AWR2243BOOST: Power Received Calculation.

Ajit Yadav

Prodigy 110 points

Part Number: AWR2243BOOST
Other Parts Discussed in Thread: AWR2243

Tool/software:

Hello,

I am calculating Pr for a corner reflector with rcs 10 m2.

Chirp Config:

c_ms = 299792458; % Speed of light in m/s

sigma_dbsm = 10; % RCS in dBsm

fc = 77e9; % Carrier frequency in Hz

Pt_dBm = 13; % Transmitted power in dBm

Gt_dB = 10.85; % Transmitter gain in dB

Gr_dB = 10.85; % Receiver gain in dB

R_m = 3.2217; % Range in meters

Ramp_End_Time = 88.07e-6; % Ramp end time in seconds

ADC_Start_Time = 6.4e-6; % ADC start time in seconds

Nc = 255; % Number of chirps

NF_dB = 13; % Noise figure in dB

RX_gain_dB = 94; % Receiver gain in dB (Seen in Post processing Data)

So these are the config i used and on right is the output i got.
Pr what i am getting is -66.801 dBFS which is far from the fft output.What could be the reason behind it?

I am using this formula for calculation.
I have doubt regarding the value of Gr, Gt values. Where to get these values for awr2243?

what i did is, take value from this graph as 10.85 db for both antenna gain.Please correct me if i am wrong.

Also after post processing the Rx gain that is showing is 94 db.(I have kept it as 30db in chirp config which can be seen in above fig)
How is it even possible when what max Rx gain possible for awr2243 radar is 52db as mentioned in data sheet.

Lastly the values i put in that equation are in units respectively:

c_ms = 299792458; % Speed of light in m/s

sigma_dbsm in m2

fc = 77e9; % Carrier frequency in Hz

Pt_in Watt

Gt in linear scale

Gr in linear scale

R_m = 3.2217; % Range in meters

Ramp_End_Time = 88.07e-6; % Ramp end time in seconds

ADC_Start_Time = 6.4e-6; % ADC start time in seconds

Correct me if any unit conversion is to be needed.

Regards,
Ajit

over 1 year ago

0 Aydin Kiasat over 1 year ago

TI__Expert 5461 points

Hi Ajit,

I went through the same calculation with your parameters and my theoretical received power comes to ~-45 dBFS which is very close to your measurement. A couple of points I would like to highlight is the rxGain measurement (94) that is shown in the studio should not be in dB. This number is in decimal and it is the addition of Rx gain and RF gain target in binary. In this case, if we add (0001 1110)+(0100 0000) = (0101 1110)-> (94). To understand this in detail, you could refer to the Interface Control Document, search for "PF_RX_GAIN".

Second point is, when we are calculating for the received power, we also need to consider additional loss due to antenna transition loss. In addition to that, if you are looking at real data, there is a 13 dBm conversion factor that you will need to account in your calculation. Please refer to the following link to read more about it /cfs-file/__key/communityserver-discussions-components-files/1023/RadarStudio_5F00_matlab_5F00_scaling-_2800_2_2900_.pdf

It might take some experimentation to get the right angle of elevation. Please refer to the following parameters I used to calculate the power in the following table.

Regards,

Aydin

0 Ajit Yadav over 1 year ago in reply to Aydin Kiasat

Prodigy 110 points

Hi Aydin,

Thanks for doing the calculations. I have doubt regarding the value of Gt and Gr as in mmWave sensing estimator the values taken by default is 7 db(see fig below).

And i have taken the Gt as 10.85 dbi from the AWR2243 userguide.

So which value is to be taken as Gt and Gr, please provide an explanation if any.

Also regarding the calculations you did, can you please share the exact formula like where to use the ant loss value -4db.
Because from the formula i am using i still get -57.7234206693 dbm.

1.68911e-9 after linear calculation, then i convert it to dbm.
Also while substituting the rcs value in formula we put it in m2 right?(correct me if wrong).

Regards,
Ajit

0 Aydin Kiasat over 1 year ago in reply to Ajit Yadav

TI__Expert 5461 points

Hi Ajit,

I am following up internally on the 7dB that is fixed in the calculator so please give me some time to get back to you on that. Please use the 10.85dB from the HFSS simulation and that is what I used in the calculation.

Regarding your question on 4dB loss, there is not a specific equation, and this is just an approximation for package to antenna transition and PCB loss that we account for. Typically, we add 1.5dB-2dB of loss each way, so that is where the 4dB is coming from.

That is correct, the RCS would be 10 square meters. Please check the numbers in the linear value calculations or type it here so I can compare your values in the equation.

