Kalman Combining Based Iterative Detection and Decoding for MIMO Systems With Hybrid ARQ

Abstract

This study proposes Kalman combining-based iterative detection and decoding (KC-IDD) schemes for multiple-input multiple-output (MIMO) systems with hybrid automatic repeat request (HARQ). The conventional Kalman filtering (KF) operation for Kalman combining performs the linear minimum mean-square error (LMMSE) detection with symbol-level combining (SLC), but it is unable to utilize <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information of retransmitted symbols. Therefore, a new KF operation is derived, wherein an observation adjustment is employed to adjust the observation for a given state of the state-space model with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information instead of directly utilizing it into the KF operation. Based on the modified KF operation, two KC-IDD schemes are developed: i) KC-IDD with the single-state observation adjustment, i.e., the observation adjustment for the current HARQ round, and ii) KC-IDD with multi-state observation adjustment (KC-IDD-MS), i.e., the observation adjustments throughout the HARQ rounds of a packet. Therefore, the proposed schemes can perform SLC-based LMMSE-IDD, where the complexity for a given number of turbo iterations is similar or smaller to that of the conventional LMMSE-IDD scheme with bit-level combining (BLC). Furthermore, the simulation results show that regardless of the retransmission strategy, the proposed schemes, especially the KC-IDD-MS scheme, outperformed the conventional LMMSE-IDD scheme in terms of error performance and decoding convergence speed for retransmissions.