# A Sparse Bayesian Approach for Forward-Looking Superresolution Radar Imaging
## 3 Sparse Bayesian Algorithm for High Cross-Range Resolution
### Simulation of Point Targets  
We first consider examples of point scatterers with different platform velocities. Suppose that three targets with the same unit amplitude are located at the forward-looking region of the platform. The cross-range angles of the three targets are \(-3.5^{\circ}\), \(-2.5^{\circ}\), and \(3^{\circ}\), respectively. The distance between the original position of platform and the center target is 20 km. Figures 2 and 3 show the simulation results in different conditions. Figure 2 shows the simulation results processed by the proposed sparse Bayesian algorithm and Poisson-based MAP algorithm when the SNR is 25 dB. The added noise obeys a zero mean and circular complex Gaussian distribution. We use a single cross-range signal profile to show the performance of the proposed algorithm in different platform velocities. Figure 2 includes the simulation results when the platform velocities are 0 m/s, 100 m/s, 200 m/s, and 300 m/s, respectively. The top of each subfigure shows the received cross-range signal after motion compensation. The middle and bottom of the subfigures are the simulation results processed by the Poisson-based MAP algorithm and the proposed sparse Bayesian algorithm, respectively. Figure 1(a) shows that the isolated point target is sharpened and the adjacent targets are resolved by both algorithms when the platform is stationary. Although the assumption that the noise distribution obeys a Poisson distribution is different from the practical added noise, the superresolution performance of the Poisson-based MAP algorithm is still high because the SNR is high in this set of simulations. The location error of the Poisson-based MAP algorithm appears in the superresolution results with the motion platform. With the influence of the Doppler phase, the received signal of the motion platform in the cross-range dimension is not the real signal convolution. We can clearly find the shape-shifting of received signals under different motion velocities. The Poisson-based MAP algorithm is a real-valued signal deconvolution algorithm. We need to do the modulus operator before applying \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Units** \\ \hline Carrier frequency & 9.6 & GHz \\ Band width & 50 & MHz \\ Beamwidth & 3 & \({}^{\circ}\) \\ Antenna scanning velocity & 30 & \({}^{\circ}\)/s \\ Antenna scanning area & \(-10\) to \(+10\) & \({}^{\circ}\) \\ Pulse repetition frequency & 1000 & Hz \\ Platform height & 1000 & m \\ Incident angle & 30 & \({}^{\circ}\) \\ Working distance & 20 & km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. this method to the cross-range signal superresolution, which causes the location error. The isolated point target did not have any location error because this target did not have any overlap among other targets. However, the location error of adjacent point targets is about 0.2\({}^{\circ}\) in motion platform simulation. For instance, the working distance is 20 km in the simulations, so the location error of the 20-km-away targets is about 70 m. This is a significant error in practical applications. This problem is overcome by the proposed sparse Bayesian algorithm. For both the stationary platform and the moving platform scenario, the proposed algorithm achieves higher target location accuracy. Besides, the proposed Bayesian superresolution algorithm has better superresolution performance than the Poisson-based MAP algorithm. It sharpened the point targets approximately four times more than the Poisson-based MAP algorithm. Figure 3 shows the simulation results when the SNR is 15 dB. From this figure, we can find that the Poisson-based MAP algorithm has a performance degradation. First, the location error still exists, and the angle location error almost reaches 0.3\({}^{\circ}\) when the platform velocity is 200 m/s. Besides, the phenomenon of noise amplification in the superresolution results appeared.