(21 votes, average: 4.29 out of 5)

by on October 1, 2008

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:
Existing subscribers can contact me 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

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

## Symbol error rate for 4PAM

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

## Symbol error rate for 4-QAM (QPSK)

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

## Symbol error rate for 16-QAM

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

## Symbol Error Rate for 16PSK

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

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

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

## References

D id you like this article? Make sure that you do not miss a new article by subscribing to RSS feed OR subscribing to e-mail newsletter. Note: Subscribing via e-mail entitles you to download the free e-Book on BER of BPSK/QPSK/16QAM/16PSK in AWGN.

rohini March 16, 2013 at 10:59 am

Dear Krishna Sankar
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Krishna Sankar March 16, 2013 at 4:25 pm

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Grekhov April 10, 2012 at 8:24 pm

I have simulated in Simulink (Bernoulli, Hamming Encoder, BPSK Modulator, AWGN, BPSK Demodulator, Hamming Decoder) BPSK with AWGN and have obtained that Hamming (7,4) code has lower BER than Hamming (31,26).
Is it connected with noncoherent demodulation?
I have subscribed but do not know how to get your book. Please send me the book.

Krishna Sankar April 11, 2012 at 5:17 am

@Grekhov: Replies
1. Hmm.. where you comparing Eb/N0? Would expect that you are using coherent demodulation
Did you want to look at http://www.dsplog.com/tag/hamming/
2. Emailed you the instructions

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hi krishna sankar

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Hi,

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Bharg January 4, 2012 at 11:35 pm

hi, can you please tell me what are the changes to be made in the symbol error probability code for QPSK if I want the bit error rate instead?

The question is- bit error probability for QPSK

Krishna Sankar January 5, 2012 at 5:12 am

@Bharg: For QPSK, one needs to send information on both real and imaginary components
http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/

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i want downllod simulation book .plz send to me.tnx

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Good book.

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I have subscribed but when I replied to get a free ebook it was failed to send email to your address. Could you please send me ebook by email please. Thank you so much.
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I am also member, please can you email the instruction of downloading the e book of calculating the BER of awgn/rayleigh channel. Thanks

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Hi Krishna,

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putria March 22, 2011 at 8:02 pm

hi..
im student of final year telecommunication..
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thanks

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Alex December 2, 2010 at 4:22 pm

Hi Krishna!
Thanks!

Krishna Sankar May 26, 2011 at 6:04 am

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Ideal November 15, 2010 at 5:47 am

Hi Krishna,
I am also member, please can you email the instruction of downloading the e book of calculating the BER of awgn/rayleigh channel. Thanks

Krishna Sankar November 15, 2010 at 9:18 pm

@Ideal: I emailed you the instructions

Rohit Nandan Prasad November 11, 2010 at 8:18 pm

Hi Krishna

Rohit

Krishna Sankar November 14, 2010 at 10:31 am

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barbadosa November 11, 2010 at 4:22 am

Hi, I have subscribed, please send me the ebook
regards,

Krishna Sankar November 15, 2010 at 1:44 am

Raja April 8, 2011 at 12:22 am

Hi,
I subscribed to dsplog and got the confirmation mail, but it is a ‘no-reply’ maid ID. I did try to reply, but it bounced
Can you please send me the e-book on AWGN…
Thanks a lot.
Raja

Krishna Sankar May 26, 2011 at 5:52 am

Rohit Prasad November 8, 2010 at 9:40 am

Hi Krishna. I am already a member of DSP log. Could you please send me the e book? Thanks in advance

Krishna Sankar November 15, 2010 at 1:49 am

john nash October 6, 2010 at 4:20 pm

thanks

Krishna Sankar November 19, 2010 at 5:58 am

@john: I emailed you the instructions

Anthony September 28, 2010 at 6:31 pm

Krishna Sankar November 19, 2010 at 5:59 am

@Anthony: I emailed you the instructions

junaid September 28, 2010 at 12:45 am

well sir i must say u hv a very big heart ………..

manaroff September 12, 2010 at 12:25 am

Sorry, Krishna. I subscribed, but nothing happened!

