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Posted By Krishna Sankar On October 1, 2008 @ 9:42 pm In Modulation | 339 Comments

We have quite a few articles discussing bit and symbol error rates for popular digital modulation schemes in Additive White Gaussian Noise (AWGN) channel. This post summarizes the articles discussing the theoretical and simulated error rates for the digital modulation schemes like BPSK, QPSK, 4-PAM, 16PSK and 16QAM. Further, Bit Error Rate with Gray coded mapping, bit error rate for BPSK over OFDM are also discussed.

The links to the individual articles and the Matlab/Octave simulation models are listed below. Alternatively, I have made a e-book discussing all the below mentioned articles to a single PDF file. If you wish, you can download the free e-book by subscribing to the free email newsletter.

Note:
contact me [1] to access the e-book.

The links to articles discussing and the Matlab/Octave simulation models are listed below.

Bit error probability for BPSK modulation[2]

$P_{s,BPSK}=\frac{1}{2}erfc\left({\sqrt{\frac{E_b}{N_0}}}\right)$.

Click here for Matlab simulation for bit error rate (BER) curve with BPSK modulation [3].

Symbol error rate for 4PAM[4]

$P_{s,4PAM}=\frac{3}{4}erfc\left({\sqrt{\frac{E_s}{5N_0}}}\right)$.

Click here for Matlab simulation for symbol error probability with 4PAM modulation [5]

Symbol error rate for 4-QAM (QPSK)[6]

$\begin{eqnarray}\mathbf{P}_{s,4QAM} = erfc\left({\sqrt{\frac{E_s}{2N_0}}}\right)\end{eqnarray}$

Symbol error rate for 16-QAM[8]

$P_{s,16QAM}=\frac{3}{2}erfc\left(\sqrt{\frac{E_s}{10N_0}}\right)$

Click here for Matlab simulation of symbol error rate curve with 16QAM modulation [9]

Symbol Error Rate for 16PSK [10]

$P_{s,16PSK}=erfc\left[\sqrt{\frac{E_s}{N_0}}sin(\frac{\pi}{16})\right]$.

Click here for Matlab simulation for symbol error rate with 16PSK modulation [11]

Note: The formula derived in the post is for a general M-PSK case. For an M-PSK scheme, the symbol error rate is,

$P_{s,MPSK}=erfc\left[\sqrt{\frac{E_s}{N_0}}sin(\frac{\pi}{M})\right]$.

16QAM Bit Error Rate (BER) with Gray mapping [12]

$P_{b,16QAM}=\frac{3}{2k}erfc\left(\sqrt{\frac{kE_b}{10N_o}}\right)$

References

URLs in this post:

[1] contact me: http://www.dsplog.com/contact-us/

[2] Bit error probability for BPSK modulation: http://www.dsplog.comwww.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/

[3] Matlab simulation for bit error rate (BER) curve with BPSK modulation: http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/#Simulation Model

[4] Symbol error rate for 4PAM: http://www.dsplog.com/2007/10/07/symbol-error-rate-for-pam/

[5] Matlab simulation for symbol error probability with 4PAM modulation: http://www.dsplog.com/2007/10/07/symbol-error-rate-for-pam/#Simulation Model

[6] Symbol error rate for 4-QAM (QPSK): http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/

[7] Matlab simulation for symbol error probability with 4QAM (QPSK) modulation: http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/#Simulation Model

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

[9] Matlab simulation of symbol error rate curve with 16QAM modulation: http://www.dsplog.com/2007/12/09/symbol-error-rate-for-16-qam/#Simulation Model

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

[11] Matlab simulation for symbol error rate with 16PSK modulation: http://www.dsplog.com/2008/03/18/symbol-error-rate-for-16psk/#Simulation Model

[12] 16QAM Bit Error Rate (BER) with Gray mapping: http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/

[13] Matlab simulation for bit error rate for 16QAM modulation with Gray mapping: http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/#Simulation Model

[14] BPSK BER with OFDM modulation: http://www.dsplog.com/2008/06/10/ofdm-bpsk-bit-error/

[15] Matlab simulation for BER with OFDM modulation: http://www.dsplog.com/2008/06/10/ofdm-bpsk-bit-error/#Simulation Model