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 is less than or equal to 0, then the receiver assumes 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,

is 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] Digital Communications by John Proakis

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.*

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i am trying to calculate the BER for an ADC, but all what i found online is that formula, which seems not accurate at all

BER = number of error/ total no. of bits sent

i will compare between to sinecures

Tx Rx

1- 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0

2- 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

in both cases the BER is 0.2 or 20%. in example one the error is insignificant as the error is on LSB and can be easily ignored. in example two the error occurs on MSB bit which makes the whole information different. in both cases, the formula says there are two errors, without mentioning which bits are damaged.

is there another formula which can be more accurate i can use??

any help would be greatly appreciated,

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I had one query regarding the error probability (Pe).

I have a set of values:

Y=[4.0829

45.2948

60.4492

0.6844

1.6557

6.4594

5.0681

5.2660

5.2568

5.4682

4.0257

3.8263

4.0347

5.4421

4.6136

0.4129

0.1094

0.0957

5.3773

1.4608

2.8782

0.3875

0.4000

33.6456

33.4021

46.8380

74.1583

45.4767

1.5635

45.9417

10.2164

45.5156

56.0098

17.0093];

I want to plot the error probability (Pe) as a function of ‘mu’ (threshold). Can you please help me regarding the same?

Waiting to hear ASAP.

Kind regards,

Rohan

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Hi, mr. Krishna, is a long time since I follow his posts, so thank you for the valuable information that I found in the blog. I have a question about the code, in particular with regard to the following line :

theoryBer = 0.5*erfc(sqrt(10.^(Eb_N0_dB/10))).

my doubt is regard the use of exponential term 10.^(Eb_N0_dB/10). why is written in this way?

thanks in advance for your attention.

can any1 pls help me calulate ber for the following direct sequence spread spectrum code using bpsk modulation??

clc;

clear all;

close all;

R=7;

T = [zeros(1,R), ones(1,R)];

T = T(randperm(2*R));

x=T;

[T]

z=length(x);

x(x==0)=-1;

for i=1:1:z

q((i-1)*100+1:i*100)=x(i);

end

b=length(q);

t=0.01:0.01:z;

c=2*cos(2*pi*t);

y=c.*q;

hpn = comm.PNSequence(‘Polynomial’,[3 2 0], …

‘SamplesPerFrame’, 14, ‘InitialConditions’,[0 0 1]);

x1 = step(hpn);

xw=x1′;

xw=xw(:)’;

[xw]

N=length(xw);

for i=1:1:N

m((i-1)*100+1:i*100)=xw(i);

end

h=y.*m;

figure;

plot(t,m);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘pn code modulated signal’);

figure;

plot(t,c);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘sinusoidal signal’);

figure;

plot(t,y);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘PSK modulated signal’);

r=randn(1,length(h));

k=h+r;

figure;

plot(t,k);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘noise added PSK signal’);

t1=0:0.01:.99;

r1=cos(2*pi*t1);

r2=fliplr(r1);

l=length(k)+length(r2)-1;

d1=fft(k,l);

d2=fft(r2,l);

d=d1.*d2;

p=ifft(d,l);

figure;

plot(p);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘correlated signal’);

for j=1:length(x)

q(j)=p(100*j);

if q(j)>0

n(j)=1;

else

n(j)=0;

end

end

op=n.*xw;

[op]

op(op==0)=-1;

figure;

len1=0:1:length(op)-1;

stairs(len1,op);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘demodulated signal’);

i=length(x)

for i=1:1:i

q((i-1)*100+1:i*100)=x(i);

end

figure;

ftr1=fftshift(abs(fft(q)));

plot(ftr1);

xlabel(‘frequency’);

ylabel(‘amplitude’);

title(‘signal spectrum’);

figure;

ftr=fftshift(abs(fft(h)));

plot(ftr);

xlabel(‘frequency’);

ylabel(‘amplitude’);

title(‘spreaded signal in frequency domain’);

figure;

stairs(x);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘input signal’);

figure;

stairs(xw);

xlabel(‘time’);

ylabel(‘amplitude’);

title(‘pn seq’);

figure;

