MATLAB Programming Language Tutorial

This MATLAB programming language tutorial covers the basics of MATLAB, including how to start and quit MATLAB, flow control, matrices, arrays, arithmetic operators, matrix operations, the load function, the save function, plotting functions, scripts and functions in MATLAB, and a sample MATLAB program.

MATLAB Introduction

This section covers the basics of MATLAB, including the benefits and applications of MATLAB.

Basics of MATLAB

MATLAB is a scientific numerical analysis programming language widely used for mathematical algorithm development requiring complex operations. It’s developed by Mathworks Inc. (www.mathworks.com).

The strengths of MATLAB lie in matrix operations, data manipulation, plotting, and interfacing with other programming languages (FORTRAN, Java, C, C++). GUIs can also be built with MATLAB GUI tools for easy user interaction with the backend MATLAB code.

In this MATLAB programming tutorial, we’ll go through MATLAB programming syntax and a sample MATLAB program.

MATLAB Work Environment

This section covers how to start and quit MATLAB, load/save operations, plots/figures, scripts and functions, and creating and working with arrays, vectors, and matrices.

How to Start and Quit MATLAB

You can start MATLAB either using the shortcut icon created during installation or from program files.

Once MATLAB opens, a window with the following sub-windows will appear:

1. Command window
2. Workspace
3. Command history
4. Menu/icons

To exit MATLAB, type quit in the command window or go to File > EXIT MATLAB.

Load/Save Operation

To save MATLAB workspace variables with a .mat extension, use either of the following:

• File > Save
• Save function

To save in any other format, use a proper extension other than .mat, such as .dat.

Syntax for the Save function:

• save filename -> Used to save all the workspace variables to the file specified by filename.
• save filename var1 var2 -> Used to save var1 and var2 to the file filename.
• save ... option -> Used to save with the specified option.

To load MATLAB variables from a file to the MATLAB workspace, use either of the following:

• File > Import Data
• load function

Syntax for the load function:

• load filename -> Loads all the variables from the file to the MATLAB workspace.
• load filename X Y Z -> Loads variables X, Y, and Z from the file filename.

Plots and Figures, Creating Simple 2D Plots

figure and plot are the functions used for plotting variables on x, y, z coordinates based on need.

plot is used for 2D plotting, and plot3 is used for 3D plotting.

mesh and meshc are useful functions for plotting in 3D.

Script and Functions

There are two ways .m files are created for different applications.

A script is a set of commands stored as a .m file. It executes all the commands stored in the sequence when the user calls the .m file by its name.

Scripts don’t take or return any arguments and operate mainly on the data available in the MATLAB workspace.

MATLAB functions can take and return arguments. Local variables are also defined, which will be local to the respective function. Global variables can be defined in the main .m file.

Just type help in the command prompt or help function_name to get a detailed description of the command or function to use.

Operators and Built-in Functions

This section covers Arithmetic Operators, Relational Operators, Logical Operators, Built-in functions, and Input and Output in MATLAB.

Arithmetic Operators:

• + Add
• - Subtract
• * Multiply
• / Divide
• \ Left division
• ^ Power or exponent
• ' Complex conjugate transpose
• ( ) Evaluation Order in an expression

Relational Operators:

• < Less than
• <= Less than or equal
• > Greater than
• >= Greater than or equal
• == Equal
• ~= Not equal

Logical Operators:

• & Logical AND
• | Logical OR
• ~ Logical complement (NOT)
• xor Exclusive OR

Built-in Functions:

There are built-in MATLAB functions for various matrix operations, such as:

• reshape
• sum
• rot90
• transpose
• diag
• fliplr
• flipud

Control Flow in MATLAB

This section covers the while loop, if-elseif-else statement, and for loop.

