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Comparing BPSK, QPSK, 4PAM, 16QAM, 16PSK, 64QAM and 32PSK

Posted By Krishna Sankar On July 8, 2008 @ 5:47 am In Modulation | 112 Comments

I have written another article in DSPDesginLine.com [1]. This article can be treated as the third post in the series aimed at understanding Shannon’s capacity equation.

For the first two posts in the series are:

The article summarizes the symbol error rate derivations in AWGN for modulation schemes like BPSK, QPSK, 4PAM, 16QAM, 16PSK, 64QAM and 32PSK.

The article in DSPDesignline.com [4] details the following:

• Based on the knowledge of bandwidth requirements for each type of modulation scheme, the capacity in bits/seconds/Hz is listed.
• Using the knowledge that the symbol to noise ratio $\frac{E_s}{N_0}$ is $k=\log_2(M)$ times the bit to noise ratio $\frac{E_b}{N_0}$, the symbol error rate vs $\frac{E_b}{N_0}$ curves are plotted.
• Using symbol error rate versus $\frac{E_b}{N_0}$ plots, the $\frac{E_b}{N_0}$ required for achieving symbol error rate of $10^{-5}$is identified.
• Upon having the capacity and $\frac{E_b}{N_0}$ requirement, the requirements for BPSK, QPSK, 4PAM, 16QAM, 16PSK, 64QAM and 32PSK are mapped on to the Shannon’s capacity vs Eb/No curve [5].
• Assuming Gray coded modulation mapping, each symbol error causes one bit out of $k=\log_2(M)$ bits to be in error. So, the relation between symbol error and bit error is,$P_b \approx \frac{Ps}{k}$.
• Using this assumption, the Bit Error Rate (BER) for BPSK, QPSK, 4PAM, 16QAM, 16PSK, 64QAM and 32PSK are listed and the BER vs Eb/No curve plotted.

URL to article: http://www.dsplog.com/2008/07/08/compare-bpsk-qpsk-4pam-16qam-16psk-64qam-32psk/

URLs in this post:

[1] DSPDesginLine.com: http://www.dspdesignline.com/howto/208801783;jsessionid=KQBZX4ZJRFCX0QSNDLRSKHSCJUNN2JVN

[2] Understanding Shannon’s capacity equation: http://www.dsplog.com/2008/06/15/shannon-gaussian-channel-capacity-equation/

[3] Bounds on Communication based on Shannonâ€™s capacity: http://www.dsplog.com../../2008/06/18/bounds-on-communication-shannon-capacity/

[4] DSPDesignline.com: http://www.dspdesignline.com/howto/208801783;jsessionid=KQBZX4ZJRFCX0QSNDLRSKHSCJUNN2JVN?pgno=1

[5] mapped on to the Shannon’s capacity vs Eb/No curve: http://www.dspdesignline.com/howto/208801783;jsessionid=KQBZX4ZJRFCX0QSNDLRSKHSCJUNN2JVN?pgno=3