Abstract
In conventional multiple-input multiple-output systems, each antenna is connected to a radio-frequency (RF) chain. Due to the tiny wavelength of millimeter waves (mmWave), tens of antennas can be packed into a small area in mmWave transceivers. However, implementing an RF chain for each antenna is impractical due to the high cost and power of mixed-signal devices. In order to reduce the cost and get benefit from the antennas, an analog RF beamformer is implemented using variable gain amplifiers and analog phase shifters. In this paper, we propose a novel spatial diversity scheme for mmWave RF beamforming. The transmitter is assumed to have partial knowledge of the channel to the receiver. We formulate the spatial diversity problem as maximizing the geometric mean of the projections of the RF precoder on the transmit steering vectors and the geometric mean of the projections of the RF combiner on the receive steering vectors. To solve the optimization problem of the RF beamformers, we propose two solution algorithms. The first algorithm is based on semidefinite relaxation (SDR). Due to the high computational complexity of the SDR algorithm, we propose a simpler second algorithm, which is gradient ascent algorithm. Simulation results show that the proposed spatial diversity scheme outperforms the conventional spatial diversity schemes in case of no blockage and in case of blockage to any propagation path regardless of the number of propagation paths.