ftr2=fftshift(abs(fft(p)));

plot(ftr2);

xlabel(‘frequency’);

ylabel(‘amplitude’);

title(‘correlated signal spectrum’);

p=length(op)

for i=1:1:i

s((i-1)*100+1:i*100)=x(i);

end

figure;

ftr3=fftshift(abs(fft(s)));

plot(ftr3);

xlabel(‘frequency’);

ylabel(‘amplitude’);

title(‘signal spectrum at receiver or despreaded spectrum’);

figure;

ftr4=fftshift(abs(fft(y)));

plot(ftr4);

xlabel(‘frequency’);

ylabel(‘amplitude’);

title(‘bpsk modulated spectrum’);

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I want the matlab code for probability of symbol error for BFSK modulation

hai krishna

This is Karthik sharma. doing my Masters in communication..

in my final year project i implemented a MIMO-OFDM WiMAX system using matlab simulink. The SNR vs BER graph for the model is showing a straight line instead of a waterfall graph.. kindly help me .

waiting for your reply..

Regards

@karthiksharma: are you getting a zero ber in the no-noise case?

Hi Krishna,

Thank you for this website

i have two question please

1- Why the WGN (n) is outside the statement (for) while in other your program (script_ber_bpsk_rayleigh_channel) is inside (for).

2- Please can you give me the equation of WGN or give me the name of reference

@supas: Replies

1/ ideally, one would want to give different noise realization for each snr point. with that in mind, having the wgn statement inside the for loop is better

2/ wgn is created using randn function

hello sir,

I want matlab codings for SOVA algorithm,could you please help me for successful matlab codings

@kavitha: SOVA is soft output viterbi alogrithm – used in turbo coding. i have not discussed turbo codes yet in the blog.

I have a doubt regarding the scaling of noise power you have put in the code..

clearly, variance= sigma^2= No/2;

hence, while writing y= x+ n

since MATLAB generates unit variance noise, we should multiply it by sigma to get our scaled noise ,

y= x+ sigma*N

i.e. y= x+ sqrt(No/2)*n,

where n is randn(1,1) or 1/sqrt(2)*[randn(1,N) + j*randn(1,N)] doesn’t matter both are unit variance,

but in your code you have multiplied n with sqrt(No) rather than sqrt(No/2) so an extra divide by sqrt(2) is needed.

#in your code

taking signal energy as unity,

No= 10^(-Eb_N0_dB(ii)/10)

sqrt(No)= 10^(-Eb_N0_dB(ii)/20);

y = s + 10^(-Eb_N0_dB(ii)/20)*n;

Please correct me if I am wrong and clear the doubt.

@marvellous: Hmm.. isn’t the code doing 1/sqrt(2) first and then sqrt(N0)? The term sqrt(N0/2) is for real and imaginary arm

http://www.dsplog.com/2012/03/25/thermal-noise-awgn/

Hi Krishna

I have a question regrading “sigma” the standard deviation of noise:

We know that sigma = sqrt(No/2), for complex noise. right?

But how about real noise? Is sigma = sqrt(No)?

where No is noise power spectral density.

I look forward to hear from you soon.

Many Thanks

@Ravinder: The term 1/2 comes because the noise is symmetric across +ve and -ve frequencies. Hope the post on thermal noise and awgn gives additional pointers

http://www.dsplog.com/2012/03/25/thermal-noise-awgn/

Thank you very much for your reply Krishna.

pls can you help solve this question; Given a stationary transmitter is sending at a center frequency of 900 MHz, the receiver is

travelling at speeds of (a) 1 km/hr; (b) 10 km/hr; (c) 100 km/hr; or (d) 500 km/hr. Draw

a graph of four curves that show deviation of spectral frequencies from the center frequency

for the above four scenarios. Use a legend properly to distinguish different scenarios.

5. Suppose that a mobile node is moving at a speed of 150 km/hr in a typical urban environment

(e.g., highway). It transmits a signal to the base station at a center frequency of fc = 1 GHz

using a binary modulation at a data rate R. It is known that the typical RMS delay spread

of multipath propagation in this scenario is around 5 s. For each of the following cases,

decide if the received signal is best described as undergoing fast/slow fading, frequency

selective fading or flat fading.

