# How to detect multipath?

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).

My responsibility: how to detect multipath?

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 )))

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.

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

Thank you very much.

Matlab:
% *****************************************************************
%%%%%%%%%%%% 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');

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Related Electrical Engineering News on Phys.org
berkeman
Mentor
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)
I am used to using antenna spatial diversity to deal with multipath and ensure good RX signal levels. Your antenna spacing does not appear to be optimum to provide you spatial diversity at 500MHz. Is there a reason you are using that spacing?

berkeman,

Thank you for the reply, the list I showed above that the information I have until now. I do not know to use them all, just list them out, and try to ask everyone who have done multipath problem before can tell me that I did right or wrong? and if I did wrong or not make sense, I would like to have suggestions.

I also have sample code in the book which I purchased in Amazon, it shows the rayleigh fading solution, but they are also applied Doppler effect option. In this case, I am making the simplest situation with 1 direct signal and 1 multipath, and also no Doppler effect.

In addition, there are 3 main parameters are known, these are: θ (angle), ζ (time delay), a (amplitude).

Any other suggestions, berkeman? And if you have done different ways as I did, please share your ideas.

I am happy to discuss with you.

Thank you.

berkeman
Mentor
Hi Nate,

So what do you think the optimum spacing between RX antennas should be for the best handling of multipath issues? That doesn't exactly answer your overall question, but I think it's important for you to understand how you would design an RF system to be robust in the face of mutipath issues.

Hi Nate,

So what do you think the optimum spacing between RX antennas should be for the best handling of multipath issues? That doesn't exactly answer your overall question, but I think it's important for you to understand how you would design an RF system to be robust in the face of mutipath issues.
Hi berkeman,

The spacing between RX antennas is set up by default, it could be the best handling of multipath issues.

I know that my answers are not make sense to you. I am sorry.

I am trying to learn and trying to understand how to detect multipath signal? what lecture should I look at? That will also help me to learn and understand more about this.

jim mcnamara
Mentor
I'm trying to help.
@berkeman is trying tell you two things:
1. you are not looking at the problem in a way to allow you to learn how to do this problem.
2. you may solve some badly defined data correctly but get a poor answer.

In order to get your attention:
Poor answers are a proven way to lose jobs. Focus on problem set up first. Solution last.

Hope you got the message, you seem very earnest.

I'm trying to help.
@berkeman is trying tell you two things:
1. you are not looking at the problem in a way to allow you to learn how to do this problem.
2. you may solve some badly defined data correctly but get a poor answer.

In order to get your attention:
Poor answers are a proven way to lose jobs. Focus on problem set up first. Solution last.

Hope you got the message, you seem very earnest.
Hi jim mcnamara,

Thank you for converting the meaning of @berkeman , now I got his message. I know my codes are not right, just for the raw ideal. Therefore, I am here to ask.

And allow me to tell you my problem set up, fix me if you have chance.

GOAL: able to detect multipath.

And here is my problem set up which attached on the pdf file. Fix me if you have a chance.

Thank you.

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berkeman
Mentor
Hi berkeman,

The spacing between RX antennas is set up by default, it could be the best handling of multipath issues.

I know that my answers are not make sense to you. I am sorry.

I am trying to learn and trying to understand how to detect multipath signal? what lecture should I look at? That will also help me to learn and understand more about this.
No worries. I'm not comfortable with spacing the antennas less than optimally, but whatever. So to detect a multipath issue, you just need to set an RSSI difference threshold between the two RX antennas, right?

Baluncore
2019 Award
I am used to using antenna spatial diversity to deal with multipath and ensure good RX signal levels.
Strictly speaking, spatial diversity involves selecting one of several antennas at different times in different places to improve the reliability of reception.
To eliminate a reflection involves a phased array of antennas that are coupled to provide one signal to the receiver. The separation of the antennas in the array and the phase of coupling determines the position of the first null and so rejection of the reflection.

To receive the direct signal while rejecting the reflected signal (that has been delayed) use the following procedure.
Place two antennas Ant1 and Ant2, next to each other, separated by a distance s.
Knowing the angle of arrival of the reflection is θ from the LOS, and the centre frequency, FMHz;
Calculate; s = 150 / ( FMHz * Sin(θ) ) metres.
The direct path will be in phase and sum, while the reflection will be in anti-phase and so cancel. Strictly speaking, spatial diversity involves selecting one of several antennas at different times in different places to improve the reliability of reception.
To eliminate a reflection involves a phased array of antennas that are coupled to provide one signal to the receiver. The separation of the antennas in the array and the phase of coupling determines the position of the first null and so rejection of the reflection.

