Range Estimation

Range Estimation Overview

Radar determines the range of the target by measuring the trip time of the electromagnetic signal it radiates. It is known that EM wave travels at a known speed (300,000,000 m/s), so to determine the range the radar needs to calculate the trip time. How?

Answer : By measuring the shift in the frequency.

Range Estimation Equation

The FMCW waveform has the characteristic that the frequency varies linearly with time. If radar can determine the delta between the received frequency and hardware’s continuously ramping frequency then it can calculate the trip time and hence the range. We further divide Range estimate by 2, since the frequency delta corresponds to two way trip.

It is important to understand that if a target is stationary then a transmitted frequency and received frequency are the same. But, the ramping frequency within the hardware is continuously changing with time. So, when we take the delta (beat frequency) between the received and ramping frequency we get the trip time.

Here, f_b is the beat frequency, which is measured by the radar by subtracting the received frequency from the hardware’s ramping frequency:

As seen in the equation, the range calculation requires chirp time T_s and chirp Bandwidth B_{sweep} . Those values are determined as we define the configuration of the radar based on its range resolution and trip time for Radar’s maximum range.

System Level Range Calculation

As seen in the image above, the Synthesizer generates FMCW chirp for a given B_{sweep} and T_s . Let’s say the signal gets transmitted at 77GHz and it returns to the radar after hitting the target in a certain time duration. The radar receiver captures the signal, processes (subtraction) and measures the frequency delta between received signal and linearly ramping signal. This delta in frequency is called as beat frequency and it is proportional to the trip time. So based on the equation above, the radar calculates the range.

Range Estimation Exercise

Using the following MATLAB code sample, complete the TODOs to calculate the range in meters of four targets with respective measured beat frequencies [0 MHz, 1.1 MHz, 13 MHz, 24 MHz].

You can use the following parameter values:

• The radar maximum range = 300m
• The range resolution = 1m
• The speed of light c = 3*10^8

Note : The sweep time can be computed based on the time needed for the signal to travel the maximum range. In general, for an FMCW radar system, the sweep time should be at least 5 to 6 times the round trip time. This example uses a factor of 5.5:

T_{chirp} =5.5\cdot 2 \cdot R_{max}/c
​

Print your answer using the disp function.

% TODO : Find the Bsweep of chirp for 1 m resolution


% TODO : Calculate the chirp time based on the Radar's Max Range


% TODO : define the frequency shifts 


% Display the calculated range
disp(calculated_range);

Solution