Conventionally, subcarrier based beamforming was used in an OFDM (Orthogonal Frequency Division Multiplexing) system under MIMO (Multiple-Input and Multiple-Output) channels to achieve optimal performance, where many DFT/IDFT (Discrete Fourier Transform/Inverse DFT) blocks, each corresponding to one antenna, are required. To reduce the complexity induced by the DFT/IDFT processing, symbol based beamforming was recently proposed with only one IDFT block at the transmitter and one DFT block at. the receiver. However, this approach results in a significant performance loss especially when the number of distinct paths in the channel is large. In this paper, we propose a multi-stage beamforming (MSB) scheme for MIMO-OFDM systems employing both the principles of subcarrier level beamforming and symbol level beamforming to effectively tradeoff system performance and complexity. Using the proposed MSB scheme and with a little complexity increase compared with the symbol based beamforming, system performance can be significantly improved. Under some channel conditions, the proposed MSB scheme can achieve a performance close to the optimal subcarrier based beamforming scheme but with much lower complexity. For the MSB scheme, we propose an iterative algorithm to jointly optimize the symbol level and subcarrier level weighting coefficients. To reduce the complexity of the joint weighting coefficients calculation algorithm, we propose a reduced complexity algorithm to first obtain the symbol level weighting coefficients and then the subcarrier level weighting coefficients. Simulation results show that good performance can be achieved using the proposed weighting coefficients calculation algorithms with reasonable complexity.
Li, S., Huang, D., Letaief, K. B., & Zhou, Z. (2007). Multi-Stage Beamforming for Coded OFDM with Multiple Transmit and Multiple Receive Antennas. IEEE Transactions on Wireless Communications, 6(3), 959-969. https://doi.org/10.1109/TWC.2007.05251