Hierarchical Beamforming for Broadcast Channels

For massive multi-input multi-output (mMIMO) cellular communications, the conventional discrete Fourier transform (DFT) based beamforming yields narrow beams of high directional gain, but it usually requires too many time slots for sweeping the beams to broadcast common messages. To reduce the time of beam sweeping while maintaining sufficient beamforming gain, this letter proposes a hierarchical beamforming (HierBF) scheme. By partitioning a large uniform rectangular array (URA) into multiple sub-URAs, first we apply the omnidirectional beamforming (OBF) to each sub-URA to transform it into a virtual high-power antenna, thus, the large URA is virtually transformed into a smaller array; second we apply the DFT codebook on the smaller virtual array to obtain wider beams, thus, the beam sweeping can be completed in fewer time slots. The HierBF scheme can accommodate to more flexible antenna array sizes than a similar technique termed array-size invariant (ASI). Besides, the HierBF scheme has a complexity of O(1) , and can be implemented using an analog phase shifter network (PSN) with a coarse phase resolution.