Krishna Sankar November 19, 2010 at 6:00 am

manaroff September 7, 2010 at 9:11 pm

Hello, Mr. Sankar

Can you send me the URL.

Thanks alot.

Krishna Sankar September 8, 2010 at 6:06 am

@manaroff: Thanks for the comment. Have you subscribed to email newsletter from dsplog.com.
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Abu Noor-Eddin September 7, 2010 at 6:53 pm

Hi Krishna,

Krishna Sankar September 8, 2010 at 6:06 am

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DIEP DANG September 7, 2010 at 9:10 am

Hi Krishna,

I’m already member of dsplog and i’m interested with your website and the free e-book. Would you kindly please send me the free e-book? Thanks in advance,Khrisna.

Krishna Sankar September 8, 2010 at 6:02 am

@DIEP DANG: emailed you the details

V.Venkataramanan August 13, 2010 at 10:23 pm

Hello Sir Can u send me the book error probability in AWGN

Krishna Sankar November 19, 2010 at 6:03 am

@Venkataramanan: I emailed the instructions

Alex August 7, 2010 at 11:12 pm

Hi Krishna, would you share the ebook please…thanks a lot.

Krishna Sankar August 10, 2010 at 5:06 am

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Nisa August 7, 2010 at 3:02 pm

Hi Krishna,

I’m already member of dsplog and i’m interested with your website and the free e-book. Would you kindly please send me the free e-book? Thanks in advance,Khrisna.

Krishna Sankar August 10, 2010 at 5:05 am

@Nisa: I emailed you the instructions

Daniel August 3, 2010 at 1:07 pm

Krishna Sankar August 4, 2010 at 6:09 am

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sal July 31, 2010 at 9:48 pm

Hi Krishna
Can you please send me the copy of the ebook !
I am doing my report on OFDM and I would like to thank you for your work!

Krishna Sankar August 2, 2010 at 5:50 am

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Harsha July 27, 2010 at 5:09 pm

Can you send me the link for the Ebooks

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mohamed saber June 21, 2010 at 7:16 pm

Krishna Sankar June 23, 2010 at 6:00 am

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Ivy June 17, 2010 at 2:40 pm

Thank you!

Krishna Sankar June 18, 2010 at 6:21 am

mohamed June 15, 2010 at 3:10 pm

Krishna Sankar June 16, 2010 at 6:08 am

Peng Li June 8, 2010 at 6:37 pm

Dear Krishna Sankar:
I am a student from China. Your work helps me a lot. Please send me a copy of the book. Thanks.

Best Regards

Yours Peng Li

Krishna Sankar June 14, 2010 at 6:25 am

@Peng Li: I emailed you the instructions.

landfox May 18, 2010 at 4:12 pm

May I get a copy of the ebook?

Thank you

Krishna Sankar June 24, 2010 at 4:12 am

uma mahesh May 11, 2010 at 8:06 am

Hi , can you please send me the pdf file

Krishna Sankar June 24, 2010 at 4:16 am

@uma: I emailed you the instructions.

R uma mahesh May 10, 2010 at 5:52 pm

can u send me a copy of the pdf file

Krishna Sankar June 24, 2010 at 4:16 am

@uma: I emailed you the instructions

Nan May 8, 2010 at 12:08 am

can u please send me a copy of the pdf file, I really very neeeeed that!
I must simulate the OOK BER in the Nakagami-m channel(energy detection)….I really dont know how to finish it…..confluent hypergeometric function,such of things make me headache…

and THANK YOU for the cool work!

