The Effect of the Eigenvalues of the Zero-Forcing Detector on Its Performance in the Space-Division Multiplexing System

Abstract

Zero-Forcing (ZF) detector is used in Space-Division Multiplexing (SDM) receiver to remove interference among the received symbols. Previous works showed that the power of channel noise is enhanced in the output of the ZF detector. They recommend using the ZF detector when the received Signal-to-Noise Ratio (SNR) is high. This work proves that the performance of the ZF detector depends on the eigenvalues of the channel correlation matrix. The paper shows that if the sum of the eigenvalues of this correlation matrix is equal to the rank of the channel matrix, the ZF detector will not enhance noise power at its outputs. Moreover, if the sum of the eigenvalues is smaller than the rank of the channel matrix, the ZF detector will reduce noise power at its outputs. In this work, a theorem, which demonstrates the performance of the ZF detector in SDM receiver, is introduced and proved. The proposed work uses smart antennas in the transmitter and receiver to control the elements and eigenvalues of the channel matrix. The introduced theorem and a complete SDM receiver with ZF detector are simulated and evaluated at different conditions with different criteria. A real-time SDM receiver with ZF detector is also implemented and evaluated. The simulation and implementation results are shown at the end of this study. The results of the proposed systems show that a ZF detector can be used to remove interference in the SDM system without enhancing the channel noise.