# Towards Deep Radar Perception for Autonomous Driving: Datasets, Methods, and Challenges
## 2 Radar Signal Processing Fundamentals
### FMCW Radar Signal Processing
Suppose one object is located in direction \(\theta\). Similar to Doppler processing, the induced frequency change between two adjacent receive antennas can be neglected, while the induced phase change can be used for calculating the direction of the angle. This phase change is given by \(\Delta\phi=2\pi d\sin\theta/\lambda\), where \(d\) is the inter-antenna spacing. To achieve the maximum unambiguous angle, the spacing can be set to \(\lambda/2\). Then, a third FFT can be applied to the receive antenna dimension. For conventional radar with a small number of Rx antennas, the sequence is often padded with \(N_{\text{FFT}}-N_{Rx}\) zeros to achieve a smooth display of the spectrum. The angle at index \(\eta\) is given by  
\[\theta_{\eta}=\arcsin\frac{\eta\lambda}{N_{\text{FFT}}} \tag{4}\]  
The angular resolution of a SIMO radar depends on the number of Rx antennas. The maximum number of Rx antennas is limited by the additional cost of signal processing chains on the device [11]. Multiple-input multiple-output (MIMO) radar operates with multiple channels in both Tx and Rx. As illustrated in Figure 4a, a MIMO radar with \(N_{\text{Tx}}\) Tx antennas and \(N_{\text{Rx}}\) Rx antennas can synthesise a virtual array with \(N_{\text{Tx}}N_{\text{Rx}}\) channels. In order to separate the transmit signals at the receiver side, the signals from different Tx antennas should be orthogonal. There are multiple ways to realise waveform orthogonality, such as time-division multiplexing (TDM), frequency-division multiplexing (FDM), and Doppler-division multiplexing (DDM) [12; 13]. TDM is widely used for its simplicity. In this mode, different Tx antennas transmit chirp signals in turns, as shown in Figure 4b. Therefore, at the receiver side, different Tx waveforms can be easily separated in the time domain. An additional phase shift compensation [14] is required to compensate for the motion of detections during the Tx switching time. Another shortcoming of TDM is the reduced detection range due to the loss of transmitting power. DDM is also supported by many radar devices. As shown in Figure 4c, DDM transmits all Tx waveforms  
Figure 3: Radar Tx/Rx signals and the resulting range-Doppler map. simultaneously and separates them in the Doppler domain. In order to realise waveform orthogonality, for the \(k\)-th transmitter, a Doppler shift is added to adjacent chirps as  
\[\omega_{k}=\frac{2\pi(k-1)}{N} \tag{5}\]  
where \(N\) is usually selected as the number of Tx antennas \(N_{\mathrm{Tx}}\). One drawback of DDM is that its unambiguous Doppler velocity is reduced to \(\frac{1}{N}\) of the original one. Empty-band DDM [15] can achieve more robust velocity disambiguation by introducing several empty Doppler sub-bands. Some example codes are provided in the RADIal dataset [16]. After decoupling the received signals, we can obtain a 3D tensor by stacking RD maps with respect to Tx-Rx pairs. Then, the DOA can be estimated through the angle FFT along the virtual receiver dimension. Some super-resolution methods [17], such as Capon, MUSIC, and ESPRIT, can be applied to improve angular resolution. The resulting 3D tensor is referred to as the range-azimuth-Doppler (RAD) tensor or radar tensor. In the radar detection pipeline, RD maps are integrated coherently along the virtual receiver dimension to increase the SNR. Then, a constant false alarm rate (CFAR) detector [18] is applied to detect peaks in the RD map. Finally, the DOA estimation method is applied for angle estimation. The output is a point cloud with measurements of range, Doppler, and angle. For conventional radars, only the azimuth angle is resolved, while 4D radars output both azimuth and elevation angles. Since radar is usually used in safety-critical applications, a lower CFAR threshold (\(\lesssim\)10 dB) is set to achieve high recall. The accuracy of detection is affected by road clutter, interferences, and multi-path effects in complex environments. Therefore, additional spatial-temporal filtering is required to improve accuracy.