# Knowledge enhanced compressive radar ranging

In the era of 5G, faster network connections speed up the development of self-driving cars. For the self-driving cars, the key point to success is high resolution ranging/imaging. In general, automobile radars transmit wideband signals for high range resolution. According to Nyquist sampling theorem, consequently, the radar receiver requires to adopt high-rate analog-to-digital converter (ADC). In most cases, the high-rate ADCs and corresponding hardware are costly and power consumption. For example, in order to increase sampling rate by a factor of 10, the ADC would consume about 7.5 times more power and increase cost by a factor of approximately 35.

How to obtain the high resolution with a low-rate ADC? Compressive sensing (CS). The success of CS is based on two principles: sparsity and incoherence. It is well known that random sensing kernels, e.g., Gaussian and Bernoulli kernels, satisfy the incoherence requirement with signal sparse representation. However, besides sparsity, random sensing does not exploit any prior knowledge that may be available in specific applications. In automobile radar, the interested range is from 0 meter to 200 meters, which can be utilized for CS kernel optimization.

We adopt the mutual information maximization criterion to optimize the CS kernel for range estimation. The optimization problem can be formulated as $\max\limits_{\boldsymbol{\varPhi}} I(\boldsymbol{y}; d) = h(\boldsymbol{y}) - h(\boldsymbol{y}|d), \nonumber$

where the optimization variable $\boldsymbol{\varPhi}$ is the compressive measurement matrix, and $I(\boldsymbol{y}; d)$ is the mutual information between the measurement vector $h(\boldsymbol{y})$ and the range $d$. Here, $h(\boldsymbol{y})$ denotes the differential entropy of the measurement $\boldsymbol{y}$, $h(\boldsymbol{y}|d)$ denotes the conditional differential entropy of the measurement $\boldsymbol{y}$ conditioned on the range $d$, respectively. With custom defined constraints, we provide the best solution to the CS kernel optimization.

Simulation

In our simulations, the ADC is assumed to be operating at a fixed sampling rate of $B = 1$ MHz. The radar transmit waveform is of bandwidth $CR \times B$ MHz, where $CR$ is the compression ratio of the CS radar receiver. Meanwhile, a 1-MHz waveform is also adopted for the baseline Nyquist result, which waveform bandwidth is matched to the receiver sampling rate.