Optimum Synthesis of Pencil Beams with Constrained Dynamic Range Ratio

Algorithm 1

Search for pencil beam array with minimum DRR and specified beam efficiency.

(1)	specify N, BW, BEdes, and εtol
(2)	for specified N and BW calculate
	coefficients aDPSS of DPSS array
	coefficients a1 by using method in Section 2.6 with D = 1
(3)	calculate
	BEhigh as beam efficiency of array with coefficients aDPSS
	BElow as beam efficiency of array with coefficients a1
(4)	if BEdes > BEhigh then
	error: BEdes is too large for given N and BW
	end if
(5)	if BEdes < BElow then
	error: BEdes is too small for given N and BW
	end if
(6)	calculate DRRhigh as dynamic range ratio of aDPSS
(7)	set DRRlow = 1 // dynamic range ratio of a1
(8)	while (DRRhigh − DRRlow) > εtoldo
	calculate D = (DRRlow + DRRhigh)/2
	calculate coefficients a by using method in Section 2.6
	calculate BE as beam efficiency of array with coefficients a
	if BE < BEdesthen
	DRRlow = D
	else
	DRRhigh = D
	end if
	end while
(9)	set aopt = a, DRRopt = D, and BEopt = BE
(10)	return aopt, DRRopt, and BEopt