Optimization Methods in Electromagnetic Radiation

Optimized arbitrary wireless device arrays for emergency response communications

“…In addition, Reference [5] provides a highly mathematical approach to the problem of optimizing electromagnetic radiation in a particular direction. References [6] through [9] consider probabilistic approaches to antenna array design, while References [10] and [11] The example configuration in figure 1 consists of four z-directed dipole elements over a perfect electric conductor (PEC) ground plane.…”

“…However, we want to optimize the electromagnetic radiation intensity for a particular direction, i.e., the z-direction, at a specific observation point within or near the boundaries of the (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16) of Reference [13], since that definition uses an R value corresponding to the far field of the array and assumes all the array elements are located at the origin. In our case, the distance between the observation points and the elements is not in the far field of the array, hence using /?^^p rovides a better mathematical representation of the overall behavior than simply using some nominal R value, such as the distance to the farthest observation point.…”

“…'n, =^l ix-x"f+{y-y"f +{z-z"f , (m* dipole source location) (4) m =^| ix -x"y +{y-y^f +{z + z" f , (image of the m* dipole source) (5) and r = V777^, (6) where F is the distance from the origin to the observation point. Other variables in eq (2) are k, which is the wavenumber, j = V^, and a, , which is the unit vector in the z- where co is the radian frequency, //q it the permeability of free space, and d{) is the impulse or delta function.…”

“…Using eq (11), the elements of e are given as _ R £ = . * Rn £"(r)andr=-^£:(F) (12) We want to maximize the ratio p = -, which equates to finding the largest B eigenvalue of Aa = AjBa , (13) where a represents a scaling of the current vector. Due to the structure of the matrices A and B, only one nonzero eigenvalue exists for eq (13).…”

“…Computation of the A and B matrices follows from eq (10) and eq (12), while optimization of the resulting gain is calculated from eq (14). Note in all the simulation runs, the radiating or array elements are located within the notional building volume, whereas the observation points may be either interior Number of Elements Figure 13 illustrates the gain obtained from using only the optimized phase information from eq (15) 13), as compared to approximately 1 dB per doubling of the elements when using the optimized magnitude information (see figure 1 0).…”