Krishna Sankar July 2, 2012 at 5:29 am

@Nan: emailed you the instructions

sndi April 19, 2010 at 1:56 am

could u plz send me the .pdf… B4 2 days, got exams coming, so pllzzzz hurry…

BTW this site is really really what i need !!!

continue the great work

Krishna Sankar April 21, 2010 at 5:44 am

@sndi: I emailed you the instructions.

lakshmi narayana April 13, 2010 at 10:20 am

sir i require qpsk mod/demod using pn sequence in cdma environment

Krishna Sankar April 14, 2010 at 4:33 am

@lakshmi narayana: Sorry, I have not discussed CDMA scenarios in the blog. However, I would guess it will be reasonably simple to adapt the QPSK mod/demod post to the CDMA case.
http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/
At the transmitter, multiply each symbol by the PN chips. Correspondingly, at the receiver convolve with the PN chip and pick the maxima.

MAH April 10, 2010 at 1:47 am

Dear Krishna Sankar

I have paper (journal ) but I dont know simulate it, pleaze help me to send me the code to summerize it.(this is homework)

Peak Power Reduction of
Masoud Sharif, Vahid Tarokh, and Babak

thank you

Krishna Sankar April 14, 2010 at 5:27 am

@MAH: Sorry, I wont be able to code for you. However, you can ask queries in the comments section. I will try answer to the best of my knowledge

MAH April 6, 2010 at 1:51 pm

Dear Pillai

Ineed Derivation of FSK BER in Rayleigh channel

and Ihave paper (journal ) but I dont know simulate it, pleaze help me to send me the code to summerize it.

Peak Power Reduction of
Masoud Sharif, Vahid Tarokh, and Babak

thank you

Krishna Sankar April 13, 2010 at 5:28 am

@MAH: I have derived BPSK BER in Rayleigh channel @
http://www.dsplog.com/2008/08/10/ber-bpsk-rayleigh-channel/
http://www.dsplog.com/2009/01/22/derivation-ber-rayleigh-channel/
I am not sure whether FSK results will be 3dB poorer that the BPSK case, but I would guess so.

Sorry, I do not have simulation for the mentioned paper.

Nana April 6, 2010 at 7:38 am

can u send me a copy of the pdf file, i just registered

Krishna Sankar April 13, 2010 at 5:15 am

swamy jsv March 25, 2010 at 10:39 am

Hello please tell me how can i get the e book. ur blog is very informative. good work..!!

Krishna Sankar March 28, 2010 at 1:47 pm

@swamy jsv: I emailed you the details.

Lester Heng March 18, 2010 at 1:01 pm

Hi Krishna,
How do I get a copy of the ebook? Thank you

Krishna Sankar March 28, 2010 at 2:22 pm

@Lester Heng: I emailed you the instructions

shreedhar A Joshi March 9, 2010 at 9:12 am

sir, please send me QPSK based matlab code with alamouti code and decode facility

Krishna Sankar March 29, 2010 at 6:48 am

@shreedhar A Joshi: I posted BPSK based Alamouti coding and decoding http://www.dsplog.com/tag/alamouti
It should be easy to adapt to QPSK case

Eric March 7, 2010 at 11:05 am

Thanks!
Eric

Krishna Sankar March 30, 2010 at 4:25 am

@Eric: I emailed you the instructions

cin6 February 21, 2010 at 12:59 pm

hai
can you mail to me too? i very appreciate it

Krishna Sankar March 31, 2010 at 5:34 am

@cin6: I emailed you the details

rajesh February 17, 2010 at 11:13 pm

How do I get a copy of the ebook? Thank you

Krishna Sankar March 31, 2010 at 5:45 am

@rajesh: I emailed you the instructions

srikanth February 16, 2010 at 8:13 pm

can any one send me the matlab lab coding for link budget analysis

mj February 15, 2010 at 12:51 am

plzz send me the book it would be very nice of u

Krishna Sankar February 15, 2010 at 5:41 am

isa February 9, 2010 at 3:05 pm

thanx

Krishna Sankar April 4, 2010 at 4:11 am

@isa: I emailed you the instructions

Preppy January 29, 2010 at 6:30 am

Hi Krishna,
I would really appreciate if you could send me the ebook.

