FMCW Radar, Backscattering Analysis

Importance
FMCW radars main applications are as altimeters, placed in aircraft, but also in the investigation of atmosphere, thanks to the sensitivity and spatial resolution that they provide in comparison with their pulsed counterparts. In addition, the FMCW radars are more compact and less expensive than the pulsed ones, which make them more suitable for aerial applications.
Source: Radar Theory
In this post we are going to analyze the backscattering effect, a very important phenomenon considered in many applications, as we will describe later.
FMCW Radar Principle, Overview
In a previous post, we saw a Matlab tutorial to study the the main theoretical principles of the FMCW Radar, summarized in the image below:
As shown in the previous image, the echo from a single target will arrive with a time delay of
where c is the speed of light and R is the range or distance to the target.
Assuming a stationary target, the beat frequency is:
If the target is moving, we would superimpose the Doppler frequency shift, fd, on the beat frequency.
Signal to Noise Ratio and Clutter Backscatter Coefficient
The general expression for a radar SNR is:
where is the radar cross section (RCS) , k is the Boltzmann’s constant, T0=290K is the standard temperature, and is the noise bandwidth.
The processing gain due to the beat frequency for FMCW radars is . This is the pulse compression ratio in a pulsed radar system. Inserting this gain in the previous formula, we can write the SNR as:
The cluttertonoise ratio (CNR) can be calculated by replacing the RCS in the SNR equation by the clutter backscatter coefficient of the illuminated surface, .
If we know the beat frequency and the range resolution, we can use a resolution cell for the illuminated surface, instead of a swath. Approximating this cell by a rectangle, we have:
where is the RCS per unit area of the illuminated cell. Combining this equation with the SNR equation, we cam determine the CNR as:
Bear in mine, the importance of defining what a clutter and what a target is. The targets usually refer to point scatterers and the clutters to extended scatterers (a surface/volume). The analysis of the backscatter from a clutter is made with the aim of separating it from the information signal.
Sources
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