## MIMO radar

MIMO radar systems employ multiple transmitters, multiple receivers, and multiple waveforms to exploit all available degrees of freedom [31]. MIMO radars can be classified as widely separated or colocated. In widely separated MIMO radar, transmit-receive antennas capture different aspects of the RCS of a target. In other words, the target appears to be spatially distributed, providing a different RCS at each antenna element. This RCS diversity can be utilized to improve the radar performance [32]. On the other hand, with colocated MIMO radar, the RCS observed by each antenna element is indistinguishable [10].

Automobiles typically use colocated MIMO radars, which are compact in size [33]. For proper transmitter spacing, the colocated MIMO radar can emulate a larger aperture phased array radar (see Figure 8). This larger array is called a virtual array. Recall of the range-azimuth estimation problem given in (8). For the MIMO radar processing, as depicted in Figure 8, a 1-D receiver array with two transmit antennas is considered. Let L_{T} and L_{R} denote the number of transmit and receive antenna elements, respectively. Suppose that d_{T} and d_{R} represent corresponding transmit and receive antenna spacings. Also, assume that transmit and receive antenna positions in Cartesian coordinates are given by l_{T} and l_{R}. Hence, the 2-D FMCW mixer output signal across fast time and aperture is given by

From (10), it is evident that if d_{T} =L_{R} X d_{R}, then MIMO radar imitates a regular 1-D array radar with single transmit and LT X LR receive antenna elements. This is known as virtual array representation. Hence, the spatial resolution of FFT-based target imaging can be improved by the factor of LT . With virtual array representation and substituting l =l_{T} X L_{R}+l_{R}, the expressions similar to (8) can be obtained and the estimation algorithms discussed in the sections “Basic Automotive Radar Estimation Problems” and “Advanced Estimation Techniques” can be applied.

The challenging aspect of MIMO radar is the selection of waveforms. The waveforms can be made orthogonal in the frequency, time, or code domain [34], [35]. Consequently, the matched filter design at the receiver varies, which is necessary to separate the reflected waveforms originating from different transmitters. From the FMCW radar signal given in (4), various orthogonal waveforms can be constructed in the following manner [36]:

- Beat frequency division: s (t) = e
^{jπ2[(fc-Δfb)t + 0.5Kt20.5(Δf2b/K)}. Here, Δf_{b}is the frequency offset introduced for waveforms orthogonalization. The last term in the exponential corresponds to residual video phase compensation, which is necessary for coherent receiver processing. - Modulation constant division: s(t)=e
^{j2π(fc+0.5[K+ΔK]t)t}The modulation constant or chirp rate offset is given by ΔK, which is obtained by varying the pulse period. The bandwidth at each transmitter remains the same to maintain the range resolution. The reset time between the pulses ensures the synchronization at the receiver. - Code division: s(t)= e
^{jπ2[(fc0.5Kt)t+0.5β(t)]}, where β(t) corresponds to the binary phase-shift keying (BPSK) signal with a low update rate that assumes values ±1. The bandwidth of the BPSK signal is kept smaller to ensure the proper operation of the FMCW radar.

Following the waveform selection, the waveform design can be used for further optimization of the radar performance. For the wideband radar waveforms with high-range resolution, a planar target appears to be a cluster of point targets. The extended target exhibit random reflectivity (impulse response) as its reflection consists of several waveforms added together. From the known extended target statistics, the transmitted waveform can be adapted (see Figure 9). The mutual information between a random extended target and the reflected received signal is used to optimize the radar waveform < title="M. R. Bell, “Information theory and radar waveform design,” IEEE Trans. Inform. Theory, vol. 39, no. 5, pp. 1578–1597, Sept. 1993." href="#">[38]. Under the constraint on the transmit power, the waveforms can be designed to minimize the mean square error in the target impulse response estimation. The solution to this problem consists of water-filling power allocation, distributing more power to target exhibiting significant scattering [39]. As shown in [40], multiuser MIMO principles can be applied to waveform design in the context of multiple target estimation and tracking.

## Robust estimation techniques

So far, we have assumed that the automotive radars only receive the reflection from the targets of interest such as a vehicle traveling in front. However, in addition to direct reflections from the target of interest, the radar also receives reflections from the road debris, guard rails, and walls. This unwanted return at the radar is called clutter. The amount of clutter in the system changes as the surrounding environment of the vehicle varies. Hence, adaptive algorithms such as constant false alarm rate (CFAR) processing and space-time adaptive processing (STAP) can be used to mitigate the effect of clutter.

To identify valid targets in the presence of clutter, the threshold for the target detection should be properly chosen. If the amplitude of the spectrum at an estimated range is greater than some threshold, the target is said to be detected. Thus, the threshold should depend on the noise or in other words on the clutter in the given system. As clutter increases, a higher threshold may be chosen. A simple CFAR method based on cell averaging can use a sliding window to derive the local cluster level by averaging the multiple range bins. As multiple targets make this detection method intricate, sophisticated techniques based on ordered statistics can be used [41], [42].

