(41 votes, average: 4.12 out of 5)
Loading ...
In this post, we will derive the theoretical equation for bit error rate (BER) with Binary Phase Shift Keying (BPSK) modulation scheme in Additive White Gaussian Noise (AWGN) channel. The BER results obtained using Matlab/Octave simulation scripts show good agreement with the derived theoretical results.
With Binary Phase Shift Keying (BPSK), the binary digits 1 and 0 maybe represented by the analog levels and
respectively. The system model is as shown in the Figure below.
Figure: Simplified block diagram with BPSK transmitter-receiver
Channel Model
The transmitted waveform gets corrupted by noise , typically referred to as Additive White Gaussian Noise (AWGN).
Additive : As the noise gets ‘added’ (and not multiplied) to the received signal
White : The spectrum of the noise if flat for all frequencies.
Gaussian : The values of the noise follows the Gaussian probability distribution function,
with
and
.
Computing the probability of error
Using the derivation provided in Section 5.2.1 of [COMM-PROAKIS] as reference:
The received signal,
when bit 1 is transmitted and
when bit 0 is transmitted.
The conditional probability distribution function (PDF) of for the two cases are:
.
Figure: Conditional probability density function with BPSK modulation
Assuming that and
are equally probable i.e.
, the threshold 0 forms the optimal decision boundary.
- if the received signal is
is greater than 0, then the receiver assumes
was transmitted.
- if the received signal is
was transmitted.
i.e.
and
.
Probability of error given 
was transmitted
With this threshold, the probability of error given is transmitted is (the area in blue region):
,
where,
isĀ the complementary error function.
Probability of error given 
was transmitted
Similarly the probability of error given is transmitted is (the area in green region):
.
Total probability of bit error
.
Given that we assumed that and
are equally probable i.e.
, the bit error probability is,
.
Simulation model
Matlab/Octave source code for computing the bit error rate with BPSK modulation from theory and simulation. The code performs the following:
(a) Generation of random BPSK modulated symbols +1′s and -1′s
(b) Passing them through Additive White Gaussian Noise channel
(c) Demodulation of the received symbol based on the location in the constellation
(d) Counting the number of errors
(e) Repeating the same for multiple Eb/No value.
Click here to download Matlab/Octave script for simulating BER for BPSK modulation in AWGN chnanel.
Figure: Bit error rate (BER) curve for BPSK modulation – theory, simulation
Reference
[DIGITAL COMMUNICATION: PROAKIS]
Related posts
- Symbol Error Rate (SER) for QPSK (4-QAM) modulation
- Symbol Error Rate (SER) for 4-PAM
- Bit error rate for 16PSK modulation using Gray mapping
- Symbol Error Rate for 16PSK
- BPSK BER with OFDM modulation
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.
{ 371 comments… read them below or add one }
Hey your BPSK theory and simulation is very useful.Do you have it for FSK modulation too?If you don’t mind please send to me. thanks.
close all
clear all
clc
N = 10^6 % number of bits or symbols
rand(‘state’,100); % initializing the rand() function
randn(‘state’,200); % initializing the randn() function
% Transmitter
ip = rand(1,N)>0.5; % generating 0,1 with equal probability
s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0
n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; % white gaussian noise, 0dB variance
Eb_N0_dB = [-3:10]; % multiple Eb/N0 values
for ii = 1:length(Eb_N0_dB)
% Noise addition
y = s + 10^(-Eb_N0_dB(ii)/20)*n; % additive white gaussian noise
% receiver – hard decision decoding
ipHat = real(y)>0;
% counting the errors
nErr(ii) = size(find([ip- ipHat]),2);
end
simBer = nErr/N; % simulated ber
theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))); % theoretical ber
theoryBer1 = 0.5*erfc(sqrt(0.5.*(10.^(Eb_N0_dB/10)))); % theoretical ber
figure
semilogy(Eb_N0_dB,theoryBer,’b.-’);
hold on
axis([-3 10 10^-5 0.5])
grid on
legend(‘theory’);
xlabel(‘Eb/No, dB’);
ylabel(‘Bit Error Rate’);
title(‘Bit error probability curve for BPSK modulation’);
figure
semilogy(Eb_N0_dB,theoryBer1,’b.-’);
hold on
axis([-3 10 10^-5 0.5])
grid on
xlabel(‘Eb/No, dB’);
ylabel(‘Bit Error Rate’);
title(‘Bit error probability curve for BFSK modulation’);
In bfsk need double bit error rate to maintain the same avarage error rate in BPSK.
Feeel the difference..
@srinivas: It is not double the bit error. Infact the BER result with BFSK is 3dB poorer than BPSK. You may look @
http://www.dsplog.com/2007/08/30/bit-error-rate-for-frequency-shift-keying-with-coherent-demodulation/
Hey Krishna,
I need help regarding the simulation for the fig 1 for the IEEE 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.
I am getting stuck with the simulation code. Can you please give a possible MATLAB code.
kk
@kk: Sorry, I do not have time to simulate that work. Good luck.
I want to change the spatial resolution in dots per inches of an image.
Do u have any code regarding this problem?
if so plz send me
regards,
@RAO: Sorry, no
do you have this program write by c++ ?
upload for me ???
@pvt: Sorry, I do not have the c code version
One who is interested in including his/her name in 3 research conferences in international IEEE conference should reply on email address me_researcher@yahoo.com. Both papers are related to mobile communication. Total of 3 authors list will be included in each Paper. 2 author names have already been included. Interested candidates who want to include his/her name at 3rd position will be required to pay for the registration fee.
Matlab Code as well as the full paper will be sent to the individual after acceptance of paper from the conference.
Fee submission will be through Freelancer and elance. Candidate name will be included in Paper after milestone payment is released by him/her. Milestone payment is one which is in the custody of broker (Freelancer or Elance authority) and not in the custody of either party. After the paper is accepted and the client is conformed about the acheivement, only then he will be allowed to pay. Time is short so the policy of 1st come 1st serve will be entertained.
Thanks.
I have not checked for FSK modulation. Once I understand, hopefully will be try put together a post.
Thanks a lot, your BPSK BER was very useful, i got to know about the errors i made when i did the code
@sus: Thanks
Dear Krishna,
Your simulation and theory prgram is very usefull and helpfull.
Could you please send me the syntax matlab comand of QPSK modulation for OFDM under multipath (i.e 3 path) fading.
Very thanks in advance.
shareef
@shareef:
Thanks. The next post is planned to be on OFDM.
thanks alot or this article . it really helped me alot .
and I am waiting the ofdm article.
@mariam: The post on BER for BPSK with OFDM modulation
http://www.dsplog.com/2008/06/10/ofdm-bpsk-bit-error/
Hey,
I found theBit error curve for BPSK modulation – theory, simulation very useful. How do we demodulate , decode and compare it with the input signal
@ David: Thanks
Oh… were you unable to find the Matlab/Octave code? The link to the code is under the heading Simulation model.
Anyways, for BPSK it is simple. We observe the real part of the received symbol. If the real part is greater than 0 decode as +1, if the real part is less than 0 decode as -1.
Once we have the decoded symbols available, the number of differing symbols can be obtained by
nErr = size(find([ip- ipHat]),2);
Ofcourse, using find() is only one among the many different ways to compute this.
Thanks,
Krishna
why are we using this term 10^(-Eb_N0_dB(ii)/20) in the code to get the final signal y. why cant we write y=s+n; ???????????????
sorry for my previuos question i got it just after posting my previuos mesg…its coz we want to add the noise to the signal so we need to convert it to dB … right? thnx
nope i didnt get it plz explain it a bit i shal be thankful
hello! i am unable to understand the FOR loop operation in this code kindly explain a bit
thnaks in advance
@babar:
The term 10^(-Eb_N0_dB(ii)/20) is for scaling the noise power as per the defined bit to noise ratio. The for loop is for computing the bit error rate for each Eb/N0 value.
Hi..
Why you are multiplying ‘n’ with The term 10^(-Eb_N0_dB(ii)/20).
The didnot understans the concept behind this from the previous posts..
@srinivas: This is to scale the noise term ‘n’, so that we can obtain BER for different values of Eb/No. In the simulations, we define Eb/No in dB. To convert dB to define a scaling term for noise voltage, we use 10^(Eb_N0_dB/20).
Hope this helps.
hi
hope you are doing fine…in the matlab program u have given here, why didnt you use the awgn matlab function to introduce the noise? why have we taken this formula? thanks
@Jhony: Thanks. Am doing good. How are u? Glad to notice that you are not desperate now
Typically, to keep the code simple, I tried to avoid in-built functions. The randn() function + scaling the does the job. Thats all.
hi krishna pillai i am doing project on viterbi decoder i want the matlab code for the viterbi decoder if u have the code please send me
@Sitharam: Plz check out
http://www.dsplog.com/tag/viterbi/
yeah ! trying to get hold of things slowly now… i hope u dnt mind me asking foolish and lots of Qz…
about the formula u uzed for awgn … i didnt get how it produces awgn …
@Jhony: The randn() function generates a random variable having Gaussian distribution and the spectrum of this random variable is same across frequencies. Hence the name White Gaussian Noise (WGN).
This is then Added to the signal, hence the name Additive White Gaussian Noise (AWGN)….
1/sqrt(2)*[randn(1,N) + j*randn(1,N)];
1/sqrt(2) ==> this is the scaling term?
j*randn(1,N) ==> this is to generate complex noise values?
I am thankful to u for helping me
[randn(1,N) + j*randn(1,N)] generates complex Gaussian noise with mean 0 and variance 2. To make the variance to 1, the scaling factor of 1/sqrt(2) is used.
yes, the j term is for complex noise.
thanks alot … u helped me alot i m very happy to learn all this … thanks once again … and plz keep helping me as i want to learn …
hi i hope you are in good health. Can you please tell me what a fading co-efficient is? and what does it signifies in few lines. I shall be very thankful to you.
@Jhony: If I may put very briefly, fading is the characteristic of the wireless channel. The channel (read enviornment) will vary with time and will exhibit different behaviour for differnt frequencies.
One of the most simplest and useful model of fading is to visualize it as filter whose coefficients change in time.
Ofcourse, this is a simplistic description. For a detailed overview, may I recommend chapter 2 from the book
Fundamentals of Wireless Communication – David Tse, Pramod Viswanath
please send me a source code for bpsk modulation in matlab
@marjano:
The link to the code is provided just above the figure. Anyhow attaching the link again
Please click here to downlod
thank you but it is not exactly what I’m schearching about :/
I need code for modulation BPSK/PM or only BPSK
thanks a lot code is very useful
even i want a code using upsampling and pulse sampling in BPSK mod and downsampling and pulse sampling in BPSK demod
@rahul: Thanks.