(a) The mobile node is sending at a data rate of R = 1 Mbps.

(b) The mobile node is sending at a data rate of R = 500 kbps.

(c) The mobile node is sending at a data rate of R = 50 kbps.

@ruby: wont be able to help directly, but can point you to the following wikipedia links:

http://en.wikipedia.org/wiki/Doppler_effect

http://en.wikipedia.org/wiki/Rayleigh_fading

Why is my comment not appeared

@Ozgee: There is moderation enabled.

First of all, congratulations for this helpful and nice explanation. I’m dealing with the similar task (maybe the same) these days. I determine two waveforms, Tb and BW, then I’m trying to draw the plot of Pe versus BW. Is yours exactly the same thing that I want to do? However, in my design, there are two integrators. I couldn’t get the point that whether you used integrator in your matlab code or not. Also, if we use lowpass filter, instead of AWGN is there a change? I’m very new at digital communication, so I’m sorry for these bad questions

@Ozgee: Replies:

1/ This simulation is doing bit error rate vs SNR (not vs Bandwidth)

2/ This code does not have any integrator – but a typical implementation will need a matched filter

see the following example : http://www.dsplog.com/2009/05/08/ber-with-matched-filtering/

3/ Loop filter and awgn two independent aspects.

Hi ,I need program for BER reduction using SSPA(solid state power amplifer ) model .or else BER reduction using PTS scheme.

@Vishnavi: Sorry, I do not know the topic.

could u send me the matlab code .plz

@karim: the link is provided in this post.

Hi!

You’ve calculated the BER with a message of 1exp6 bits, and the curve obtained is perfectly over the reference, but if you take less than 1exp6 (e.g. 1exp4) apears irregulats peaks on the curve.

My question is……that’s something that I have to worry? Or it’s correct the response of the curve?

Thank you very much!

Yamsha

@Yamsha: To get confidence in the simulated results, one need to get sufficient number of errors. For eg, to get a bit error rate of the order of 10^-6, one needs to send atleast 10^7 bits.

Thanks a lot!

Thats the information that i need!

Yamsha

Hi Krishna,

Can we use importance sampling to measure the BER very small (below 10^-10) ?

@trung tong: To get a BER of 10^-10, need to send atleast 10^11 bits. Do not use this code, use C model to do the simulation (will be faster)

Hi Sir…

Can you Provide the matlab code for Analysis and design of OFDM-IDMA systems

it’s very urgent….!

@phani: sorry, do not know about ofdm-idma topic

Dear Mr Krishna.

Im trying to draw the same function, BPSK with AWGN, in excel.

I get a completely different graph, so i must be doing something wrong.

May i contact you by mail to send you my table?.

Thanks very much.

@Tony: In excel, make sure that you are selecting log-scale for the y-axis.

Can you please provide the code for 2×2 MIMO with spatial diversity and different reciever combining schemes for a system using m-PPM modulation. Using gamma-gamma channel model.

@BALA MURTHY: Please check out post @

http://www.dsplog.com/category/mimo

I need this in matlab with expalnation.

Compute the error probability of a BPSK as a function of Es/NodB (in decibel)

{1; 2; 3; 4; 5; 6; 7; 8; 9; 10}.

1.What is the energy of a BPSK symbol (Es)? And the Energy per bit (Eb)?

Comment.

2.The noise variance is

sigma^2 =N0/2

hence for each value of Es/NodB you can derive the associated sigma^2 that you

need to generate your additive white gaussian noise.

3.Generate a vector x representing N=1000000 BPSK equiprobable symbols.

4.Estimate the transmitted symbol x based on the received signal y = x + n.

Show the histogram of y for Es/NodB = 1 and Es/NodB = 10 (comment the

figures)

5.Compute the average error probability as the number of errors over the total

number of transmitted symbols N.

6.Repeat the steps for each value of Es/NodB and plot the corresponding P(e) in

a log scale (use the function semilogy with “blue” line). Comment the results.

