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

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

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:
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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:
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>> 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.