I believe you are looking for the code for transmit pulse shaing filter. You can look at the article and the code in the posts with the tag ‘pulse-shaping’
http://www.dsplog.com/tag/pulse-shaping/
That should help you get going.
Btw, what is pulse sampling?
i m very satisfy to this site, bcause it is very hepful to me to make mmy project. if u have bpsk matlab code then send me .
@Vinay:Thanks.
The code is present in this post. Click here to download
http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/#Simulation%20Model
hi, hope every1 doing well. all the posts are very useful
thanks
Hi,
I do not understand why a complex gaussian noise is required. The source here belongs to a BPSK modulation so I think, in practice we have a real noise, because we do just activate the in phase component and not the quadrature phase component.
@antiwina: You are right, the imaginary component is ignored. Infact if you see the simulation model, for demodulating the symbol, we use only the real part of the received signal.
However, our definition of noise is with a variance of N0/2 on the real arm and N0/2 on the imaginary arm.
hi,
I do not understand why the BER curves for both BPSK and BPSK with OFDM are almost same where the BPSK with OFDM get
advantage i.e., decrease in BER in case of BPSK with OFDM.
So please give me the idea by differentiate the two curves and how the BER can be decreased with OFDM as soon as possible. iam waiting for u r response hopefully,thanku
hi,
Is there a demodulation matlab code which i can apply on most modulation methods like 8 psk, QPSK, 16QAM..etc.
Also do you have 8psk and 16 QAM modulation and demodulation codes in matlab?
thank you
@ravi kumar: In AWGN, there should not be any advantage by using OFDM modulation. OFDM can be thought of as a simple up-conversion scheme where each information gets multiplied on different sub-carrier frequencies.
However, the BER difference should come in multipath simulations.
@farie: The demodulation approaches for PSK is a different from QAM. For 16-PSK case, you can find two posts:
Symbol Error Rate for 16PSK
http://www.dsplog.com/2008/03/18/symbol-error-rate-for-16psk/
Bit error rate for 16PSK modulation using Gray mapping
http://www.dsplog.com/2008/05/18/bit-error-rate-for-16psk-modulation-using-gray-mapping/
You should be able to modify the code for 16-PSK to 8-PSK case.
For 16-QAM case, there are two posts on error rate computation:
16QAM Bit Error Rate (BER) with Gray mapping
http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/
Symbol Error Rate (SER) for 16-QAM
http://www.dsplog.com/2007/12/09/symbol-error-rate-for-16-qam/
Hope this helps.
hey krishna,
can you please help me with the case of DPSK
@siddhartha: I have written a post on Coherent deomdulation of DBPSK (Differential Binary Phase Shift Keying).
URI: http://www.dsplog.com/2007/09/30/coherent-demodulation-of-dbpsk/
Please check out. Hope this helps.
Hello Krishna
Your simulation and theory prgram is very useful. Do you have the matlab code with qpsk symbols ? Would be great !
I want to compare the theoretical bit error curve for qpsk with a simulated bit error curve with a zero force equalizer. Can you please give me an advice of how to implement this.
Thank you in advance
Best regards
Micman
@Micman: Thanks. I have written a post on symbol error rate computation for QPSK in AWGN.
Symbol Error Rate (SER) for QPSK (4-QAM) modulation
URI: http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/
Maybe that helps.
Hi Krishna
thank you very much for Your simulation and theory prgram, really they are very useful. Do you have the matlab code for OFDM with 16-QAM in AWGN and Rayleigh Channels.
Best Regards
Hussien
@Hussein: Thanks. I do not have the codes, but I would think that it will be reasonable to extend the available simulation models to 16QAM case.
For 16-QAM in AWGN (without OFDM) you may look at the posts,
URI: http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/
URI: http://www.dsplog.com/2007/12/09/symbol-error-rate-for-16-qam/
For extending them to OFDM, you may use the following posts as reference:
http://www.dsplog.com/2008/06/10/ofdm-bpsk-bit-error/
http://www.dsplog.com/2008/08/26/ofdm-rayleigh-channel-ber-bpsk/
Hope this helps.
Nice graphics and derivation.
Might want to consider using a separate integration variable for the definition of the erfc function, since the variable x was used for both the erfc argument and integration variable.
Perhaps just use ‘z’ or ‘y’ for the erfc integration variable, i.e., erfc(x) = 2/sqrt(pi) * Integral_x_inf { exp(-z^2/2)*dz } . This will then make it clear that the erfc argument ‘x’ is used to modify the integration limits, as opposed to the actual function being integrated.
@grad student: Yeah, thanks for the suggestion. I agree that your proposal will make the text even more readable.
Anyhow, may I recommend to keep status quo given that the current text is not making it very difficult for the reader.
exelent!
for QPSK modulation, the variance is
sigma = 1/sqrt(10.0^(snr/10.0));
sigma=sigma/2;
Do you have any idea why it has to devide by 2?
Thanks alot
@Sky Stradlin: There is noise on the real and imaginary dimension. So, to make the total variance of the complex noise to unity, there is scaling by 1/2.
Dear Krishna,
I have made a program for BER of BPSK in AWGN and Rayleigh fading channel, now I want to combine the both results in one graph, when I combine the results, the curve for rayleigh change but for awgn not change, can you give any idea what should i do, either i make a functions of both separately and call in one program or i should do something else?
anyone have idea about it plz comment
@Ideal: So you are able to plot both the curves using independent functions/scripts, but not able to combine them. Correct? This should be a reasonably easy aspect to resolve.
You can have a main script which generates the transmit symbol, Eb/No values etc. Pass it two function
(a) for awgn channel y = x + n,
(b) for rayleigh channel y = hx+n
Each function will count equalize, count the errors and report the number of errors for each value of Eb/No.
That should address your concern. Hope this helps.
hi
Dear Krishna,
% receiver – hard decision decoding
ipHat = real(y)>0;
here what do you mean by hard decision decoding? plz reply in brief.
@Ideal: It just means that any value of y (real component) greater than 0 is assigned to 1 and if less than 0 is assigned as 0. This is called hard decision decoding.
Soft decisions – where we do not decide on what was transmitted based on the received constellation – are used typically when there is a decoder block (like Viterbi) following the constellation demapping.
Does this help?
Hi Krishna,
Thanks for the good information.
Could you shade light on the derivation of Sigma^2 = No/2 from correlation and spectral density of noise stand point?
Thanks,
Zoe
@Zoe: The term N0/2 corresponds to the spectral density of white noise. In typical systems, we experience white noise filtered by an ideal LPF. The variance of this filtered noise contributes to the noise term in the system.
You may look at chapter 9 in Communication Systems – An introduction to Signals and noise in Electrical Communication by A. Bruce Carlson, Paul Crilly, Janet Rutledge for further details.
Hope this helps
Hi all
hope u all r f9
can any one help me for BER performance of adaptive modulation
(QPSK,4QAM,16QAM)in AWGN only I need to draw them in single graph
thankz in advance
@mak: As I understand from your query, you want to switch from one modulation scheme to another based on a defined error rate constraint. For eg, for lower SNR’ you would want to use BPSK, then move on to QPSK/4QAM for medium SNR’s and then hit 16QAM at high SNR’s.
I do not have any code explicitly doing this, but I would think that it would be reasonably easy to build using the following posts:
(a) Bit Error Rate (BER) for BPSK modulation
(b) Symbol Error Rate (SER) for QPSK (4-QAM) modulation
(c) Symbol Error Rate (SER) for 16-QAM
(d) 16QAM Bit Error Rate (BER) with Gray mapping
Hope this helps.
dear sir
i want simulation for adaptive modulation
please if have such code send it to me
thanks
@leth; Sorry, I have not discussed adaptive modulation
hi..how 2 generate -ve rectangular pulse 4 bin sym 0 & +ve rectangular pulse 4 bin sym 1
@manju: You may use the following steps provided in the Matlab code snippet
clear all
N = 7; % number of bits
ipBit = rand(1,N) > 0.5; % random 1′s and 0′s
ipMod = 2*ipBit – 1; % converting 1′s to 1 and 0′s to -1
os = 4; % oversampling factor
ipMod_os = [ipMod; zeros(os-1, length(ipMod))]
ipMod_os = ipMod_os(:).’;
ipMod_filter = conv(ipMod_os,ones(1,os)/os);
Does that help?
Hi krishna
can any one help me for code SIC (Successive Interference Cancellation).i will tray it for study…..
thanks………………..
@wap: I have written some posts on Successive Interference Cancellation with a 2×2 MIMO system. The URI are:
http://www.dsplog.com/2008/11/09/mimo-zero-forcing-successive-interference-cancellation/
http://www.dsplog.com/2008/11/29/mimo-zf-sic-optimal-order/
http://www.dsplog.com/2008/12/06/mimo-with-mmse-sic-and-optimal-ordering/
Hope this helps.
who can help me to find the formula bit error rate when coding for bpsk…?
@bullah: It depends on the coding which is applied. There are couple of posts discussing BPSK in AWGN with rate 1/2 convolutional coding.
Convolutional coding
http://www.dsplog.com/2009/01/04/convolutional-code/
Hard decision Viterbi
http://www.dsplog.com/2009/01/04/viterbi/
Soft input Viterbi
http://www.dsplog.com/2009/01/14/soft-viterbi/
Hope this helps.
hi hope you are fine. In your code you have scaled the noise with the term 10^(-Eb_N0_dB(ii)/20)
my question is why we do this?I mean why we need to scale the noise power as per the defined bit to noise ratio? Any references will help me a lot
fire back soon plz !!!
@invizible soul: Sorry for the delayed response. I am traveling with out a reliable access to internet.
In this analysis, our objective is to analyze the impact of noise on the reliable decoding of BPSK modulation. To analyze the impact, we need to find out the performance (bit error rate) for different values of noise. Hence we scale the noise by noise power.
Hope this helps.
thanx alot krishna … sorry i missed it …
@manju I got a better solution for your question.We need to untilmately multiply with standard deviation of noise so we get 20 there.
SNRdB = 20 log (Asignal / Anoise)
-SNRdB = 20 log(Anoise / Asignal)
-SNRdB/20 = log(Anoise / Asignal)
10^(-SNRdB/20) = Anoise/Asignal <——— noise amplitude scaling factor.
@T-dog: Thanks.
thanks khrishna with your help………..
i late reply n visit your site coz im busy….
how abaut this???