What is the minimum Es/NodB to guarantee a P(e) < 10^-5? In the same

gure plot ("red" line) the theoretical P(e) of a BPSK (see slides). Comment

Dear krishna sankar sir,

could you please help me regarding the question i posted

@Manoj: The matlab code in this article should be able to address most of your queries.

@Manoj: This post (and the matlab code) on BER of BPSK in AWGN is addressing most of your queries. Good luck!

thankyou very much sir

books

could you please explain the relationship between the BER and the Eb/No and why we get this graph shape

looking for your reply

Nada

@Nada: The derivation is explained in this post

hey

How do you calculate the SNR if given bit error rate of 10^-3.

Secondly if now i am given a symbol like P which when converted to binary is equal 011. How do i calculate the snr if i need a symbol error rate of less than 10 ^-4 ??

thanks

@pawan: you can either use the visual information from the ber plot to find the minimum snr required to hit a given bit error rate. for eg, bpsk in awgn requires around 7dB of Eb/N0 to hit 10^-3 ber. One can also use the erfinv() function.

can you exaplan about curve of error performance of BPSK over AWGN and Rayleigh channel?

@ebtesam jumma: For the BPSK BER in Rayleigh channel case, please take a look at

http://www.dsplog.com/2008/08/10/ber-bpsk-rayleigh-channel/

http://www.dsplog.com/2008/08/26/ofdm-rayleigh-channel-ber-bpsk/

http://www.dsplog.com/2009/01/22/derivation-ber-rayleigh-channel/

Hi, Krishna

Would like to ask how to add attenuation to the transmitted signal?

which line of code should i edit? is it from ”y = s + 10^(-Eb_N0_dB(ii)/20)*n;”

In case if attenuation = 0.3

@vanness: Well, shouldn’t it be straightforward

attn = 0.3;

y = attn*s + 10^(-Eb_N0_dB(ii)/20)*n;

Hi Krishna,

I want to demo about DSSS spread spectrum systems by MATLAB. it’s my project

it uses modBPSK and PN

but i’m not good at matlab programming

can you help me about it ?

thankyou very very much !!

my email : phuc0605bk@gmail.com

@phucmv: sorry, wont be able to help you with the matlab programming. good luck

Hi Krishna,

In this post, it is very useful that you show the relationship between BER and SNR. Actually, I want to describe the relationship between BER and transmission distance for BPSK in AWGN channel. Please give some advices for this.

Thank you so much!!

@candy: To convert to a distance, one needs to know – Transmit power, Path loss, Receive noise power

The SNR, dB at the receiver is = Tx Power, dBm – Path Loss, dB – Rx Noise Power, dBm

The transmit power is chosen by the designer. The path loss depends on the square of the carrier frequency and square of the distance in free space. Check out http://en.wikipedia.org/wiki/Free-space_path_loss.

The receiver noise power depends on the bandwidth of the receiver. For eg, a receiver with a 20MHz bandwidth will have a thermal noise power of -174dBm/Hz + 10*log10(20e6) = -101dBm.

http://www.dsplog.com/2012/03/25/thermal-noise-awgn/

Hope this helps.

Dear Krishnan,

Thank you so much for your help!

I have another problem that I can not understand as:

I used the formula: BER = 0.5*erfc(SNR) for BPSK in AWGN channel to plot the picture which show relationship between BER and propagation distance through the relationship between SNR and distance based on free space path loss model. But I can not explain why BER can not be greater than 0.5 even the distance is increased up top very large value. I think that this result is not suitable with the fact that when BER will be increased to 1 when distance increased from 0 to infinite.

I hope you give me some advices for this.

Thanks.

@candy: well, when we flip a coin we have a 50% chance of getting the call correct.

Thank you so much!

Dear Krishnan,

Could you help me writing the code for this question.

Simulate 4-PAM (k = 2,M = 4). Pairs of bits are mapped into symbols s, where s belongs to the alphabet S = (3A, A,-A,-3A). Note that the input symbols are equiprobable, and there is no need to generate individual bits. Additive noise n is real AWGN process (same as in (1)). The input into the detector is r =s + n. The

detector finds the closest point in S to r. The average symbol SNR s = 5A square / 2. The bit SNR b = SNR s / 2. Simulate performance of this system for SNR b = 7, 8, 9, 10, 11 dB and find the symbol and bit error rates.

