Arbitrary beam synthesis of hybrid beamforming systems for beam training

For future millimeter wave mobile communication systems, the use of analog/hybrid beamforming is envisioned to be an important aspect. The synthesis of beams is a key technology to enable the best possible operation during beam search and data transmission. The method for synthesizing beams developed in this letter is based on previous work in radar technology considering only phased array antennas. With this technique, it is possible to generate a desired beam of any shape with the constraints of the desired target transceiver antenna frontend. It can cope with 1-D, 2-D, and even 3-D antenna array geometries, e.g., cylindrical arrays. The numerical examples show that the method can synthesize beams by considering a user defined tradeoff between gain, transition width, and passband ripples. Since this beam synthesis method is computationally complex, it is only suitable for offline calculation during the design or calibration of a device.