5. Synthesis of time-modulated antenna arrays

## 5.1 Pattern synthesis parameters

In Section 3.3, it is observed that, though the conventional amplitude tapering methods such as Dolph-Chebyshev and Taylor series can be used to obtain the power pattern of the desired SLL with minimum beamwidth at the operating frequency of time-modulated antenna arrays, these methods are not useful to control the undesired power radiated at different sidebands. Similarly, it is also observed that application of the stochastic computational technique, such as GA, for suppressing side lobe level of the center frequency pattern without taking into account the sideband radiation, cannot reduce sideband signal power. Also, the beamwidth of such patterns is unpredictable. The power pattern with low SLL and suppressed sideband is preferred for the different communication systems.

Therefore, the parameters to be considered to synthesize pencil beam pattern in TMAAs as shown in Figure 5 are SLL, FNBW, and SBL. However for the shaped beam pattern such as flattop and cosec squared, in addition to these three parameters, ripple level in the desired shaped region is another parameter to be taken into account. Further, it can be observed that while SLL is reduced, FNBW is increased and SBL is significantly large. In this regard, SLL, SBL, and FNBW for pencil beam pattern and SLL, SBL, FNBW, and ripple level for synthesizing shaped beam patterns are the conflicting parameters.

### 5.2 Multiple objectives

In Eq. (13), the cost function is defined to synthesize the power pattern with a single objective that is to achieve the desired value of SLL in the synthesized power pattern. Conversely, the synthesized pencil beam patterns at the operating frequency should have reduced SLL along with sufficiently suppressed SBL and narrow beamwidth. Thus, TMAA synthesis problems are multi-objective optimization problems where the multiple objectives are low SLL and narrow beamwidth (BW)

of the main beam at operating frequency and low value of maximum sideband level (SBLmax) for synthesizing pencil beam pattern while one more objective is low ripple level for synthesizing shaped beam patterns.
