This post is the next part of our previous post Financial Calculations in MATLAB named as Implementation of Black Litterman Approach in MATLAB, so if you haven't read that then you can't understand what's going on here so, its better that you should first have a look at that post. Moreover, as this code is designed after a lot of our team effort so its not free but we have placed a very small cost of $20. So you can buy it easily by clicking on the above button.In the previous post, we have covered five steps in which we first get the financial stock data, then converted it to common currency and after that we calculated the expected returns and covariance matrix and then plot the frontiers with and without risk free rate of 3%. Now in this post, we are gonna calculate the optimal asset allocation, average return after the back test, calculation of alphas and betas of the system and finally the implementation of black-litterman approach. First five steps are explained in the previous tutorial and the next four steps for Implementation of Black Litterman Approach in MATLAB are gonna discuss in this tutorial, which are as follows:
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In this part of the problem,I calculated the optimal asset allocation in the different years by choosing a constant required return. I chose the constant required return equal to 0.01 and used the highest_slope_portfolio function and plot the graphs. The code used in MATLAB is shown in the below:
ConsRet=0.010 for w=1:10 [xoptCR(:,w), muoptCR(w), sigoptCR(w)] = highest_slope_portfolio( covmat{1,w}, ConsRet , estReturn(w,:)', stdRet(w,:) ); End
The result for this part is shown in the Figure 3. For a constant required return of 0.01, portfolio turnover for each year has increased approximately by 2%.
In this part of the assignment, it was asked to perform a back test for the optimized portfolios and calculate the average return and the standard deviation for this portfolio. Average return is the average of expected return for the corresponding year and it is calculated by the below code in MATLAB, where w is varying from 1 to 10 to calculate for all the 10 years.
BTreturn(w,:)=estReturn(w,:)*xoptCR(:,w);Results obtained after the back test for the optimized portfolios for average return are shown in table3 below:
Average Return after the back test | |
1st year | 0.1158 |
2nd year | 0.0889 |
3rd year | 0.0797 |
4th year | 0.0628 |
5th year | -0.0660 |
6th year | -0.4323 |
7th year | -5.1212 |
8th year | -0.6820 |
9th year | 0.2891 |
10th year | 0.1691 |
Table : Average return after the back test
The standard deviation of the rate of return is a measure of risk. It is defined as the square root of the variance, which in turn is the expected value of the squared deviations from the expected return. The higher the volatility in outcomes, the higher will be the average value of these squared deviations. Therefore, variance and standard deviation measure the uncertainty of outcomes. Symbolically,
BTstd(w,:)=sqrt(stdRet(w,:).^2*(xoptCR(:,w).^2));The results of standard deviation for the 10 years are as follows:
Standard Deviation after the back test | |
1st year | 0.2942 |
2nd year | 0.1833 |
3rd year | 0.1799 |
4th year | 0.1733 |
5th year | 0.4026 |
6th year | 1.5834 |
7th year | 16.1279 |
8th year | 2.1722 |
9th year | 1.0430 |
10th year | 0.4949 |
FTLC= hist_stock_data('01111993','01112013','^FTLC','frequency','m'); LRFTLC=diff(log(FTLC.Close));After that I calculated the expected return of one unit of each asset based on the model which gave me the total covariance matrix for the single and multi indexed model. Finally, I calculated the alpha and beta for the model. The MATLAB code used for performing these actions is shown below:
for i = 1:7 mdl_si{i} = LinearModel.fit(LRFTLC, logRet(:,i), 'linear'); mdl_ret_s(i) = mdl_si{i}.Coefficients.Estimate(1:2)' * [1; 12*mean(LRFTLC)]; mdl_cov_s(i) = mdl_si{i}.RMSE^2; alpha_s = [mdl_si{i}.Coefficients.Estimate(1), alpha_s]; beta_s = [mdl_si{i}.Coefficients.Estimate(2), beta_s]; endAs a result, alphas and betas of the system are obtained which are shown in the table below:
Aplha | Beta |
0.0068 | 0.1748 |
0.0057 | 0.0335 |
0.0050 | 0.0528 |
0.0063 | 0.0552 |
0.0030 | 0.0249 |
0.0035 | 0.0083 |
0.0047 | 0.0289 |
Table: Alpha & beta of the model
In this part, I have finally implemented the Black Litterman approach on the data available. Black Litterman approach involves the below steps:
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gamma = 1.9; tau = .3; for w=1:10 ind=[(w-1)*12+1 (w+10)*12]; logRet2=logRet(ind(1):ind(2),:); for i=1:7 OplogRet(:,i)=logRet2(i,:).*xoptCR(i,w)'*100; end covmatOP{1,w}=12*cov(OplogRet); end for w=1:10 Opweig(:,w)=xoptCR(:,w); Pi{w}= gamma *covmatOP{1,w}* Opweig(:,w); end figure for w=1:10 title('BL'); hold on; bar(Pi{w}) hold on; endThat's all for today, hope it will help you all in some way. If you have any questions then ask in comments and I will try my best to resolve them.
After that I calculated Expected Returns & Covariance Matrix for all these data for the last 10 years and finally plot them. Moreover, I have also plotted the frontiers with risk free rate of 3% so that the ideal and realistic conditions can be compared. So, here are the overall steps we are gonna cover in this project:
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Stocks = hist_stock_data('X', 'Y', 'Z', 'frequency', 'm')
snp500 = hist_stock_data('01111993','01112013','^GSPC','frequency','m'); NDX=hist_stock_data('01111993','01112013','^NDX','frequency','m'); GSPTSE=hist_stock_data('01111993','01112013','^GSPTSE','frequency','m'); DAX = hist_stock_data('01111993','01112013','^GDAXI','frequency','m'); CAC40=hist_stock_data('01111993','01112013','^FCHI','frequency','m'); FTAS=hist_stock_data('01111993','01112013','^FTAS','frequency','m'); SSMI=hist_stock_data('01111993','01112013','^SSMI','frequency','m');
The first two values were in US dollars, while third one was in CAD dollars, fourth and fifth values were in Euros, sixth were in GBP and the last one was in Swiss France. Hence, there was a need to convert all these currencies into one currency as instructed. I converted all of them into US dollars. In order to convert them, I first defined the exchange rate between these currencies and the US dollars using the below code:
GBP2USD=1.6; EURO2USD=1.34; CAD2USD=0.95; SF2USD=1.08;After defining the exchange rate, I applied it to all the currencies using the below code:
GSPTSE=CurrencyConvert(GSPTSE, CAD2USD); DAX=CurrencyConvert(DAX, EURO2USD); CAC40=CurrencyConvert(CAC40, EURO2USD); FTAS=CurrencyConvert(FTAS, GBP2USD); SSMI=CurrencyConvert(SSMI, SF2USD);Now all the currencies for the financial stock indices for 7 sectors are obtained in US dollars.
