## 4 A Method of Improving the Radiation Efficiency of an MAA  
In general, resonant elements with varying amplitude responses in frequency are realistically achievable. Specifically, different amplitude distributions of the elements on an MAA are represented by the varying radiation efficiencies on the aperture. However, there is a trade-off between the \(Q\)-factor and the radiation efficiency of these elements [19]. Additionally, an increase in the \(Q\)-factor of the element on the metamaterial aperture causes \(\mu_{g}\) to decrease [13]. Hence, a trade-off between the average mutual coherence \(\mu_{g}\) and the radiation efficiency of the MAA must be made. Usually the MAA is composed of all the strongly resonant elements, such as a CELC [15]. Figure 4 shows the radiation characteristic of a CELC element. The PMC (Perfect Magnetic Conductor) boundary used here is meant to represent the periodic boundary condition that is used to model an infinite metamaterial aperture antenna in practice. It can be seen that, when size parameters \(g\) and \(l\) decrease, the resonant frequency of the CELC increases and the CELC element has an agile radiation efficiency response across the frequency band. However, the element has a very low radiation efficiency, with a peak value of approximate 50% and a bandwidth of \(\Delta f\approx\) 0.1 GHz. In this case, a low \(Q\)-factor element can be introduced to increase the radiation efficiency without significantly destroying \(\mu_{g}\). The CJC unit cell [16] is adopted, which has a low quality factor but a radiation efficiency that is superior to that of the CELC element, as shown in Figure 5.  
In this paper, the improved strategy of the MAA design is a combination of CELC and CJC elements. However, the ratio of the CJC elements distributed on the aperture is crucial, which causes a balance problem between the \(\mu_{g}\) and the radiation efficiency of the antenna. To illustrate this, we analyze the performances of the MAA with 20 \(\times\) 20 elements, when the ratio of CJC elements  
Figure 3: Comparison of the average mutual coherence \(\mu_{g}\) between phase and amplitude modulation. changes from 0 to 50%. On the aperture, the CELC elements are used to generate frequency-diverse field patterns. The CJC elements that are used to improve the radiation efficiency are placed on the remaining part of the aperture with a certain ratio. Using a full-wave simulation tool, the radiation efficiency of the CJC element is obtained in the frequency band from 33 to 37 GHz, as shown in Figure 5b. It can be seen that the CJC element has a good radiation ability. When the filling ratio of CJC elements on the MAA is changed from 0 to 50%, as shown in Figure 6, the average mutual coherence \(\mu_{g}\) will vary from 0.115 to 0.377, as shown in Figure 7a. The radiation efficiency of the MAAs with different ratios of CJC elements is shown in Figure 7b. We can see in Figure 7 that the increase in radiation efficiency causes \(\mu_{g}\) to increase. As a result, to obtain a relatively high radiation efficiency and a low \(\mu_{g}\), the ratio of CJC elements must be selected as 20% since its radiation efficiency has been improved to around 60% and its capability of imaging reconstruction approaches that of a metamaterial aperture without CJC elements. Figure 4: The complementary electric-field-coupled (CELC) element with a unit cell size of 2 mm: (**a**) full-wave simulation model; (**b**) its top view; (**c**) the variation in radiation efficiency when \(l\) and \(g\) change. Figure 5: (**a**) Top view of complementary Jerusalem cross (CJC) element with a unit cell size of 2 mm and (**b**) a radiation efficiency of the element. Thus, the prototype of a metamaterial aperture antenna, with 120 \(\times\) 120 randomly distributed CELC and CJC elements, whose total size is 250 mm \(\times\) 250 mm \(\times\) 0.5 mm was fabricated, measured, and analyzed. The fabricated MAA consisted of 80% CELC elements and 20% CJC elements, as shown in Figure 8b,c.