**1. Introduction**

Conformal antenna arrays are beneficial for applications that need an antenna to be placed on a non-flat surface, for example, on the fuselage of a UAV/airplane in the aerospace industry [1–3], implantable sensors in wearable networks [4–8], and satellite communications [9–11]. One of the main advantages of using conformal antenna is its structural integration ability on singly curved (e.g., a wedge/cylinder) [12–15] and doubly curved (like a sphere) surfaces [16]. This can be very useful in applications where using definite flat surface may not be a practical design choice. Another exciting application of conformal antenna array is at the base station in a cellular mobile communication system. Today, mobile service providers are utilizing three separate antenna panels (dipole or monopole array) in a cell for a 120° sector coverage. What about, if one cylindrical array is used instead of three dipole arrays [17]? This can result in a much smaller transmitter requirement with 360° azimuthal coverage plus reduced base station size at a lower cost (specifically beneficial in crowded residential areas where cellular companies have to rent the space for base station installation).

On the other hand, these curved surfaces may be subjected to intentional (e.g., flexing wings of a UAV/aircraft) and/or unintentional (bending of aircraft wings due to severe weather conditions/vibrations) forces that change the shape of the

surface [12]. As a result, the radiation pattern of the conformal antenna array is changed as shown in **Figure 1**. The results in [18] indicate that directivity of conformal antenna array can be reduced by 5–15 dB. In the literature, various methods have been proposed to compensate the reduction in directivity and to improve/correct the radiation pattern of a conformal antenna array. In [1–3, 11, 19–21], mechanical calibration techniques have been used to steer the main beam on a conformal surface in the desired direction. In [12, 13, 15, 16, 22–25], projection method of [26] is used to correct the main beam direction of a deformed/flex surface. In [27–30], various optimization algorithms have been used to control the radiation pattern of conformal antenna arrays. In summary, it has been shown that the radiation pattern of a conformal antenna array can be improved with different calibration techniques, signal processing algorithms, sensor circuitry, and phase and amplitude adjustments.

This chapter will focus on phase compensation of four-element conformal cylindrical antenna array using (1) projection method and (2) convex optimization method. First, a brief introduction and working principle of phase compensation is presented using projection method. Then, array factor expression will be derived to compensate the radiation pattern of conformal cylindrical array. Then, the convex optimization algorithm will be discussed to compute the array weights for pattern recovery of conformal cylindrical array. Then, compensated gain using both the methods will be compared to linear flat array to explore the gain limitations of these compensated techniques for conformal antenna arrays. Finally, conclusion and future work are presented.