If Statement

if cond==1
    M = sum(a,b)
elseif cond==2
    M = multiply(a,b)
else
    M = divide(a,b)
end

Switch Statement

switch (cond)
    case 1
        M = sum(a,b)
    case 2
        M = multiply(a,b)
    case 3
        M = divide(a,b)
    otherwise
        error('This is impossible')
end

For Loop

for i = 1:m
    for j = 1:n
        H(i,j) = 1/(i+j);
    end
end

While Statement

i=0;
while cond1 > cond2
    i= i+1;
end

continue and break statements are also used similarly as they are used in the C programming language.

Matrices and Vectors

This section covers creating matrices and vectors, indexing matrices, initializing and reshaping, and manipulation of matrices.

Matrices and Array

A = [1 2 3; 5 6 7; 9 10 11; 13 14 15];

This will store A as a matrix in the MATLAB workspace, a 4 x 3 matrix (4 rows and 3 columns), as shown below:

1    2    3
5    6    7
9   10   11
13  14   15

A(i,j) will extract the element at the ith row and jth column. For example, A(2,2) equals 6. A(:,1) represents all the rows of the 1st column. A(2:3,2) represents the 2nd and 3rd rows of the 2nd column.

A matrix with a single row is called an array. The following is an example of array A with 5 elements:

A=[1 2 3 4 5];

Matrix Operations

• A+B -> Addition of two matrices
• A-B -> Subtraction of two matrices
• A*B -> Multiplication of two matrices
• A.*B -> Element-wise multiplication of two matrices
• A/B -> Right Division of two matrices. The result of B/A is equal to the result of B*inv(A)
• A./B -> Array Right Division. A and B should be of the same size.
• A\B -> Left Division of two matrices. The result of A\B is equal to the result of inv(A)*B.
• A.\B -> Array Left Division. A and B should be of the same size.
• x^P -> If x is a scalar and P is a matrix, x^P is x raised to the matrix power P using eigenvalues and eigenvectors. If both are matrices, it will result in an error.
• A.^B -> Array power
• A' -> Transpose of the matrix
• A.' -> Array transpose

length and size functions will give the dimensions of the matrix/array.

Structure and Cell in MATLAB

This section covers Creating/Manipulating structures and Creating/Manipulating cells.

A structure will have several fields; the fields will have different types of data. A single field must contain data of the same type. We will see an example of the structure named Springsem with fields course and score, as shown below:

Springsem.course = 'MS';
Springsem.score = [70 80 90];

Typing the following at the command prompt will produce all the fields of the structure.

>>Springsem

Springsem =
    course: 'MS'
    score: [70 80 90]

A cell is the most versatile data object in MATLAB. It can contain any type of data, for example, arrays, strings, structures, or cells. Let us create a cell as mentioned below.

C=cell(2,2);                                   % create  2 by 2 cell % cell(2) will do the same
C(1,1) = rand(2);                      % Put a 2x2 random matrix in the 1st box
C(1,2) = char('mohan','john');           % put a string array in the 2nd box
C(2,1) = Springsem;                             % put a structure in the 3rd box
C(2,2) = cell(2,2);                    % put a 2x2 cell in the 4th box

Sample Large MATLAB Program

This section covers an example of a large MATLAB program using multiple .m files.

This program adds various impairments (AWGN, frequency offset, Rayleigh channel, and DC offset) to the ideal modulated data and plots the constellation diagram.

• main.m -> Main MATLAB file
• frequency_offset.m -> Will incorporate frequency offset to the input vector
• wimax_mapping.m -> Will convert the input binary vector to the complex data output based on the modulation scheme selected

Run the main.m file to see the results.

