In its most basic form, a radar transmits an electromagnetic pulse, and if a target is present within a certain angle and range, it will receive an echo, as shown
The task at hand at the receiver is to decide if a target is present at a particular range. Therefore, it creates a so-called range map, obtained by sampling the received signal after some processing.
Range map example:
The Doppler effect describes the difference between the observed frequency and the emitted frequency of a wave when the source moves relative to the observer. The received frequency is higher when the source moves towards you and lower when moving away.
A Doppler radar is a special radar that utilizes the Doppler effect to produce velocity data about objects at a distance. Regular radars send out pulses of radio waves and detect the returned pulses. The time difference between the transmission and reception of a pulse is used to determine an object's range (distance). In addition, Doppler radars look at the phase change of the received pulse due to the Doppler effect. In this way, Doppler radars can also determine the velocity of objects. The range map is thereby extented by the Doppler dimesnion, resulting in a range-Doppler map. This video could help you understand more in detail:
https://www.youtube.com/watch?v=NtyU6aKZ-cY
The detection efficiency of a radar is characterized by the probability of detection Pd and the probability of false alarm Pfa. According to the Neyman-Pearson criterion, the optimal detector of a radar target signal against noise should maximize Pd for a given Pfa. In general, the signal strength of the echo is unknown, and thus, we cannot define the probability of detection Pd. However, if we assume we know the statistics of the noise created by the receiver hardware, we can calculate Pfa. For a Pfa, we can define a thrershold, and the presence of the target is declared whenever the signal exceeds the threshold, as shown in Range Map figure. In many practical scenarios, the noise statistic is not known as a priori and may vary temporally and spatially. Moreover, echoing objects may not be located in front of a clear or empty background. Instead, there will be clutter presesent in the received signal. In such situations, a detector designed to adapt its threshold is advantageous. In other words, the threshold level is raised and lowered to maintain a constant probability of false alarm. This is known as CFAR detection.
The basic 1D CFAR architecture is shown in figure bellow. The CFAR window comprises a leading and a lagging window, guard cells, and a cell under test (CUT). The CUT is located in the center of the CFAR window. The term CUT refers to the current cell to which the CFAR threshold is to be applied. Measurements contained in the guard cells are not used to estimate the interference statistics, as they may contain returns associated with the target in the CUT, which will bias the interference estimate. The CFAR window is moved through the data window one sample or cell at a time. At each position, a detection decision is made regarding the measurement in the CUT. The detection threshold applied to the CUT is derived from measurements in the leading and lagging window (also called training cells). The threshold is calculated as: ZT = a * hat{g} where the CFAR constant is a function of the desired . is the estimated statistics from the leading and lagging windows which makes the threshold adaptive.
The dataset used is "radar.mat". This is one of the real-life datasets measured on the A13 highway by the PARSAX Radar (see figure). The measurment setup is shown as well. The Data_out matrix contains 30208 consecutive range measurements. Each range measurement comprises 270 range bins. The correspondoing range values are provided in the range vector. The consecutive measurements are obtained by transmitting a radar signal ever milisecond (variable Ts). The time axis for the consecutive measurements is referred to as slow time.