In this part, we calculated the expected returns and covariance matrix in annual steps for a period of 10 years. I used the data for 7 markets or sectors were obtained in the first step and calculated their expected returns and covariance matrix. The expected rate of return is a probability-weighted average of the rates of return in each scenario. We may write the expected return as:
Where,First of all, I initialized a column matrix and filled it with the above data and took log of each data separately by using MATLAB commands as follows:
covmat=cell(1,11); ret=flipud([log(SSMI.Close) log(FTAS.Close) log(CAC40.Close) log(DAX.Close) log(GSPTSE.Close) log(snp500.Close) log(NDX.Close)]);
Further, I calculated the differences between adjacent elements of each data using the diff command in MATLAB.
logRet=[diff(ret(:,1)) diff(ret(:,2)) diff(ret(:,3)) diff(ret(:,4)) diff(ret(:,5)) diff(ret(:,6)) diff(ret(:,7))];
Expected return is nothing other than a guaranteed rate of return. However, it can be used to forecast the future value of a market, and it also provides a guide from which to measure actual returns. Hence to calculate the expected return, I first take two indices with w as a variable where w = 1:10 and calculated these indices for all the values of w and finally took mean value of each data with these two indices as follows:
ind=[(w-1)*12+1 (w+10)*12]; estReturn(w,:)=[mean(logRet(ind(1):ind(2),1)) mean(logRet(ind(1):ind(2),2)) mean(logRet(ind(1):ind(2),3)) mean(logRet(ind(1):ind(2),4)) mean(logRet(ind(1):ind(2),5)) mean(logRet(ind(1):ind(2),6)) mean(logRet(ind(1):ind(2),7))];
The above values calculated for all the 10 times and hence it is placed within a for loop. estReturn gives us the estimated return for a single month and now there’s a need to convert it to annual return, which is accomplished by below command, simply by mutilpying it with 12.
estReturn(w,:)=estReturn(w,:)*12;
After the calculation of expected return annually, I used the command var(X) to calculate the variance of the data. Although it was not asked to calculate in the problem but in order to calculate the covariance, it is required to first obtain the data such that each row of the matrix becomes an observation and each column is a variable. The command used for the calculation of variance is as shown below:
stdRet(w,:)=sqrt(12*var([ logRet(ind(1):ind(2),1) logRet(ind(1):ind(2),2) logRet(ind(1):ind(2),3) logRet(ind(1):ind(2),4) logRet(ind(1):ind(2),5) logRet(ind(1):ind(2),6) logRet(ind(1):ind(2),7)]));
Finally, I used the MATLAB command cov(x) to calculate the covariance of the data. The syntax used is:
Y = cov(X)Where,
Expected Return | SSMI | FTAS | CAC40 | DAX | GSPTSE | SNP50 | NDX |
1st year | 0.0625 | 0.0373 | 0.0524 | 0.0632 | 0.0700 | 0.0848 | 0.0644 |
2nd year | 0.0954 | 0.0531 | 0.0762 | 0.0846 | 0.0884 | 0.0921 | 0.1290 |
3rd year | 0.0872 | 0.0506 | 0.0972 | 0.0940 | 0.0915 | 0.0763 | 0.1004 |
4th year | 0.0742 | 0.0457 | 0.0814 | 0.0925 | 0.0747 | 0.0610 | 0.0835 |
5th year | 0.0006 | -0.0064 | 0.0122 | 0.0147 | 0.0321 | -0.0058 | 0.0110 |
6th year | -0.0112 | 0.0007 | -0.0039 | 0.0103 | 0.0537 | -0.0055 | 0.0115 |
7th year | -0.0144 | -0.0069 | -0.0356 | 0.0115 | 0.0494 | -0.0148 | -0.0307 |
8th year | -0.0314 | -0.0034 | -0.0573 | -0.0041 | 0.0295 | -0.0048 | -0.0080 |
9th year | 0.0081 | 0.0180 | -0.0209 | 0.0359 | 0.0454 | 0.0198 | 0.0470 |
10th year | 0.0431 | 0.0529 | 0.0228 | 0.0907 | 0.0644 | 0.0575 | 0.1007 |
Table 1: Expected Returns for 10 years
Covariance Matrix for 1st year | ||||||
SSMI | FTAS | CAC40 | DAX | GSPTSE | SNP50 | NDX |
0.0334 | 0.0191 | 0.0285 | 0.0324 | 0.0168 | 0.0190 | 0.0196 |
0.0191 | 0.0201 | 0.0234 | 0.0271 | 0.0155 | 0.0169 | 0.0257 |
0.0285 | 0.0234 | 0.0434 | 0.0444 | 0.0211 | 0.0226 | 0.0380 |
0.0324 | 0.0271 | 0.0444 | 0.0609 | 0.0252 | 0.0280 | 0.0527 |
0.0168 | 0.0155 | 0.0211 | 0.0252 | 0.0268 | 0.0198 | 0.0342 |
0.0190 | 0.0169 | 0.0226 | 0.0280 | 0.0198 | 0.0234 | 0.0379 |
0.0196 | 0.0257 | 0.0380 | 0.0527 | 0.0342 | 0.0379 | 0.1411 |
Covariance Matrix for 2nd year | ||||||
SSMI | FTAS | CAC40 | DAX | GSPTSE | SNP50 | NDX |
0.0318 | 0.0179 | 0.0273 | 0.0322 | 0.0162 | 0.0185 | 0.0235 |
0.0179 | 0.0180 | 0.0213 | 0.0258 | 0.0151 | 0.0161 | 0.0269 |
0.0273 | 0.0213 | 0.0404 | 0.0427 | 0.0209 | 0.0219 | 0.0390 |
0.0322 | 0.0258 | 0.0427 | 0.0590 | 0.0255 | 0.0279 | 0.0503 |
0.0162 | 0.0151 | 0.0209 | 0.0255 | 0.0265 | 0.0193 | 0.0367 |
0.0185 | 0.0161 | 0.0219 | 0.0279 | 0.0193 | 0.0230 | 0.0394 |
0.0235 | 0.0269 | 0.0390 | 0.0503 | 0.0367 | 0.0394 | 0.1014 |
Covariance Matrix for 3rd year | ||||||
SSMI | FTAS | CAC40 | DAX | GSPTSE | SNP50 | NDX |
0.0314 | 0.0181 | 0.0280 | 0.0320 | 0.0164 | 0.0186 | 0.0237 |
0.0181 | 0.0181 | 0.0214 | 0.0261 | 0.0152 | 0.0160 | 0.0270 |
0.0280 | 0.0214 | 0.0397 | 0.0433 | 0.0212 | 0.0224 | 0.0399 |
0.0320 | 0.0261 | 0.0433 | 0.0579 | 0.0259 | 0.0282 | 0.0509 |
0.0164 | 0.0152 | 0.0212 | 0.0259 | 0.0266 | 0.0194 | 0.0371 |
0.0186 | 0.0160 | 0.0224 | 0.0282 | 0.0194 | 0.0227 | 0.0395 |
0.0237 | 0.0270 | 0.0399 | 0.0509 | 0.0371 | 0.0395 | 0.1014 |
