Calculation of the Total Radiated Power for 4-D Antenna Arrays With Arbitrary Time Modulated Waveform

When it comes to four-dimensional (4-D) antenna arrays, calculating the power in sideband radiation is a tough nut to crack since there exists an infinite summation of all the harmonics and the more complicated time modulated waveforms (TMWs). In this communication, we derived some simple but general expressions to tackle the problem of the power calculation in 4-D antenna arrays. On the one hand, the expressions are appropriate for 4-D antenna arrays with arbitrary TMWs and arbitrary array geometry. On the other hand, the proposed expressions can be directly used for accurately and efficiently evaluating the array performance, and discussing the performance of antenna arrays with different TMWs. Some examples are given to illustrate their universality and accuracy for time modulated arrays (TMAs) with real-valued, complex-valued and nonuniform period TMWs.