% BER_sic=sim_sic_fn(SNR_dB, P, Nb, code_matrix, chan_type)
% return bit error rate of the sic receiver in AWGN or rayleigh fading
%
% PARAMETER:
% SNR_dB=signal-ti-nopise ratio in dB
% P=power control vector, P(i)=transmitted power of i-th user
% Nb=number of transmitted bit
% code_matrix=matrix of the spreading code used
% chan_type=channel type(1=AWGN, 2=rayleigh fading channel)
%
% output:
% BER_sic=bit error of the sic receiver
%
function BER_sic=sim_sic_fn(SNR_dB, P, Nb, code_matrix, chan_type)
BER_sic=zeros(size(SNR_dB));
K=length(P); %number of user
N=size(code_matrix,2); %spreading factor
G(:,1)=code_matrix(33,:)’;
G(:,2:K)=code_matrix(1:K-1,:)’;
@Wap: Sorry, I did not get your question
kindly reply me !!! i am still waiting … from where we get this expression:
10^(-Eb_N0_dB(ii)/20)
thnx
hello..
who will help me to understand the function of a filter in a block diagram of a basic communication system in BPSK?
What the purpose of finding the value of delay in the program of BPSK?
@nyna: Filter is used for controlling the spectrum of the transmission. However, when doing the filtering we do not want to introduce ISI. Hence we typically go for filters like raised cosine etc. You may find some more details @
http://www.dsplog.com/2008/04/14/transmit-pulse-shape-nyquist-sinc-rectangular/
http://www.dsplog.com/2008/04/22/raised-cosine-filter-for-transmit-pulse-shaping/
http://www.dsplog.com/2008/05/01/eye-diagram-plot-matlab-raised-cosine-filter/
Hope this helps.
hi … i think my username “invizible soul” has really made me invizible
… as no one has answered my questions …
waitinn……
@invizible soul:
I thought I replied already. Plz check my response @
http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/comment-page-2/#comment-5038
thanks krishna…i’m really appreciate it..thanks so much
hi i have plotted the results for some coding
i just want is biterr with no coding
i.e. simply take msg, modulate add noise and demodulate
now find the biterr or symerr for oiginal msg and recovered msg
pls help as early as possible
@mansi: You may refer to the following posts on error rate computation for BPSK, QPSK, 16QAM and 16PSK in AWGN.
http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/
http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/
http://www.dsplog.com/2008/03/18/symbol-error-rate-for-16psk/
http://www.dsplog.com/2007/12/09/symbol-error-rate-for-16-qam/
http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/
http://www.dsplog.com/2008/05/18/bit-error-rate-for-16psk-modulation-using-gray-mapping/
sdadasdad
The term 10^(-Eb_N0_dB(ii)/20) is for scaling the noise power as per the defined bit to noise ratio, why divided it by 20 >>??to convert it to voltage
@mohamed: Yes, divided it by 20 is to convert to voltage.
I want to do a matlab simulation for the the GFSK. Plot the BER vs. EbNo.
@Einstein: Sorry, I do not have Matlab simulations with GFSK. However, you may check up the post on BER for FSK in AWGN @
http://www.dsplog.com/2007/08/30/bit-error-rate-for-frequency-shift-keying-with-coherent-demodulation/
Hope this helps.
sir,
i want matlab programs for MCCDMA,whtever u hve on dis topic ,plz mail me as soon as possible,since MCCDMA is my thesis topic, but i m facing many prblms regarding matlab programs
thank u,
pragya
@pragya: Sorry, I have not written Matlab models on MC-CDMA.
hai..krishna..i want ask you the function of hamming code and bCh code..it because i already simulate the block using that coding…can you give me the formula for i’m calculate theory the bit error rate when using coding for i compare between theory and simulate…..also can you give me the graph ber vs Eb/No when coding..tq
@bullah: Sorry, I have not discussed hamming codes or BCH codes till date. You may look at the posts describing convolutional coding and Viterbi decoding @
http://www.dsplog.com/tag/viterbi
Hope this helps.
krishna can u help to understand more about the function of transmitter filter in BPSK and also how the ISI(intersymbol interference)will occur at transmitter filter??
@nyna: In the transmitter, we will first be converting bits into analog voltage (+1/-1 in the case of BPSK). However, we cannot transmit them as is, as it will occupy lots of spectrum (which is not desirable). Hence we need to do filtering. However, when doing filtering, we introduce ISI (inter symbol inteference) i.e each symbol may interfere with the next symbol and so on.
So, the question is: can we do filtering without introducing ISI? The answer is YES. There are simple filters like rectangular, ideal filter like sinc and practical filters like raised cosine, which can do the job. You may read more about them @
http://www.dsplog.com/2008/04/14/transmit-pulse-shape-nyquist-sinc-rectangular/
http://www.dsplog.com/2008/04/22/raised-cosine-filter-for-transmit-pulse-shaping/
http://www.dsplog.com/2008/05/01/eye-diagram-plot-matlab-raised-cosine-filter/
Hope this helps.
hi
I wanna matlab simulation code for AODV routing protocol. Can you help me ….
@shoumi: Sorry, I have not worked on AODV protocol.
Hey krishna,
I am new here. I find this site really very useful. Thanks for everything. I have a question reg BPSK sim. I did it with awgn function and I am not getting theo and sim graphs overlapping. Please answer this as soon as you get time . thanks
@Aditya: You should have got similiar curves with awgn() function too. Is the slope of the graphs matching. Then its quite likely some power normalization issue.
tq krishna…i understand it more than before..i really appreciate it..
however can i ask u bout the graph of BPSK between simulation and theoretical in term of BER vs SNR…
how the shape of graph become like that?
@nyna: The shape of the curve is determined by the probability of error which we have defined in the post.
Hi there, very useful site. I have a couple of questions regarding the BPSK:
1) Could you go in to a little more detail why you use complex noise vs. real. Although it doesn’t make a difference for BPSK, I’m assuming it actually will with other modulation methods. I didn’t see this in any of my textbooks.
2) In your code for the BPSK, you divide by 20. Shouldn’t that be 10? Given an SNR in dB, we get S/N0 = 10*log(SNR-dB / 10).
This gives N0 for a given signal power S.
The variance^2 = N0/2 and if we assume 0 mean, this gives us our AWGN, which is a random variable describing the noise amplitude. In my simulation, if I use 10 instead of 20, my results were way off, but 10 gives a perfect match with theory.
Thanks much,
Matt
@ Matt K: My replies
1). Yes, for BPSK the noise component on the imaginary arm is ignored. To make the noise model same as with other modulation schemes, I kept it as complex.
2). The division by 20 is to convert the dB to scale the voltage signal. In my simulation model, the noise term n is a Gaussian random variable with mean 0 and variance 1. Therefore, I am scaling the noise voltage by 10^(-Eb_N0_dB(ii)/20)*n. Thats why I used 20.
In general, it depends on how one creates the model. Different people have different coding style. However, its the end result which matters.
Hope this helps.
Thanks for your codes.It’s helped me a lot.But I want to replace Eb/N0 as SNR how can I do it.Could you pls help me urgently.
Thanking you
@Nafis: For BPSK. Eb/N0 is same as SNR. Agree?
hi
How can i calculate throughtput for a multi-hop wireless network using matlab. please give me some suggestion ragarding this….
thanks
@shoumi: Sorry, am not familiar with modelng multi-hop networks.
@shoumi: Sory, I have not worked on modeling multihop wireless networks.
@shoumi: Sorry, I have not worked on modeling multihop wireless networks.
Can someone pls provide me the matlab code for the below mentioned project work:
A randomly generated bit stream should be transmitted through an AWGN channel using BPSK. THe received symbols should then be converted again to a bit stream. The received bit stream should be compared with the original one to determine the total number of errors and hence the bit error probability. The probability of error should be calculated for several values of EB/No.
Once the above system is succesfully simulated an additional block of channel coding should be incorporated in the system. A (15,11) Hamming code should be used for this purpose. Simulation of this should be performed to increase the performance of the system.
RESULT to be DISPLAYED:
1. Bit error probability versus EB/No graph of BPSK
2. Bit error probability versus Eb/No graph of BPSK using equation
3.Bit error probability versus Eb/No graph of BPSK system with channel coding/decoding
The written code shuld allow the user to perform simulation for any number of bits and for any range of Eb/No.
THANKS..
Looking forward for your assitance.
@Shahrukh: My replies:
1. Example Matlab code is provided in this post
2. The equation for BER for BPSK for a given value of Eb/N0 is provided in this post
3. I have not tried simulating with Hamming code. However, you may check the article on convolutional coding
with Viterbi decoding
http://www.dsplog.com/2009/01/04/viterbi/
Hope this helps.
pls sumbody help me out!!!…………:(….
Hi Krishna,
All your posts have been very helpful and easily understandable. I was looking for a code that has all the modulations(bpsk,qpsk,mpsk,ask,bfsk,msk etc…) in a single program and to compare their BER, PSD curves. please let me know if you have any.
Thanks
@Murali: No, I have not posted a single code putting all the BER curves in a single plot. However, I have discussed about multiple modulation schemes in dspdesignline.com
http://www.dsplog.com/2008/07/08/compare-bpsk-qpsk-4pam-16qam-16psk-64qam-32psk/
Hope this helps.
Hi, can you help with this issue,consider QPSK transmission over flat fading Rayleigh channels and a 1×2 system.The channels on the different diversity branches are assumed to have the same variance and the noise samples are assumed to be uncorrelated and circularly symmetric Gaussian variables with the same variance.
Consider three combining schemes: MRC, EGC and SC, for plot the BER versus the average signal-to-noise ratio (SNR).
I hope you can help me
@R@y: Using BPSK modulation, I have written articles for a 1 transmit, 2receive system in a flat fading uncorrelated Rayleigh channel.
http://www.dsplog.com/2008/09/06/receiver-diversity-selection-diversity/
http://www.dsplog.com/2008/09/19/equal-gain-combining/
http://www.dsplog.com/2008/09/28/maximal-ratio-combining/
Hope this helps.
Hello,
Do you know how you can build a zero-crossing detector or delay-and-multiply detector for the FSK.
Thanks.
@Einsein: I have written a post on BER computation for FSK using coherent demodulation. That may provide some pointers
http://www.dsplog.com/2007/08/30/bit-error-rate-for-frequency-shift-keying-with-coherent-demodulation/
Hope this helps.
