Transmit beamforming for frequency-selective channels with decision-feedback equalization

In this paper, we propose beamforming schemes for frequency-selective channels with decision-feedback equalization (DFE) at the receiver and with, respectively, perfect and quantized channel state information (CSI) at the transmitter. For beamforming with perfect CSI and infinite impulse response (IIR) beamforming Alters (BFFs) we provide a closed-form expression for the optimum BFFs. We also devise two efficient numerical methods for recursive calculation of the optimum finite impulse response (FIR) BFFs with perfect CSI. For beamforming with quantized CSI and finite-rate feedback channel, we propose a global vector quantization (GVQ) algorithm for codebook design. This algorithm is deterministic and independent of initial conditions and does not impose any constraints on the number of transmit and receive antennas, the antenna correlation, or the fading statistics. Our simulation results for typical GSM/EDGE channels show that in general short FIR BFFs are sufficient to closely approach the performance of IIR BFFs even in severely frequency-selective channels. Furthermore, finite-rate feedback beamforming with only a few feedback bits achieves significant performance gains over single-antenna transmission, transmit antenna selection, and optimized delay diversity in frequency-selective fading.