# Towards Deep Radar Perception for Autonomous Driving: Datasets, Methods, and Challenges
## 2 Radar Signal Processing Fundamentals
### Radar Performances  
The performance of automotive radar can be evaluated in terms of maximum range, maximum Doppler velocity, and field of view (FoV). Equations for these attributes are summarised in Table 2. According to the radar equation, the theoretical maximum detection range is given by  
Figure 4: MIMO radar principles. (**a**) Virtual array configuration of a 2 Tx4 Rx MIMO radar (**b**) In TDM mode, Tx1 and Tx2 transmit signals in turns. (**c**) In DDM mode, a Doppler shift is added to Tx2. \[R_{\max}=\sqrt[4]{\frac{P_{t}G^{2}\lambda^{2}\sigma}{(4\pi)^{3}P_{\min}}} \tag{6}\]  
where \(P_{t}\) is the transmit power, \(P_{\min}\) is the minimum detectable signal or receiver sensitivity, \(\lambda\) is the transmit wavelength, \(\sigma\) is the target RCS, and \(G\) is the antenna gain. The wavelength is 3.9 mm for automotive 77 GHz radar. The target RCS is a measure of the ability to reflect radar signals back to the radar receiver. It is a statistical quantity that varies with the viewing angle and the target material. According to the test results [20], smaller objects, such as pedestrians and bikes, have an average RCS value of around 2-3 dBsm, whereas normal vehicles have an average RCS value of around 10 dBsm and large vehicles of around 20 dBsm. The other parameters, such as transmit power, minimum detectable signal, and antenna gain are design parameters aimed at meeting product requirements, as well as regulations. Some typical values for these parameters are summarised in Table 3. In practice, the maximum range is limited by the supported IF bandwidth \(B_{\rm IF}\) and ADC sampling frequency. The maximum unambiguous velocity is inversely proportional to the chirp duration \(T_{c}\). For MIMO radar, the maximum unambiguous angle is dependent on the spacing of antennas \(d\). The theoretical maximum FoV is 180\({}^{\circ}\) if \(d=\lambda/2\). In practice, the FoV is determined by the antenna gain pattern. Another important characteristic is resolution, i.e., the ability to separate two close targets with respect to range, velocity, and angle. As shown in Table 2, high-range resolution requires a large sweep bandwidth \(B\). High Doppler resolution requires a long integration time, i.e., the frame time \(N_{c}T_{c}\). The angular resolution depends on the number of virtual receivers \(N_{R}\), the object angle \(\theta\), and the inter-antenna spacing \(d\). For the case of \(d=\lambda/2\) and \(\theta=0^{\circ}\), angular resolution is in a simple form of \(2/N_{R}\). From the perspective of antenna theory, angular resolution can also be featured by the half-power beamwidth, i.e., the 3-dB beamwidth [13], which is a function of the array aperture \(D\). In practice, different types of automotive radar are designed for different scenarios. Long-range radar (LRR) achieves a long detection range and a high angular resolution at the cost of a smaller FoV. Short-range radar (SRR) uses MIMO techniques to achieve a \begin{table}
\begin{tabular}{c c} \hline \hline
**Definition** & **Equation** \\ \hline Max Unambiguous Range & \(R_{m}=\frac{cB_{\rm IF}}{2\lambda^{2}}\) \\ Max Unambiguous Velocity & \(v_{m}=\frac{1}{4T_{c}}\) \\ Max Unambiguous Angle & \(\theta_{\rm FoV}=\pm\arctan(\frac{1}{2d})\) \\ Range Resolution & \(\Delta R=\frac{c}{2B}\) \\ Velocity Resolution & \(\Delta r=\frac{\lambda}{2N_{c}T_{c}}\) \\ Angular Resolution & \(\Delta\theta_{\rm Res}=\frac{1}{N_{d}\delta\cos(\theta)}\) \\
3 dB Beamwidth & \(\Delta\theta_{\rm 3 dB}=2\arcsin\frac{14A}{\pi D}\) \\ \hline \hline \end{tabular} The meaning of parameters is consistent in this section. Refer to Table 11 (in Appendix A) for a quick check of the meaning.  
\end{table} 
Table 2: Equations for radar performance.