## 3 Full-Wave Validation and Discussion
Figure 4 shows that the \(\mu^{\rm T}\) of matrix \(\mathbf{H}\) increases with the increasing of the \(\mu^{\rm T}\) of matrix \(\mathbf{S}\), validating the predicted positive relationship. It is also obvious that in the positive relationship the mutual coherences in the measurement matrix upsurges with the increasing of the imaging range, which can be interpreted by the shrinking spectral low-pass filter. The \(\mu\) relationship possesses the same characteristics with \(\mu^{\rm T}\), although it represents the coherence level in the column space of the matrix. Therefore, this simulation proves that the proposed coherence relationship is still valid in a general situation. At last, we perform a full-wave simulation in a commercial electromagnetic simulation environment (Ansoft HFSS), in which a set of Complementary Electric-Field-Coupled (CELC) arrays as shown in Figure 5 is introduced in sequence as the radiation source. This simulation shares the same intention with the numerical simulations, although the fictitious sources are replaced with the equivalent sources generated by the near-field scanning of these arrays. The number of the elements in this set of arrays varies as 25, 100, 225 and 400, while resonant frequencies of the elements are randomly distributed from 26 to 34 GHz. The elements are placed in the same polarization direction. In addition, we randomly select the rows of the source matrix \(\mathbf{S}\) and correspoding \(\mathbf{H}\) to reassemble a new sample. Eventually, the number of the samples is enlarged to 648. The results are shown in Figure 6, where (a) demonstrates the relationship \(\mu^{\rm T}(\mathbf{H})\leftarrow\mu^{\rm T}(\mathbf{S})\) and (b) \(\mu(\mathbf{H})\leftarrow\mu(\mathbf{S})\):  
Figure 4: The coherence relationships obtained in the third numerical simulation via Monte Carlo method: (**a**) \(\mu^{\rm T}(\mathbf{H})\leftarrow\mu^{\rm T}(\mathbf{S})\) and (**b**) \(\mu(\mathbf{H})\leftarrow\mu(\mathbf{S})\). The sources are modulated by random spatial frequencies. Figure 5: The complementary electric coupled (CELC) array in the Ansoft HFSS simulation. As is shown Figure 6, the average mutual coherence of \(\mathbf{H}\) keeps an approximately linear relationship with the average mutual coherence of \(\mathbf{S}\) at the imaging range of 1 m. The former coherence obviously upsurges with the increasing of the imaging range. The characteristics of the \(\mu^{\mathrm{T}}\) and the \(\mu\) relationship in this result coincide with previous numerical simulation, validating that the proposed coherence relationship still holds for actual antennas. Before we end up with the section of simulation, in order to clearly demonstrate how the coherences in the measurement matrix affect the reconstruction, we generate the point-spread-functions (PSF) of four measurement matrices with the \(\mu\) of 0.081, 0.135, 0.275 and 0.550 respectively. These matrices are selected from the samples in previous numerical simulations. The result is shown in Figure 7, where the resolution is significantly improved with the reduction of \(\mu\), validating that the number of independent measurements is enlarged by the reduction. Therefore, the reduction of the coherences improves the resolution of microwave computational imaging systems. The above simulations validate that antennas can be optimized for MCI by reducing the spectral coherences of their equivalent radiation sources; however, it should be noted that how the reduction can be realized on actual antenna structures still remains unknown. In this paper, we focus on the investigation of the coherence relationship based on antennas' equivalent radiation sources rather than actual structures. This work is a first step towards the antenna optimization for MCI. The spatial modulation implemented in the numerical simulations avoids  
Figure 6: The coherence relationships obtained in the Ansoft HFSS simulation: (**a**) \(\mu^{\mathrm{T}}(\mathbf{H})\leftarrow\mu^{\mathrm{T}}(\mathbf{S})\) and (**b**) \(\mu(\mathbf{H})\leftarrow\mu(\mathbf{S})\).