How to detect multipath signal?

Hi everyone,

I am a new engineer just work in the real industry, so I would like to collect more experience from the real project.

I am working on the Multipath problem, but I've not done before in the University, and really do not know how to solve it.

During the discussion from the professor which I can wrote down from the pdf file (attached below). 

[B]My responsibility: how to detect multipath? [/B]

Here are what I have?

0. Choose the simplest situation that is 1 direct signal and 1 multipath signal.
1. Center frequency of the TV station: fc = 533 MHz, and bandwidth: B = 6 MHz
2. Equation for electromagnetic:  k = 2*pi/λ
3. Distance between 2 RX antennas : d1 = 10 cm (Software Define Radio with dual antenna)
4. Time delay indoor : ζ from 10 - 1000 (ns)
5. Angle θ = ± pi/2 ( everytime turn the angle pi/2 or -pi/2) (angle between RX and TX)
6. Distance between 2 RX antenna to TX antenna d2 = 4.3 km
7. Amplitude: a0 = 1        (a0 is amplitude for direct signal LOS)
                   a1 = [0 1)   (a1 is amplitude for multipath signal 1)


8. Equation for multipath: MUL = ∑ an * exp(j*(k*(x*cosθ + y*sinθ) - w( t - ζ )))

[B]I do not know I did right or wrong? But If anyone who has done this before, please confirm with me, I would appreciate so much.[/B]

and If I did not do right, how I can fix it. Please give me suggestions.

Thank you very much.
    

% *****************************************************************
%%%%%%%%%%%% here is my code and plot %%%%%%%%%%%%%%
% *****************************************************************
%% multipath with 2 signals : Direct signal (Light Of Sight) and reflected signal
clear all; %close all
f_c             = 533e6; 
speed_of_light  = 3e8 ;                         % m/s
d               = 0.01;                         % distance between 2 rx antenna 10cm
lamda           = speed_of_light / f_c;         % wave length
k               = (2 * pi) / lamda;             % notation for electro-magnetic
w               =  2 * pi * f_c;
a               = [1 1/3];                      % attenuation
x               = [-d/2  d/2];
y               = [0  0];
alpha           = [0   pi/2];                   % turn every time by (pi/2)
tau             = [0  0.1e-6];                  % time delay
t               = 0 : (pi / 100) : (pi * 1);
N_path          = length(tau);

% *****************************************************************
% %%%%%%%%%%%%%%  simple calculation %%%%%%%%%%%%%
% *****************************************************************
a0      = a(1);
a1      = a(2);
x0      = x(1);
x1      = x(2);
y0      = y(1);
y1      = y(2);
tau0    = tau(1);
tau1    = tau(2);
alpha0  = alpha(1);
alpha1  = alpha(2);

plane0 = x0 * cos(alpha0) + y0 * sin(alpha0); % 
plane1 = x1 * cos(alpha1) + y1 * sin(alpha1); % 3.417721599179047e-18

complex0 = k * plane0 - w * (t - tau0);
z_Direct_signal    = a0 * exp(j*complex0);

complex1 = k * plane1 - w * (t - tau1);
z_Reflected_signal = a1 * exp(j*complex1);

z_total            = z_Direct_signal + z_Reflected_signal;

figure, subplot(2,2,1)
plot(real(z_Direct_signal),'r')
title('Direct Signal in Real');
subplot(2,2,2)
plot(imag(z_Direct_signal))
title('Direct Signal in Imaginary');
subplot(2,2,3)
plot(abs(z_Direct_signal));
title('Magnitude of LOS');
subplot(2,2,4)
plot(angle(z_Direct_signal));
title('Phase of LOS');

figure, subplot(2,2,1)
plot(real(z_Reflected_signal),'r')
title('Reflected Signal in Real');
subplot(2,2,2)
plot(imag(z_Reflected_signal))
title('Reflected Signal in Imaginary');
subplot(2,2,3)
plot(abs(z_Reflected_signal));
title('Magnitude of Reflected');
subplot(2,2,4)
plot(angle(z_Reflected_signal));
title('Phase of Reflected');

figure, subplot(2,2,1)
plot(real(z_total),'r')
title('total Signal in Real');
subplot(2,2,2)
plot(imag(z_Reflected_signal))
title('total Signal in Imaginary');
subplot(2,2,3)
plot(abs(z_Reflected_signal));
title('Magnitude of total');
subplot(2,2,4)
plot(angle(z_Reflected_signal));
title('Phase of total');

21. Ask more questions for multipath equation