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Articles

Symbol and Bit error rate computation for various modulation scheme in AWGN

  1. Bit error rate for BPSK
  2. Bit error rate for FSK (frequency shift keying)
  3. Bit error rate for differential binary phase shift keying (DBPSK)
  4. Symbol error rate for 4-PAM
  5. Symbol error rate for QPSK
  6. Symbol error rate for 16-QAM
  7. Symbol error rate for 16-PSK
  8. Comparing symbol error rate for 16QAM and 16PSK modulation

Orthogonal signals

  1. Minimum frequency spacing for having orthogonal sinusoidals
  2. OFDM transmission
  3. Cyclic prefix in orthogonal frequency division multiplexing
  4. Peak to average power ratio in OFDM signalling

Receiver synchronization

  1. Frequency offset estimation using 802.11a short preamble
  2. First order PLL for tracking constant phase offset

Filters

  1. Cascaded Integrator Comb (CIC) filter
  2. Digital implementation of RC low pass filter
  3. Transmit pulse shaping filter

Hardware efficient signal processing circuits

  1. Polyphase filters for interpolation
  2. Using CORDIC for phase rotation
  3. Using CORDIC for phase and magnitude computation

Miscellaneous

  1. Straight line fit using Least Squares (LS) estimate
  2. Interpreting the output of FFT()

MIMO

  1. MIMO with Zero Forcing equalizer
  2. MIMO with MMSE equalizer
  3. MIMO with ZF Successive Interference Cancellation equalizer
  4. MIMO with ML equalization
  5. MIMO with MMSE SIC and optimal ordering

Hope you like the blog.

Related posts

  1. Back!
  2. Simulating Minimum Shift Keying Transmitter
  3. BER for BPSK in ISI channel with Zero Forcing equalization
  4. Bit Error Rate (BER) for frequency shift keying with coherent demodulation
  5. BER for BPSK in ISI channel with MMSE equalization

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{ 70 comments… read them below or add one }

1 sam July 30, 2009 at 2:30 pm

hi
i need simulink’s (matlab) block for accunting BPSK BER
thanks

Reply

2 Krishna Sankar July 31, 2009 at 4:53 am

@sam: Sorry, I do not have Simulink.

Reply

3 vanitha August 31, 2009 at 12:42 pm

my question is how to demodulate the SSB-SCsignals.

Reply

4 Selvi Rajan October 13, 2009 at 12:32 pm

Sir, while converting data into OFDM signal , it is observed that Subcarrier index is used. Inthis for standndard 802.11a , 64 subcarriers are used ,of which 52 is for data. The subcarrier index used is -26 to +26 . I want to know Why it is used so? Why 0 is not included in this.

Reply

5 Krishna Sankar October 15, 2009 at 5:25 am

@Selvi Rajan: Answer for one of the queries in http://www.dsplog.com/2009/10/07/quiz-ieee-80211a-specifications/ address this.
DC is not used because, there can be DC in the system due to RF impairments. Hence will corrupt the information send on DC subcarrier. The edge subcarriers are not used to allow the spectrum to roll-off.

Reply

6 Fritzou October 31, 2009 at 10:39 pm

sorry about the incomplete comment !!
I meant that the variance will be changed or not if I didn’t use a complex part ?

Reply

7 SREENU November 18, 2009 at 11:05 am

sir
please give me the suggestion to calculate throughput in WLAN OFDM systems

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8 Krishna Sankar December 6, 2009 at 3:50 pm

@SREENU: I would recommend you to go over the paper
Throughput and Delay Limits of IEEE 802.11, Yang Xiao, Jon Rosdahl, IEEE COMMUNICATIONS LETTERS, VOL. 6, NO. 8, AUGUST 2002
Its available online and you should be able to find it by quick googling. Good luck.

Reply

9 manisha February 22, 2010 at 7:39 pm

sir i am able to do matlab program for papr calcaulation for 7 carriers

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10 Krishna Sankar March 31, 2010 at 5:30 am

@manisha: Thats nice

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11 SREENU November 18, 2010 at 10:11 am

thank you sir

Reply

12 thilini December 10, 2009 at 6:49 pm

Plz it is urgent I need it today

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13 rama krishna December 14, 2009 at 11:35 am

iam dioing simulation to find ber of bpsk modualtion for pass band case in awgn channel. i am using a carrier with some perticular frequency.

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14 Krishna Sankar December 22, 2009 at 5:40 am

@rama: Please ask queries. I will try to answer to the best of my knowledge.

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15 gul December 22, 2009 at 4:46 pm

thank you for sharing such information.