To receive the direct signal while rejecting the reflected signal (that has been delayed) use the following procedure.
Place two antennas Ant1 and Ant2, next to each other, separated by a distance s.
Knowing the angle of arrival of the reflection is θ from the LOS, and the centre frequency, FMHz;
Calculate; s = 150 / ( FMHz * Sin(θ) ) metres.
The direct path will be in phase and sum, while the reflection will be in anti-phase and so cancel.

View attachment 111103
@Baluncore : Where did get those equations? Especially, The equationtion: (lamda = 300/ Fc) ? did you mean 3*10^8 speed of light?
And also, the device that I have is B200 ettus, this one have 2 antennas with distance set up by default (10 cm). it means S=10cm. Therefore, the angle theta will be too small, about 0.00016 degree.

Last edited:
Baluncore
2019 Award
The equationtion: (lamda = 300/ Fc) ? did you mean 3*10^8 speed of light?
I specify frequency is measured in MHz.
So 3x108/Fc becomes 300/FMHz

From the geometry we have equation(1); Sin(θ) = (λ/2) / s
You know that; λ = 300x106 / Fc
Therefore equation(2) is; λ = 300 / FcMHz
Substitute equation (2) into equation (1); s = 150 / ( FcMHz * Sin θ )

Last edited:
Baluncore
2019 Award
The “B200 ettus” does not include an option of two receive antennas with 10 cm separation. It has separate receive and transmit connectors. Either you are confusing the RX and TX antenna terminals, or the two antennas come from somewhere else. A different model, the “B210 ettus” has two receive channels, but I do not know how you can combine them in phase.

I think you must get an appropriate pair of dipole antennas for the TV frequency band and mount them on a beam with the correct separation and polarisation. You must get some form of phasing harness to combine the two antenna signals in phase into one cable, to go to one receiver antenna connector.

I specify frequency is measured in MHz.
So 3x108/Fc becomes 300/FMHz

From the geometry we have equation(1); Sin(θ) = (λ/2) / s
You know that; λ = 300x106 / Fc
Therefore equation(2) is; λ = 300 / FcMHz
I specify frequency is measured in MHz.
So 3x108/Fc becomes 300/FMHz

From the geometry we have equation(1); Sin(θ) = (λ/2) / s
You know that; λ = 300x106 / Fc
Therefore equation(2) is; λ = 300 / FcMHz
Substitute equation (2) into equation (1); s = 150 / ( FcMHz * Sin θ )
Substitute equation (2) into equation (1); s = 150 / ( FcMHz * Sin θ )
@Baluncore : Assume I have that angle, delay, and amplitude. I am using the equation above with those parameters. In the simplest case, that is 1 LOS and 1 reflected signal, I can calculate:

angle_ = [0 pi/2 pi 3*pi/2]; % same set up, same angle of the reflected signal but now rotate

t = 0:1e-9:50e-9;
alpha = [0 pi/4]; % angle betweet RXs and TX
f_c = 533e6; % center freq.
speed_of_light = 3e8 ; % m/s
d = 0.1; % 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 0.5]; % attenuation/ amplitude
x = [-d/2 d/2]; % center of 2 RX
y = [0 0];
tau = [0 10e-9]; % time delay

general = zeros(1,length(t));

for i = 1:length(angle_)
% assume (1) for direct signal, (2) for multipath signal

multipath1 = a(1)*exp(j*(k*(x(1)*cos(alpha(1)+ angle_(i)) + y(1)*sin(alpha(1)+angle_(i))) - w*(t-tau(1)))); % for direct signal
multipath2 = a(2)*exp(j*(k*(x(2)*cos(alpha(2)+ angle_(i)) + y(2)*sin(alpha(2)+angle_(i))) - w*(t-tau(2)))); % for multipath signal

tot_multi = (multipath1 + multipath2);
end

Is this right or wrong?

Please give me suggestions. Thank you.

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The “B200 ettus” does not include an option of two receive antennas with 10 cm separation. It has separate receive and transmit connectors. Either you are confusing the RX and TX antenna terminals, or the two antennas come from somewhere else. A different model, the “B210 ettus” has two receive channels, but I do not know how you can combine them in phase.

