Codebook Design for Millimeter-Wave Channel Estimation With Hybrid Precoding Structure
In this paper, we study hierarchical codebook design for channel estimation in millimeter-wave (mmWave) communications with a hybrid precoding structure. Due to the limited saturation power of the mmWave power amplifier, we consider the per-antenna power constraint (PAPC). We first propose a metric, termed generalized detection probability (GDP), to evaluate the quality of an arbitrary codeword . This metric not only enables an optimization approach for mmWave codebook design, but also can be used to compare the performance of two different codewords/codebooks. To the best of our knowledge, GDP is the first such metric, particularly for mmWave codebook design. We then propose a heuristic approach to design a hierarchical codebook exploiting beam widening with the multi-RF-chain sub-array (BMW-MS) technique. To obtain crucial parameters of BMW-MS, we provide two solutions, namely, a low-complexity search (LCS) solution to optimize the GDP metric and a closed-form (CF) solution to pursue a flat beam pattern. Performance comparisons show that BMW-MS/LCS and BMW-MS/CF achieve very close performances, and they outperform the existing alternatives under the PAPC.