On the Performance of a Multi-User Multi-Antenna System with Transmit Zero-Forcing Beamforming and Feedback Delay

This paper considers zero-forcing beamforming (ZFBF) at the transmitter for a downlink multi-user multiple-input single-output (MU-MISO) system. Transmit beamforming as a simple yet efficient technique can exploit the benefits of multiple transmit antennas provided that the instantaneous channel state information (CSI) is known at both sides of transmission link. In order to have such improvements, the CSI at both link ends must be updated timely. However, the updating process is always subject to non-ideality such as feedback delay and estimation error, which destroy the orthogonality of the parallel channels and cause the mismatch between the actual channel characteristic and the modulation matrices used. By analyzing the effect of feedback delay on the performance of capacity with spectral efficiency and outage probability as benchmarks, we design a cross-layer scheduler combining semi-orthogonal user selection (SUS) algorithm at the medium access control (MAC) layer to reduce the inter-user interferences and an adaptive proportional weighted modulation (APWM) algorithm at the physical (PHY) layer to address the problem of such mismatch, and compare the proposed scheduler (APWM-SUS) with the naive scheduler (the rate modulation matrices designed for the perfect CSI). Finally, simulation and numerical results reveal significant gains and high feasibility.