TIDEP-01012: Maximum Range for one Antenna (MIMO-Mode)

Andreas Baumann

Part Number: TIDEP-01012
Other Parts Discussed in Thread: AWR1243

Dear sir or madam,

I would like to compute the maximum range of the TIDEP-01012 in MIMO-Mode.From a data processing point of view the maximum range is limited to:

r_max = (c * f_sampling) / (2 * chirp_slope)

with:

c = speed of light

f_sampling = sampling frequency

chirp_slope = slope of the chirp

However, there is also an other formula to compute the maximum range:

r_max = sqrt4( (P_r * sigma * c^2 * G_r^2) / ( (4*pi)^4 * f_0^2 * P_min) )

with:

P_r = Power output of the radar [W]

sigma = radar cross section of an object, e.g. car/corner reflector [m^2]

c = speed of light [m/s]

G_r = radar antenna gain [linear]

f_0 = radar signal frequency [Hz]

P_min = minimum detectable power [W]

I wanted to ask, where could I find the related numbers for these properties?

P_r was already replied in another thread post (https://e2e.ti.com/support/sensors/f/1023/t/892866) with 20 dBm for one antenna. With P[W] ) 10^( (P[dBm]-30)/10)=0.1W

Sigma depends on the actual object and c is a constant for the speed of light.

G_r would be written in the Lua configuration script and in the AWR1243 document (chapter 5.7, https://www.ti.com/lit/ds/symlink/awr1243.pdf?ts=1604525689951) and would be equal to 48dB or 63095.7 with ratio = 10^(G_r/10)

f_0 would be the center frequency, e.g. 79 GHz

I could not find information about P_min .

Thank you very much for your help.

Best,

Andreas

over 4 years ago

0 Cesar over 4 years ago

TI__Guru*** 148654 points

Hi,

I will need a few days to get back to you

Thank you

Cesar

0 Cesar over 4 years ago in reply to Cesar

TI__Guru*** 148654 points

Hi,

Could you double check the equation:

r_max = sqrt4( (P_r * sigma * c^2 * G_r^2) / ( (4*pi)^4 * f_0^2 * P_min) )

I believe the (4*pi)^4 should be (4*pi)^3?

Regarding P_min

I checked with our systems team and we have not been explicitly computing minimum detectable power (P_min) when doing the Radar link budget.

Please see an example of Radar Link Budget computation

Does this answer your question?

Thank you

Cesar

0 Andreas Baumann over 4 years ago in reply to Cesar

Intellectual 470 points

Dear Cesar,

thank you very much! Yes, it is a typing error with the ^4. It should be ^3.

Your inputs would also answer my question and would help me a lot with the estimations. Thank you very much for checking out a solution.

All the best,

Andreas

0 Andreas Baumann over 4 years ago in reply to Cesar

Intellectual 470 points

Dear Cesar,

I tried to reproduce the given equations/figures and I was not able to do it

clear all
close all
clc

c = 299792458; % Speed of Light [m/s]
rcs = 0.1;%5.44; % Radar Cross Section [m^2]
P_tx = 10; % TX Power [dbm]
G_tx = 8; % TX Antenna Gain [dB]
G_rx = 8; % RX Antenna Gain [dB]
lambda = c/(79*10^9); % Wavelength [m]
T_chirp = 9.5*10^-5; % Chirp Duration [s]
G_Nchirps = 32; % Number of Chirps per Frame [-]
G_RXArray = 9; % Number of Antennas Gain [dB]
k = 1.38064852*10^-23; % Boltzmann Constant [m^2*kg*s^-2*K^-1]
T = 290; % Temperature [K]
N = 15; % Noise Figure [dB]
L_bumber = 3; % Bumper Loss [dB]
L_additional = 4; % other Loss [dB]
SNR_detection = 12; % Detection Signal-to-Noise-Ratio [dB]

r_max = nthroot((rcs*P_tx*G_tx*G_rx*lambda^2*T_chirp*G_Nchirps*G_RXArray)/...
                ( (4*pi)^3*k*T*N*L_bumber*L_additional*SNR_detection),4)

This would give me for

rcs=0.1m^2 a r_max of 196m instead of 29m and for

rcs=1.0m^2 a r_max of 348m instead of 52m.

Could it be that G_rxArray is not equal to the "Number of antennas gain" mentioned in the table?

Thank you very much,

Andreas

0 Cesar over 4 years ago in reply to Andreas Baumann

TI__Guru*** 148654 points

Hi,

Usually the Rx Gain is higher.

Let me check with the team that provided this information and get back to you

Thank you

Cesar

0 Cesar over 4 years ago in reply to Cesar

TI__Guru*** 148654 points

HI,

I have received the feedback on your computation

All the dB values and the dBm value need to be converted to linear units before plugging in the equations

Please see added code below

thank you
Cesar

clear all

close all

clc

c = 299792458; % Speed of Light [m/s]

rcs = 0.1;%5.44; % Radar Cross Section [m^2]

P_tx = 10; % TX Power [dbm]

G_tx = 8; % TX Antenna Gain [dB]

G_rx = 8; % RX Antenna Gain [dB]

lambda = c/(79*10^9); % Wavelength [m]

T_chirp = 9.5*10^-5; % Chirp Duration [s]

G_Nchirps = 32; % Number of Chirps per Frame [-]

G_RXArray = 9; % Number of Antennas Gain [dB]

k = 1.38064852*10^-23; % Boltzmann Constant [m^2*kg*s^-2*K^-1]

T = 290; % Temperature [K]

N = 15; % Noise Figure [dB]

L_bumber = 3; % Bumper Loss [dB]

L_additional = 4; % other Loss [dB]

SNR_detection = 12; % Detection Signal-to-Noise-Ratio [dB]

% All the dB values and the dBm value need to be converted to linear units before plugging in the equations

P_tx_watt = (10^(P_tx/10)*1e-3); % dBm to watts

num = rcs*P_tx_watt*(10^((G_tx+G_rx+G_RXArray)/10))*lambda^2*T_chirp*G_Nchirps

den = ((4*pi)^3)*k*T*(10^((N+L_bumber+L_additional+SNR_detection)/10))

r_max = nthroot(num/den,4)

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TIDEP-01012: Maximum Range for one Antenna (MIMO-Mode)