def ber_vs_es_over_n0_qam(snr, M):
"""
Bit-error-rate vs signal to noise ratio after formula in _[1].
Parameters
----------
snr : array_like
Signal to noise ratio in linear units
M : integer
Order of M-QAM
Returns
-------
ber : array_like
theoretical bit-error-rate
References
----------
...[3] Shafik, R. (2006). On the extended relationships among EVM, BER and SNR as performance metrics. In Conference on Electrical and Computer Engineering (p. 408). Retrieved from http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4178493
"""
L = np.sqrt(M)
ber = 2 * (1-1/L) / np.log2(L) * q_function(np.sqrt(3 * np.log2(L) / (L ** 2 - 1) * (2 * snr / np.log2(M))))
return ber
def ber_vs_evm_qam(evm_dB, M):
"""Calculate the bit-error-rate for a M-QAM signal as a function of EVM. Taken from _[1]. Note that here we miss the square in the definition to match the plots given in the paper.
Parameters
----------
evm_dB : array_like
Error-Vector Magnitude in dB
M : integer
order of M-QAM
Returns
-------
ber : array_like
bit error rate in linear units
References
----------
...[1] Shafik, R. (2006). On the extended relationships among EVM, BER and SNR as performance metrics. In Conference on Electrical and Computer Engineering (p. 408). Retrieved from http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4178493
Note
----
The EVM in dB is defined as $EVM(dB) = 10 \log_{10}{P_{error}/P_{reference}}$ (see e.g. Wikipedia) this is different to the percentage EVM which is defined as the RMS value i.e. $EVM(\%)=\sqrt{1/N \sum^N_{j=1} [(I_j-I_{j,0})^2 + (Q_j -Q_{j,0})^2]} $ so there is a difference of a power 2. So to get the same plot as in _[1] we need to enter the log of EVM^2
"""
L = np.sqrt(M)
evm = dB2lin(evm_dB)
ber = 2 * (1-1/L) / np.log2(L) * q_function(np.sqrt(3 * np.log2(L) / (L ** 2 - 1) * (2 / (evm * np.log2(M)))))
return ber