Thanks,
Preppy

Krishna Sankar April 4, 2010 at 4:47 am

@Preppy: Have you subscribed to email newsletter from dsplog.com.
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Thanks,
Krishna

Amjad January 27, 2010 at 11:10 am

Hi,

Krishna Sankar January 28, 2010 at 5:31 am

@Amjad: Sorry, I need more study to reply to your queries. And due to time constraints, am unable to allocate time. Kindly excuse.

ZhangRui January 22, 2010 at 8:17 am

Hi Krishna,
How do I get a copy of the ebook? Thank you

Krishna Sankar January 25, 2010 at 5:24 am

fariha January 13, 2010 at 3:28 pm

Krishna Sankar January 25, 2010 at 5:23 am

Ishwinder January 13, 2010 at 11:35 am

Hi Krishna,

Request you for the Ebook.

Thanks
Ishwinder

Krishna Sankar January 25, 2010 at 5:22 am

Choe January 12, 2010 at 5:56 pm

Hello Mr. Krishna,
I need to get the e-book (I am already a member)
If you O.K. can you send to me e-book?

Krishna Sankar January 25, 2010 at 5:20 am

gul December 22, 2009 at 4:42 pm

thank you for sharing such information.it is helpful in acquiring the knowledge about programminig in MATLAB.

can u help me in the topic use of wavelet transform in OFDM .
i m doing a project on it.

Krishna Sankar December 23, 2009 at 5:53 am

@gul: Sorry, am not familiar with wavelet transform in OFDM

vijay j December 8, 2009 at 4:39 pm

I am already a member, could you please send me the ebook?

Thanks

Krishna Sankar December 10, 2009 at 6:02 am

@vijay: I emailed you the details.

girish November 21, 2009 at 11:19 pm

Krishna Sankar December 6, 2009 at 4:30 pm

Anis November 18, 2009 at 2:14 pm

Hi Krishna,

Please send me the ebook, thankS!

Krishna Sankar December 6, 2009 at 3:56 pm

ahishek November 16, 2009 at 7:53 am

hi!
we are doing a project to implement adaptive channel equalizer using MAT LAB.
can you provide us coding of adaptive channel equalizer.

Krishna Sankar December 6, 2009 at 3:26 pm

@ahishek: I have not yet posted articles on adaptive equalizer. good luck.

aisha November 7, 2009 at 3:28 pm

hi im student of final year telecommunication
i need the matlab simulation codes of the following data
mobile wimax(error detection,correction,modulation)
same for hsdpa

Krishna Sankar November 8, 2009 at 9:02 am

@aisha: Sorry, I have not discussed specific to 802.16e. However, you may find posts on QAM and Viterbi @
http://www.dsplog.com/tag/qam/
http://www.dsplog.com/tag/viterbi/

ReiRok October 27, 2009 at 7:39 am

Hi,

I have subscribed for the e-book, but i haven’t received any. Can you tell me the procedure to download it?

Krishna Sankar November 8, 2009 at 7:16 am

rasi October 7, 2009 at 9:11 pm

I need equations on QPSK so that i can calculate bit error and eye diagram using matlab. Can u help me?

Krishna Sankar October 8, 2009 at 5:41 am
Ryan October 5, 2009 at 1:03 pm

Hi Krishna,
Your blog helps me to learn OFDM , thank you very much for that.
I am try to simulate BER for OFDM using 16QAM
Thanks!

Krishna Sankar October 8, 2009 at 5:22 am
Pit Dagostino September 16, 2009 at 11:33 pm

Hi Krishna

Could you send me the link?

Pit

Krishna Sankar September 18, 2009 at 5:51 am

@Pit: I emailed you the instructions. Plz check.

