Multi-Resolution Codebook Based Beamforming Sequence Design in Millimeter-Wave Systems

There is growing interest in using millimeter wave (mmWave) communication for fifth generation (5G) wireless systems because of the large bandwidth available in these frequencies. To overcome the higher path loss at mmWave bands, highly directional beamforming using large-scale, or massive, multiple-input multiple-output (MIMO) systems is critical. In this scenario, the problem of channel estimation becomes challenging due to the substantial training overhead needed to sound all possible beam directions using a high-resolution narrow beam. To tackle the issue of beam search in a mmWave system, we consider the use and design of multi-resolution beamforming sequences, which can quickly search out the dominant channel direction in a bisection manner. Given the multi-resolution codebook, the proposed multi-resolution beamforming sequence is designed to strike a balance between minimizing the training overhead and maximizing beamforming gain. We discuss how the multi-resolution codebook can be designed using a phase-shifted version of a {\em discrete Fourier transform} (DFT) matrix. Numerical results show the effectiveness of the proposed algorithm.