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Comparing 16PSK vs 16QAM for symbol error rate

Posted By __Krishna Sankar__ On March 29, 2008 @ 6:05 am In __Modulation__ | __56 Comments__

In two previous posts, we have derived theoretical symbol error rate for 16-QAM and 16-PSK modulation schemes. The links are:

(a) Symbol error rate for 16-PSK ^{[1]}

(b) Symbol error rate for 16-QAM ^{[2]}

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?**

** 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 .

** 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,

.

Comparing both,

.

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

clear

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))));

close all

figure

semilogy(Es_N0_dB,theorySer_16PSK,'bs-','LineWidth',2);

hold on

semilogy(Es_N0_dB,theorySer_16QAM,'mx-','LineWidth',2);

axis([0 25 10^-5 1])

grid on

legend('theory-16PSK', 'theory-16QAM');

xlabel('Es/No, dB')

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 .

No wonder we find 16-QAM modulation instead of 16-PSK in typical specifications like IEEE-802.11a ^{[3]}, IEEE802.16d ^{[4]} etc.

Hope this helps.

Thanks,

Krishna

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URL to article: **http://www.dsplog.com/2008/03/29/comparing-16psk-vs-16qam-for-symbol-error-rate/**

URLs in this post:

[1] Symbol error rate for 16-PSK: **http://www.dsplog.com/2008/03/18/symbol-error-rate-for-16psk/**

[2] Symbol error rate for 16-QAM: **http://www.dsplog.com/2007/12/09/symbol-error-rate-for-16-qam/**

[3] IEEE-802.11a: **http://standards.ieee.org/getieee802/download/802.11a-1999.pdf**

[4] IEEE802.16d: **http://standards.ieee.org/getieee802/download/802.16-2004.pdf**

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