I think you must get an appropriate pair of dipole antennas for the TV frequency band and mount them on a beam with the correct separation and polarisation. You must get some form of phasing harness to combine the two antenna signals in phase into one cable, to go to one receiver antenna connector.
I am sorry, I typed wrong, B210 ettus is the one I am using now. I believe that rx1 and rx2 can give you spectrum density, and from there we have phase.

Baluncore
2019 Award
During the discussion from the professor which I can wrote down from the pdf file (attached below).
Where is that file.pdf ?

The thread title “how to detect multipath?” could mean several things.
What are you trying to do?
1. To receive the direct path while rejecting the reflected path. Or;
2. To detect the presence of a multipath signal. Or;
3. To receive and demodulate a reflected signal while rejecting the direct signal.

Where is that file.pdf ?

The thread title “how to detect multipath?” could mean several things.
What are you trying to do?
1. To receive the direct path while rejecting the reflected path. Or;
2. To detect the presence of a multipath signal. Or;
3. To receive and demodulate a reflected signal while rejecting the direct signal.
@Baluncore:

Number "2" : "To detect the presence of a multipath signal" is my goal.

Because of the pdf file is too large, so I can not upload in here, therefore I broke up into single images.

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tech99
Gold Member
For the case where the multipath delay is long compared with a carrier cycle, the max and mins of the field which are noticed as the receiver is moved are spaced nearly half a wavelength apart. So receiving antennas spaced about a quarter of a wavelength provide good diversity action, as one is in a min when the other is in a max. They are well decorrelated. This is still the case when signals are arriving by several paths, as in a typical mobile environment.
For a case where the multipath delay is small, maybe less than one carrier cycle, the max and mins of the pattern are widely spaced. This is not the case with mobile systems but occurs with microwave links, where diversity antenna spacings of a hundred wavelengths or so might be found.
The performance will also depend somewhat on how the antennas are combined. For instance, they may be added via an intelligent phase shifter, or selected by a switch, or selected after demodulation. It is not possible to just connect them in parallel because it forms an array which itself still suffers from fading as the receiver moves.

• Nate Duong
tech99
Gold Member
For the case where the multipath delay is long compared with a carrier cycle, the max and mins of the field which are noticed as the receiver is moved are spaced nearly half a wavelength apart.
Clarification: successive maxima or minima are nearly half a wavelength apart.

• Nate Duong
Where is that file.pdf ?

The thread title “how to detect multipath?” could mean several things.
What are you trying to do?
1. To receive the direct path while rejecting the reflected path. Or;
2. To detect the presence of a multipath signal. Or;
3. To receive and demodulate a reflected signal while rejecting the direct signal.
@Baluncore : What do you think?

Baluncore
2019 Award
I think that; with the small fixed antenna separation you have no deep nulls in the array pattern. It is not possible to rotate the antenna array to look for a deep null of the direct signal which would identify the presence of other propagation paths.

With a compact array of antennas there is a possibility that array orientation will chance on an axis of interference pattern symmetry. I think you must change the orientation of the array while sampling the signal several times. A difference in spectral power density between channels will then identify the presence of an interference pattern.
Traditionally, cyclic switching between the two antennas or the sum and difference of the two antennas would generate a cyclic variation in the received signal power if multipath was present.

With one antenna you could autocorrelate the received signal. That would identify the time delay in the reflected path(s). You have not identified if you are applying this to analogue or digital TV signals, each of which has a time repetitive pattern that gives it a distinctive autocorrelation function. It would be deviations from the standard autocorrelation function that would be important. Echo detection of repetitive signals will pose problems. With only one antenna you would need to know what the signal format was before extracting the indirect delay information.

A RAKE receiver would need more antennas in a larger array to identify and separate multiple signals.
There are parallels with Passive RADAR here, but the target is static and so would be classed as ground clutter.
I'm still thinking.

• Nate Duong and berkeman
I think that; with the small fixed antenna separation you have no deep nulls in the array pattern. It is not possible to rotate the antenna array to look for a deep null of the direct signal which would identify the presence of other propagation paths.

With a compact array of antennas there is a possibility that array orientation will chance on an axis of interference pattern symmetry. I think you must change the orientation of the array while sampling the signal several times. A difference in spectral power density between channels will then identify the presence of an interference pattern.
Traditionally, cyclic switching between the two antennas or the sum and difference of the two antennas would generate a cyclic variation in the received signal power if multipath was present.

