**4.2 Cylindrical surface with radii of curvatures** *r* **= 10, 12, 15 cm**

When radii of curvatures of cylindrical surface array increase (less deformation), both the projection and convex optimization (phase correction only) methods recover the broadside radiation pattern with decreasing gap between corrected and uncorrected gains as shown in **Figures 5–7** and are also tabulated in **Table 1**. The gain *Gc* (between uncorrected and corrected) and *Gref* (between corrected and linear) decreases with increase in *r*. However, it is obvious that in all cases, the

#### **Figure 4.**

*(a) Analytical results for phase compensation of a conformal cylindrical antenna array with r = 8 cm. (b) CST simulation results for phase compensation of a conformal cylindrical antenna array with r = 8 cm.*

**Figure 5.**

*(a) Analytical results for phase compensation of a conformal cylindrical antenna array with r = 10 cm. (b) CST simulation results for phase compensation of a conformal cylindrical antenna array with r = 10 cm.*

compensated gain is less than the ideal gain (linear array) for both projection and convex optimization methods. This is an important finding and must be kept in design stages of conformal antenna arrays.
