Exact BER for Gray-coded 2^2n-QAM modulation with AWGN
Generates MatLab-code expressions describing the exact theoretical (raw) bit error ratio vs. Eb/N0 and Es/N0 for the transmission of symmetrical binary signals using Gray-coded 2^2n-QAM modulation over an AWGN channel with a coherent detection receiver.
Use:
===
ExactBER(n)
ExactBER(n, 'details')
n = 1: QPSK
n = 2: QAM16
n = 3: QAM64
n = 4: QAM256
n = 5: QAM1024
n = 6: QAM4096
n = 7: QAM16384
n = 8: QAM65536
etc.
Example:
=======
>> ExactBER(2)
Theoretical AWGN Raw BER for QAM16:
EsN0 = 4 * EbN0
F = sqrt(EsN0/10)
BER = (3/8) * erfc(F) + (1/4) * erfc(3*F) - (1/8) * erfc(5*F)
NOTE: The theoretical BER values as generated by MatLab's berawgn function (also applied by MatLab's bertool) are approximations which deviate from the exact values especially at low Eb/N0.
Cite As
Paul A.M. Bune (2024). Exact BER for Gray-coded 2^2n-QAM modulation with AWGN (https://www.mathworks.com/matlabcentral/fileexchange/19717-exact-ber-for-gray-coded-2-2n-qam-modulation-with-awgn), MATLAB Central File Exchange. Retrieved .
MATLAB Release Compatibility
Platform Compatibility
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- Wireless Communications > Communications Toolbox > Propagation and Channel Models >
- Wireless Communications > Communications Toolbox > PHY Components > Modulation > QAM >
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Version | Published | Release Notes | |
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1.0.0.0 |