# Designing Advanced Multistatic Imaging Systems with Optimal 2D Sparse Arrays
## 5 Results
### Optimal 2D Sparse Array  
To evaluate the performance of the method, an architecture with NTX = 64 and NRX = 49 was used. As previously described in Section 3.2.1, the desired aperture size, both in range and cross-range, was set to 1 m. To precisely meet this design criterion, \(d_{rx}\) was set to 14.3 cm. Additionally, it is critical to consider the minimum inter-element separation, which was set to 2 cm due to the physical characteristics of the hardware available for prototype construction. As described in Section 2  
can be understood as the spatial resolution of the imaging system [44]. In this equation, \(D_{x,z}\) represents the aperture size of the array, \(\lambda\) represents the wavelength of the electromagnetic waves being used, and \(L\) is the distance between the OUT and the array.  
The PSF effectively defines the smallest resolvable detail or spot size in the resulting images produced by the system. According to the given equation, this PSF results in a spot with an approximate diameter of 6 mm centered at the origin (0,0). This means that, in ideal conditions, the imaging system can resolve features in the object as small as this 6 mm spot size, allowing for detailed observation and analysis of the OUT's characteristics.  
It is also desirable to eliminate additional contributions and minimize the presence of secondary lobes, which can have several negative effects, such as degradation of resolution, contamination of the image with unwanted artifacts, and difficulty in accurate interpretation of the image, which in turn can hinder the identification of specific objects or details. However, due to the inherent characteristics of these architectures, which do not strictly adhere to the Nyquist criterion, achieving this is unattainable. These diffraction lobes will inevitably appear as a direct consequence of the architectural features and impose constraints on the FoV during the reconstruction process. The objective is to position them as far away as possible from the main lobe and minimize their magnitude.  
Secondary lobes are observed at a distance of approximately 13 cm from the main lobe and have a magnitude of 24.6 dB less than the main lobe. Although the PSF is not ideal, it comes quite close. The secondary lobes are distant enough and at a low enough level to not negatively impact the reconstructions that the system can perform.  
Figure 5 shows the PSF at a distance of 3 m of the architecture resulting from the GA optimization.  
The goal of the optimization is to obtain a PSF that is as clean as possible, with the aim of keeping the secondary lobes as far away and as low as possible. Without the assistance of these optimization tools, the most intuitive way to design the architecture would be to evenly distribute the transmitters and receivers along the X and Z axes. For example, to achieve a 1 m aperture, the spacing between elements should be 13.33 cm. Figure 6a shows the resulting configuration, and Figure 6b shows the PSF at 3 m. Multiple secondary lobes are observed, located extremely close to the main lobe, and furthermore, they have a significantly high level, nearly of the same order of magnitude as the main lobe. This is an unfavorable result as it predicts a significant degradation in the quality of the recovered images, making it difficult to clearly distinguish any objects. Comparing Figures 5a and 6b, there is a significant improvement of the optimized system with respect to the unoptimized one.  
Figure 5: PSF of optimal architecture at a standoff distance of 3 m. (**a**) PSF in XZ—plane. (**b**) X—Cut at Z = 0.