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Exact BER for Gray-coded 2^2n-QAM modulation with AWGN

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25 Apr 2008 (Updated )

Generates a MatLab-code expression for the exact theoretical BER for Gray-coded 2^2n-QAM modulation

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Description

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.

MATLAB release MATLAB 7.2 (R2006a)
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Comments and Ratings (2)
31 Jan 2012 Paul A.M. Bune

Hello Esuabom Dijemeni, what is exactly your problem? You could contact me directly ...

19 Jan 2012 David Dijemeni

Not getting the correcting graphs...

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