I. Introduction
Retro-directive beamforming technique has been investigated for decades with the aim of accomplishing efficient wireless power transmission over long distance. Its best-known application is space solar power, in which solar power is scavenged by satellites in the outer space and then transmitted to the earth using microwave beam [1]. When retro-directive beamforming is applied to space solar power, ground station on the earth sends pilot signal to the satellite and the satellite adjusts its power beam's direction to be opposite to the pilot signal's incoming direction. Because space solar power involves a large number of economic and societal issues in addition to technical issues, its feasibility is still under discussion at present. In recent years, research efforts on wireless power transmission are strongly motivated by the practical demand to charge mobile/portable electronic devices (such as wireless sensors) wirelessly. As a distinctive difference from space solar power applications, mobile/portable devices do not require the wireless power transmitter to reside far away, typically closer than 10 meters [2]. In scenarios that call for wireless power transmission over several meters, it is sometimes impossible to identify one explicit direction to characterize the interaction between wireless power transmitter and wireless power receiver. Consequently, retro-directive beamforming cannot be directly applied and it is more appropriate to employ retro-reflective beamforming [3]. Retro-reflective beamforming and retro-directive beamforming share the same fundamental principle, which is using pilot signal to guide power propagation. Whereas the wireless power transmitter in retro-directive beamforming behaves as a conventional phased array antenna, the wireless power transmitter in retro-reflective beamforming is more like a near-field focusing antenna. In other words, the wireless power transmitter in retro-reflective beamforming is desired to construct a focal point at the wireless power receiver's location, which resides in the transmitter's near-zone (rather than far-zone). To be more important, the wireless power transmitter in retro-reflective beamforming is not desired to construct any focal points other than the wireless power receiver's location and its far-zone gain must be minimized to prevent electromagnetic interference.