Your cooperation in this regard will highly be appreciated

Thanks

Anil

@Anil: Long back, I have written a post on symbol error rate for 4-PAM.

http://www.dsplog.com/2007/10/07/symbol-error-rate-for-pam/

Hope this helps.

I want the code for IEEE project of “Error correction between convolutional codes using Chaotic switching.

@megha: what is chaotic switching? the regular convolutional code with viterbi decoder is discussed in

http://www.dsplog.com/tag/viterbi

Hello Sir

I am new here and i need your help.Please give me answers of my few questions. I will be thankful to you.:

1. ip = rand(1,N)>0.5

how it generate only +1 and -1

what is the concept of using the term>0.5

2. Eb_N0_dB = [-3:10]

how the range of Eb/No is chosen and what is the need of this?

3. for ii = 1:length(Eb_N0_dB)

what is the concept of this function?

@khushi: my replies

1. rand() generates a uniformly distributed number in the range from [0 to 1). The >0.5 allows to generate a input sequence with approximately equal probabilities for 0 and 1.

Then 2*0 – 1 = -1 and 2*1 – 1 = +1

2. This is the region where the BER for BPSK modulation changes from from very high ber (>0.1) to very low ber (<10^-4)

3. To find the ber for different Eb/N0 values

Thank you very much Sir for solving my problems

One more thing I want to know that how do we know that in which range BER changes from from very high ber to very low ber.

@khushi: From the theoretical bit error rate equation

sir will u please tell me that from where I can see that equation

Hi Krishna,

Could you answer the following q’s please if you have the time? Thanks. Zoe

1. I don’t know how the following counts. Is nErr(ii) an array?

And I don’t precisely know what ‘size’ and ‘find’ functions do?

(I know ip-ipHat = 0 is no error)

nErr(ii) = size(find([ip- ipHat]),2);

2. In the following is the decimal version of EbNo getting multiplied with n, mean of the Gaussian noise? (of course then added with s, -1 or 1, depending on what was sent)

y = s + 10^(-Eb_N0_dB(ii)/20)*n

3. The following is confusing. Why two real and imaginary component Gausian functions added and normalized by inverse of “sqrt(2)”

Could you write the formula or equation it is derived from?

n=1/sqrt(2)*[randn(1,N) + j*randn(1,N)]

@Zoe:

1. nErr is the count of errors.

find() finds the index of elements which are different between ip and ipHat

size() counts the number of elements which are reported by find()

2. it is the Eb/N0 in linear scale applied to the noise voltage to produce the desired Eb/N0 ration

3. one can possibly send information on the two dimensions together. Hence we model as two randn() variables each with variance 1/2. Hence the normalization by 1/sqrt(2) on the voltage signal.

hi , iam new here i need disscision about ber performance of bpsk over awgn and rayliegh channel

@ebtesam: Please look at

http://www.dsplog.com/2008/08/10/ber-bpsk-rayleigh-channel/

http://www.dsplog.com/2007/08/05/bit-error-probability-for-bpsk-modulation/

Hi dear,

how are you.I need a help from you because I have a project and there some points i don`t understand it.

It is about the square root raised cosine pulse ,we need to plot it with different roll-off factor(B=0.25,B=0.5,B=1.

After that consider a binary antipodal signaling over an ideal AWGN channel at the normalized bit rate of 1 bit second where TB =1

x(t)=+or-p(t) +w(t)

where w(t) is an additive white gausian noise ,simulate model for this system and plot the resulting BER (B=0.5)

@Aisha: Please check out

http://www.dsplog.com/tag/pulse-shaping/

Hello Krishna Pillai,

thanks alot for the wonderful work you did here.please can i have d privilege to have your personal email address. I have something personal to email to you with respect to my undergraduate project work.Thanks.

@Arinze : Please use the email listed in http://www.dsplog.com/contact-us/

hi,

how can I plot the bpsk waveform for the sequence [1 0 1 1 0 1 0] please .

Thanks.