In this part, it was asked to plot the 11 different frontiers in one figure. The concept of efficient frontier was introduced by Harry Markowitz and it is defined as if a portfolio or a combination of assets has the best expected rate of return for the level of risk, it is facing, then it will be referred as “efficient”.
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In order plot them, I used the below code in MATLAB, I used different markers for different plots so that they could be distinguished from one another quite easily. Moreover, I used the command legend in order to show the respective years for which the graphs are plotted. RF is a variable which indicate the risk-free rate and as it is asked to operate under efficient frontier that’s why risk-free rate is equal to zero.
RF=0; for w=1:10 [xopt(:,w), muopt(w), sigopt(w)] = highest_slope_portfolio( covmat{1,w}, RF, estReturn(w,:)', stdRet(w,:) ); end mker=['o' '+' '*' '.' 'x' 's' 'd' '^' '>' '<'] figure for w=1:10 plot (sigopt(w), muopt(w) ,'Marker', mker(w)); hold on; plot (0, RF, 'o'); hold on; RF_p1 = [0 sigopt(w) 2* sigopt(w)]; opt1_p = [.02 muopt(w) (2 * muopt(w) - RF) ]; line(RF_p1, opt1_p ); end legend('Year 1994', 'Year 1995', 'Year 1996', 'Year 1997','Year 1998','Year 1999','Year 2000', 'Year 2001', 'Year 2002', 'Year 2003')In this code, first of all I used highest_slope_portfolio function. This function finds the portfolio with the highest slope. Results are shown in the below figure annually:
The plot in Part (c) was about the efficient frontier with risk rate equal to zero i.e. operating in an ideal condition while in this part, it was asked to plot the same graphs but this time include a risk-free rate of 3%. Hence I used the same code as for the previous part but only this time I used RF = 0.03 as I needed to include a risk free rate of 3%. The code used in MATLAB for this part is shown below:
RF=0.03; %the risk free rate for w=1:10 [xoptRF{w}, muoptRF(w), sigoptRF(w)] = highest_slope_portfolio( covmat{1,w}, RF, estReturn(w,:)', stdRet(w,:) ); end figure for w=1:10 plot (sigoptRF(w), muoptRF(w) ,'Marker', mker(w)); hold on; plot (0, RF, 'o'); hold on; RF_p1 = [0 sigoptRF(w) 2* sigoptRF(w)]; opt1_p = [.02 muoptRF(w) (2 * muoptRF(w) - RF) ]; line(RF_p1, opt1_p ); end legend('Year 1994', 'Year 1995', 'Year 1996', 'Year 1997','Year 1998','Year 1999','Year 2000', 'Year 2001', 'Year 2002', 'Year 2003')
The result for this part i.e. after including a risk-free rate of 3% is shown in the figure below. If the Figure 1 and Figure 2 are closely examined then one can see the clear difference. When the risk-free rate was considered zero, all the expected estimate graphs were in positive direction depicting the profit annually while after adding a risk-free rate of 3%, few of the graphs went in the negative direction depicting the loss in those years. Hence adding the risk factor may cause the business to get deceased and it may even cause it to decline continuously which results in disaster.
That's all for today, in the coming post, I will calculate more financial terms like Optimal asset allocation, average return, standard deviation and much more, so stay tuned and have fun.
Before starting this project, you must have first integrated the Arduino Lilypad Library as without it you wont be abe to do this project. So, if you haven't downloaded it yet then you should read the previous post Arduino Lilypad / Nano Library for Proteus first. Lets get started with this project.
int analogPin = A0; int ledCount = 3; int ledPins[] = { 2, 3, 4}; void setup() { // loop over the pin array and set them all to output: for (int thisLed = 0; thisLed < ledCount; thisLed++) { pinMode(ledPins[thisLed], OUTPUT); } } void loop() { // read the potentiometer: int sensorReading = analogRead(analogPin); // map the result to a range from 0 to the number of LEDs: int ledLevel = map(sensorReading, 0, 1023, 0, ledCount); // loop over the LED array: for (int thisLed = 0; thisLed < ledCount; thisLed++) { // if the array element's index is less than ledLevel, // turn the pin for this element on: if (thisLed < ledLevel) { digitalWrite(ledPins[thisLed], HIGH); } // turn off all pins higher than the ledLevel: else { digitalWrite(ledPins[thisLed], LOW); } } }
In today's post, we will first simulate the Relay in a simple circuit in which when you run the simulation, the relay will automatically got activated and after that we will go in a bit detail and will control relay using a logic, i.e. when you provide +5V to it then the relay will go activated and when you give GNd then it will de-energize. I will explain it below in detail how to use it with Microcontroller. Moreover, if you are planning to work on Relay then you should also check What is a Relay and How to use it? and should also have a look at Relay Interfacing with Microcontroller using ULN2003 and finally must check this one as well Relay Control using 555 timer in Proteus ISIS.If you have any questions. related to it then ask in comments and I will try my best to reply your queries. Let's get started with designing of control relay in Proteus ISIS.
