Lattice-based Linear Equalization for Single Carrier and Multi Carrier Transmission over Doubly Selective Channels

This paper studies a lattice-based linear equalization (LLE) approach over doubly selective channels (DSCs). At the transmitter, the message sequence is encoded using a ring code, which is also a simple yet powerful lattice code. The resultant coded digits are one-to-one mapped to PAM symbols. The receiver carries out linear filtering and computes the a posteriori probabilities (APPs) of some integer linear combinations (ILCs) of the coded digits. Next the APPs of the ILCs are converted into APPs of the coded digits, which are then utilized for channel-code decoding. The optimized linear filter and and integer coefficient matrices for the proposed LLE based scheme are presented. Featuring a parallel processing architecture, our proposed LLE approach outperforms the traditional linear equalizers, such as linear minimum mean square error (MMSE) without significantly increased complexity. Further, we put forth a double-layer iterative (DLI) decoding method for a linear block codes coded LLE scheme. The integer coefficient matrices and the paritycheck matrix code are concatenated to form the effective Tanner graph, and based on which the soft-in-soft-out (SISO) decoding is carried out. Extensive numerical results demonstrate that the developed LLE approach achieves considerably improved bit error rate performance over DSCs for both single-carrier and multi-carrier systems.