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

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16 Krishna Sankar December 23, 2009 at 5:54 am

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

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17 manisha February 22, 2010 at 7:52 pm

can u pls mail me matlab program for papr calculation
i hav prefferd iee paper of jones and wiliksons paper

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18 Krishna Sankar March 31, 2010 at 5:30 am

@manisha: You can refer articles on PAPR at http://www.dsplog.com/tag/papr

Reply

19 gul December 23, 2009 at 9:23 am

is there any book for digital communication and wireless/mobile communication using MATLAB?

Reply

20 gul December 31, 2009 at 2:28 pm

why u r not using the builtin functions for modulation,demodulation etc.

Reply

21 rezgui January 2, 2010 at 10:09 pm

thanks a lot for the demonstration

Reply

22 Umashankar Dewangan January 4, 2010 at 9:56 pm

Hello sir,
i subscribed dsplog but i didn’t get ber e-book. i got mail to download book but its not working. its giving corrupted pdf. Kindly send me.

Reply

23 Krishna Sankar January 25, 2010 at 5:18 am

@Umashankar: I mailed you the download instructions. please check.

Reply

24 gurinder February 27, 2010 at 11:31 am

plz sir help me in providing matlab code for interleaver using rs using qam or any other modulation scheme in awgn . its urgent. plz help
thanks in advance

Reply

25 Krishna Sankar March 30, 2010 at 5:18 am

@gurinder: Sorry, I have not made any posts involving interleaver

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26 gul January 12, 2010 at 1:55 pm

i subscribed dsplog but i didn’t get BER e-book. i received the mail to download the book but its not working. Kindly send me.

Reply

27 Krishna Sankar January 25, 2010 at 5:19 am

@gul: I re-checked the download link, its working. I mailed the same to you again.

Reply

28 gul January 25, 2010 at 4:31 pm

thank you for the same.
i m doing a project on OFDM. i want to implement wavelet transform in place of FFT.can u suggest am i on right track or not?
is it little possible to do this.

Reply

29 ZhangRui January 22, 2010 at 8:22 am

Can you demodulate the co-channel AIS signals(GMSK signals) and does there exists any methods to separete the co-channel AIS signals(GMSK signals) ?thanks very much

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30 kishore January 25, 2010 at 9:11 pm

hi krishna!
I need matlab code to obtain BER vs SNR curve for binary on-off keying modulation.
also, i need code for SER vs SNR curve for 3ASK modulation.

Reply

31 surjeet January 31, 2010 at 10:49 pm

hw i will generate multipath channel coefficient in ofdma

Reply

32 Krishna Sankar April 4, 2010 at 4:35 am
33 Ahmed February 12, 2010 at 7:05 pm

Hi
Krishna
If the channel became Nakagami-m in OFDM system, how change the value of ht in program simulation of BER of multipath OFDM in Relaigh fading channel
Thank you

Reply

34 Krishna Sankar April 4, 2010 at 4:00 am

@Ahmed: Sorry, I have not tried to model Nakagami systems

Reply

35 shah February 14, 2010 at 8:01 am

im new in matlab.
Hello Krishna, thanks for ur nice work on OFDM.
i want to design an OFDM simulator using matlab GUI so that we can easily to find out the BER vs SNR when i change any parameter on the modulation..
can u give me some idea which part i need to change mybe on the sampling freq or mybe on the no of sample..
and lastly from ur code which part i must to do so…please teach me…-shah-

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36 Krishna Sankar April 4, 2010 at 3:58 am

@shah: Well, the concept of sampling is notional in Matlab

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37 manisha February 22, 2010 at 7:54 pm

i wan to know how can we find papr for 7 caiiers
suppose by block coding code is 1100110 then how to find papr

Reply

38 Krishna Sankar March 31, 2010 at 5:29 am

@manisha: Please look at the post http://www.dsplog.com/2008/02/24/peak-to-average-power-ratio-for-ofdm/. The article discuss the N carrier case, which you can adapt to 7 carrier case.

Reply

39 deepak February 24, 2010 at 9:36 pm

hi krishna
i m new to matlab and i need to know tht ur code for ml equalisation uses viterbi algo aur something else,please tell i m not able to figure it out.

thanks

Reply

40 Krishna Sankar March 31, 2010 at 5:11 am

@deepak: which is the code which you are referring to?

Reply

41 Karthick February 25, 2010 at 4:36 pm

I need to compute 24 point dft using 8 point dft chips……. pls help!!!!!!

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42 Krishna Sankar March 31, 2010 at 5:06 am

@Karthick: Did you try looking into the FFT equations?

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43 Krishna Sankar March 31, 2010 at 5:09 am

@Karthick: Have you tried looking into the FFT equations?