% -----------------------------------------------------main.m function------------------------------------------------
len=input('Enter the length of the payload:');
mod=input('Enter 1 for bpsk, 2 for qpsk, 4 for 16qam, 6 for 64qam:');
if mod==1
    c1=sqrt(1);
elseif mod==2
    c1=sqrt(1/2);
elseif mod==4
    c1=sqrt(1/10);
elseif mod==6
    c1=sqrt(1/42);
else
    printf('wrong entry');
end

%This part will generate binary vector as per length entered by user
data=floor(rand(1,len)+0.5);

%Mapping of binary data
mapper_out=wimax_mapping(data',mod,c1);
figure;plot(real(mapper_out),imag(mapper_out),'r+');title('ideal constellation');

%Adding AWGN
snr=input('Enter SNR:');
map_out_awgn=awgn(mapper_out,snr,'measured');
figure;plot(real(map_out_awgn),imag(map_out_awgn),'r+');title('constellation with Added AWGN');

%Adding Frequency Offset
foff=input('Enter Frequency offset:');%= 10e3; % Hz
foff=(foff)/20e6;   % 20MHz is the Bandwidth of the system
map_out_foff=frequency_offset(mapper_out,foff);
figure;plot(real(map_out_foff),imag(map_out_foff),'r+');title('constellation with Frequency offset');

%Adding Rayleigh channel
choice=input('Enter 1 to apply the channel, other no. to bypass:');%10 Hz;sample time=0.1e-3;
if(choice==1)
    ts=(256/4e6);
    doppler=0.1;
    tau=[0.0 0.4 0.9];
    pdb=[0 -15 -20];
    chan = rayleighchan(ts,doppler,tau,pdb);
    %TS is the sample time of the input %0.1e-3; %signal, in seconds.  FD is the maximum Doppler shift, in Hertz. %100 Hz
    map_out_chl=filter(chan,mapper_out);
    figure;plot(real(map_out_chl),imag(map_out_chl),'r+');title('constellation with channel');
else
    disp('no channel applied proceed to DC offset');
end

%Adding DC offset
DCO=input('Enter DC offset:');  %2.5; %map_out_dc= (real(mapper_out)+DCO) +i*(imag(mapper_out)+DCO);
map_out_dc= mapper_out* DCO;
figure;plot(real(map_out_dc),imag(map_out_dc),'r+');title('constellation with DC offset');

% figure;plot(abs(fft(mapper_out,256)));title('spectrum ideal');
% figure;plot(abs(fft(map_out_dc,256)));title('spectrum with DC offset');
matlab
% ----------------------------frequency_offset.m function ------------------
function [d1] = frequency_offset(d1,CFO)
m = length(d1);
d1 = d1.*exp(1i*2*pi*(0:m-1)*CFO);
matlab
%---------------------------- wimax_mapping.m function-----------------------
function [map_out]=wimax_mapping(data,mode,fact)
input_seq = data;

switch mode
    case 1
        b=fact*[1 -1];
    case 2
        b=fact*[1+1i -1+1i 1-1i -1-1i];
    case 4
        b=fact*[1+1i 1+3i 1-1i 1-3i 3+1i 3+3i 3-1i 3-3i -1+1i -1+3i -1-1i -1-3i -3+1i -3+3i -3-1i -3-3i];
    case 6
        b=fact*[3+3i 3+1i 3+5i 3+7i 3-3i 3-1i 3-5i 3-7i 1+3i 1+1i 1+5i 1+7i 1-3i 1-1i 1-5i 1-7i 5+3i 5+1i 5+5i 5+7i 5-3i 5-1i 5-5i 5-7i 7+3i 7+1i 7+5i 7+7i 7-3i 7-1i 7-5i 7-7i -3+3i -3+1i -3+5i -3+7i -3-3i -3-1i -3-5i -3-7i -1+3i -1+1i -1+5i -1+7i -1-3i -1-1i -1-5i -1-7i -5+3i -5+1i -5+5i -5+7i -5-3i -5-1i -5-5i -5-7i -7+3i -7+1i -7+5i -7+7i -7-3i -7-1i -7-5i -7-7i];
    otherwise
        error('wrong choice');
end

count=1;
count1=1;
for i=1:(ceil(length(input_seq)/mode))
    temp=0;
    for j=1:mode
        temp=bitor(temp,bitshift(input_seq(count),(j-1)));
        count=count+1;
        if(count>length(input_seq))
            break;
        end
    end
    map_out(count1)=b(temp+1);
    count1=count1+1;
end