Microcontrollers Programming is difficult because usually engineers and students doesn’t have the required tools for debugging of their codes and electronic circuits, that the main reason, they got into trouble while designing projects. On the other hand, we are highly equipped withh all sorts of tools to deal with such problems and we not only design projects but also put our full effort in explaining these projects to engineers and students so that they also get technical knowledge and can easily debug or increase the projects’ technicality in future.
Note:
We have designed projects in almost every field. Embedded projects belong to different fields and if you are not master of all trades then you can’t complete in embedded fields. That’s the main reason, we have a batch of engineers in our research depart who continuously work on research new fields. We have worked on many different technologies taking from simple keypad, LCD to high complex modules such as WiFi, Ethernet etc. We have worked on many different technologies, such as:
In embedded projects, motors are normally used, especially in robotics. Without motors, its unable to drive robots. We have worked on many different motors, such as:
Apart from these motors, few motors are used in electrical projects for controlling purposes, such as:
Arduino Wifi Shield is used to connect Arduino board with Wifi. After connectivity with Wifi, one can perform many tasks using this shield. We can built a complete server on it and can also use it as a client. Server designed on an Arduino Wifi Shield are usually quite simple as it doesn’t have much processing power to support heavy server. Arduino Wifi Shield is mostly used in home automation projects where home appliances are controlled by Wifi or can also be used for security purposes. In short, it has numerous applications and is widely used.
In today’s project, we will use Arduino UNO board for programming purposes, and will interface two leds with it and then we will control these leds via an online web server. Using that online web server, we will ON and OFF these leds on command. For controlling leds from an online server, we have to design two things:
Their arrangement and pin configuration is shown in the Arduino Web Client section. We will arrange them in such a way that two leds will be mounted on the Arduino UNO shield. In web server, we will design a simple page, which will be having four buttons on it, which will be:
When someone will open this web page and will pres any of these buttons, respective task will be performed on the Leds. i.e. if someone pressed the LED 1 ON button then Led 1 present on the Arduino board will get ON and when someone press LED 1 OFF button, that Led will go OFF and same function will be performed for second led. There won’t be any connection between the hardware and that web server, the only connection will be the Wifi. The Arduino Shield must have a Wifi connection available and one sitting from across the world can control them. Now let’s discuss these two parts, one by one.
I have designed the online web server on my own site The Engineering Projects. This is a php page which I have uploaded on my web server. In order to make this page, simply follow the below steps:
Note:
#include <SPI.h> #include <WiFi.h> char ssid[] = “EvoWingle-12F3“; // your network SSID (name) char pass[] = “093B3453“; // your network password (use for WPA, or use as key for WEP) int keyIndex = 0; // your network key Index number (needed only for WEP) int status = WL_IDLE_STATUS; char server[] = “www.theengineeringprojects.com“; // name address for Google (using DNS) String location = “/Examples/data.txt HTTP/1.0“; char inString[500]; // string for incoming serial data int stringPos = 0; // string index counter byte statusLed = 0; char c; int led1 = 3; int led2 = 4; WiFiClient client; unsigned long lastConnectionTime = 0; // last time you connected to the server, in milliseconds boolean lastConnected = false; // state of the connection last time through the main loop const unsigned long postingInterval = 10*1000; // delay between updates, in milliseconds void setup() { //Initialize serial and wait for port to open: Serial.begin(9600); pinMode(led1,OUTPUT); pinMode(led2,OUTPUT); digitalWrite(led1, LOW); digitalWrite(led2, LOW); // check for the presence of the shield: if (WiFi.status() == WL_NO_SHIELD) { Serial.println(“WiFi shield not present”); // don’t continue: while(true); } // attempt to connect to Wifi network: while ( status != WL_CONNECTED) { Serial.print(“Attempting to connect to SSID: “); Serial.println(ssid); // Connect to WPA/WPA2 network. Change this line if using open or WEP network: status = WiFi.begin(ssid, pass); // wait 10 seconds for connection: delay(10000); } Serial.println(“Connected to wifi”); printWifiStatus(); Serial.println(“nStarting connection to server…”); // if you get a connection, report back via serial: if (client.connect(server, 80)) { Serial.println(“connected to server”); // Make a HTTP request: client.print(“GET “); client.println(location); client.println(“Host: theengineeringprojects.com”); // client.println(“Connection: close”); client.println(); //readPage(); }else{ Serial.println(“connection failed”); } } void loop(){ while (client.available()) { c = client.read(); Serial.write(c); CheckingStatus(); } if (!client.connected() && lastConnected) { Serial.println(); Serial.println(“disconnecting.”); client.stop(); } if(!client.connected() && (millis() – lastConnectionTime > postingInterval)) { PingRequest(); } lastConnected = client.connected(); } void PingRequest(){ if (client.connect(server, 80)) { // Serial.println(“connected to server”); // Make a HTTP request: client.print(“GET “); client.println(location); client.println(“Host: theengineeringprojects.com”); client.println(“Connection: close”); client.println(); //readPage(); lastConnectionTime = millis(); }else{ //Serial.println(“connection failed”); client.stop(); } } void CheckingStatus(){ inString[stringPos] = c; if(c == ‘*’) { statusLed = inString[stringPos - 1]; stringPos = 0; // Serial.write(statusLed); delay(500); UpdatingStatus(); // delay(500); // client.flush(); // delay(10000); //PingServer(); } stringPos ++; } void UpdatingStatus(){ if(statusLed == ’1') { digitalWrite(led1, HIGH); // Serial.write(‘OK’); } if(statusLed == ’2') { digitalWrite(led1, LOW); } if(statusLed == ’3') { digitalWrite(led2, HIGH); } if(statusLed == ’4') { digitalWrite(led2, LOW); } } void printWifiStatus() { // print the SSID of the network you’re attached to: Serial.print(“SSID: “); Serial.println(WiFi.SSID()); // print your WiFi shield’s IP address: IPAddress ip = WiFi.localIP(); Serial.print(“IP Address: “); Serial.println(ip); // print the received signal strength: long rssi = WiFi.RSSI(); Serial.print(“signal strength (RSSI):”); Serial.print(rssi); Serial.println(” dBm”); }
That’s all for today, Stay Blessed, take care. :))
Hello friends, today I am going to post a complete project designed on MATLAB named as Modelling of DVB-T2 system using Consistent Channel Frequency in MATLAB. This project is designed by our team and it involved a lot of effort to bring it into existence that's why its not free but as usual I have discussed all the details below related to it, which will help you understanding it and if you want to buy it then you can click on the Buy button shown above.