Reply

44 taona March 3, 2010 at 1:09 pm

Help hw do i generate E/No curve for ASK modulation

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45 Krishna Sankar March 30, 2010 at 4:35 am

@taona: I have discussed symbol error rate for 4-PAM case http://www.dsplog.com/2007/10/07/symbol-error-rate-for-pam/
Hope that serves as a good reference

Reply

46 venkat March 13, 2010 at 5:51 pm

Hello Krishna,
I have referred your example on first order PLL for constant phase tracking.It was very useful.
http://www.dsplog.com/2007/06/10/first-order-digital-pll-for-tracking-constant-phase-offset/
But in the example a complex carrier is being used at the transmitter and receiver.Practically , when I use a cosine carrier at Tx. and cosine,sine carriers at Rx.(as in costas loop) , can the same loop filter be used ?
I have tried to simulate the above situation in the following script but was unable to estimate the phase. Please help me……….

% MODULATION

clc;
clear all;
close all;

[b,a] = butter(1,0.0156,’low’); % low pass filter to remove
nterm_i = 0; % double frequency component
dterm_i = 0;
nterm_q = 0;
dterm_q = 0;

n_sym = 10; % number of symbols
fs = 12.8e6;
t = 0:1/fs:100e-6 – 1/fs;
fc = fs/8; % carrier freuency
theta = 70*pi/180; % phase offset
r = 0.1e6; % symbol rate
oversamp = fs/r;
sym = randint(n_sym,1)*2-1;
in = 0;
for ind=1:1:n_sym
tmp(1:oversamp) = sym(ind);
in = [in tmp];
end
tx = in(2:end);
tx_carrier = cos(2*pi*fc*t + theta);

tx_out = tx.*tx_carrier;

% first order pll
alpha = 0.05;
phiHat = 0;

for ii = 1:1:length(t)

% Remove carrier
rx_i(ii) = tx_out(ii)*cos(2*pi*fc*t(ii) + phiHat);
rx_q(ii) = tx_out(ii)*sin(2*pi*fc*t(ii) + phiHat);

% low-pass IIR filter for I-channel
iir_in_i(ii) = rx_i(ii);
iir_out_i(ii) = b(1)*iir_in_i(ii)+ nterm_i + dterm_i;
nterm_i = b(2)*iir_in_i(ii);
dterm_i = a(2)*iir_out_i(ii);

% low-pass IIR filter for Q-channel
iir_in_q(ii) = rx_q(ii);
iir_out_q(ii) = b(1)*iir_in_q(ii)+ nterm_q + dterm_q;
nterm_q = b(2)*iir_in_q(ii);
dterm_q = a(2)*iir_out_q(ii);

% demodulating circuit
xHat = 2*(iir_out_i(ii)>0) -1 ; % symbol estimate
phiHatT =angle(conj(xHat)*rx_i(ii)); % phase error estimate angle(iir_out_i(ii) + i*iir_out_q(ii));%

% accumulation
phiHat = alpha*phiHatT + phiHat; % phase accumulator output
% dumping variables for plot
phiHatDump(ii) = phiHat;
end

plot(phiHatDump*180/pi,’-');

Reply

47 Krishna Sankar March 28, 2010 at 3:42 pm

@venkat: Does the transmitted symbol has phase information?

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48 uma March 16, 2010 at 10:37 pm

hello sir..
how to downsample received UWB signal ???kindly help us with matlab code sir

Reply

49 Krishna Sankar March 28, 2010 at 2:28 pm

@Uma: Sorry, I have not tried modeling UWB signals

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50 gul March 29, 2010 at 10:54 am

hello krishna,

i m making code for PTS scheme for PAPR reduction. i m facing some problems in that……
1. how to implement oversampling in ofdm?
2. how do we calculate CCDF for PAPR calculation?

thanx in advance.

Reply

51 Krishna Sankar March 30, 2010 at 4:19 am

@gul: My replies
1/ For oversampling by a factor of 2 insert 1 zero inbetween samples; for oversampling by factor of 3 insert 2 zeros inbetween samples; and so on. Note: Oversampling need to be followed by filtering
2/ Take the histogram of the time domain samples to find the PDF. Use cumsum to find the CDF. Then 1- CDF gives CCDF. In the post on PAPR in OFDM, I have plotted the CDF of the time domain waveform http://www.dsplog.com/2008/02/24/peak-to-average-power-ratio-for-ofdm/

Reply

52 ben April 13, 2010 at 8:22 pm

Hello,

I have a question about plotting BER vs SNR in MIMO systems. Lets say i have a 2×2 MIMO system, and i perform an SVD on the channel, so i can encode and decode the signal with V and U, respectively, such that i am left with 2 uncoupled SISO channels. now each channel has its own singular value, and let us assume for now that the noise power is the same in both channels. So we have SNR1 in the first channel, and SNR2 in the second channel, and they are different.
Q1: How would you define the SNR of this system? is it the average SNR of both channels?