STAP is another technique that can robustify target position estimation [43], [44]. The key idea is to use an adaptive filter that selects the target amid clutter from the road and other objects. The weights of the filter change adaptively with clutter statistics. In FMCW radar (7), this filter operates on the mixer output across different chirps (i.e., P slow time samples) as well as across spatial domain (L samples from 1-D aperture). The clutter statistics are recorded with the interference covariance matrix C_{LPXLP}, which is calculated by averaging over the range bins surrounding the target of interest. Let e_{LPX1}(Θ_{t}, f_{d}_{t}) be the spatiotemporal steering vector pointing to the possible target. The weights of space-time adaptive filter are given by minimum variance distortionless (MVDR) beamformer [44] as

The presence of the target is then tested by passing the spatiotemporal data through the filter with coefficients w(Θ_{t}, f_{d}_{t}). This process is conducted for all possible targets of interest.

Additionally, STAP can benefit from extra degrees of freedom in MIMO radar by using multiple transmitter antenna elements to reduce the clutter. The MIMO radar with increased virtual array size can process both direction of arrival and departure information, which shows mismatch if the signal is reflected from the clutter [11], [45].

## Target tracking problem

Target tracking is an essential part of the ADAS subsystems such as collision avoidance and lane assist. In the tracking, a state (x,y, z,v_{x},v_{y},v_{z}), which indicates the 3-D position of the target in Cartesian coordinates and corresponding directional velocities is determined based on the current observation (R,Θ,∅) and previous state information.

A key step in tracking is to associate separately estimated parameters of Q targets, particularly velocities (v_{1},v_{2}….,v_{Q}) and ranges (R_{1},R_{2},….,R_{Q}) with each other [(R_{1},v_{1}),(R_{2},v_{2})…,(R_{Q},v_{Q})]. After linking estimated parameters with targets, the targets are associated with tracks. For example, if each target follows a separate track, then there are Q tracks in the system. The association problem becomes complex when two tracks cross each other. Different methods to perform data association include joint probabilistic data association (JPDA), nearest neighbor (NN), and fuzzy logic [46].

A realistic simulation setup should include radiation patterns of the transmit and receive antenna elements, which count for the direction dependent scaling of the transmitted and reflected signals according to the geometry of the system.

Following the data association, tracking can be performed using well-known algorithms such as Kalman filtering. For

each track, a separate filter is implemented. These filters operate in parallel. Since the observation vector (R,Θ,∅) has a nonlinear relationship with the state vector (x,y,z,v_{x},v_{y},v_{z}), an extended Kalman filter (EKF) is used. The state equation that captures the effect state transition over time [47]. is given by

where T is the observation interval. The observation vector is related with state vector via

From the knowledge of the previous state, the present state is predicted based on the state equation (12). Using (13) and the present observation, the predicted value is updated. The amount of correction depends on the SNR of the observations; see [47] for more details. Vehicle tracking problems are also addressed in [48] [49] [50] [51].

## Pedestrian detection

Pedestrian, bike, and wild life detection is essential for a driver assist and collision avoidance system. As a pedestrian walks, a small change in range produces very low Doppler shift. In other words, the micromotion of a target produces what is known as a micro-Doppler [52]. Likewise, the periodic motion of limbs creates a periodic pattern in velocity over time, which is also known as the micro-Doppler signature. This signature, along with other feature extraction and matching algorithms, can be used to uniquely identify pedestrian walking. More details about an analysis of human gait using range-Doppler plots are given in [53].

Moreover, the pedestrian detection task becomes more challenging due to a smaller RCS of the human body [54]. To make the pedestrian detection robust, the radar based on micro-Doppler estimation can be combined with inputs from a vision sensor [55]. Also, the tracking algorithms discussed previously can help predict pedestrian movement [56].

Let us discuss how the micro-Doppler signature is extracted using FMCW radar processing in (5). First, 2-D signal samples obtained across slow and fast time are converted into single dimensional signals by range gating. Typically, FFT is performed across fast time n and only the frequency corresponding to the range of interest R0 is retained (assume single target with micromotion at R0 ). Neglecting range-Doppler coupling and effect of finite length FFT, (5) can be rewritten as

where Ω(.) is the function characterizing the micromotion of the target. As explained in [52], the short-time Fourier transform (STFT) of (14) gives the instantaneous variation of Doppler across time. Detail analysis regarding micro-Doppler vibration measurements using FMCW radar is done in [57]. In addition to pedestrian detection, micro-Doppler also can be used to identify the type of a vehicle (truck, sedan, etc.) by characterizing its vibration pattern on top of Doppler shift produced by its bulk motion [58], [59].