Dear Krishna Pillai :
How can I change Amplitude Modulation to BPSK(y1 = ammod(x1,Fc1,Fs) to bpsk . I hope for a positive response.
clc
close all
clear all
t = 0:0.00001:0.001;
Fc1 = 1000;
Fs = 12000;
y1 = 1;
x1 = cos(2*pi*1000*t);
in_p = input(‘\nDo you want to enter user Y/N: ‘,’s');
if(in_p == ‘Y’ | in_p == ‘y’)
y1 = ammod(x1,Fc1,Fs);
end
@Student: Sorry, I do not have the functions ammod(). Maybe the post on symbol error rate computation using 4-PAM be of help.
http://www.dsplog.com/2007/10/07/symbol-error-rate-for-pam/
Please i dont know how i can acess the e book.
I am working on super orthogonal space time turbo codes in OFDM systems and will need this e book .Thank u
@ Oluwafemi: I had mailed you the instructions. Please check your inbox.
Dear Krishna Pillai
How can I correlate demodulated signal and binary code in BPSK ?I mean reteriving back of binary code.
@Student: At the receiver, using hard decision decoding you can find out whether the received symbol is +1 or -1. Then we can easily map to +1 to bit1 and -1 to bit0 respectively.
Hi,
I would need equations of bit error probability for this modulation technique: MSK, GMSK, QPSK, ASK. Do you know it?
Thank for answer
@bwk: I have not tried simulating MSK/GMSK. Something to do in future. However, you may look at the posts:
a/. Symbol error rate for QPSK
http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/
b/. Symbol error rate for 4-PAM
http://www.dsplog.com/2007/10/07/symbol-error-rate-for-pam/
Dear Krishna Pillai
Thanks a lot for ur suggestion.When I domodulate following code it gives a simple sine wave.How can I demodulate it?
close all
b=[0 1 1 0 1 0 1 0 0 1];
fc=10;
n=1;
while n<=length(b)
if b(n)==0 %0 is -1
tx=(n-1)*0.1:0.1/100:n*0.1;
m=(-1)*sin(2*pi*fc*tx);
plot(tx,m,’LineWidth’,1.5);grid on;
else
tx=(n-1)*0.1:0.1/100:n*0.1;
m=(1)*sin(2*pi*fc*tx);
subplot(2,1,1)
plot(tx,m,’LineWidth’,1.5);grid on;
hold on;
end
n=n+1;
end
title(‘BPSK modulated Signal’)
How coherent detection can be applied on it?
Thanks in advance.
Regards,
@Student: hmm..let me try to understand. For bit0 you are sending -ve sine wave, and for bit1 you are sending +ve sinewave right. At the receiver you cmay undo the effect of the sine wave by multiplying the received signal with the sine wave and taking the mean. Then perform hard decision decoding on that signal.
Does that help?
Bonjour
Je cherche des programmes MATLAB pour la gƩnƩration des codes LDPC Quasi Ciclique
Alors si vous avez des programmes ou des liens utiles priĆØre de me les envoyer a ce mail
eliasknopfler@hotmail.com
Je vous remercie
@Elias: Sorry, I have not discussed LDPC coding till date. Hopefully in the near future.
wah ini dia data yang aku cari-cari akhirnya menemukan yang namanya BPSK
thanks yaaaaaaaaaaaaaaaa…
sip sip sip sip
@bowang: good
Dear Krishna Pillai :
Please reply my question dated April 30, 2009 at 9:37 am.
Regards,
@Student: I just did. Hope you are happy with the response. Sorry for the delay in my reply. Good luck.
Dear Krishna Pillai
Thank u. I am really happy and trying to do what u have suggested.
hello sir
i am doing my project in cdma can u tell me the purpose of rake receiver and details about maximum ratio combining
@kanchana: Well, I have not quite discussed about cdma in the blog till date. Hope to do so in future.
I beleive the intent of the rake receiver is to coherently combine information from all the multipath taps such that the bit-error rate is reduced. I have posted about maximal ratio combining for a 1 transmit 2 receive receive diversity case.
http://www.dsplog.com/2008/09/28/maximal-ratio-combining/
Though the context is different, I think you should be able to adapt that to suit your needs.
Good luck.
Dear Krishna
how can we simulat the angular delay profile. can you just give me simple example plz?
@Ideal: Sorry, am not familiar with modeling angular profile.
Dear krishna
I hope you are fine. I am in 5th semister of my bachelors of telecommunications. So I am new to this field and facing lots of difficulties. I find your site very impressive and have joined it recently. Can you kindly tell me why we normalize things? thnx
@aam_log: Good luck for your studies. We normalize, because we want to have a fair comparison when trying out different approaches….
For eg, if we are comparing 100apples with 100grapes, we would want to know the price per kilogram, no?
HEY sir can u plzz help me in getting the main concept of vblast detection scheme,,i am not geting how it estimates the data…
@maya: Well, understanding V-BLAST with Zero Forcing equalization is the most simplest way. From our linear algebra days, we know that if we have two unknowns, we need atleast two equations to solve them.
Adapting them to MIMO V-BLAST, the two unknowns are the unknown transmitted data, and the two equations are provided by the two receive antennas. Just putting a simple example,
y1 = a*x1 +b*x2
y2 = c*x1 + d*x2
where
y1, y2 are received symbols
a,b,c,d are channel taps (which are known) and
x1, x2 are unknown transmit symbols.
The following post might be of bit more help.
http://www.dsplog.com/2008/10/24/mimo-zero-forcing/
Hope this helps.
thnx for ur response,,it means dat u need to have atleast 2 no of rcvd bits at da reciever 2 be compared..but my confusion is that how to use vblast when i am considering diversity mimo,where i have to use combing technique first?? can i implement vblast in dat case or not???
@maya: Well, try to write the equation in matrix form. For eg, consider a simple case where we have two transmit antennas and 3 receive antennas. The matrix dimensions will be of:
y = Hx + n, where
y – received symbols of dimension [nrx x 1]
H – channel matrix of dimension [nrx x ntx]
x – transmit symbols of dimension [ntx x 1]
n – noise of dimension [nrx x 1]
If we write the zero forcing equalizer for this equation, then we can find that
W = (H^H*H)-1*H^H
This equalization also performs the diversity combining via Maximal Ratio Combining way. Does this help?
hi every body can any one tell me the code for “signal to noise ratio using autocorrelation in time domain” using MATLAB
thanks in advance…..
@sasidhar: The question is not clear to me. Can you please provide some more details….
i have a question..
i have a program wich makes bpsk modulation and i need to show Bit error curve for BPSK modulation – theory, simulation (both) as you do here in this page at top.
ok but there is something that happens with simulation curve that appears a little bit more to the right side of teoric curve.
i wanna know a reason why does it happens.
@Eduardo Solano: If the simulation curve is happening to the right of the theoretical curve, it typically means that you are adding more noise than what is required. Also make sure that you simulate for atleast 10^6 bits, such that you get statistically accurate results.
Dear Krishna, thanks for your codes. I am plotting BER for BPSK and QPSK but i am not getting same BER curve. As it should be same for both. I know that the plot should be BER vs EbN0. But how to get EbN0 from SNR? In your codes you have written Eb_N0_dB, is this EbN0?? I think it is SNR. If this is EbN0, why am i not getting same curve for BPSK and QPSK… Please Help
@Assad Abbasi: Well, as you said BER vs EB/N0 curve for both BPSK and QPSK should be comparable. In general,
Es/N0 = kEb/N0, where k = log2(M) and M is the constellation size.
I have discussed a post comparing BPSK, QPSK, QAM etc @ http://www.dsplog.com/2008/07/08/compare-bpsk-qpsk-4pam-16qam-16psk-64qam-32psk/
Hope this helps.
Have you got any code to 16-apsk?
@Mathew: Did you mean 16-PSK? You may check out the posts on symbol error rate for 16PSK @
http://www.dsplog.com/2008/03/18/symbol-error-rate-for-16psk/
http://www.dsplog.com/2008/03/29/comparing-16psk-vs-16qam-for-symbol-error-rate/
http://www.dsplog.com/2008/07/08/compare-bpsk-qpsk-4pam-16qam-16psk-64qam-32psk/
I mean 16-apsk modulation sth like that http://commons.wikimedia.org/wiki/File:Const_16APSK.gif
@Mathew: Sorry, I have not tried simulating 16-APSK. Thanks to you, I just realized that it is used in DVB-S2. I will try to do a write up in future.
Hello.
I need matlab code for DPSK and also its BER.
regards,
@RAO: I have a post on Coherent Demodulation of DBPSK
http://www.dsplog.com/2007/09/30/coherent-demodulation-of-dbpsk/
Hope this helps.
thanks Krishna.
Actually i need matlab code for non-coherent detection of either bpsk or dpsk and also corresponding BER vs Eb/No plots.
regards,
sorry. in addition, i want noncoherent detection of bpsk or dpsk for both AWGN AND RAYLEIGH channel.
regards,
@RAO: Sorry, I have not tried simulating non-coherent detection dpsk.
Thanks Krishna for reply.
I want to plot BER vs Eb/No for MPSK and MDPSK. Can u help me in this regard ?
Also do u have code for FSK coherent and non-coherent with corresponding BER vs Eb/No plot?
first of all, thanks a lot for ur job, itĀ“s really useful for all the DSP internet communty.
here my question, IĀ“m carrying out some simulations on simulink. modulating BPSK, spreading w/ gold code, going through awgn, despreading and demodulating BPSK, and at the end I measure the BER.
using simple BPSK mod/demod provided in the communications block set, IĀ“ve got a relative high BER (.5), then I found the so-called “Real BPSK mod/demod” which basically a “real-imag to complex”/”complex to real-imag” block is added to the BPSK mod/demod, and the resulting BER is around .1.
IĀ“ve tried to find unsuccessfully an explanation to this on technical literature.
maybe you know something about that.
Thanks in advance.
@Olguin: Well, having BER of 0.5 means there is some error in the simulation code. If you wish you refer the post on
(a) BPSK BER with matched filtering
http://www.dsplog.com/2009/05/08/ber-with-matched-filtering/
Hope that helps you to debug the code.
Thanks Krishna for reply.
I want to plot BER vs Eb/No for MPSK and MDPSK. Can u help me in this regard ?
Also do u have code for FSK coherent and non-coherent with corresponding BER vs Eb/No plot?
Your early response will b highly appreciated.
Hi All,
Can any one guide me to good source…
How to calculate Bit error probability for given SNR, any modulation technique with error correcting codes(convolution coding).
Please give some information on this.
-Thanks
Swetha
@Sweta: The book Digital Communications by John Proakis is a good reference
please can you tell me what does this instruction do exactly
ipHat = real(y)>0;
is it equivalent to
if (real(y)>0)
ipHat = 1
else
ipHat = 0
end
Thanks
@komari: Your explanation is correct.