This project aims to implement a DVB-T2 (Digital Video Broadcasting for terrestrial television) system using consistent channel frequency responses. Tthe code is designed to use the same output from a channel model for different transmitter configurations so that consistency of performance results can be obtained. After that the overall project will be modified to repeat an experiment “n” times collecting data so that “x%” confidence intervals can be calculated. Historically, DVB is a project worked by more than 250 companies around Europe at first and now worldwide. DVB-T2 is the world’s most advanced digital terrestrial television (DTT) system, offering more robustness, flexibility and at least 50% more efficiency than any other DTT system. It supports SD, HD, mobile TV, or any combination thereof. The GUI for DVB-T2 parameters selection in MATLAB is shown on the left.
DVB-T2 is the second generation standard technology used for digital terrestrial TV broadcasting. As it’s a new technology so it has many fields to explore and research, and the best way of researching on any new technology is via simulations. Simulations provide an easy and efficient way to evaluate the performance of any system. For simulation purposes, MATLAB software was chosen in this thesis because of its wide range of tools and ability to show graphical results in a very appropriate form. . Further, this DVB-T2 simulation model could be extended easily to simulate DVB-H, which shares many features with DVB-T2 (only the physical layer that needs modification). The most important feature, I discussed in my simulations are:
DVB-T2 scheme can handle wide range of sub carriers from a range of 1k to 32k; these sub carriers can be fixed or mobile. In this thesis, experiments are performed on mobile transmission of signals to 4000 sub carriers. Below are discussed three different mobile scenarios, for different speeds of mobiles user, which are:
In all the scenarios, the factors mentioned below are kept constant so that a real comparison can be obtained and it could be checked that whether the speed affects the signal or not. These constant factors are:
During this thesis, help was taken from a MATLAB model of DVB-T2 transmission system designed by a student at Brunel University. First this initial model was studied and then enhanced it to a higher level. The first model designed by the student at Brunel University, performed the iterations on the DVB-T2 system and gives the results for just one cycle. Explanation of this initial model is discussed in detail below.
After the user input all the values in the GUI, this model first calculates the below three values depending on the number of subcarriers attached to the DVB-T2 system.
After getting this information, the model performs the QAM modulation over the signal so that it could be sent from the transmitter to the receiver. Next, depending on the value of Pilot Pattern given by the user, it calculates the scattered Pilot Amplitudes for the system. After that, it calculates the distortion in transmission depending on area in which the signal is propagating.
In order to calculate the distortion, FFT technique is performed on the signals to get their frequency response. As the signal has already sent from the transmitter after QAM modulation so demodulation on the receiver side is necessary. The model performs the same and demodulates the signal and finally it calculates the value of Signal to noise ratio (SNR) and Bit Error Rate (BER). At the end, it simply plots the graphs of SNR and BER for the visual representation.
Different experiments were performed on the initial model and checked its results. The results are given below for three different experiments, which are:
Results of these experiments are shown in figure 6.1, 6.2 and 6.3 respectively. Table 6.1, 6.2 and 6.3 gives the values of BER and average BER for all the values of SNR. If these three graphs are closely examined then it can be shown that the band limited impulse response increases as the speed increase and so as the BER and SNR.
The reason for such behavior is that because as the speed of the mobile increase, signal distortion also increases and it becomes difficult for the receiver to catch the signal, that’s the main reason that user travelling in high speed vehicle faces more distortion as compared to a pedestrian.
SNR | BER & Average BER |
SNR: 0 | BER:0.103833 |
SNR: 0 | NoAvrg_BER:0.160358 |
SNR: 5 | BER:0.014366 |
SNR: 5 | NoAvrg_BER:0.033706 |
SNR: 10 | BER:0.000206 |
SNR: 10 | NoAvrg_BER:0.001528 |
SNR: 15 | BER:0.000002 |
SNR: 15 | NoAvrg_BER:0.000107 |
SNR: 20 | BER:0.001543 |
SNR: 20 | NoAvrg_BER:0.002319 |
SNR: 25 | BER:0.000076 |
SNR: 25 | NoAvrg_BER:0.000184 |
SNR: 30 | BER:0.000000 |
SNR: 30 | NoAvrg_BER:0.000164 |
BER & Average BER Vs. SNR for experiment 1
SNR | BER & Average BER |
SNR: 0 | BER:0.140855 |
SNR: 0 | NoAvrg_BER:0.195596 |
SNR:5 | BER:0.046527 |
SNR:5 | NoAvrg_BER:0.071364 |
SNR:10 | BER:0.011363 |
SNR:10 | NoAvrg_BER:0.019860 |
SNR:15 | BER:0.003815 |
SNR:15 | NoAvrg_BER:0.006448 |
SNR:20 | BER:0.000604 |
SNR:20 | NoAvrg_BER:0.001222 |
SNR:25 | BER:0.000214 |
SNR:25 | NoAvrg_BER:0.000404 |
SNR:30 | BER:0.000233 |
SNR:30 | NoAvrg_BER:0.000503 |
SNR | BER & Average BER |
SNR: 0 | BER:0.128177 |
SNR: 0 | NoAvrg_BER:0.182924 |
SNR:5 | BER:0.056198 |
SNR:5 | NoAvrg_BER:0.084254 |
SNR:10 | BER:0.023229 |
SNR:10 | NoAvrg_BER:0.035131 |
SNR:15 | BER:0.006793 |
SNR:15 | NoAvrg_BER:0.010362 |
SNR:20 | BER:0.001748 |
SNR:20 | NoAvrg_BER:0.002801 |
SNR:25 | BER:0.000425 |
SNR:25 | NoAvrg_BER:0.000691 |
SNR:30 | BER:0.000354 |
SNR:30 | NoAvrg_BER:0.000515 |
BER & Average BER vs. SNR for experiment 3
Although the results given by these simulations were quite accurate but they were not accurate enough to be trusted, as they were performing the process just for one period and getting the results on the basis of that.