@Justin: If you want to pulse shape with a rectangular filter,

>>os = 4

>>x = [1 0 1 1 0 1 0];

>>xp = kron(x,ones(1,os));

>>plot(xp)

Please help me with simulating BPSK with direct-sequence spreading using m-sequence .I have tried doing the spreading and the despreading as well as noise addition but the BER vs. EbN0 curve is higher!!!! than the theoretical one ,which is the same as BPSK without spreading .

the problem could be with the addition of the noise ; I did multiply the transmitted chips by 1/sqrt(N) ,where N is spreading factor ,in order to make sure that the bit power is 1 .

Here is my code:

clear

b = 10000; % number of bits or symbols

%—————– Transmitter————–

%Message signal

ip = rand(1,b)>0.5; % generating 0,1 with equal probability

%generating m-sequence

polynomial=[6 1 0];

[pnSequence,chipIndex,N]=genPNSequence(polynomial);

signal = 2*ip-1; % BPSK modulation 0 -> -1; 1 -> 1 (polar)

mseq=2*pnSequence-1; % PN sequence in polar form

%spreading message signal ‘signal’ using pn sequence ‘mseq’,the processing gain

%’N';length of the PN sequence.

spreadedSig=zeros(1,N*b);

w=mseq’*signal;

spreadedSig=(1/sqrt(63))*reshape(w,1,N*b);

n = randn(1,N*b) ; % white gaussian noise, 0dB variance

Eb_N0_dB = [-3:10]; % multiple Eb/N0 values

for ii = 1:length(Eb_N0_dB)

% Noise addition

y = spreadedSig + 10^(-Eb_N0_dB(ii)/20)*n; % additive white gaussian noise

%despreading

q=reshape(y,N,b);

despreadedSig=q’*(mseq’);

despreadedSig= despreadedSig’;

% receiver – hard decision decoding

ipHat = real(despreadedSig)>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

% plot

close all

figure

semilogy(Eb_N0_dB,theoryBer,’b.-’);

hold on

semilogy(Eb_N0_dB,simBer,’mx-’);

%axis([-3 10 10^-5 0.5])

grid on

legend(‘theory’, ‘simulation’);

xlabel(‘Eb/No, dB’);

ylabel(‘Bit Error Rate’);

title(‘Bit error probability curve for BPSK modulation’);

end of code

So please can you check what is wrong with my code??

@Asia: I couldn’t play with the code. However, if you are getting zero BER for no noise case, it points to a scaling error.

@Krishna: Hello Krishna

I have tried the no noise case and gave me zero BER . I couldn’t figure out what is the problem with the scaling ??!! Do you have any code for spreading and despreading ?

I need the correct coe for my final project on my Bachelor degree. So I should be very grateful if you can help me with this.

pleas Mr I would like to help me to find calculation BER vs SNR when using 64DAPSK modulation with DWT-OFDM in simulation MATLAB, thanks.

@yahya: Sorry, I have not tried 64DAPSK modulation

Your article really open my eyes.

Is there anyone about calculate theory BER value of frequency selective channel in your BLOG?

Thanks,

Yushi Chen

@Fargo: Thanks. Please take a look at

http://www.dsplog.com/2008/08/26/ofdm-rayleigh-channel-ber-bpsk/

i want code on CDMA transimeter and reciver with AWGN for multi user by LLR log like ratio in receiver iterative decoding ,…….i make it but without LLR can u help me plz also i put spreader but not coded as block thx

@medo: Good luck with the assignment

I want the code for error correction between convolution codes using chaotic switching

@megha: Sorry, nothing handy

why

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/

Dear Mr. Krishna

Would you help me in my project!!!

I study this paper in IEEE for satrting my thesis in master degree. “Cross-Layer combining of adaptive Modulation and coding with truncated ARQ over wireless links” .1343909 abstract

This paper appears in: Wireless Communications, IEEE Transactions on

Issue Date: Sept. 2004

Volume: 3 Issue:5

On page(s): 1746 – 1755

but I have som misunderstand whith this paper and manye other papers like this .

The first problem is finding average SNR in mode(n).

