In order to reduce the cost and power consumption of radio frequency (RF) chains in a millimeter-wave (mmWave) multiple-input multiple-output (MIMO) system, hybrid analog/digital beamforming (HBF) can be utilized to reduce the number of RF chains. The HBF consists of an analog beamforming (ABF) stage and a digital beamforming (DBF) stage. The ABF is always realized by using phase shifters and the DBF is done in a low-dimensional digital domain. However, phase shifters have several drawbacks, such as high power consumption and inconsistency of insertion loss. In this paper, we propose an energy-efficient HBF structure to handle these problems, which utilizes the Butler phase shifting matrix in the ABF stage. With the Butler-matrix-based ABF, several fixed beam directions can be obtained, and the best beam directions of different Butler matrices can be chosen by using exhaustive search. To reduce the high complexity of exhaustive search, we further provide a low complexity HBF algorithm. Simulations under the conditions of perfect channel state information (CSI) and estimated CSI verify the effectiveness of our proposed Butler-matrix-based HBF structure and related algorithms.
Figure 1
The Butler-matrix-based HBF structure for mmWave MIMO systems.
Figure 2
(Color online) The ergodic achievable downlink sum SE vs. $\rho$ under the condition of perfect CSI: $N_\text{s}= N = 4, M = 8, N_{\rm t}= 32, K = 2, N_{\text{s}k}= N_k = 2, M_k = 4, N_{\text{r}k}= 8$.
Figure 3
(Color online) The ergodic achievable downlink sum SE vs. $\rho$ under the condition of estimated CSI: $N_\text{s}= N = 4, M = 8, N_{\rm t}= 32, K = 2, N_{\text{s}k}= N_k = 2, M_k = 4, N_{\text{r}k}= 8$.
Figure 4
(Color online) EE vs. SE under the condition of perfect CSI: $N_\text{s}= N = 4, M = 8, N_{\rm t}= 32, K = 2, N_{\text{s}k}= N_k = 2, M_k = 4, N_{\text{r}k}= 8$.
Figure 5
(Color online) EE vs. SE under the condition of estimated CSI: $N_\text{s}= N = 4, M = 8, N_{\rm t}= 32, K = 2, N_{\text{s}k}= N_k = 2, M_k = 4, N_{\text{r}k}= 8$.
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