With one antenna you could autocorrelate the received signal. That would identify the time delay in the reflected path(s). You have not identified if you are applying this to analogue or digital TV signals, each of which has a time repetitive pattern that gives it a distinctive autocorrelation function. It would be deviations from the standard autocorrelation function that would be important. Echo detection of repetitive signals will pose problems. With only one antenna you would need to know what the signal format was before extracting the indirect delay information.

A RAKE receiver would need more antennas in a larger array to identify and separate multiple signals.
There are parallels with Passive RADAR here, but the target is static and so would be classed as ground clutter.
I'm still thinking.
@Baluncore: your suggestions are valuable for me, I hope you will have more ideas soon.
Thank you very much, Baluncore!

I think that; with the small fixed antenna separation you have no deep nulls in the array pattern. It is not possible to rotate the antenna array to look for a deep null of the direct signal which would identify the presence of other propagation paths.

With a compact array of antennas there is a possibility that array orientation will chance on an axis of interference pattern symmetry. I think you must change the orientation of the array while sampling the signal several times. A difference in spectral power density between channels will then identify the presence of an interference pattern.
Traditionally, cyclic switching between the two antennas or the sum and difference of the two antennas would generate a cyclic variation in the received signal power if multipath was present.

With one antenna you could autocorrelate the received signal. That would identify the time delay in the reflected path(s). You have not identified if you are applying this to analogue or digital TV signals, each of which has a time repetitive pattern that gives it a distinctive autocorrelation function. It would be deviations from the standard autocorrelation function that would be important. Echo detection of repetitive signals will pose problems. With only one antenna you would need to know what the signal format was before extracting the indirect delay information.

A RAKE receiver would need more antennas in a larger array to identify and separate multiple signals.
There are parallels with Passive RADAR here, but the target is static and so would be classed as ground clutter.
I'm still thinking.
@Baluncore: Can I now do the simplest case that is only direct signal (LOS), no multipath effect? then change the phase as turning the antenna around to calculate the delay via the equation from this website? http://www.sengpielaudio.com/calculator-timedelayphase.htm

That is: delta_t = phase(i) / (360 * 533MHz)

Baluncore
2019 Award
I have not found a programming manual for the Ettus B210 radio you have. I do not know how the front-end switching is arranged, or if you can use the same local oscillator for the front-end down-converters of both receive channels so the two IFs will be phase locked. Without that information it is hard to see how to proceed.
Must the antenna separation be fixed at 10 cm?
Is the transmitted TV sgnal digital or analogue?
Is it vertical or horizontal polarisation?

• Nate Duong
I have not found a programming manual for the Ettus B210 radio you have. I do not know how the front-end switching is arranged, or if you can use the same local oscillator for the front-end down-converters of both receive channels so the two IFs will be phase locked. Without that information it is hard to see how to proceed.
Must the antenna separation be fixed at 10 cm?
Is the transmitted TV sgnal digital or analogue?
Is it vertical or horizontal polarisation?
@Baluncore:
1. Must the antenna separation be fixed at 10 cm?
ans: it does not need to be 10 cm, it depends on how we set up the distance between 2 RX.
2. Is the transmitted TV signal digital or analogue?
ans: transmitted TV signal.
3. Is it vertical or horizontal polarization?
ans:horizontal polarization

Mention: This is a static situation, I say that because most the document I read in the books, pdf files ... people mentioned just only for movable cases, such as: high speed train, vehicle moving,... I think this case is much simpler than movable case, but my problems are not to understand how they look like? and I am trying to understand as much as I can.

This is attached pdf file which I am reading and I think this file almost close to what I am trying to understand.

It's only take you 2 minutes to scan it. And if you can see any ideal by your experience, could you please share with me.

Thank you very much for the reply.

Best regards,

Nate Duong.

I have not found a programming manual for the Ettus B210 radio you have. I do not know how the front-end switching is arranged, or if you can use the same local oscillator for the front-end down-converters of both receive channels so the two IFs will be phase locked. Without that information it is hard to see how to proceed.
Must the antenna separation be fixed at 10 cm?
Is the transmitted TV sgnal digital or analogue?
Is it vertical or horizontal polarisation?
@Baluncore: I hope you read it, and if so, please tell you opinion.