As you may be aware, Matlab provides lots of ‘quick one liner’ ways to do things.
Ok Thanks very much krishna
Hello
i just want to ask about this statement in the code
ipHat = real(y)>0;
what exactly it do
is it equivalent to
if real(y)>0
real(y)=1
else
real(y)=1
end
Thx
@ahmed: No, your explanation is not correct. As komari mentioned, it is equivalent to
if (real(y)>0)
ipHat = 1
else
ipHat = 0
end
i wanna know what does this statement exactly do
ipHat = real(y)>0;
is it equivalent to
if real(y)>0
real(y)=1
else
real(y)=0
end
thanks
@jo: Plz refer the reply provided to ahmed
Can anyone help me out with a matlab code for this.
For ISI channel with L real coeffnts and BPSK modulation write a Viterbi algo decoder with decoding delay >0
@Srinivas: I have not done MLSE equalization in multipath channel, but plan to do that in near future.
Can someone help me out with a Matlab code for this.
For ISI chanell with real coeffnts and BPSK modulation write a Viterbi algo decoder with decoding delay >0 (say ‘delta’)
plot BER vs SNR for varying ‘delta’s
Thank you for your effort…
i have some question
1. y = s + 10^(-Eb_N0_dB(ii)/20)*n;
2. theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10)))
i don`t know why Eb_N0_dB(ii) has minus value…
and
At first term,^(-Eb_N0_dB(ii) is divided by 20 but, at second term Eb_N0_dB is divided by 10.
Why Eb_N0_dB is divided by diferrent value??
My question is very poor, nevertheless i will wait for your comment
Have a nice day
@Moon: My replies
1/ Before this scaling, the signal term s and the noise term n has the same variance of 1. The term -Eb_N0_dB reduces the noise variance
2/ The scaling is happening on the noise voltage signal, hence the factor of 1/20. In the theoretical equation, note that there is a square root term outside the 1/10 factor. This is equivalent to having 1/20 factor. Agree?
please simulation for BER MIMO (2,2)
@BOUHAFS: Please refer to the post
http://www.dsplog.com/2008/10/24/mimo-zero-forcing/
Hi, I am want to plot the pdf for various SNR(Symbol Error) for various modulation schemes. Do you have matlab code for it.
The derivation in this link is SER Vs SNR, How to change the SER to PDF(of SNR)?
Thanks in advance
@Vijay: I have written an article on error rate for various modulation schemes in dspdesignline.com @
http://www.dspdesignline.com/howto/208801783;jsessionid=3ISGUXHINOVIAQSNDLRSKHSCJUNN2JVN?pgno=1
Further, you may also check out the post
http://www.dsplog.com/2008/10/01/download-free-e-book/
hi
i need matlab code for adaptive modulation from BPSK,QPSK,16QAM,64QAM
so if you have not such code, i hope to guide me how to make it , as you know for low SNR we use like BPSK and for high SNR use like 64QAM
so how to make this via matlab?
regards
@leth: I do not have a code combining BPSK/QPSK/QAM etc to do adaptive modulation. However, you may find individual posts describing these modulation schemes @ http://www.dsplog.com/2008/10/01/download-free-e-book/
As you said, one way to make an adaptive modulation scheme is to define a BER threshold (lets say 10^04) to switch from one modulation scheme to another.
hi can you tell me how to make adaptive modulation ?
thanks
plz help me for changing code rate and delay spread in bpsk modulation used in hiperlan/2
@gdkorde: Quick questions:
1/ What is the coding technique used ? Convolutional coding?
2/ What is the model of the multipath channel? Exponential model?
hi kirishna pillai
i need simulink’s (matlab) block for accunting BPSK BER
thanks
@sam: Sorry, I do not have Simulink.
Hi, my english is not very good looking, but…what is the noise variance for 16QAM and 64QAM?, AWGN channel.
@Diego: The noise variance is independent of the modulation scheme. However, I think you might be looking for error rate for different modulation schemes for a given value of noise variance. You may refer posts:
http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/
http://www.dsplog.com/2008/03/29/comparing-16psk-vs-16qam-for-symbol-error-rate/
http://www.dsplog.com/2007/12/09/symbol-error-rate-for-16-qam/
http://www.dsplog.com/2008/07/08/compare-bpsk-qpsk-4pam-16qam-16psk-64qam-32psk/
hi everybody
i need simulinkās (matlab) block for accunting BPSK BER
Hi Pillai
I would like to ask you a simple question. I am trying to make a simple simulation using a matlab. It is about that one node using SF(spreading factor)=2, and another node using SF = 8 (orthogonal to each) are encoding the data and sending to one node (asynchronous network) with same power but from different distance at the same time. how can i simulate it? when decoding at the receiver, it uses same ovsf code as the node using SF = 8.
Thanks in advance.
@Alex: Well, let me try to write the pseudo code for this case
y1 = x1*code1; % code with SF=2
y2 = x2*code2; % code with SF=8
n = noise; % AWGN noise, lets take mean=0, variance = 1
r1 = y1*scaling1; % scaling factor for first signal
r2 = y2*scaling2; % scaling factor for second signal
r = r1+r2+n; % receiver collects both signals corrupted by noise
x2Hat = r*code2 % receiver tries to correlate r with code2 to recover x2.
Makes sense?
hi,can any one help me to derive BER for physical layer network coding(PNC) modulation scheme…:-)
@Selvadenniz: Sorry, have not studied PNC coding.
hiii… you have BER for physical layer network coding(PNC) modulation schemeā¦.
@tommy: Sorry, no
Hi Krishna,
I am working on Forward error correction codes. I have plotted the BER performance curve for Reed solomon codes using BPSK modulation over an AWGN channel from EbNo 0 – 1 . However, the curves are overlapping at the begining between EbNo values 0 and 1 and also in the middle.
Also the curves for convolutional codes overlap at the begining between 0 and 1. and also in the concatenated codes.
Could you please give me a detailed explanationc on the reason why the overlapping occurs and the significance.
The RS codes used were RS(255,191), RS(255,223), RS(255,239) and RS(255,247).
Thanks, hope to hear from you soon.
@Tito: Firstly, a clarification. When you mentioned about “curve-overlapping”, I guess you meant that – “with coding, the BER becomes poorer than no coding for very low values of Eb/N0″. Agree?
At-least with respect to convolutional codes, I think it can be attributed to the large number of errors in received coded bits, which makes the Viterbi algorithm go haywire.
Thanks that is exactly what i mean. Why does this occur.
And i also have an curve RS curve with and without an interleaver, these curves are overlapping at two points. Why does this occur.
can you send me the matlab coding for physical layer network coding modulation
@thenmozhi: Sorry, I do not have matlab code for physical layer network coding modulation
Thanks a lot, man.
Was very useful.
hello Krishna Pillai!
I’m a student in Ho Chi Minh City, Viet Nam. I’m searching about “the impact of real channel over MiMo system”. your code is useful. So, we assume that receiver is unknown h matrix and we must explore channel by channel estimation. Do you help me?
Hope you will response me!
@Hung: Yes, the receiver is trained to estimate the MIMO channel by sending known preamble.
I knew that OFDM technique, improve the BER performance in frequency selective fading channel, Can you help me in writing code using matlab program show that , I have probem in how write code for frequence selective fading.
Thank you .
@ahmed: In OFDM, though the channel is frequency selective, channel as seen by each subcarrier is flat. Hence the expression for flat fading holds good. Please refer to the post http://www.dsplog.com/2008/08/26/ofdm-rayleigh-channel-ber-bpsk/
Dear Krishna:
I knew that OFDM technique, improve the BER performance in frequency selective fading channel, Can you help me in writing code using matlab program show that , I have probem in how write code for frequence selective fading.
Thank you .
This Krishna Pillai guy is a great help and his website undoubtedly very good resource on communication system topic. I got necessary informations about Vitervi Algorithm, Hard and soft decision.
Ajay Pratap Singh apts
@Ajay: Thanks for the nice words.
Thank you for this website ,it is awesome
could you help me to know what is the role of the following
rand(‘state’,100); % initializing the rand() function
randn(‘state’,200); % initializing the randn() function
thank you
@christine: The random numbers generated by the program can be initialized to enable us to run multiple simulations with the ‘exact same’ random numbers
. Setting the state of the rand() or randn() enables one to do so.
Use >>help rand or >> help randn to get more information.
Hi Krishna,
thanx a lot for your website
i have a simple question:
what about the unequally probable, e.g. when P(s0)=0.25 & P(s1)=0.75 ??
@3mor: If the probabilities are un equal, we would want to shift the threshold for making the decision. The chapter 5.1.3 Digital Communications by John Proakis discuss that case.
Hi krishna, I have actually read the answers given to you by the concerns generated by the formula below
10^(-Eb_N0_dB(ii)/20)*n
for further clarification, i have actually divided by 18,16,14,12——3 to get different plots that actually decreases down the graph . Want to know if is how one can plot for BER with variable noise in the channel. I will appreciate if you reply me soon. Thanks
@Egerue: Do not change the division factor. Rather change the value of Eb_N0_dB. The division by 20 is required to convert dB into voltage.
Hi krishna, I have actually read the answers given to you by the concerns generated by the formula below
10^(-Eb_N0_dB(ii)/20)*n
for further clarification, i have actually divided by 18,16,14,12āā3 to get different plots that actually decreases down the graph . Want to know if is how one can plot for BER with variable noise in the channel. I will appreciate if you reply me soon. Thanks
Hi Krishna.
Thank you very much. God will bless you. Below is the answer you gave me for my concern on this formular 10^(-Eb_N0_dB(ii)/20)*n
“Do not change the division factor. Rather change the value of Eb_N0_dB. The division by 20 is required to convert dB into voltage”.
Please give me more direction, by giving me an example of what you mean by changing the VALUE of Eb_No_dB.
Am thinking is Eb_No_dB =[0:10], [0:20], [0:30] and so on, but am not very sure. Pls, you are indeed a very good teacher, help me out
Thanks, you are really very helpful, you must really reap the fruit of your efforts.
NNAMDI
@Egerue:
You are right.
Eb_No_dB =[0:10], –> 0 to 10dB in steps of 1dB
Eb_No_dB =[0:20], –> 0 to 20dB in steps of 1dB
Eb_No_dB =[0:30], –> 0 to 30dB in steps of 1dB
Hi Krishna.