The initial MATLAB model is modified in this thesis, in order to use the same output from the channel model with different transmitter configurations to obtain more consistent results that can be compared with each other. Then theDVB-T2model will be modified so that it can be simulated using Matlab n times collecting data so that an x% confidence interval can be measured.
The results obtained after modifications were very consistent as they were performing the whole scenario for N times (defined by the user), this attribute lacks in the initial model as it was performing the complete task just for one cycle of time and any kind of distortion could fluctuate the results. While in modified model, the same process was performed by N times defined by the user and the results obtained are actually the average of all the cycles and hence providing a very consistent output, which couldn’t be distorted by any external factors.
Moreover, this new model further enhanced the initial model to calculate the Mean BER as it will give the overall performance of BER and average BER. Furthermore, calculates the standard BER on the basis of which global BER is also calculated.As the simulation of DVB-T2 requires a lot of input parameters from the user, that’s why a GUI is also designed in MATLAB, which makes the working of this project user friendly. User can easily change the parameters of the system using that GUI. On startup, the GUI looks like as shown in figure 4.2:
As mentioned above, taking all the other parameters constant, three experiments are performed for the mobile user moving at different speeds with different Iterations and no. of repeats, which are:
Results of the first experiment are shown in the figure 6.5, 6.6 and 6.7 respectively. While the theoretical values of BER and average BER for the corresponding SNR are shown in table 6.4 and the Mean BER and std BER are shown in table 6.5.
For N=1 | For N=2 | ||
SNR: 0 | BER:0.131272 | SNR: 0 | BER:0.131542 |
SNR: 0 | NoAvrg_BER:0.185916 | SNR: 0 | NoAvrg_BER:0.186218 |
SNR:1 | BER:0.107086 | SNR:1 | BER:0.106672 |
SNR:1 | NoAvrg_BER:0.157698 | SNR:1 | NoAvrg_BER:0.157319 |
SNR:2 | BER:0.086805 | SNR:2 | BER:0.086459 |
SNR:2 | NoAvrg_BER:0.129841 | SNR:2 | NoAvrg_BER:0.129562 |
SNR:3 | BER:0.087178 | SNR:3 | BER:0.086924 |
SNR:3 | NoAvrg_BER:0.128066 | SNR:3 | NoAvrg_BER:0.127755 |
SNR:4 | BER:0.081465 | SNR:4 | BER:0.081709 |
SNR:4 | NoAvrg_BER:0.116619 | SNR:4 | NoAvrg_BER:0.116581 |
SNR:5 | BER:0.028071 | SNR:5 | BER:0.028074 |
SNR:5 | NoAvrg_BER:0.051596 | SNR:5 | NoAvrg_BER:0.051751 |
SNR:6 | BER:0.016450 | SNR:6 | BER:0.016439 |
SNR:6 | NoAvrg_BER:0.030762 | SNR:6 | NoAvrg_BER:0.030725 |
SNR:7 | BER:0.012705 | SNR:7 | BER:0.012607 |
SNR:7 | NoAvrg_BER:0.022399 | SNR:7 | NoAvrg_BER:0.022108 |
SNR:8 | BER:0.036446 | SNR:8 | BER:0.036612 |
SNR:8 | NoAvrg_BER:0.052421 | SNR:8 | NoAvrg_BER:0.052642 |
SNR:9 | BER:0.026200 | SNR:9 | BER:0.026378 |
SNR:9 | NoAvrg_BER:0.039987 | SNR:9 | NoAvrg_BER:0.040434 |
SNR:10 | BER:0.014162 | SNR:10 | BER:0.014155 |
SNR:10 | NoAvrg_BER:0.023779 | SNR:10 | NoAvrg_BER:0.023805 |
SNR:11 | BER:0.007526 | SNR:11 | BER:0.007539 |
SNR:11 | NoAvrg_BER:0.013874 | SNR:11 | NoAvrg_BER:0.013838 |
SNR:12 | BER:0.015524 | SNR:12 | BER:0.015382 |
SNR:12 | NoAvrg_BER:0.023693 | SNR:12 | NoAvrg_BER:0.023602 |
SNR:13 | BER:0.005303 | SNR:13 | BER:0.005448 |
SNR:13 | NoAvrg_BER:0.008758 | SNR:13 | NoAvrg_BER:0.008764 |
SNR:14 | BER:0.008712 | SNR:14 | BER:0.008823 |
SNR:14 | NoAvrg_BER:0.014517 | SNR:14 | NoAvrg_BER:0.014421 |
SNR:15 | BER:0.013224 | SNR:15 | BER:0.013144 |
SNR:15 | NoAvrg_BER:0.019547 | SNR:15 | NoAvrg_BER:0.019305 |
SNR:16 | BER:0.001919 | SNR:16 | BER:0.001890 |
SNR:16 | NoAvrg_BER:0.003767 | SNR:16 | NoAvrg_BER:0.003703 |
SNR:17 | BER:0.002873 | SNR:17 | BER:0.002907 |
SNR:17 | NoAvrg_BER:0.004932 | SNR:17 | NoAvrg_BER:0.005001 |
SNR:18 | BER:0.000610 | SNR:18 | BER:0.000641 |
SNR:18 | NoAvrg_BER:0.001197 | SNR:18 | NoAvrg_BER:0.001243 |
SNR:19 | BER:0.006294 | SNR:19 | BER:0.006231 |
