We propose a low-complexity closed-loop spatial multiplexing method with limited feedback over multi-input-multi-output (MIMO) fading channels. The transmit adaptation is simply performed by selecting transmit antennas (or substreams) by comparing their signal-to-noise ratios to a given threshold with a fixed nonadaptive constellation and fixed transmit power per substream. We analyze the performance of the proposed system by deriving closed-form expressions for spectral efficiency, average transmit power, and bit error rate (BER). Depending on practical system design constraints, the threshold is chosen to maximize the spectral efficiency (or minimize the average BER) subject to average transmit power and average BER (or spectral efficiency) constraints, respectively. We present numerical and Monte Carlo simulation results that validate our analysis. Compared to open-loop spatial multiplexing and other approaches that select the best antenna subset in spatial multiplexing, the numerical results illustrate that the proposed technique obtains significant power gains for the same BER and spectral efficiency. We also provide numerical results that show improvement over rate-adaptive orthogonal space-time block coding, which requires highly complex constellation adaptation. We analyze the impact of feedback delay using analytical and Monte Carlo approaches. The proposed approach is arguably the simplest possible adaptive spatial multiplexing system from an implementation point of view. However, our approach and analysis can be extended to other systems using multiple constellations and power levels.
Ko, Y., & Tepedelenlioglu, C. (2008). Threshold-based substream selection for closed-loop spatial multiplexing. IEEE Transactions on Vehicular Technology, 57(1), 215. https://doi.org/10.1109/TVT.2007.905392