Thank you very much. God will bless you. Below is the answer you gave me for my concern on this formular 10^(-Eb_N0_dB(ii)/20)*n
āDo not change the division factor. Rather change the value of Eb_N0_dB. The division by 20 is required to convert dB into voltageā.
Please give me more direction, by giving me an example of what you mean by changing the VALUE of Eb_No_dB. or how do we get the value
Am thinking is Eb_No_dB =[0:10], [0:20], [0:30] and so on, but am not very sure. Pls, you are indeed a very good teacher, help me out
Thanks, you are really very helpful, you must really reap the fruit of your efforts.
NNAMDI
Hi krishna
Pls in essence how and where do we set the different values for EbNo/ or S/N or SNR to achieve different BER plots using your simulation example. Pls i will appreciate ur reply.
Thanks
@Egerue: Change Eb_N0_dB
Hi krishna
Pls in essence how and where do we set the different values for EbNo/ or S/N or SNR to achieve different BER plots using your simulation example. Pls i will appreciate ur reply.
Thanks
Hi Krishna,
I was working on a IEEE paper titled”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.”.
Since you have also worked on similar field, I hope u can help me..
I was stuck with re creating the 1st fig in the paper.
SO, can you please look into it and help me out..
Thanks,
Student
@student: Sorry, due to time constraints, may I pass that opportunity. Good luck.
Hi…
I need to Simulink Probability of error for PSK, 16QAM & MFSK. but don’t know how to simulink the equation: Pe=0.5*erfc(sqrt(snr)).
I tried to call the fuction from Matlab using Embedded Function Block in Simulink. But, the program din’t work. Can u suggest me a Block for finding Pe or a Program to call from .m file..?
@Jatin: Does this help?
Eb_N0_dB = [-3:10];
theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))); % theoretical ber
close all; figure;
semilogy(Eb_N0_dB,theoryBer,’b.-’);
I am working on an adaptive modulation model on Simulink. For that first I am trying to get probability of error rate vs snr of different modulation techniques. On modelling 16 QAM modem I have problem plotting its graph by getting bit err rate from simulink model and performing graph plotting on matlab. following is the code im using in matlab..
clear; clf;
M=16; % for simulink
snr=0:10;
err_vec=[];
for i=1:length(snr)
EbNo=snr(i);
sim(‘QAM_16′);
err_vec(i)=bit_err_rate(1);
end;
semilogy(EbNo,err_vec,’b-*’);
grid on
please guide what is the error in this code… thanks
@Faisal: For BPSK,
Eb_N0_dB = [-3:10];
theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))); % theoretical ber
close all; figure;
semilogy(Eb_N0_dB,theoryBer,āb.-ā);
hi
Why you are using 10^(-Eb_No_db(ii)/20) the minus sign in this formula because for voltage scaling it should be 10^(Eb_No_db(ii)/20).
@Hamid: The negative sign came as I am scaling the noise voltage. I am keeping the signal swing the same and reducing the swing of noise voltage to simulate various Eb/N0 values.
Please guys I am having trouble writing a code for non coherent detection, I am required as part of my project to Assume Rayleigh fading channel with BPSK modulation. Using MAT-LAB plot bit error probability (BEP) under non-coherent de-tection. Your ĀÆgures should include plots from both analysis and simulation.Use average SNR (complex) from -5 to 20 dB.
Thanks a lot, i will be very grate ful to get help from you guys.
@Obinna O: Hope you have finished the project by now. Hope this post might be of help
http://www.dsplog.com/2008/08/10/ber-bpsk-rayleigh-channel/
hi sir
i have problem in BPSK with RS codes…..when i/p is given to pskmod function it says that “does not support complex airthmatic”.however i/p given is in 1 0 form
@alok joshi: Sorry, I do not have the pskmod() function.
is erfc equal Q function?
@rai: No, erfc is not equal to Q function, but both are related.
http://en.wikipedia.org/wiki/Q-function
hi krisna,
i hope you are fine.plz could you send me BPSK,QPSK,16QAM,64QAM modulation and demodulation simulation in matlab and simulation of adaptive modulation of convolutionaly coded for BPSK,QPSK,16QAM,64QAM?please help me.
@shadat: Please refer to the post
http://www.dsplog.com/2008/07/08/compare-bpsk-qpsk-4pam-16qam-16psk-64qam-32psk/
http://www.dsplog.com/tag/viterbi
@shadat: Please refer to the post
http://www.dsplog.com/2008/07/08/compare-bpsk-qpsk-4pam-16qam-16psk-64qam-32psk/
http://www.dsplog.com/tag/viterbi
Hi Krishna
I need to Simulink Probability of error for binary symmetric channel if you don’t mind.
@fatima: I believe it should be reasonably straightforward to modify the gaussian channel used in this post to a binary symmetric channel. good luck.
Hi Krishna,
Actually, im studying about your coding for BER vs SNR for BPSK modulation. For simulation, when i changed the value for EbNodB = [-3:10] to [1:10], i cant get the result. why this problem happened?
@adah: What is the error which you are getting?
i am doing simualtion to find the ber of bpsk modulation in pass band case.could you help me.
@rama: Please ask queries. I will try to answer to the best of my knowledge.
i want matlab programs for ‘BER MIMO’,thank u,please help me
@mouhamed: Please look at http://www.dsplog.com/tag/mimo
Hello friends: i am working on MAP , ML decoding for convolutional codes..is there any one who too work on similar field ..?
@waheed: For the Viterbi way of ML decoding, you may look at
http://www.dsplog.com/tag/viterbi
dear krishna…
From my past question, actually i got my result and understand..but..i have a problem with my coding…can you help me please…
My coding…
%directional antenna
d=100;
Pt=100:100:1000;
theta10=10*pi/180;
v=int(‘cos(x)*sin(x)’,0,pi/2);
x=int(v,’x',0,2*pi);
gt10=(4*pi)*cos(theta10)/double(x);
grd=180*pi/180;
c=3e8;
f=2.4e9;
L=1;
lamda=c/f;
Pr10=(Pt.*gt10.*grd)./(((4.*pi.*d)./lamda).^2)*L;
%power noise
k=1.38e-23; %k=Boltzman’s constant
t=300; %t=noise temperature in Kelvin
b=5e6; %b=bandwidth
Pn=k*t*b;
%directional antenna
snr10=Pr10/Pn;
Rb=54e6;
ebno10=snr10/Rb;
ebno101=10.*log10(ebno10);
N = 10^6; % number of bits or symbols
rand(‘state’,100); % initializing the rand() function
randn(‘state’,200); % initializing the randn() function
% Transmitter
ip = rand(1,N)>0.5; % generating 0,1 with equal probability
s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0
n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; % white gaussian noise, 0dB variance
% Eb_N0_dB = [-3:10]; % multiple Eb/N0 values
% k=1:1:10;
%
% for ii = 1:length(k)
% % Noise addition
% yomni = s + 10.^(-k(ii)./20)*n; % additive white gaussian noise
%
% % receiver – hard decision decoding
% ipHatomni = real(yomni)>0;
%
% % counting the errors
% nErromni(ii) = size(find([ip- ipHatomni]),2);
%
% end
for ii = 1:length(ebno101)
% Noise addition
y10 = s + 10.^(-ebno101(ii)./20)*n; % additive white gaussian noise
% receiver – hard decision decoding
ipHat10 = real(y10)>0;
% counting the errors
nErr10(ii) = size(find([ip- ipHat10]),2);
end
simBer10 = nErr10./N;
k1=1:1:10
figure
%semilogy(k,simBeromni,k1,simBer10)
semilogy(k1,simBer10)
grid on
legend(‘theta=10′)
xlabel(‘Eb/No, dB’);
ylabel(‘Bit Error Rate’);
title(‘Bit error probability curve for BPSK modulation in simulation’);
when i changed the Pt=10:10:100; actually i got the result..can you help me pliz….
thanks a lot…
@adah: what is the problem which you are seeing?
dear krishna…
In theory, when i applied my SNR into your coding, i got the result.
But, when i applied my SNR into your coding for simulation, i got the problem. I think that problem occurred at SNR or BER. But i dont know where my coding is problem? Can you help me pliz…
Thanks a lot..
please can u help me in this project ::::–
2) final report(OFDM):
* genearte large no of bits using randint
* modulate the data once with bpsk & then 16-QAM
* bpsk mod is 2*data-1
* after modulation u should loop on the data with step of 64′s
each time calculating their ifft
* add the noise to each 64
* if u remeber how to add noise then do it as u know,
else use awgn
sigandnoise=awgn(signal, SNR in dB , ‘measured’ )
* do fft with steps of 64′s , the same groups of symbols that were ifft’ed
* demodulate the data ( if bpsk then bits= recdata > 0)
*calculate ber using
ber=sum(xor( transmitted bits , received bits ) )
* the whole program should be done in a large loop that loops over
SNR -5 -> 15
* in case of fading
multiply with channel before ifft then divide after ifft
* multiplication is done using (.*) not just (*)
Hi Krishna,
I know the BER of BPSK is 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))),
if I put channel coding before the modulation,and the code rate is R,
then if the BER equals 0.5*erfc(sqrt(R*10.^(Eb_N0_dB/10)))?
then BER with code rate 1/2 is higher than 3/4,but acturally ,it should be
lower. where is my mistake ?
Hoping for your help, thank you
Student
please give help about matlab code in optimization for co channel and adjacent channel interference using ANN
haiiiiiii
i need Matlab code for digital modulation techniques.
plz give reply to me….plz
‘
Dear Krishna,
Can you little bit tell me how to simulate the Uncoded BER and ergodic capacity for webb channel using QPPM modulation.
Dear Krishna,
I already ask this question please. reply
Can you little bit tell me how to simulate the Uncoded BER and ergodic capacity for webb channel using QPPM modulation.
Hi krishna!
I need matlab code to obtain BER vs SNR curve for binary on-off keying.
also ,code for generating SER vs SNR curve for 3ASK modulation
Hi there,
i just wondering why we need to initialize the rand and randn function?
@anis: If we initialize, we can ensure that the same random numbers are generated in any run
hi,
I would like to demodulate QPSK but using soft decision. can you help me or guide me how I want to do this? I try the matlab function using
demodh= modem.pskdemod(ht, ‘outputType’, ‘bit’,'DecisionType’, ‘LLR’, ‘NoiseVariance’, sigma);
dec_inputt=demodulate(demodh,rt);
but the bit that I’m receive sort like it have inverse sign.
for example: if I transmit bit : 1; 0; 1 ,
I received : -10.8; +9.7; -11.2.
I’m expecting that : +10.8;-9.7;+11.2.
Or is it LLR gives this inverse sign? TQ so much if you can help me.
