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Introduction to Radar Processing and Deep Learning

At the end of this chapter, reader will have understanding on

• How radar data cubes are processed to extract range, velocity, and angle of the multiple detected targets and are tracked over time.
• Different target representations used for radar target recognition.
• Introduction to deep learning architectures used for radar target recognition.

1.1 Basics of Radar Systems

Radar is an acronym that stands for radio detection and ranging. It is basically an electromagnetic system used to detect the presence of one or more targets of interest and estimate their range, angle, and velocity relative to the radar. Instead of just measuring the target's location and velocity, modern radars can predict the target given the reflected radar signals. The main objective of radar compared to infrared and optical sensors is to discover distant targets under difficult climate conditions and to determine their spatial location while tracking them over time with precision. The general working principle and signal processing fundamental details are explained in the following sections.

1.1.1 Fundamentals

The radar system generally consists of a transmitter that produces an electromagnetic signal, which is radiated into space by the transmit antenna. When this signal strikes an object, it gets reflected or re-radiated in many directions. This reflected echo signal is received by the receive antenna, which delivers it to the receiver circuitry, where it is processed to detect the target and also localize it over time along with certain characteristics of the target. A simplified version of a typical continuous wave radar front-end with the most important building blocks can be seen in Figure 1.1. The chosen waveform is generated by a local oscillator (LO) and transmitted via the transmit (Tx) antenna. The receive (Rx) antenna then captures the incoming signal reflections from the target at a distance. After amplifying the received signal, it is mixed with the original transmitted waveform and is passed through subsequent analog bandpass filtering (BPF). This removes any high-frequency components that could cause aliasing as well as low-frequency components from direct coupling of the LO signal into the receiver. After mixing and filtering the signal that has been shifted to an intermediate frequency (IF), and it is referred as . The IF bandwidth is determined by the upper cut-off frequency of the bandpass filter, which is typically in the order of tens of kHz to few MHz.

Figure 1.1 Block diagram of the continuous wave radar front-end and its receive chain including the mixer, band pass filter, and analog-to-digital converter. The digitized samples are stored into a data matrix . The radar in this case is sensing a human target in the field of view.

1.1.2 Signal Modulation

To detect and differentiate multiple targets along its range, relative velocity, and azimuth-elevation angle dimensions, linear frequency modulated continuous wave (FMCW) is used as the most standard sensing waveform [1]. Usually, consecutive identical chirps are transmitted within a frame with a predefined time spacing referred to as chirp repetition time. The received IF signal is arranged within a two dimensional matrix, and the intratime, i.e., within a chirp, is referred as fast-time, while the intertime, i.e., across chirps, is referred to as slow-time. If the target is static, the round trip delay in the received signal is manifested as a frequency offset along the fast-time dimension after down-mixing at the receiver. But if the target or the radar is not stationary, the received signal will have an additional frequency offset caused by the Doppler shift manifested across slow-time dimension.

Figure 1.2 shows the concept of a FMCW modulation in detail. The LO generates a chirp signal with starting frequency , bandwidth , duration , and resulting sweep rate . By taking advantage of time integral over Tx frequency, instantaneous phase is calculated as shown in Eq. (1.1), where corresponds to the initial phase of the LO:

Figure 1.2 Illustration of typical modern radar sensors with several identical transmit chirps within a frame and the digitized IF samples are then stored chirpwise in a data matrix for coherent processing.

Assuming unity amplitude for a single chirp, can be formulated by

If this transmit signal gets reflected by some object, also referred to as target, the reflection will be received at the radar with a time delay , which is proportional to the target's distance to the radar. Additionally, signals of multiple reflections, like extended targets, are superimposed on each other at the receiver. For an arbitrary number of point targets composing a spatially distributed target, the received signal can thus be expressed as follows:

where represents thermal receiver noise or clutter and is the round trip delay to the th target located at distance and moving with a relative radial velocity of . As a result, can be described as , where is the speed of light. For ease of notations, the noise term is dropped for all the following considerations. The received and amplified signal is mixed with the original transmitted signal (). As discussed before, both transmitted and received signal follows cosine waveform. Thus, the down-mixed signal can be transformed into two components using trigonometric formulation.

here contains the difference of Tx and Rx signal frequencies and contains the sum frequencies respectively. The sum component is removed by the following BPF and the resulting IF signal is obtained as follows:

This shows that intermediate received signal contains both distance-dependent frequency and also speed-dependent frequency shift which are factors of modulation parameters. This includes chirp duration , chirp repetition time , sweep frequency or bandwidth , and number of chirps in a frame as main configuration parameter for the design of a FMCW waveform. As a result, these parameters control the range and Doppler resolution, as presented in Eqs. (1.6) and (1.7), respectively. The maximum observable range and the maximum unambiguous Doppler is given in Eqs. (1.8) and (1.9).

1.2 FMCW Signal Processing

The IF signal, obtained from Eq. (1.5), is then digitized by an analog-to-digital converter with sampling period at the discrete time instants , where . Consequently, the discrete time signal contains samples per chirp. Typically, modern short-range radar sensors rapidly transmit several identical chirps in a so-called chirp sequence modulation. The digitized IF samples are then stored chirp wise in a data matrix for coherent processing. Figure 1.3 summarizes the FMCW signal processing multistage pipeline, where is first preprocessed in time-domain for removal of spectral leakage or static targets followed by interference mitigation. Later, the preprocessed is transformed to frequency domain for target detection. Once a target is detected, then the measurement is fed into a tracking algorithm for temporal smoothening. At the end, the tracked target's features are extracted using their motion or spatial signature in the form of images or point-clouds, respectively, which are used for target recognition.

Figure 1.3 Summary of FMCW signal processing pipeline including both pre- and postprocessing over chirp matrix for target detection, tracking, and classification.

The frequency domain analysis for range-Doppler processing is explained in the following section.

1.2.1 Frequency-Domain Analysis

As indicated by Eqs. (1.6) and (1.7) both range and radial velocity information of the target are functions of frequency shifts in the received signal. As a result, frequency-domain analysis is used to determine respective target's parameters instead of time-domain analysis. In contrast to time-domain signals where signal changes over time (amplitude or power) can be observed, frequency-domain analysis reveals how much of the signal lies within each given frequency band over a range of frequencies, which also include change in phase information. The most common frequency-domain transform methods are Fourier transform, short-time Fourier transform (STFT) and wavelet transforms. All three transforms are inner products of a family of basis functions with a time-domain signal. The parameterization and the basis functions determine the properties of the transforms.

Before delving into details, Figure 1.4 illustrates all the three transforms pictorially. While the classical technique to represent time signals in the frequency domain by calculating discrete Fourier transformation (DFT), it fails to detect time variant frequency effects, which are important for extended targets. As an...