This paper focuses on studying the fundamental performance limits and linear dispersion code design for the MIMO-ARQ slow fading channel. Optimal average rate of well-known HARQ protocols is analyzed. The optimal design of space-time coding for the MIMO-ARQ channel is discussed. Information-theoretic measures are used to optimize the rate assignment and derive the optimum design criterion, which is then used to evaluate the optimality of existing space-time codes. A different design criterion, which is obtained from the error probability analysis of space-time coded MIMO-HARQ, is presented. Examples are studied to reveal the gain of ARQ feedback in space-time coded MIMO systems.

Abstract—This paper presents a comprehensive study on the problem of decoding complexity in a Multi-Input Multi-Output (MIMO) Hybrid Automatic Repeat reQuest (HARQ) system based on Space-Time Block Codes (STBCs). We show that there exist two classes of fast-decodable MIMO HARQ systems: independent and dependent STBC structures. For the independent class, two types of protocols namely, fixed and adaptive threshold-based are presented and their effectiveness in both computational complexity reduction and spectral efficiency preservation are discussed. For the dependent class, a fast Sphere Decoder (SD) algorithm with a low computational complexity is proposed for decoding process of HARQ rounds. Two new concepts are introduced to leverage the fast-decodable notion in MIMO HARQ systems. Simulation results show that the proposed fast-decodable MIMO HARQ protocols in both classes provide a significant reduction in the decoding complexity as compared with the original MIMO HARQ method.