In two previous posts, we have derived theoretical symbol error rate for 16-QAM and 16-PSK modulation schemes. The links are:
Given that we are transmitting the same number of constellation points in both 16-PSK and 16-QAM, let us try to understand the better modulation scheme among the two, i.e. to answer the following question:
For the same signal to noise ratio , will 16-PSK or 16-QAM give a lower symbol error rate?
Distance between the constellation points for 16-PSK
Figure: Distance between constellation points for 16-PSK modulation
As can be seen from the above figure, the distance between symbols and can be approximated as,
, where .
Distance between the constellation points for 16-QAM
Figure: Distance between constellation points for 16-QAM modulation
As can be seen from the above figure, the distance between the constellation points for 16QAM modulation is,
The distance between the constellation points fo 16QAM modulation is around 1.6x the value for 16PSK modulation. Expressing in dB’s, this comes to around .
More the distance between the constellation, lesser is the chance of a constellation point getting decoded incorrectly. This implies that for the same symbol error rate, 16QAM modulation requires only 4.19dB lesser signal to noise ratio , when compared with 16PSK modulation.
% Matlab/Octave code for comparing the symbol error rate for 16PSK and 16QAM modulation
M = 16;
Es_N0_dB = [0:25]; % multiple Es/N0 values
theorySer_16PSK = erfc(sqrt(10.^(Es_N0_dB/10))*sin(pi/M));
theorySer_16QAM = 3/2*erfc(sqrt(0.1*(10.^(Es_N0_dB/10))));
axis([0 25 10^-5 1])
ylabel('Symbol Error Rate')
title('Symbol error probability curve for 16-PSK and 16-QAM modulation')
Figure: Symbol Error Rate for 16PSK and 16QAM modulation
As can be observed, at a symbol error rate of , 16QAM requires only arond 19dB whereas 16PSK requires around 23dB of .
Hope this helps.
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