Regards,

Aydin

0 Ajit Yadav over 1 year ago in reply to Aydin Kiasat

Prodigy 110 points

Hi Aydin,

I am sharing you the matlab code for Pr calculation and the studio output is Pr = -47.487 dBFS.

function Pr_dBFS = radar_power_received()

% Constants

Kb = 1.38e-23; % Boltzmann constant in J/K

T = 290; % System temperature in K

sigma_dbsm = 10; % RCS in dBsm

Pt_dBm = 13; % Transmitted power in dBm

Gt_dB = 10.85; % Transmitter gain in dB

Gr_dB = 10.85; % Receiver gain in dB

R_m = 4.2163; % Range in meters

rangeFFTSize = 242; % Range FFT size/no. of samples

DopplerFFTSize = 255; % Doppler FFT size/no. of chirps in frame

Rx = 30; %receive Gain in dB

% Convert dB values to linear scale

Pt = 10^((Pt_dBm - 30) / 10); % Convert dBm to Watts

Gt = 10^(Gt_dB / 10);

Gr = 10^(Gr_dB / 10);

sigma = 10^(sigma_dbsm / 10);

% Wavelength calculation

c_ms = 299792458; % Speed of light in m/s

fc = 77e9; % Carrier frequency in Hz

lambda_m = c_ms / fc; % Wavelength in meters

% Calculate received power in linear scale

Pr = Pt * Gr * Gt * lambda_m^2 * sigma / ((4 * pi)^3 * R_m^4);

% Convert received power to dBm

Pr_dBm = 10 * log10(Pr) + Rx;

% Convert received power to dBFS

dBmTodBFs_conversion = -10;

% Pr_dBFS = Pr_dBm + dBmTodBFs_conversion - 4 + 10 * log10(rangeFFTSize) + 10 * log10(DopplerFFTSize);

% Pr_dBFS = Pr_dBm +13-4;

Pr_dBFS = Pr_dBm + dBmTodBFs_conversion - 4; %here 4 is compensated for antenna loss

% Display results

fprintf('Received Power (linear): %e W\n', Pr);

fprintf('Received Power (dBm): %f dBm\n', Pr_dBm);

fprintf('Received Power (dBFS): %f dBFS\n', Pr_dBFS);

end

% Call the function to calculate and display the received power

Pr_dBFS = radar_power_received();

% REPRESENT COMMENTED OUT JUST FOR REFERENCE

The output from this code is Received Power (linear): 7.133528e-10 W
Received Power (dBm): -61.466957 dBm
Received Power (dBFS): -75.466957 dBFS

As you can see it is far from what is needed.

The formula which i got from trail and error method that leads to studio output is

Pr_dBm = 10 * log10(Pr) + Rx;

dBmTodBFs_conversion = 13 ;

Pr_dBFS = Pr_dBm + dBmTodBFs_conversion - 4; %here 4 is compensated for antenna loss

So the output from this comes out to b e -47.53 which matches with studio output. But here the dbm to dbfs conversion needed to be subtracted right instead of that i added the same and got the correct answer.

What may be the reason for this?

Rectify any part of this code and if possible please give an explanation for the same.

Regards,
Ajit

0 Aydin Kiasat over 1 year ago in reply to Ajit Yadav

TI__Expert 5461 points

Hi Ajit,

I edited the code you could check it in the bottom. Distance in the measurement shows less then 4 meters, so changed the range to about 3.4m. Please note that the -4dB antenna loss should be multiplied in your main received power calculation as shown in below to account for the loss. In addition, when converting from dBm to Watts, there should be a factor of 1mW in the denominator which I did not find and added it the main power equation. Finally, you will need to add the receiver gain back while subtracting the conversion factor, line 32.

function Pr_dBFS = radar_power_received()
% Constants
Kb = 1.38e-23; % Boltzmann constant in J/K
T = 290; % System temperature in K
sigma_dbsm = 10; % RCS in dBsm
Pt_dBm = 13; % Transmitted power in dBm
Gt_dB = 10.85; % Transmitter gain in dB
Gr_dB = 10.85; % Receiver gain in dB
R_m = 3.4; % Range in meters
Antenna_LOSS = -4; %Antenna Loss
%rangeFFTSize = 242; % Range FFT size/no. of samples
%DopplerFFTSize = 255; % Doppler FFT size/no. of chirps in frame
Rx = 30; %receive Gain in dB
% Convert dB values to linear scale
Pt = 10^((Pt_dBm - 30) / 10); % Convert dBm to Watts
Gt = 10^(Gt_dB / 10);
Gr = 10^(Gr_dB / 10);
sigma = 10^(sigma_dbsm / 10);
% Wavelength calculation
c_ms = 299792458; % Speed of light in m/s
fc = 77e9; % Carrier frequency in Hz
lambda_m = c_ms / fc; % Wavelength in meters
%Antenna Loss
AL = 10^(Antenna_LOSS / 10);
% Calculate received power in linear scale
Pr = Pt * Gr * Gt * lambda_m^2 * AL * sigma / ((4 * pi)^3 * R_m^4)*1000;
% Convert received power to dBm
Pr_dBm = 10 * log10(Pr);
% Convert received power to dBFS
%dBmTodBFs_conversion = -10;
%Pr_dBFS = Pr_dBm + dBmTodBFs_conversion - 4 + 10 * log10(rangeFFTSize) + 10 * log10(DopplerFFTSize);
Pr_dBFS = Pr_dBm -13+ Rx;%Subtracting conversion factor and adding 30dB RX receiver gain
%Pr_dBFS = Pr_dBm + dBmTodBFs_conversion - 4; %here 4 is compensated for antenna loss
% Display results
fprintf('Received Power (linear): %e W\n', Pr);
fprintf('Received Power (dBm): %f dBm\n', Pr_dBm);
fprintf('Received Power (dBFS): %f dBFS\n', Pr_dBFS);

