Tutorial20: modulation2.pdf 16-QAM BER

[Krishna]

Hi Charan,

Brief comment on Table II BER equations (in Tutorial 20). My understanding of BER for 16-QAM is different from the BER equation for 16QAM mentioned in Table II.

My understanding;
As I understand, the symbol error probability for 16QAM modulation is SER_{16QAM} = (3/2)*erfc(sqrt(Es/10No));

To find BER, typically we can assume that the bits assigned to constellation points are grey coded . Which means that each symbol error causes only 1 out of 4 bits to be incorrectly detected. Given so, the bit error probability is 1/4th the symbol error probability.

Additionally, since we are transmitting 4 bits in a symbol,
the each symbol carries energy of four bits i.e Es/No = 4*Eb/No.

Combining, the bit error probability comes to
BER_{16QAM} = (3/8)*erfc(sqrt(4Eb/10No)).

More details on how I arrived at this @ my blog @
www.dsplog.com/2007/12/09/symbol-error-rate-for-16-qam/

Do you agree to my observations?
Kindly share your thoughts.

Thanks,
Krishna
~ Blog on digital signal processing
~ www.dsplog.com