Alhad September 14, 2009 at 1:05 am

Krishna Sankar September 14, 2009 at 5:33 am

smoodliar September 14, 2009 at 12:03 am

Hi Krishna

Krishna Sankar September 14, 2009 at 5:33 am

vanitha August 31, 2009 at 12:39 pm

Krishna Sankar September 7, 2009 at 5:28 am

@vanitha: Sorry, the two days have long passed Hope you found the required information.

Raymond August 23, 2009 at 7:05 pm

Hi,
Could you give a copy of free ebook ?
You really set up a good website of communication system.
Thanks.

Krishna Sankar August 24, 2009 at 5:01 am

Tahir Abbas August 20, 2009 at 11:18 pm

AOA
Dear friend!
i am doing thesis of ms, my topic is
Channel State Information Enhanced Adaptive MC CDMA.
can u people help me, specially in matlab coding………

Krishna Sankar August 22, 2009 at 5:23 am

@Tahir Abbas: Good luck for your thesis.

Mak_m August 12, 2009 at 11:16 pm

hi , i hav tried qpsk with half rate convolutional coding with trellis structure of t = poly2trellis(7,[171 133]); i have also applied it with and without gray coding but still i m getting ber of 0.5.. why it does not match theoritical ber theortical ber……plzzz can any body tell me where i m wrong ….i had also tried 2/3 rate coding it works fine but ber at lower EbNo values is little bit higher after that remaining ber values are ok..but i m more intereted in 1/2 rate coding
any help will be appreciated

farrakh August 10, 2009 at 2:06 am

hi krishna,
i want to plot different modulation schemes BER vs Es/No in awgn channel on a single plot.for example, 0 to 9 db QPSK modulation, 10 to 11 db 16 QAM modulatio,12 to 19 db 32PSK modulation and so on. its output will be a single line at series of Es/No values.can u help me about this?
thnx

Krishna Sankar August 11, 2009 at 4:51 am

@farrakh: From your question, it sound like you want to build an adaptive modulation simulation. Though I do not have posts discussing this explicitly, hope you will be able to adapt the QPSK, 16QAM and 16PSK simulations to meet your need.
http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/
http://www.dsplog.com/2007/12/09/symbol-error-rate-for-16-qam/
http://www.dsplog.com/2008/03/18/symbol-error-rate-for-16psk/

Kabir August 3, 2009 at 6:50 pm

Hi Krishna, I am working with mobile location in IS-95 CDMA system. Could you please send me matlab simulation m-file for QPSK modulation and demodulation of Pilot signal in IS-95 CDMA for Pilot channel acquisition. It would be a great help in my research.
Best wishes,

Kabir

Krishna Sankar August 5, 2009 at 5:51 am

@Kabir: Sorry Kabir. I have not tried modeling IS-95 systems.

Girish August 1, 2009 at 3:35 pm

hi,
i am working for bit error rate for BPSK, QPSK and 16 QAM modulation techniques for different code rate 1/2, 3/4, 9/16 using AWGN and Rayleigh channel so plz help me for changing code rate and delay in hiperlan/2

Krishna Sankar August 5, 2009 at 5:48 am

@Girish: How do you achieve different code rate – by puncturing the convolutional code?

saianand July 17, 2009 at 6:28 pm

its good

Gazi faisal Ahmed Jubair July 16, 2009 at 8:28 pm

I need to build a code of probability of Bit Error rate of BPSK, 16 QAM and 256 QAM and QPSK. I need some help. where could I get help . Can you Please help me on that regards.