Now we now that according to the Water Filling algorithm, we can transmit more power (and thus, more bits) in channels with higher SNR. so if come to conclusion that the first channel can carry QPSK, and the second channel can only carry BPSK, i have different contelations in both channels… So the SNR which were calculated earlier for each channel, should now be modified in order to reflect the number of bits which are transmitted via those channels, by: SNR_bit=SNR_sym/k, where k=log_2(M).

Q2: How should plot 1 graph which describes the BER vs. SNR_bit of this system? Should i calculate SNR_bit for each SISO channel, and BER for each SISO channels separately, and the average the results?

Thanks

Reply

53 Krishna Sankar April 14, 2010 at 4:56 am

@ben: My replies
1.a) As I recall, when we are multiplying by V, we are not introducing any gain in the transmitter. In that case, signal power at the transmitter remains the same irrespective of multiplication by V. Agree?
Having said that reporting SNR information from both the streams and average SNR is useful. I believe most MIMO test instruments report both
1.b) The signal to noise ratio is independent of the constellation used. If you want to compare using Eb/N0, then yes, need to factor in the constellation
2) Hmm…. you can defined Es/N0 = ratio of total power at tx / total noise power at rx. Then depending on the number of bits which are pumpre through, Es/N0_dB = Eb/N0_dB + 10*log10(number of bits per symbol across all tx chains)

Agree? Your thoughts please.

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54 avdhut August 26, 2010 at 9:07 pm

hey…
will u plz giv me code for gmsk….

thanks..
avdhut

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55 Krishna Sankar September 1, 2010 at 7:03 am
56 AHMED October 23, 2010 at 6:33 am

Hello;
How can i cacluate the SNR between two nodes A and B if they used BPSK
B.R

Reply

57 Krishna Sankar November 18, 2010 at 5:23 am

@Ahmed: Sorry, the question is not clear

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58 Willie February 11, 2011 at 11:15 pm

How do I get access to the download site for the e-book?

Reply

59 Krishna Sankar May 26, 2011 at 6:00 am

@Willie: Emailed you the download instructions

Reply

60 Usman April 20, 2011 at 12:33 pm

plz send me the book…

Reply

61 Krishna Sankar May 24, 2011 at 5:39 am

@usman: Have you subscribed to email newsletter from dsplog.com.
If not, please click here to subscribe.
http://www.feedburner.com/fb/a/emailverifySubmit?feedId=1348583&loc=en_US

Once you have subscribed, you should have received a confirmation email. Please reply to that
email and you will receive email instructions on how to download the eBook.

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62 shu May 17, 2011 at 11:39 pm

hi krishna sir

I saw ur example of ber -bpsk-rayleigh channel but i need the the qpsk for the rician channel I dont know coding sir so please help me sir give some hints where to change thats enough for me sir .please sir

Reply

63 Krishna Sankar May 23, 2011 at 2:46 am

@shu: My replies:
1/ For QPSK, send data on I channel as well as Q channel
2/ I have not discussed Rician channel model

Reply

64 jinumadhavan November 22, 2011 at 2:04 pm

Nice Article,i Appriciate u=r Knowledge

Reply

65 Ari Endang Jayati January 2, 2012 at 9:39 am

Hello. Thanks for your posts.
I have a question.

When I simulated 2by2 MIMO system, the 4PAM-ZF system has same SER of 4PAM-MMSE system.
(Rayleigh ch./AWGN noise/BER vs SNR
But, there is a little difference
So, I am very confusing.

Please answer my question
Thanks

Reply

66 Krishna Sankar January 3, 2012 at 4:37 am

@Ari: When you try to reduce the modulation from 4PAM to 2PAM (BPSK), are you seeing differences in the MMSE behaviour vs ZF behaviour. Further, in AWGN the difference might not be present, as there is no interference terms.
Do reply back with your findings.

Reply

67 Gayathri January 6, 2012 at 11:49 am

hello sir ,
pls help me with me , with a code for MIMO with MMSE equaliser in QAM-16 modulation technique

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68 Krishna Sankar January 7, 2012 at 6:14 am

@Gayathri: Sorry, I do not have the exact matlab code handy. But I can point you to
a) MIMO with MMSE equalizer – BPSK 2×2 in Rayleigh channel
http://www.dsplog.com/2008/11/02/mimo-mmse-equalizer/

b) 16QAM in AWGN over OFDM
http://www.dsplog.com/2012/01/01/symbol-error-rate-16qam-64qam-256qam/

Hope both helps to get you what you need.

Reply

69 ammar January 26, 2012 at 7:13 pm

Hello. Thanks for your posts

i just want to ask you if you deal with matlab function named”rayleighchan”?

its great

but i have some question on it

Reply

70 Krishna Sankar January 29, 2012 at 5:51 am

@ammar: Sorry, i do not ‘deal’ with rayleighchan

Reply

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