  Satellite communications (SatComs) are anticipated to provide global Internet
access. Low Earth orbit (LEO) satellites (SATs) have the advantage of providing
higher downlink capacity owing to their smaller link budget compared with
medium Earth orbit (MEO) and geostationary Earth orbit (GEO) SATs. In this
paper, beam-broadening algorithms for uniform rectangular arrays (URAs) in LEO
SatComs were studied. The proposed method is the first of its kind that jointly
considers the path loss variation from SAT to user terminal (UT) due to the
Earth's curvature to guarantee quality of service (QoS) inspired by the
synthesis of isoflux radiation patterns in the literature, constant modulus
constraint (CMC) favored for maximizing power amplifier (PA) efficiency, and
out-of-beam radiation suppression to avoid interference. A URA design problem
is formulated and decomposed into two uniform linear array (ULA) design
subproblems utilizing the idea of Kronecker product beamforming to reduce the
computational complexity of designing URA.The non-convex ULA subproblems are
solved by a convex iterative algorithm. Simulation results reveal the
advantages of the proposed method for suppressing out-of-beam radiation and
achieving design criteria. In addition, channel capacity evaluation is carried
out and shows that the proposed ``broadened-beam" beamformers can offer
capacities that are at least four times greater than ``narrow-beam" beamformers
employing an array steering vector when beam transition time is taken into
account. The proposed method holds potential for LEO broadcasting applications
such as digital video broadcasting (DVB).
