# Blind Spot Detection Radar System Design for Safe Driving of Smart Vehicles
## 2 FMCW Radar Principle  
The BSD radar system is designed using FMCW radar, which is capable of measuring Range (R), Velocity (V), and Angle (A). The principle of FMCW radar is to determine the R, V, and A of surrounding objects by analyzing the signal transmitted by the radar's transmitter and the signal reflected by surrounding objects and received by the radar's receiver [12; 13]. The difference between the received signal and the transmitted signal is known as the beat frequency. The BSD radar system considers two main situations to analyze the accurate R, V, and A of the surrounding targets. The first situation is a stationary target, and the second situation is a moving target. Stationary targets can be further classified into two categories: Single Stationary Target and Multiple Stationary Targets. Moving targets can also be classified into two categories: Single Moving Target and Multiple Moving Targets. Figure 1 illustrates the stationary target of the FMCW radar. In Figure 1, the transmitted (Tx) signal from the system collides with the surrounding targets and the reflected signal is defined as the received (Rx) signal that enters the radar system. \(\tau\) defines the time difference between the Tx and Rx signals, while \(B\) defines the frequency bandwidth. \(T\) is the sweet time, which defines the time for the amplitude to increase from the minimum value to the maximum value. Up-chirp defines the time for the amplitude of the signal to increase, while down-chirp defines the time for the amplitude of the signal to decrease. \(f_{b}\) is the beat frequency, which defines the frequency difference between the Tx and Rx signals. The FMCW radar system analyzes the R, V, and A of the surrounding targets with respect to the moving vehicle by using the beat frequency. As Figure 1 shows a stationary target, a time difference occurs between the Tx and Rx signals, but the bandwidth is the same between the two signals because the target is stationary. Therefore, in Figure 1, the analysis of beat frequency and range is an important factor. In Figure 1, the equation for analyzing the beat frequency is shown as Equation (1):  
\[\left\{\frac{f_{b}}{\tau}=\frac{B}{T}\right\}\Rightarrow f_{b}=\tau\cdot \frac{B}{T}=\frac{2R}{C}\cdot\frac{B}{T},\left\{ \begin{array}{l}B=bandwidth \left[\mathrm{Hz}\right]\\ T=sweep\ time\ \left[\mathrm{sec}\right]\\ R=target\ range\ \left[m\right]\\ \tau=time\ delay\ \left[\mathrm{sec}\right]\\ c=3\mathcal{E}\ \left[\frac{\mathrm{m}}{\mathrm{s}}\right]\end{array} \right. \tag{1}\]  
Figure 1: Beat Frequency for Stationary Target. In the analysis of beat frequency, \(2R\) is defined considering the round-trip distance to the target, where \(C\) represents the transmission speed of the signal, defined as the speed of light. The equation for analyzing Range (\(R\)) in a stationary target is shown as Equation (2):  
\[R=\frac{cTf_{b}}{2B}R_{max}=\frac{cTf_{b,max}}{2B}\Rightarrow R_{limit}=\frac {cT}{2},(f_{b,max}=B) \tag{2}\]  
In Equation (2), the actual maximum time difference (\(\tau\)) is commonly defined as 0.1 \(\times\) T.  
When considering a stationary target, the relative speed is zero. Thus, the equation B = \(f_{b}\) is applicable. The parameter \(R\) can be defined using Equation (2). Figure 2 defines a moving target of the FMCW radar. There is a time difference between the beat frequencies of the Tx signal and the Rx signal, and a bandwidth difference occurs due to the movement of the target. In the presence of a moving target, the received signal experiences a shift due to the Doppler effect, which can be quantified by the Doppler frequency. The change in bandwidth is defined by the height on the frequency axis. The slope variation of the chirp signal, which increases the starting frequency for a certain period, is used to define the velocity.