SNR:19 | NoAvrg_BER:0.009262 | SNR:19 | NoAvrg_BER:0.009209 |
SNR:20 | BER:0.001799 | SNR:20 | BER:0.001749 |
SNR:20 | NoAvrg_BER:0.003268 | SNR:20 | NoAvrg_BER:0.003248 |
SNR:21 | BER:0.000966 | SNR:21 | BER:0.000998 |
SNR:21 | NoAvrg_BER:0.001677 | SNR:21 | NoAvrg_BER:0.001636 |
SNR:22 | BER:0.001733 | SNR:22 | BER:0.001778 |
SNR:22 | NoAvrg_BER:0.002772 | SNR:22 | NoAvrg_BER:0.002883 |
SNR:23 | BER:0.004920 | SNR:23 | BER:0.004914 |
SNR:23 | NoAvrg_BER:0.007638 | SNR:23 | NoAvrg_BER:0.007743 |
SNR:24 | BER:0.000089 | SNR:24 | BER:0.000098 |
SNR:24 | NoAvrg_BER:0.000220 | SNR:24 | NoAvrg_BER:0.000234 |
SNR:25 | BER:0.000001 | SNR:25 | BER:0.000001 |
SNR:25 | NoAvrg_BER:0.000052 | SNR:25 | NoAvrg_BER:0.000052 |
SNR:26 | BER:0.000408 | SNR:26 | BER:0.000393 |
SNR:26 | NoAvrg_BER:0.000695 | SNR:26 | NoAvrg_BER:0.000646 |
SNR:27 | BER:0.000583 | SNR:27 | BER:0.000600 |
SNR:27 | NoAvrg_BER:0.001222 | SNR:27 | NoAvrg_BER:0.001242 |
SNR:28 | BER:0.000352 | SNR:28 | BER:0.000381 |
SNR:28 | NoAvrg_BER:0.000609 | SNR:28 | NoAvrg_BER:0.000625 |
SNR:29 | BER:0.000107 | SNR:29 | BER:0.000124 |
SNR:29 | NoAvrg_BER:0.000365 | SNR:29 | NoAvrg_BER:0.000384 |
SNR:30 | BER:0.000367 | SNR:30 | BER:0.000351 |
SNR:30 | NoAvrg_BER:0.000720 | SNR:30 | NoAvrg_BER:0.000695 |
SNR Vs. BER values for Experiment 1
Mean BER | std BER |
-0.8814 | 0.0006 |
-0.9711 | 0.0012 |
-1.0623 | 0.0012 |
-1.0602 | 0.0009 |
-1.0884 | 0.0009 |
-1.5517 | 0.0000 |
-1.7840 | 0.0002 |
-1.8977 | 0.0024 |
-1.4374 | 0.0014 |
-1.5802 | 0.0021 |
-1.8490 | 0.0001 |
-2.1231 | 0.0005 |
-1.8110 | 0.0028 |
-2.2696 | 0.0083 |
-2.0571 | 0.0039 |
-1.8799 | 0.0019 |
-2.7203 | 0.0046 |
-2.5391 | 0.0035 |
-3.2039 | 0.0151 |
-2.2033 | 0.0031 |
-2.7511 | 0.0086 |
-3.0078 | 0.0099 |
-2.7556 | 0.0079 |
-2.3083 | 0.0004 |
-4.0308 | 0.0285 |
-6.1938 | 0 |
-3.3978 | 0.0118 |
-3.2281 | 0.0086 |
-3.4365 | 0.0247 |
-3.9387 | 0.0460 |
-3.4455 | 0.0137 |
Mean BER & std BER values for Experiment 1
For N = 1 | For N = 2 | ||
SNR: 0 | BER:0.144963 | SNR: 0 | BER:0.144537 |
SNR: 0 | NoAvrg_BER:0.200382 | SNR: 0 | NoAvrg_BER:0.200617 |
SNR:1 | BER:0.103536 | SNR:1 | BER:0.103496 |
SNR:1 | NoAvrg_BER:0.153318 | SNR:1 | NoAvrg_BER:0.153312 |
SNR:2 | BER:0.081079 | SNR:2 | BER:0.081874 |
SNR:2 | NoAvrg_BER:0.123080 | SNR:2 | NoAvrg_BER:0.123966 |
SNR:3 | BER:0.056279 | SNR:3 | BER:0.056618 |
SNR:3 | NoAvrg_BER:0.096223 | SNR:3 | NoAvrg_BER:0.096636 |
SNR:4 | BER:0.070647 | SNR:4 | BER:0.070241 |
SNR:4 | NoAvrg_BER:0.103436 | SNR:4 | NoAvrg_BER:0.103023 |
SNR:5 | BER:0.063094 | SNR:5 | BER:0.063427 |
SNR:5 | NoAvrg_BER:0.089725 | SNR:5 | NoAvrg_BER:0.090577 |
SNR:6 | BER:0.020785 | SNR:6 | BER:0.021318 |
SNR:6 | NoAvrg_BER:0.039970 | SNR:6 | NoAvrg_BER:0.040469 |
SNR:7 | BER:0.024660 | SNR:7 | BER:0.024455 |
SNR:7 | NoAvrg_BER:0.040979 | SNR:7 | NoAvrg_BER:0.041170 |
SNR:8 | BER:0.032986 | SNR:8 | BER:0.032662 |
SNR:8 | NoAvrg_BER:0.052140 | SNR:8 | NoAvrg_BER:0.052100 |
SNR:9 | BER:0.023306 | SNR:9 | BER:0.022988 |
SNR:9 | NoAvrg_BER:0.037168 | SNR:9 | NoAvrg_BER:0.037283 |
SNR:10 | BER:0.009120 | SNR:10 | BER:0.008878 |
SNR:10 | NoAvrg_BER:0.017749 | SNR:10 | NoAvrg_BER:0.017499 |
SNR:11 | BER:0.023258 | SNR:11 | BER:0.023224 |
SNR:11 | NoAvrg_BER:0.034964 | SNR:11 | NoAvrg_BER:0.034473 |
SNR:12 | BER:0.023534 | SNR:12 | BER:0.023745 |
SNR:12 | NoAvrg_BER:0.034579 | SNR:12 | NoAvrg_BER:0.034325 |
SNR:13 | BER:0.000103 | SNR:13 | BER:0.000101 |
SNR:13 | NoAvrg_BER:0.000588 | SNR:13 | NoAvrg_BER:0.000648 |
SNR:14 | BER:0.000016 | SNR:14 | BER:0.000010 |
SNR:14 | NoAvrg_BER:0.000196 | SNR:14 | NoAvrg_BER:0.000231 |
SNR:15 | BER:0.000009 | SNR:15 | BER:0.000014 |
SNR:15 | NoAvrg_BER:0.000209 | SNR:15 | NoAvrg_BER:0.000240 |
SNR:16 | BER:0.001996 | SNR:16 | BER:0.002008 |
SNR:16 | NoAvrg_BER:0.003367 | SNR:16 | NoAvrg_BER:0.003535 |
SNR:17 | BER:0.002367 | SNR:17 | BER:0.002430 |
SNR:17 | NoAvrg_BER:0.003467 | SNR:17 | NoAvrg_BER:0.003535 |
SNR:18 | BER:0.000002 | SNR:18 | BER:0.000004 |