@anne na: Why are you using soft decision, unless you have some decoder like Viterbi following your demapper. Anyhow, I have discussed about softbit for 16QAM @ http://www.dsplog.com/2009/07/05/softbit-16qam/
respected sir
please can u help me in providing matlab code for rs codes using interleaver &qam in awgn channel
i will be thankful to u
@gurinder: I have not discussed ReedSolomon codes in dsplog.com yet. Hope to do so
Hi There,
I need to design and develop a simulation platform in C/C++ to simulate the performance for BPSK- and 8PSK modulation through an AWGN channel and evaluate the biterror rate (BER) performance for BPSK and 8PSK in the range Eb/N0 2 [ā4, 8] dB.Can you help me with any suggestion or source code.
@DaMarco: You can use the Matlab model provided in this post as a reference for the C code
hello sir,
please give us an idea how to analyse matlab code for ofdm-awgn channel with that of theory. what are the pilots and why are they used?
@rekha: The BER performance of OFDM in AWGN is comparable to the no OFDM case. http://www.dsplog.com/2008/06/10/ofdm-bpsk-bit-error/
hello sir,
m doing ma project on ber calculation using matlab simulation for ofdm transmission for multipath wireless communication so please if u cud help me out in knowing which book wud b d best 2 go through….where i wud b getting much of d information regarding d basics of ofdm , transmission n reception of signls using ofdm, n n… ber calculation n its various graphs hw 2 plot dm n al….
please do help me out sir in dis ……m very confused abt dis…..
@Ananya: A good book to read is OFDM Wireless LANs: A Theoretical and Practical Guide by Juha Heiskala , John Terry
Hi,
Can anyone help me in my project!!!
i Have read here that there is no difference between BER vs SNR in case of BPSK and OFDM using BPSK.
But my project guide has told me to mathematically prove that BER vs SNR is better for OFDM using BPSK than simple BPSK.
Suppose there is N no. of subcarrier.Then for each subcarrier there will be BER.But if i want to calculate the total BER for n no. of sub carrier then how the BER of indivisual subcarriers are related???
@amit: In AWGN there is no difference between using BER for BPSK and BER for BPSK using OFDM.
your kind guidance on MATLAB has been really a great help for MATLAB starters. hope u will continue in future too.
@vj1892: Thanks
pls i need a matlab program for signal to noise ratio in a wireless communications system.. how do i do the write up for the matlab program??
@fizzle: Well, if you divide signal power by noise power, the resultant is signal to noise ratio
dear sir Krishna Sankar
I am very happy to find your blog … and found what I was looking for … I am a student majoring in telecommunications engineering and was doing the final tasks of rain attenuation, said supervisors told to discover how much value other than tresshold BER for MQAM rmodulasi … I want to ask how can I download the book John Proakis as an accurate reference book saya.Mohon bantuanya final … and also how the graph of the BER curve modulation 16…………
@eca: You can try purchasing Digital Communications by Proakis
Hi Krishna Pillai ..
I whant to simulate BER for BPSK but for 5 or 6 user not for 1 user
what is the changement applicated in this programme.
@STIVE CHLEF: Well, if you have 5/6 users, how are you planning to distinguish them at the receiver?
Hi sir,
I want some programmes on DAPSK(differential amplitude phase shift keying) in OFDM systems.Is there any matlab codes in DAPSK.Please reply me as soon as possible.
Thanks,
regards,
chandra
@chandra: Sorry, no posts on DAPSK. The closest which I have discussed for ASK is the 4-PAM case
http://www.dsplog.com/2007/10/07/symbol-error-rate-for-pam/
Hope this helps
hello sir …
in BPSK constallation we map bit 1 to sqrt(Eb) and 0 to -sqrt(Eb). these are real points then why to add complex noise …we can directly add real noise of unit variance as follows…
N = 10^6 % number of bits or symbols
rand(‘state’,100); % initializing the rand() function
randn(‘state’,200); % initializing the randn() function
% Transmitter
ip = rand(1,N)>0.5; % generating 0,1 with equal probability
s = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 0
n = randn(1,N) ; % white gaussian noise, 0dB variance
Eb_N0_dB = [-3:10]; % multiple Eb/N0 values
for ii = 1:length(Eb_N0_dB)
% Noise addition
y = s + 10^(-Eb_N0_dB(ii)/20)*n; % additive white gaussian noise
% receiver – hard decision decoding
ipHat = real(y)>0;
% counting the errors
nErr(ii) = size(find([ip- ipHat]),2);
end
or we can use awgn function to pass through awgn channel which will add real noise if data is real and will add complex noise if data is complex… if i proceed in that way the performance is not matching with the theoritical analasys… can u explain me clearly why should we add complex noise…
expecting early reply….
Thanking u sir
@rama krishna: Adding complex noise does not affect the end result (as we are ignoring the imaginary part at the receiver). However, just make sure that scaling is correct. You should multiply factor of 1/sqrt(2) to the noise term which you have defined.
hello sir
can you please guide me,how can i plot BER error rate of uncoded and coded BPSK
i know the formula of BER for Uncoded BPSK ,i have plotted it,but I am really cunfused about the Coded Bpsk,I am using BCH codes which are block codes
Waiting for your reply
@Ayesha: I have two posts on coded BPSK BER with
a) Hamming code :
http://www.dsplog.com/2009/09/29/hamming-74-code-with-hard-decision-decoding/
b) Convolutional code with hard/soft viterbi decoder
http://www.dsplog.com/2009/01/04/viterbi/
http://www.dsplog.com/2009/01/14/soft-viterbi/
http://www.dsplog.com/2009/07/27/viterbi-with-finite-survivor-state-memory/
Hope this helps
Thanks alot sir for your precious time and guidance
hey krushna
That really helpful for me.
but i need it’s paper too. can u send it to me plzzz
@prashant: I referred the text book Digital Communication by Proakis
Oops i am sorry if this is a total blunder.. In digital modulation techniques we modulate a sine or a cos wave using bits and transmit them as sine or cos waves.. But in this code for BPSK modulation I never found the usage of such things.. could you please clarify my doubts in simple words… Regards Ajith
@Ajith: No, its not a blunder at all, tt’s a genuine query. There are two aspects to the reply.
a) In the case of baseband transmissions, we send the information on pulses and in the most simplest case, we send out rectangular pulses of varying amplitude to convey the information (or we can do some better pulse shaping to reduce the out of band emissions, while not introducing ISI)
b) In the case of pass band transmissions, we do the pulse shaping, then upconvert to a carrier and then transmit.
In both (a) and (b), for computing BER, the results which we get even if we do not simulate pulse shaping + up conversion is same as the one without it (assuming, we undo the operations optimally). Hence did not put those in place.
Further, I have written a post doing BER computation with rectangular pulse shaping with matched filtering
http://www.dsplog.com/2009/05/08/ber-with-matched-filtering/
Thanks for your detailed post!
But I have question about the comment of this line in your codes
s = 2*m-1; % BPSK modulation 0 -> -1; 1 -> 0
I think maybe you want to change original 0 to -1, but 1 should be no change, is it?
@weather: Thanks for noticing the typo in the comment. I corrected it.
hey…
will u plz giv code for gmsk…
@avdhut: I do not have the code for GMSK, but you may refer the MSK code @
http://www.dsplog.com/2009/06/16/msk-transmitter-receiver/
http://www.dsplog.com/2008/01/19/simulating-minimum-shift-keying-transmitter/
dear krishna,
i need to simulate BPSK modulation to analyse the bit error rate in AWGN channel and reyleigh fading channel for different SNR.the carrier frequency should be 20MHz.if u hav matlab codes for dis,help me.m running out of time.
xpecting fruitful reply.
@jansi: The following posts might be of help
a) BPSK in AWGN : http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/
b) BPSK with OFDM in AWGN : http://www.dsplog.com/2008/06/10/ofdm-bpsk-bit-error/
c) QPSK in AWGN : http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/
its very useful thanx , do u know how can i get the simulink for this code ,please?
@hamdirajeh: Sorry, I do not have simulink code
hi
i m doing graduation we have a project in which we have to design the communication sysem in which data+modulation(bpsk and 8-psk)+awgn then threshold detector and then we had to compute bit error rate.. can you help me in this…..
@Ahmed:
For 8 PSK case, you may use the article on 16PSK as a reference
[symbol error rate] http://www.dsplog.com/2008/03/18/symbol-error-rate-for-16psk/
[bit error rate] http://www.dsplog.com/2008/05/18/bit-error-rate-for-16psk-modulation-using-gray-mapping/
Hi Krishna,
what about 8-PSK ?
is it the same to 16-PSK and just change M=8 only?
or there is other things that i should to change ?
becouse when i changed M to 8 i got an output and no errors
pls answer me it’s very importanat
thanks alot man
@Elayan: Yes, I guess changing M to 8 should suffice.
Hello Krishna,
I have a question.. I am hoping to design a OFDM communication system…
If you were to design an OFDM communication system.. what and where would u start from?
Regards
Sara
@Sara: You should know your available bandwidth, then chose your subcarrier spacing and so on
Dear krishna
impressive works! hay, can you provide me simulation codes for BPSK, QPSK, 16QAM & 64QAM with AWGN channel in OFDMA modulation? these would be very much helpful for my thesis. thank you.
Moyeen
@Moyeen: Please refer to the post http://www.dsplog.com/2008/07/08/compare-bpsk-qpsk-4pam-16qam-16psk-64qam-32psk/
Hi Krishna,
I am working on different modulation technique. I am badly needed BER code of QPSK, (QAM 16,64)with AWGN channel.I have to submit my paper on 30may2011.
please send me code , this very helpful for me.
moyeen
@moyeen: You can refer to the post on BER for 16QAM with Gray coding
http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/
hi krishna,
please send the matlab codes(whatever u have about that paper) for below linked paper, I am doing my project on that paper. Please help me. This is very urgent., Please click on below mentioned web address.
http://dspace.mit.edu/openaccess-disseminate/1721.1/52384
@Nikhil: Sorry, I have not looked into that paper.
Hello Krishna Sankar,
I am doing some research on chaotic carriers and I was planing to make this BER for comparison.
Your post save me a lot of time to focus on the real subject of my work.
Thank you very much for the help!
Regards from Brazil
Marcos Amaral
@Marcos: Thanks.
Hi krishna,
Could i have codings with different modulations with different subcarriers for any one user in MIMO OFDM system .output shouild be throughput versus time or ber and time.please help me sir.Thank you in advance
@Guhan: Yes, you can have independent modulation on different subcarriers.