Krishna Sankar July 17, 2009 at 5:28 am

@Gazi: You may use the following links
a) Bit error probability for BPSK modulation
http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/
b) Symbol error rate for 4-QAM (QPSK)
http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/
c) 16QAM Bit Error Rate (BER) with Gray mapping
http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/

taher July 14, 2009 at 6:18 pm

Hi Krishna,

I would really appreciate if you can help me to implement the cooperative communication (amplify and forward ) and (decode and forward) over the slowe fading channel . the system consistes of source, relay and destnation

all the best

Krishna Sankar July 15, 2009 at 5:19 am

@taher: Sorry, I have not tried modeling co-operative communications.

mrKim November 13, 2012 at 8:38 am

Dear Taher
I am also worikng on multi-hop relay network. I am new in this area and need some help from you. if you can give me ur email address please.
my email is nguyenkimhieuha@gmai.com

i’ll wait for ur reply,plz contzct me on my email.

john Franzen July 14, 2009 at 7:56 am

Hi Krishna,

Thanks!
-John

Krishna Sankar July 15, 2009 at 5:18 am

@John: I just mailed you the download instructions over email. Plz check.

Girish K. July 11, 2009 at 3:38 pm

please send me ebook for BER in AWGN
thanks
regaurds Girish K.

Krishna Sankar July 15, 2009 at 5:08 am

@Girish: I just mailed you the download instructions over email. Plz check.

Matt July 8, 2009 at 9:13 am

Hi, I’d like a copy of the e-book as well.
Thanks

Krishna Sankar July 15, 2009 at 4:48 am

@Matt: I just mailed you the download instructions over email. Plz check.

Carlos July 7, 2009 at 11:18 am

Hi Krishna,

I would really appreciate if you could send me the ebook.

Thanks,
Carlos

Krishna Sankar July 15, 2009 at 4:43 am

@Carlos: I just mailed you the download instructions over email. Plz check.

Muhammad June 30, 2009 at 6:06 pm

Hi Krishna,
I am a member; can you please send me the URL for the ebooks you have? Thanks a lot.

Krishna Sankar July 2, 2009 at 5:20 am

Ali June 28, 2009 at 11:30 am

I need errors in computing like inherent errors,absolute, relative, modeling errors…..
please send on my mail alimabrook@gmail.com
with subject as ERRORS

Krishna Sankar June 30, 2009 at 5:10 am

@Ali: Sorry

val June 23, 2009 at 3:20 am

hello sir,
am yet to get the ebook.
I would appreciate it ,if you send me the link

Krishna Sankar June 23, 2009 at 4:41 am

mukul April 29, 2011 at 12:24 am

sir

Krishna Sankar May 24, 2011 at 5:37 am

@mukul: Have you subscribed to email newsletter from dsplog.com.
http://www.feedburner.com/fb/a/emailverifySubmit?feedId=1348583&loc=en_US

hugh June 21, 2009 at 9:24 pm

thank you!

Krishna Sankar June 22, 2009 at 5:44 am

Tianhe June 18, 2009 at 7:28 am

Dear Krishna,
Plz send me the ebook ,thanks you so much before

Krishna Sankar June 21, 2009 at 12:42 pm

mya.amira June 16, 2009 at 11:38 pm

Please send me the ebook, thankS!

Krishna Sankar June 20, 2009 at 11:00 am

@mya: I just mailed you the download instructions over email. Kindly check

Sarah June 16, 2009 at 4:45 pm

Hello,

I would like to get a copy of the free e-Book on error rates in AWGN plz

Thanks

Krishna Sankar June 20, 2009 at 10:53 am

@Sarah: I just mailed you the download instructions over email. Kindly check

R.Bijukumar June 10, 2009 at 11:08 am

Dear Krishna,
Plz send me the ebook on Error Prob
thanx

Krishna Sankar June 11, 2009 at 4:25 am

apri May 28, 2009 at 2:53 am

I would really appreciate if you could send me the ebook. thanks you so much before

Bijunair May 26, 2009 at 12:34 pm

Dear Mr.Krishnapillai,
I admire your dedication and sincerity in helping others by giving useful suggestions, ample guidance and valuable advises. I am doing research in communication field and topic is to improve the performance of ofdm systems. my plan is to minimise PAPR and Frequency offset by using scrambling(PAPR Redn) in Txr and Windowing in Rxr(ICI Cancellation), plz comment on this and if you have any suggestion it will defenitely help me.