% Call the function to calculate and display the received power
Pr_dBFS = radar_power_received();

% REPRESENT COMMENTED OUT JUST FOR REFERENCE

The output from this code is Received Power (linear): 6.716062e-07 W
Received Power (dBm): -61.728853 dBm
Received Power (dBFS): -44.728853 dBFS
end

Regards,

Aydin

0 Aydin Kiasat over 1 year ago in reply to Ajit Yadav

TI__Expert 5461 points

Ajit,

Regarding the 7dBi antenna gain shown in the estimator, I've confirmed this is an error from the estimator and we are working to fix it. The correct plot is the HFSS simulation of the antenna pattern as you have attached, and it is found in the user's guide.

Regards,

Aydin

0 Ajit Yadav over 1 year ago in reply to Aydin Kiasat

Prodigy 110 points

Hi Aydin,

A big thanks to you.All of your responses were helpful.

Regards,

Ajit

0 Ajit Yadav over 1 year ago in reply to Ajit Yadav

Prodigy 110 points

Hi Aydin,

Pt = 10^((Pt_dBm - 30) / 10); % Convert dBm to Watts

This is the conversion from dbm to watt, here 30 is compensated for the milliwatt right?
So, still do we need to multifply 1000 in the denominator?

Regards,

Ajit

+1 Aydin Kiasat over 1 year ago in reply to Ajit Yadav

TI__Expert 5461 points

Hello Ajit,

A correction here, I am not sure why you were subtracting 30. That expression should be divided by 1000 to get the answer in Watts. When calculating the Received power, we want the answer to be in mW for simplicity of converting back to dBm if it makes sense. Please check the following edit.

function Pr_dBFS = radar_power_received()
% Constants
Kb = 1.38e-23; % Boltzmann constant in J/K
T = 290; % System temperature in K
sigma_dbsm = 10; % RCS in dBsm
Pt_dBm = 13; % Transmitted power in dBm
Gt_dB = 10.85; % Transmitter gain in dB
Gr_dB = 10.85; % Receiver gain in dB
R_m = 3.4; % Range in meters
Antenna_LOSS = -4; %Antenna Loss
%rangeFFTSize = 242; % Range FFT size/no. of samples
%DopplerFFTSize = 255; % Doppler FFT size/no. of chirps in frame
Rx = 30; %receive Gain in dB
% Convert dB values to linear scale
Pt = 10^((Pt_dBm) / 10)/1000; % Convert dBm to Watts
Gt = 10^(Gt_dB / 10);
Gr = 10^(Gr_dB / 10);
sigma = 10^(sigma_dbsm / 10);
% Wavelength calculation
c_ms = 299792458; % Speed of light in m/s
fc = 77e9; % Carrier frequency in Hz
lambda_m = c_ms / fc; % Wavelength in meters
%Antenna Loss
AL = 10^(Antenna_LOSS / 10);
% Calculate received power in linear scale
Pr = Pt * Gr * Gt * lambda_m^2 * AL * sigma / ((4 * pi)^3 * R_m^4)*1000;
% Convert received power to dBm
Pr_dBm = 10 * log10(Pr);
% Convert received power to dBFS
%dBmTodBFs_conversion = -10;
%Pr_dBFS = Pr_dBm + dBmTodBFs_conversion - 4 + 10 * log10(rangeFFTSize) + 10 * log10(DopplerFFTSize);
Pr_dBFS = Pr_dBm -13+ Rx;%Subtracting conversion factor and adding 30dB RX receiver gain
%Pr_dBFS = Pr_dBm + dBmTodBFs_conversion - 4; %here 4 is compensated for antenna loss
% Display results
fprintf('Received Power (linear): %e W\n', Pr);
fprintf('Received Power (dBm): %f dBm\n', Pr_dBm);
fprintf('Received Power (dBFS): %f dBFS\n', Pr_dBFS);

% Call the function to calculate and display the received power
Pr_dBFS = radar_power_received();

Regards,

Aydin

0 Ajit Yadav over 1 year ago in reply to Aydin Kiasat

Prodigy 110 points

Hi Aydin,

Almost all of my doubts are cleared.
Thankyou!

Regards,
Ajit

+1 Aydin Kiasat over 1 year ago in reply to Ajit Yadav

TI__Expert 5461 points

Hi Ajit,

Glad it helped. I will close this thread and discuss with you on your other SNR topic.

Regards,

Aydin

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AWR2243BOOST: Power Received Calculation.