Capacity lower bound and energy efficiency of training‐based MIMO systems over correlated channels

Abstract

SUMMARYThe behavior of training-based multiple-input multiple-output wireless communications over correlated channels is studied in the low signal-to-noise ratio (SNR) regime from an energy efficiency perspective. To start with, a relaxed but analytically more tractable capacity lower bound is derived where the impacts of channel spatial correlation are considered simply through the ranks of correlation matrices. It shows that, different from the independent and identically distributed case, the optimal training length no longer equals the number of transmit antennas but is just the same as the rank of transmit correlation matrix. Next, the bit energy requirements are analyzed based on the derived capacity lower bound. It shows that the minimum bit energy required for reliable communication is achieved at a nonzero SNR value below, which the bit energy grows to infinity with a zero-approaching wideband slope. Flash training and transmission scheme is also studied and shown to improve the energy efficiency. In addition, the impacts of spatial correlation, channel coherence interval and antenna number on the energy efficiency are analyzed. It shows that stronger spatial correlation leads to less bit energy, i.e. higher-energy efficiency. The minimum bit energy is achieved at lower SNR in a more correlated channel. Spatial correlation also helps to reduce the signal peakiness in the flash scheme. And larger coherence interval always improves energy efficiency at all SNR. Finally, the validity of the proposed results is verified by numerical simulations.