Krishna Sankar May 31, 2009 at 8:25 pm

@Bijunair: Well, even I have not done much on PAPR reduction rather than using scrambling at the transmitter. Am curious about how you are going to reduce the effect of frequency offset by using windowing in receiver. You may point me to some references which you are using. Thanks.

radman May 25, 2009 at 8:08 am

hi Krishna
how can i get this book? can u help me and send the downlaod link? thanks alot

Krishna Sankar May 31, 2009 at 8:15 pm

kanchana May 15, 2009 at 1:12 pm

hello sir

i am already subscribed but i did’nt get that ebook

Krishna Sankar May 20, 2009 at 5:26 am

@kanchana: If you had subscribed, you should have got the email download instructions. Maybe the email got incorrectly flagged as spam. Anyhow, I just mailed you with a fresh set of intructions.

madhu May 9, 2009 at 11:59 pm

Hai, krishna ,

Please send some information about Space time block codes.i.e introduction with two pages for the documentation.

by

Krishna Sankar May 12, 2009 at 5:33 am

@madhu: You may find two articles discussing Alamouti Space Time Block Codes @
http://www.dsplog.com/tag/stbc/

Hope this helps.

Oluwafemi April 16, 2009 at 8:46 pm

pls kindly send me the e book. thanks

Danial April 15, 2009 at 6:29 pm

Krishna Sankar April 17, 2009 at 5:59 am

@Danial: I just mailed you the instructions. Please check.

Danial August 16, 2010 at 9:46 am

Would you please resend the e-mail to me?

Krishna Sankar November 19, 2010 at 6:01 am

@Danial: Re-send

Murali Krishna April 11, 2009 at 3:45 am

Hi,

I have subscribed for the e-book, but i haven’t received any. Can you tell me the procedure to download it?

Thanks

Krishna Sankar April 11, 2009 at 7:52 am

val April 7, 2009 at 3:42 am

Hello,
You are really doing a great job!
pls send me the link to the ebook
thanks alot

Krishna Sankar April 11, 2009 at 6:18 am

Wig April 5, 2009 at 11:06 am

Krishna Sankar April 11, 2009 at 6:09 am

Munish March 30, 2009 at 5:42 pm

I too need this e-book. Please send the same

Krishna Sankar April 4, 2009 at 4:24 pm

coss March 29, 2009 at 11:44 pm

Krishna Sankar April 4, 2009 at 8:49 am

mansi March 28, 2009 at 10:19 pm

i am already a member pls send me URl i want this book

Krishna Sankar April 4, 2009 at 8:36 am

Muhammad Naveed Ahmed March 28, 2009 at 6:28 pm

Krishna plz send the above mentioned book. Thanks

Krishna Sankar April 4, 2009 at 8:35 am

pulkit March 21, 2009 at 7:23 am

hi
kindly mail me ebook

regards
pulkit

Krishna Sankar March 21, 2009 at 4:53 pm

saraviqar March 18, 2009 at 8:46 pm

hi
kindly mail me ebook

regards
sara

Krishna Sankar March 21, 2009 at 9:15 am

navya March 8, 2009 at 3:17 pm

Krishna Sankar March 8, 2009 at 7:54 pm

@navya: On a high level, effect of multiple access inteference is equivalent to a MIMO communication (V-BLAST) where each dimension interfers with the other. You may read more about MIMO with Zero Forcing equalizer @
http://www.dsplog.com/2008/10/24/mimo-zero-forcing/

Hope this helps.

Arif February 19, 2009 at 6:03 pm

Hi Krishna,
How do I get a copy of the ebook, since I am already a member ?

Krishna Sankar February 21, 2009 at 7:36 am

@Arif: I mailed you the link.

mahesh jaju February 18, 2009 at 12:11 am

Krishna Sankar February 21, 2009 at 7:32 am

A-Imam February 16, 2009 at 5:42 pm

Hi
Would like a copy of e-book onerror prob.

