Serially Connected Bidirectional EP-Based Decision Feedback Equalization in MIMO-VLC System with Signal-Dependent Noise

To accurately detect signals in multiple-input multiple-output visible light communication (MIMO-VLC) systems, this paper proposes an expectation propagation (EP)-based decision feedback equalization (EP-DEF) algorithm. A free space optical channel model incorporating signal-dependent noise (SDN) for MIMO-VLC systems, and a constellation design method combining uniform modulation and square root modulation are applied. In this work, we first present the EP-DFE using both the a posteriori moments of estimated symbols and the a priori moments of unestimated symbols, and then two fast recursive schemes are developed to reduce the computational complexity. To further reduce the error propagation, the serially connected bidirectional EP-DFE (SC-Bi-EP-DFE) is introduced, which utilizes the output of the forward EP-DFE as the input of the backward EP-DFE. Finally, with considering the channel estimation error (CEE), the new autocorrelation and the new covariance matrix of received vectors are derived to obtain the equalizer coefficients. Simulation results show that the proposed SC-Bi-EP-DFE provides good performance at an acceptable computational cost, especially for the degraded channels. With the CEE, our proposed method can achieve significant performance improvement without increasing complexity. Therefore, it is a promising candidate for application in practical MIMO-VLC systems.