# Towards Deep Radar Perception for Autonomous Driving: Datasets, Methods, and Challenges
## 2 Radar Signal Processing Fundamentals
### FMCW Radar Signal Processing  
Off-the-shelf automotive radars operate with a sequence of linear frequency-modulated continuous-wave (FMCW) signals to simultaneously measure range, angle, and velocity. According to regulations, automotive radar is allowed to use two frequency bands in millimetre waves: 24 GHz (24-24.25 GHz) and 77 GHz (77-79 GHz). There is a trend towards 77 GHz due to its larger bandwidth (76-77 GHz for long-range and 77-81 GHz for short-range), higher Doppler resolution, and smaller antennas [9]. As shown in Figure 3, the FMCW signal is characterised by the start frequency (also known as the carrier frequency) \(f_{c}\), the sweep bandwidth \(B\), the chirp duration \(T_{c}\), and the slope \(S=B/T_{c}\). During one chirp duration, the frequency increases linearly from \(f_{c}\) to \(f_{c}+B\) with a slope of S. One FMCW waveform is referred to as a chirp, and radar transmits a frame of \(N_{c}\) chirps equally spaced by chirp cycle time \(T_{c}\). The total time \(T_{f}=N_{c}T_{c}\) is called the frame time, also known as the time on target (TOT). In order to avoid the need for high-speed sampling, a frequency mixer combines the received signal with the transmitted signal to produce two signals with sum frequency \(f_{T}(t)+f_{R}(t)\) and difference frequency \(f_{T}(t)-f_{R}(t)\). Then, a low-pass filter is used to filter out the sum frequency component and obtain the intermediate frequency (IF) signal. In this way, FMCW radar can achieve GHz performance with only MHz sampling. In practice, a quadrature mixer is used to improve the noise figure [10], resulting in a complex exponential IF signal as  
\[x_{\rm IF}(t)=Ae^{i(2\pi f_{\rm IF}t+\phi_{\rm IF})} \tag{1}\]  
where \(A\) is the amplitude, \(f_{\rm IF}=f_{T}(t)-f_{R}(t)\) is referred to as the beat frequency, and \(\phi_{\rm IF}\) is the phase of the IF signal. Next, the IF signal is sampled \(N_{s}\) times by an ADC converter, resulting in a discrete-time complex signal. Multiple frames of chirp signals are assembled into a two-dimensional matrix. As shown in Figure 3, the dimension of the sampling points within a chirp is referred to as fast time, and the dimension of the chirp index within one frame is referred to as slow time. Assuming one object moving with speed \(v\) at distance \(r\), the frequency and phase of the IF signal are given by  
\[f_{\rm IF}=\frac{2S(r+vT_{c})}{c},\phi_{\rm IF}=\frac{4\pi(r+vT_{c})}{\lambda} \tag{2}\]  
where \(\lambda=c/f_{c}\) is the wavelength of the chirp signal. From (2), we can find that the range and Doppler velocity are coupled. Under the following assumptions: 1. the range variations in slow time caused by target motion can be neglected due to the short frame time; 2. the Doppler frequency in fast time can be neglected compared to the beat frequency by utilising a wideband waveform. Then, range and Doppler can be decoupled. Range can be estimated from the beat frequency as \(r=cf_{\rm IF}/2S\), and Doppler velocity can be estimated from the phase shift between two chirps as \(v=\Delta\phi\lambda/4\pi T_{c}\). Next, a range DFT is applied in the fast-time dimension to resolve the frequency change, followed by a Doppler DFT in the slow-time dimension to resolve the phase change. As a result, we obtain a 2D complex-valued data matrix called the Range-Doppler (RD) map. In practice, a window function is applied before DFT to reduce sidelobes. The range and the Doppler velocity of a cell in the RD map are given by  
\[r_{k}=k\frac{c}{2B_{\rm IF}},v_{l}=l\frac{\lambda}{2T_{f}} \tag{3}\]where \(k\) and \(l\) denote the indexes of DFT, \(B_{\text{IF}}\) is the IF bandwidth, and \(T_{f}\) is the frame time. In practice, FFT is applied due to its computational efficiency. Accordingly, the sequence will be zero-padded to the nearest power of 2 if necessary. Angle information can be obtained using more than one receive or transmit channel. Single-input multiple-output (SIMO) radars utilise a single transmit (Tx) and multiple receive (Rx) antennas for angle estimation.