Thanks

Krishna Sankar February 21, 2009 at 7:25 am

wjlwyk February 14, 2009 at 5:43 pm

3ks

Leo January 8, 2009 at 9:12 am

Hi, could you please send me the copy of the ebook Fundamentals of communication systems by John G. Proakis and Masoud Salehi. I’m studying communication systems and looking for some reference sources. Thanks a lot.

Krishna Sankar January 8, 2009 at 5:09 pm

@Leo: Well, I do not think that Fundamentals of Communication Systems may not be available online. I can point you to another book
Signal Processing for Communications – http://www.sp4comm.org/webversion.html. Nice read.

communications engineer December 23, 2008 at 7:28 pm

I am a member and I have still not received the promised pdf. Krishna can you please tell me how can I get it

Krishna Sankar December 24, 2008 at 6:17 am

@ communications engineer : Typically, the e-Book is offered for subscribers who have opted in to receive posts over email. Anyhow, since you have already joined Google FriendConnect, I have send you the link over email.

premalatha December 19, 2008 at 1:45 pm

respected sit,
your site is very useful for me
thank you
premalatha

DemetriS November 29, 2008 at 2:34 pm

Θα ήθελα πάρα πολύ αυτό το βιβλίο. Ευχαριστώ

Krishna Sankar November 27, 2008 at 6:10 am

@Fred: Is this a question or a statement?

Fred November 27, 2008 at 1:45 am

Simulate 8-PSK (k = 3, M = 8) using the mapping below:
There is no need to generate individual bits. The input to the detector is r = s + n where all numbers are complex. The input, s, is a complex number with magnitude A and phase
determined by the random input. To generate complex noise, you need two independent
Gaussian random variables. Alternatively, you can model all signals as two-dimensional
vectors. The detector finds the closest signal point to r.
For this simulation, SNRb = (A^2)/6. Simulate the performance the system for SNRb = 7, 8,
9, 10, 11 dB and find the symbol and bit error rates. The printout format is:
System:8-PSK; SNRb=___(dB); #Bits transmitted=___ (i N/10, i = 1,…,10); SER=___; BER=___
Compare your results with the theoretical estimates of symbol and bit error rates. Plot the
theoretical estimates (curves) and the simulated error rates (points) in one figure.

Krishna Sankar November 18, 2008 at 6:07 am

Hyde November 17, 2008 at 6:33 pm

Krishna Sankar November 9, 2008 at 7:29 pm

Shreyas November 8, 2008 at 12:31 pm

Hi Krishna,
I would really appreciate if you could send me the ebook.

Thanks,
Shreyas

Krishna Sankar November 7, 2008 at 6:44 am

Ramu March 14, 2009 at 10:32 am

Krishna Sankar March 21, 2009 at 7:55 am

@Ramu: I just send you instructions over email.

John Katsaris July 2, 2009 at 5:56 pm

Hi Krishna,
I would really appreciate if you could send me the ebook too.

Thanks,
John.

Krishna Sankar July 6, 2009 at 5:13 pm

Steven Wu November 6, 2008 at 8:16 pm

Please send me the ebook, thankS!

Krishna Sankar October 29, 2008 at 10:25 am

Irma May 20, 2009 at 12:24 pm

Atsiuskite ebook Matlab

ShanmukhaPriya November 7, 2009 at 1:47 am

Hello

I need matlab code for generating the diamond curve in figure 1 in the paper ,Xiaodi Zhang and N.C. Beaulieu, “A Closed-Form BER Expression for BPSK Using MRC in Correlated CCI and Rayleigh Fading,” IEEE Trans. Communications, vol. 55, no. 12, pp. 2249-2252, Dec. 2007

Krishna Sankar November 8, 2009 at 8:58 am

@ShanmukhaPriya: Sorry, I do not have time to simulate that work. Good luck.

Dule December 6, 2009 at 4:45 pm

Krishna Sankar December 7, 2009 at 5:31 am