Code link : https://paste.ubuntu.com/p/jTs672h5z7/

enter image description here

  • $\begingroup$ A couple of quick notes: (1) Your code is too complex: try to simplify it; (2) The SNR range should be from about 0 to maybe 10-12 dB; (3) The shift in the curves tells you that your SNR calculation is wrong; (4) The fact that your two curves have the same shape is encouraging; it's likely that your only error is in the SNR calculation. $\endgroup$ – MBaz Oct 18 '19 at 19:45
  • $\begingroup$ Thanks ... trying to figure a way out to simplify and find the prob with calculation of SNR @MBaz $\endgroup$ – user716190 Oct 19 '19 at 1:00

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