SNR:18 | NoAvrg_BER:0.000010 | SNR:18 | NoAvrg_BER:0.000018 |
SNR:19 | BER:0.001298 | SNR:19 | BER:0.001367 |
SNR:19 | NoAvrg_BER:0.002071 | SNR:19 | NoAvrg_BER:0.002116 |
SNR:20 | BER:0.009918 | SNR:20 | BER:0.009850 |
SNR:20 | NoAvrg_BER:0.014701 | SNR:20 | NoAvrg_BER:0.014585 |
SNR:21 | BER:0.000472 | SNR:21 | BER:0.000521 |
SNR:21 | NoAvrg_BER:0.000769 | SNR:21 | NoAvrg_BER:0.000854 |
SNR:22 | BER:0.001085 | SNR:22 | BER:0.001169 |
SNR:22 | NoAvrg_BER:0.001855 | SNR:22 | NoAvrg_BER:0.001917 |
SNR:23 | BER:0.001360 | SNR:23 | BER:0.001495 |
SNR:23 | NoAvrg_BER:0.002240 | SNR:23 | NoAvrg_BER:0.002427 |
SNR:24 | BER:0.000595 | SNR:24 | BER:0.000621 |
SNR:24 | NoAvrg_BER:0.001258 | SNR:24 | NoAvrg_BER:0.001321 |
SNR:25 | BER:0.000873 | SNR:25 | BER:0.000820 |
SNR:25 | NoAvrg_BER:0.001457 | SNR:25 | NoAvrg_BER:0.001422 |
SNR:26 | BER:0.000003 | SNR:26 | BER:0.000003 |
SNR:26 | NoAvrg_BER:0.000199 | SNR:26 | NoAvrg_BER:0.000201 |
SNR:27 | BER:0.000326 | SNR:27 | BER:0.000342 |
SNR:27 | NoAvrg_BER:0.000637 | SNR:27 | NoAvrg_BER:0.000651 |
SNR:28 | BER:0.000198 | SNR:28 | BER:0.000216 |
SNR:28 | NoAvrg_BER:0.000270 | SNR:28 | NoAvrg_BER:0.000262 |
SNR:29 | BER:0.000000 | SNR:29 | BER:0.000000 |
SNR:29 | NoAvrg_BER:0.000000 | SNR:29 | NoAvrg_BER:0.000000 |
SNR:30 | BER:0.000000 | SNR:30 | BER:0.000000 |
SNR:30 | NoAvrg_BER:0.000071 | SNR:30 | NoAvrg_BER:0.000078 |
SNR Vs. BER values for Experiment 2
Mean BER | Std BER |
0.8394 | 0.0009 |
0.9850 | 0.0001 |
1.0890 | 0.0030 |
1.2483 | 0.0018 |
1.1522 | 0.0018 |
1.1989 | 0.0016 |
1.6767 | 0.0078 |
1.6098 | 0.0026 |
1.4838 | 0.0030 |
1.6355 | 0.0042 |
2.0458 | 0.0083 |
1.6337 | 0.0005 |
1.6264 | 0.0027 |
3.9915 | 0.0072 |
4.8895 | 0.1323 |
4.9486 | 0.1512 |
2.6985 | 0.0018 |
2.6201 | 0.0081 |
5.5089 | 0.1569 |
2.8755 | 0.0159 |
2.0051 | 0.0021 |
3.3048 | 0.0302 |
2.9484 | 0.0231 |
2.8460 | 0.0291 |
3.2160 | 0.0133 |
3.0727 | 0.0192 |
5.4949 | 0 |
3.4765 | 0.0154 |
3.6850 | 0.0273 |
Inf | NaN |
Inf | NaN |
Mean BER and std BER values for Experiment 2
This thesis presents the design and Implementation of DVB-T2 system in MATLAB software. The basic purpose of this thesis is to check the bit error ratio (BER) and signal to noise ratio (SNR) for DVB-T2 system so that the system could be improved to a better quality. DVB-T2 system is evaluated for mobile users moving at different speeds. It is clearly shown that the mobility has an impact on the received signal, where the SNR goes to zero in some points. This behavior will generate high BER. If the figures for impulse responses are checked for all the three experiments then it is depicted that the Impulse is high for the third experiment where the mobility speed is higher than the first two experiments. The packet data loss is almost zero for the first experiment while it’s increasing in the second and is higher in the third. The number of packet lost confirms this behavior that high losses occurred in the case of high mobility.
I believe that you have installed the MPLAB Software which I have emailed to all the subscribed users on our site. If anyone didn't receive it yet then get subscribed on our site and I will email it to you. You should also have a look at these Top 3 PIC C Compilers. Now follow these steps carefully and if you feel any problem let me know in comments.
Although they provide some demo version as well which has some limit of hex size. Why MPLAB is better than MikroC or any other compiler is because it is very flexible. You can change any bit of your Microcontroller in MPLAB but this thing isn't possible in other compilers. But on the other side it also more difficult than other compilers. MikroC has builtin libraries using which you can save quite a lot of time. Suppose you wanna run LCD, then in MikroC you just need to write 2 lines but in MPLAB there will be quite a lot code lines need to be written. Here's a comparison of Top 3 PIC C Compilers. So, anyways its just a little comparison, now lets come back to our tutorial and start with Installation of MPLAB C Compiler.