Performance of Hybrid-ARQ in Block-Fading Channels: A Fixed Outage Probability Analysis (0811.4191v3)

Abstract: This paper studies the performance of hybrid-ARQ (automatic repeat request) in Rayleigh block fading channels. The long-term average transmitted rate is analyzed in a fast-fading scenario where the transmitter only has knowledge of channel statistics, and, consistent with contemporary wireless systems, rate adaptation is performed such that a target outage probability (after a maximum number of H-ARQ rounds) is maintained. H-ARQ allows for early termination once decoding is possible, and thus is a coarse, and implicit, mechanism for rate adaptation to the instantaneous channel quality. Although the rate with H-ARQ is not as large as the ergodic capacity, which is achievable with rate adaptation to the instantaneous channel conditions, even a few rounds of H-ARQ make the gap to ergodic capacity reasonably small for operating points of interest. Furthermore, the rate with H-ARQ provides a significant advantage compared to systems that do not use H-ARQ and only adapt rate based on the channel statistics.

• The paper demonstrates that Hybrid-ARQ enables rates to nearly approach ergodic capacity with just a few retransmission rounds despite only having statistical channel knowledge.
• It analyzes how increasing the maximum number of H-ARQ rounds substantially improves average transmission rates compared to non-H-ARQ systems.
• Numerical simulations with Gaussian approximations verify that H-ARQ integration enhances spectral efficiency in fast-fading, delay-sensitive wireless networks.

Performance of Hybrid-ARQ in Block-Fading Channels: A Fixed Outage Probability Analysis

The paper by Peng Wu and Nihar Jindal investigates the performance of Hybrid Automatic Repeat reQuest (H-ARQ) protocols in Rayleigh block-fading channels. The research focuses on assessing the long-term average transmitted rate in a fast-fading scenario, where the transmitter is only aware of the channel statistics. The analysis is conducted under the constraint of maintaining a target outage probability, which is aligned with the operational techniques of contemporary wireless systems.

Key Contributions

1. Rate Adaptation via Hybrid-ARQ: The paper demonstrates that Hybrid-ARQ provides an implicit mechanism for adapting to instantaneous channel quality, thereby enabling earlier termination if decoding becomes feasible. While H-ARQ does not achieve the ergodic capacity—obtainable with complete channel state information—it significantly narrows this gap with just a few retransmission rounds. This behavior offers a considerable performance advantage over systems that solely rely on statistics-based rate adaptation without H-ARQ.
2. Impact of Maximum H-ARQ Rounds: The authors emphasize the relationship between the number of allowed H-ARQ rounds and system performance. Specifically, as the maximum number of H-ARQ rounds increases, the operational rate approaches the ergodic capacity. This convergence is due to the enhanced capability of H-ARQ to adapt to channel variations, thus reducing the effective negative impact of the unknown instantaneous channel conditions.
3. Comparison with Non-H-ARQ Systems: It is notable that the system using H-ARQ can achieve higher average transmission rates compared to non-H-ARQ systems at the same level of diversity (determined by the number of fading blocks experienced by each codeword). The finding positions H-ARQ as a superior technique under certain fast-fading conditions, whereby traditional fixed-rate strategies mandate a conservative rate selection to meet outage constraints.
4. Numerical Verification and Theoretical Bounds: Through both theoretical derivations and numerical simulations, the paper validates its assertions. The authors use Gaussian approximations to simplify the performance analysis, offering practical insights into the achievable rates under various configurations. The analysis reveals that the gap between H-ARQ performance and the ergodic capacity diminishes as the number of rounds increases.
5. Performance with Chase Combining: The paper also evaluates Chase Combining (CC) against Incremental Redundancy (IR) H-ARQ. It concludes that while CC may offer advantages at low SNR due to SNR accumulation, it suffers at high SNR because of its inherent repetition coding strategy, thus limiting its spectral efficiency as compared to IR.

Theoretical and Practical Implications

The work presents a comprehensive view on utilizing H-ARQ for rate adaptation in environments where channel state information is limited to statistical knowledge. The insights suggest that integrating H-ARQ can enhance spectral efficiency in modern wireless systems, particularly in scenarios with fast channel variations and stringent delay constraints. This relevance is applicable in high-mobility contexts, such as vehicular networks and mobile users in urban environments, potentially guiding future protocol design in these areas.

Future Directions

Considering the implications presented, further research could explore the integration of H-ARQ with higher-layer ARQ systems, accounting for practical considerations such as feedback errors and implementation complexities. The extension of this work into multi-antenna systems or systems operating with discrete constellations would also provide deeper insights, potentially enhancing the robustness and efficiency of next-generation wireless communication systems.

In summary, Peng Wu and Nihar Jindal's paper provides significant contributions to understanding the potential benefits and limitations of H-ARQ for achieving fixed outage probabilities in fast-fading environments. The analysis presents compelling arguments for adopting H-ARQ in contemporary and future wireless systems, underscoring its efficacy in elevating average spectral efficiency while maintaining system reliability.