Do you have code on how to generate a NRZ signal?
And do you have code on how to generate the eye diagram. Thanks.
@Emmanuel: For eye diagram, you can take a look at
http://www.dsplog.com/2008/05/01/eye-diagram-plot-matlab-raised-cosine-filter/
1.10^(-Eb_N0_dB(ii)/20)*n
2.10^(-Eb_N0_dB(ii)/10)
i want to answer the confusion of /20 why not by /10?
In fact sir Krishna Pillai want to make noise variance equal to 1 or 0dB.
you can check by command max((10^(-Eb_N0_dB(ii)/20)*n))= 1.01 where as
max((10^(-Eb_N0_dB(ii)/10)*n))= 0.3251 so its clear scaling…..remember before these commands i just removed the complex part i.e n = 1/sqrt(2)*[randn(1,N)]; for my easyness.
I also noticed that this scaling change for system to system e.g for non coherent 4FSK -it becomes like (10^(-sqrt(2)*Es_2N0_dB(ii)/20))*n becoz in 4FSK i need variance 0.5.so i scaled it to 0.5 by just multiplying by sqrt(2)
@Talib: Replies:
1. The /20 is to scale the noise voltage signal. Using max is not a good idea
2. I think for FSK coherent demodulation, which uses 0/1 modulation has 3dB poorer BERwhen compared to BPSK
http://www.dsplog.com/2007/08/30/bit-error-rate-for-frequency-shift-keying-with-coherent-demodulation/
hai,
i would like to know why in y = s + 10^(-Eb_N0_dB(ii)/20) we use a negative sign her e for eb no.
Thanks in advance
@sarah: The -ve sign is to scale down the noise signal with respect to desired signal
Hello Mr.Krishna Pillai I tried to plot the BER for BPSK using the following code but didn’t get correctly..Could you please kindly correct me what went wrong..
clc
clear all
close all
ber=[];
x= randint(1,200);
y= [2];
k= log2(y);
z= reshape(x,length(x)/k,k);
d=bi2de(z);
M=[2];
s=pskmod(d,M);%Psk modulation
scatterplot(s);
snr=[-3:35];
ber1=[];
for i=snr;
p=awgn(s,i);
q=pskdemod(p,M);%psk demodulation
z1=de2bi(q);
d1=reshape(z1,1,length(x));
[r,b3]=biterr(x,d1);
ber1=[ber1,b3];
end
p;
ber=[ber;ber1];
scatterplot(p);
figure()
plot(snr,ber)
@Thiyagi: If you dont add noise, are you getting zero bit error rate?
Yes mr.Krishna i’m getting bit error rate as zero without adding noise i.e not used ‘awgn’ function to add noise
Mr.Krishna for the below code i’m achieving same BER at less SNR comparing to the theoretical value, since i used AWGN inbuilt function to add noise..Whether this approach is correct? With the program given in this website it works good, from this program I tried with my logic just want to know whether the below logic is correct..Thank u
clc
close all;
clear all;
ber2=[];
N = 10^6; % number of bits or symbols
x = randint(1,N);
for i=1:length(x)
y1(i)=1; y11(i)=-1;
if x(i)==1
s(i)=y1(i);
else
if x(i)==0
s(i)=y11(i);
end
end
end
s;
scatterplot(s);
n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)];%AWGN
ber=[];
SNR_dB = [-3:35];
snr=10.^((SNR_dB)/10);
for i = 1:length(SNR_dB)
y = awgn(s,i);
y_hat = real(y)>0;
[n,b]=biterr(x,y_hat);
ber=[ber,b];
end
ber2=[ber2;ber];
figure()
form_ber = 0.5*erfc(sqrt(snr)); % theoretical ber
semilogy(SNR_dB,form_ber,’g.-’);
hold on
semilogy(SNR_dB,ber2,’bs-’)
legend(‘theoretical BER’,'practical BER’)
axis([-3 10 10^-5 1])
grid on
@Thiyagi: The code looks ok. You can check couple of points:
a) awgn : whether the noise power is as expected. Maybe you can try with ‘measured’ option.
From Mathworks http://www.mathworks.in/help/toolbox/comm/ref/awgn.html
“y = awgn(x,snr,’measured’) is the same as y = awgn(x,snr), except that awgn measures the power of x before adding noise.”
b) Counting the number of error. That piece of code looks funny. Did not understand the need for ber and ber2.
Should be easy for you to figure out.
@Thiyagi : ok, good
hai,
i am new in working with OFDM , so can anyone help me with simulink model of OFDM, please
@vidhya: I don’t have the simulink model, but hopefully the post on BER for BPSK over OFDM helps
http://www.dsplog.com/2008/06/10/ofdm-bpsk-bit-error/
Gud morning Mr.Krishna thank u for posting ur valuable comments..
for i = 1:length(SNR_dB)
y = awgn(s,i);
y_hat = real(y)>0;
[n,b]=biterr(x,y_hat);
ber=[ber,b];
end
ber2=[ber2;ber];
I checked this one no need for ‘ber2′.. I used ‘ber’ as an array to store the values of bit error ratio since biterr is an inbuilt fuction and [n,b] where ‘b’ bit error ratio for a particular snr value and we need Bit Error Ratios for all differen SNR values, for that I used variable ‘ber’ to store the values of ‘b’
@Thiyagi: Ok. So, all your issues are resolved?
Yes Mr.Krishna…
I’m currently pursuing my M.Tech(Communication Engineering) in VIT.. I’m willing to work in wireless field.. I need ur guidelines to work in communication field or in signal processing so that I can prepare for my future… Pls do reply waiting for ur precious reply.. Thank You
@Thiyagi: All the best for your studies. With out being specific, I believe having the following knowledge will help you in good stead when trying to chart out a career in wireless communication/signal processing :
a) Understanding of RF architecture, RF impairments and it’s effect on the system performance
b) Phase/frequency syncrhronization
c) Channel effects – channel estimation/tracking
d) Channel coding
e) Multi user communication … to name a few…
Dear Mr. Krishna
I’d be grateful to you if it’s possible to provide single carrier and OFDM code (Matlab) for both timing and frequency offsets with and without cyclic prefix (both for single carrier and OFDM).
@Kabir: Sorry, I do not have all those codes handy
I am having problems simulating the BER vs SNR curve for the binary on-off keying modulation. My plot looks backwards. Do you have any suggests.
Here is my code
% EE474 Lab 1
clc;
clear all;
close all;
Es =1;
n=0:7;
count0 = 0;
%Simulated BER
for snr =0:7
count0 = count0+1;
error =0;
right = 0;
snr_number = 10^(snr/10);
N0 = Es/snr_number;
count = 0;
while(error0.5)
d=1;
else d=0;
end
S = d*sqrt(Es);
noise = randn*sqrt(N0/2);
D =S+noise;
if D>0
d_hat = 1;
else
d_hat =0;
end
if d == d_hat
right = right+1;
else
error = error+1;
end
end
ber_sim(count0) = error/count
end
semilogy(n,ber_sim,’o-’);
hold on;
xlabel(‘SNR’);
ylabel(‘BER (dB)’);
title(‘BER vs SNR BPSK’)
Your help is appreciated.
Greg
@Greg: Are you getting zero BER when no noise is present in the simulation?
the above graph shows the theoritical and simulated values for bpsk from where this theoritical values comes.thnx
@abhay: The computation of the theoretical BER is discussed in this post. Idea is to find the area under the tail of the Gaussian curve.
Hello Mr.Krishna
How to get rotated Pi/4 QPSK constellation? I got QPSK constellation how to get Pi/4 rotated constellation for QPSK
@Thiygai: I do not think I ‘ve discussed pi/4 QPSK. But discussion of a close cousin MSK is kept @
http://www.dsplog.com/2009/06/16/msk-transmitter-receiver/
For QPSK you can refer to
http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/
Thank u very much Mr.Krishna.. Could you please name a few companies recruiting in this field… I knew only the IT companies no idea about this type of companies and what will the requirements to get into those companies……
@Thiyagi: Trust that doing cursory search using google/linkedin will give you lots of pointers.
Requirement to get into any company is good knowledge of basics
Thank You
hi, this was very helpful 4 me, do you have the code for bit error rate(BER) of OOK
thanks.
@stud1: Thanks. The OOK case is very close to BFSK, you can take look at
http://www.dsplog.com/2007/08/30/bit-error-rate-for-frequency-shift-keying-with-coherent-demodulation/
@RAO: My replies;
1/ I have written a post on symbol error rate and bit error rate for 16-PSK.
http://www.dsplog.com/2008/03/18/symbol-error-rate-for-16psk/
http://www.dsplog.com/2008/05/18/bit-error-rate-for-16psk-modulation-using-gray-mapping/
The equation and code should be easily adapted to M-PSK case.
2/ I have not tried modeling MDPSK.
3/ I have written a post on coherent demodulation of FSK
http://www.dsplog.com/2007/08/30/bit-error-rate-for-frequency-shift-keying-with-coherent-demodulation/
Hope this helps.
please can you tell the differences in the code if we made it such that the noise is only Gaussian noise with 0 mean and No/2 variance
@Ali: We are discussing this case, no?
please can you tell me how that is discussed if you write this statement 0db variance
in this line of code
n = 1/sqrt(2)*[randn(1,N)] %+ j*randn(1,N)]; % white gaussian noise, 0dB variance
really , please can you illustrate me which part exactly in the code do this thing as the part the i see in the code is
n = 1/sqrt(2)*[randn(1,N)]; %+ j*randn(1,N)]; % white gaussian noise, 0dB variance
and you write as comment that the noise is 0 db variance
thanks for your great efforts
Hi Pillai..my Mtech project is Cs-OFDMa ,here we are using LAS (smart codes),pls let me know if hav any matlab simulation for the subject mentioned.
@Ali: The 0dB variance is for complex noise (on both real and imaginary part). For BPSK we use only real part and the variance is 1/2. Agree?
@hemant: Sorry, I have not worked on LAS. Infact, I was unaware of the acronym till I googled and found Large Area Synchronous.
Hi Krishna,
I just read your answers in this website.
I am working in convolutional codes with 8psk and AWGN. I have some doubts in Iterative decoding. Can you help me.
Anil
@anil: You may ask. I will reply to the best of my knowledge
Hi Krishna,
I am working on a IEEE paper titled”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.”.
Since you have worked on similar field, I was hoping you can help me.
I was stuck with re creating the 1st fig from the paper.
Can you please look into it and help me.
Student
Never mind, already found out what I did wrong… forgot to convert to dB scale
{ 5 trackbacks }