how to find the ber of qam modulation with gray coding with respect to uncoded bpsk?

how to find the ber of m-ary qam for different m with gray coding with respect to uncoded bpsk?

Answer 1

[Pooja Kumari]

Dear anna,

It is my understanding that you wanted to know the BER of m-ary QAM for different value of "m" with gray coding in comparison to uncoded bpsk. You can use the BER expression for finding BER for each modulation schemes.

Calculating BER of uncoded BPSK theoritically using the given formula:

where

• Eb/N0 is the bit energy to noise power spectral density ratio.
• Q(x) is the Q-function, which is the tail probability of the standard normal distribution and can be computed as Q(x) = (1/2) * erfc(x/sqrt(2)), where erfc is the complementary error function.

Calculating BER of m-ary QAM for different value of "m" in an AWGN (Additive White Gaussian Noise) channel with gray coding using the given formula :

where:

• m is the modulation order ( m is perfect sqaure).
• log2(m) gives the number of bits per symbol.
• Eb/N0 and Q(x) are same as defined previously.

You can refer to the below documentation of "qfunc" for more information:

https://www.mathworks.com/help/comm/ref/qfunc.html

Hope this helps!