I am currently working a tricky communication chain that I want to simulate into Matlab.

The chain is like a classic BPSK modulator/demodulator chain, but where the BPSK modulated signal has been merged with an other carrier using PM (Phase modulation) modulation method.

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So, after the PM modulation step, the signal can be expressed like this ($\mathrm{h}$ is the modulation index and $d(t)$ is the NRZ data signal):

$$\cos\left( \omega_c t + \mathrm{h} d(t) \cos(\omega_{sc} t + \varphi_{sc}) + \varphi_c \right)$$

My goal is to find the curve of the $BER = f\left(\frac{E_b}{N_0}\right)$ (Which should fit the theorical BPSK BER curve).

Well, I used to work with this kind of chain without the PM step. To simulate it, I usually just use a theorical noise power $P_n = \frac{\sigma_c^2}{\frac{E_b}{N_0} * \mathrm{BPS}}$ to create a gaussian noise of standard deviation $\sqrt{\frac{Pn}{2}}$. But I have some issue in my current case: I made this chain in Matlab, but I just cannot simulate it because I don't know how to find the standard deviation I have to apply to my gaussian noise when my signal is between the two PM steps.

Actually, I have no idea about how to find it... I just have a big mental breakdown because of the non-linearity of the PM modulation/demodulation step, and I don't know what to do to find $P_n$...

I already calculated the theorical signal autocorellation/PSD just after the PM modulation step, which use first kind Bessel functions (Something similar to the expression (9) of this paper). But honestly I don't know what to do know...

  • $\begingroup$ $N_0$ is normally assumed normalized. Therefore, you need to calculate the occupied bandwidth and the symbol energy to derive the energy per bit per Hz, which is $E_b$ in $E_b/N_0$. For PCM, linearization may be needed. Just follow the definition of SNR and EbNo. $\endgroup$
    – AlexTP
    May 18, 2020 at 9:44
  • $\begingroup$ The full statement is "in simulations, $N_0$ is normally assumed normalized" $\endgroup$
    – AlexTP
    May 18, 2020 at 10:06


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