Signal Designs for Non-negative Channels

Abstract

In this thesis, we would like to design signals for non-negative channels in some wireless communication systems such as visible light communication (VLC) systems and massive multiple-input and multiple-output (MIMO) RF communication systems. In the first part of this thesis, we consider the design of the optimal precoding matrix for an indoor multiple-input and multiple-output visible light communication system with a zero-forcing (ZF) equalizer and a threshold detector. We assume that the channel state information (CSI) is available at both transmitters and receivers. For such a system with non-negative $q$-PAM modulation, we propose an optimal precoding matrix design for transmitted signals such that the average symbol error probability (SEP) (or the bit error rate (BER)) is minimized. On the one hand, in the low SNR regime, our theoretical analysis suggests that we need to turn off one of two transmitters, and let the other work individually. Meanwhile, the constellation size should be improved to maintain the transmission rate. On the other hand, in high SNR scenario, both transmitters should transmit concurrently. The computer simulations show that in high SNR, BER for our proposed design is better than that of currently available methods.

In the second part of this thesis, considering the non-negative constraint on the transmitted signal and the channel in VLC systems, we are interested in designing a two-dimensional non-negative constellation with a specific unique decomposition. Compared with repetition coding (RC), spatial multiplexing (SMP) and spatial modulation (SM), space-collaborative constellation (CC) has the lowest average normalized optical power and better error performance in practical application for VLC. As for the multi-user situation, by using a recently developed concept called additively uniquely decomposable constellation group (AUDCG), a whole (sum) constellation can be uniquely decomposed into several sub constellations to serve multi users at the same time. However, not all the CC can be decomposed into AUDCG. Then, we introduce several new methods to design a 2-dimensional constellation based on the idea of CC and AUDCG, which can serve two users with different priority strategies. The simulation result shows that our constellation design has lower average symbol error probability than traditional SMP in all strategies.