I don’t know how can I select the average SNR in (7), (8),(15) ,…

and the second problem is ,if we select the SNR whit gama distribution in matlab for example:

gamrand(a,b)

then gama average is: ab (in gama distribution).

In fig 4, 5 ,… we have average SNR in horizontal axis and I don’t know how select from 0 to 30 db

best regards

@Zahra: Sorry, due to lack of time I wont be able to help in your project. Good luck.

Hi Krishna,

your coding’s were very useful for my simulation lab works..could you please send me the comparison of various error correcting codes for a particular modulation scheme..

@Sivaganesh: I have discussed only two error correcting codes:

a) Hamming code and decoder

http://www.dsplog.com/2009/09/29/hamming-74-code-with-hard-decision-decoding/

b) Viterbi decoder (hard and soft)

http://www.dsplog.com/tag/viterbi/

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

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/

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.

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?

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

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…

hi,i need to have m file of each modulation and the figures of error in matalb without using the order of modulation that are in matlab.

can you help me?

thankyou

@fateme: Please take a look at http://www.dsplog.com/2008/07/08/compare-bpsk-qpsk-4pam-16qam-16psk-64qam-32psk/

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/

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 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

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/

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/

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.

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,

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.

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/

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/

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

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.

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/

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

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/

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/

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.

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/

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

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

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.

The same to code of rama krishna wrote, could I modify it from BPSK to ASK. How?

Thanks for your time!

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

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?

beatiful work krishna, i wonder if you have the same simulation for QPSK in matlab…thanks

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

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

your kind guidance on MATLAB has been really a great help for MATLAB starters. hope u will continue in future too.

@vj1892: Thanks

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.

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

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/

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 [−4, 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

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,

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/

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 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

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.

Dear Krishna,

Can you little bit tell me how to simulate the Uncoded BER and ergodic capacity for webb channel using QPPM modulation.

haiiiiiii

i need Matlab code for digital modulation techniques.

plz give reply to me….plz

‘

please give help about matlab code in optimization for co channel and adjacent channel interference using ANN

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 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 (*)

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..

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

i want matlab programs for ‘BER MIMO’,thank u,please help me

@mouhamed: Please look at http://www.dsplog.com/tag/mimo

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.

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?

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 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

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 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.

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 ¯gures 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

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.

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,’b.-’);

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.-’);

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 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

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.

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. 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.

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, 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

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,

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.

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.

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.

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 .

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/

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.

Thanks a lot, man.

Was very useful.

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

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.

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 scheme….

@tommy: Sorry, no

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 everybody

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

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 kirishna pillai

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

thanks

@sam: Sorry, I do not have Simulink.

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 can you tell me how to make adaptive modulation ?

thanks

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, 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/

please simulation for BER MIMO (2,2)

@BOUHAFS: Please refer to the post

http://www.dsplog.com/2008/10/24/mimo-zero-forcing/

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?

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

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.

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

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

Ok Thanks very much krishna

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.

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

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.

first of all, thanks a lot for ur job, it´s really useful for all the DSP internet communty.

here my question, I´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, I´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.

I´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.

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?

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.

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/

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.

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.

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….

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?

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.

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?

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.

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 Pillai

Thank u. I am really happy and trying to do what u have suggested.

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.

wah ini dia data yang aku cari-cari akhirnya menemukan yang namanya BPSK

thanks yaaaaaaaaaaaaaaaa…

sip sip sip sip

@bowang: good

Bonjour

Je cherche des programmes MATLAB pour la génération des codes LDPC Quasi Ciclique

Alors si vous avez des programmes ou des liens utiles prière 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.

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?

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

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.

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 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/

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.

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.

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.

pls sumbody help me out!!!…………:(….

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.

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.

Dear Shoumi

Did you find material about calculate throughtput for a multi-hop wireless network using matlab ? Please share me if you have. I need it very much

my email: nguyenkimhieuha@gmail.com

Thank you

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 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.

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.

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.

hi

I wanna matlab simulation code for AODV routing protocol. Can you help me ….

@shoumi: Sorry, I have not worked on AODV protocol.

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.

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.

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.

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.

sdadasdad

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/200