# Survey of Deep Learning-Based Methods for FMCW Radar Odometry and Ego-Localization
## 4 Radar Representation
### Radar Processing  
Radar sensors have found utility across various applications since the 1930s and have gained particular popularity for perception tasks. This preference stems from their robustness and relatively affordable cost [5; 9]. A radar sensor functions by emitting and receiving frequency-modulated continuous waves (FMCW), usually within frequency bands centered at 24 GHz or 77 GHz with a linearly increasing frequency. To achieve this, a frequency mixer is employed, combining the transmitted and received signals to manage high-speed sampling requirements. Subsequently, a low-pass filter is applied to eliminate the summed components, resulting in the extraction of an intermediate-frequency signal (IF). This IF signal can be captured by an Analog-to-Digital Converter (ADC), yielding a discrete-time complex ADC signal. The process of determining an object's range involves analyzing the beat frequency, which emerges due to the time difference between transmission and reception [9]. Simultaneously, the Doppler velocity is ascertained by examining the phase shift within the IF signal. This phase shift arises due to the consecutive generation of FMCW waves, also referred to as chirps. The dimension of the sampling points within a single chirp is referred to as the _fast time_, and the dimension of a single chirp index across multiple chirps in a single frame is referred to as _slow time_. Under the assumptions that the range variations in slow time caused by target motion can be neglected due to a short frame time and by utilizing large frequency modulation to neglect the Doppler frequency in fast time, the range and Doppler calculations can be decoupled. A pivotal outcome of this process is a complex-valued data matrix, achieved through two discrete Fourier transforms carried out over the fast-time and slow-time dimensions. Known as the range-Doppler (RD) map, this matrix depicts power readings corresponding to specific range and Doppler values. This map offers valuable insight into the presence and motion of objects detected within the radar's scope [5]. Every FMCW radar employs the outlined scheme to calculate range and Doppler components. However, techniques diverge when it comes to determining the object's direction of arrival (DOA). This distinction hinges on the radar's positioning and configuration, leading to two main categories of methods: _automotive radars_ (AR) and _spinning radars_ (SR). Figure 3 illustrates how each radar sensor configuration can be placed on a vehicle. Spinning radar configurations have the advantage that they only consist of a single sensor placed on top of the vehicle. A sole external calibration matrix is used to project the objects into the vehicle's frame of reference. For an automotive radar configuration, radar sensors, typically 4-8 small chips, are placed at different positions around the vehicle. Here, the information recorded by the sensors needs to be transformed into the same coordinate system, often into the vehicle coordinate system, to match the same detections recorded by different sensors. As such, point cloud representations are favored when working with AR configurations [5, 9]. Table 2 provides an overview of presently utilized open-source radar datasets that are explicitly employed for ego-motion or ego-localization purposes using radar sensors. The datasets, discovered through the GitHub repository [62], were supplemented by additional datasets identified in Section 5. Figure 3: AR stands for automotive radar sensors and SR stands for spinning a radar sensor. A single spinning radar sensor is installed on top of the vehicle, while multiple radar sensors are installed in front and in the corners or sides of the vehicle in an automotive radar configuration. While mathematical expressions and derivations for variables like the IF signal, range, Doppler velocity, and DOA exist, these details are not covered here.