A New Look at Dual-Hop Relaying: Performance Limits with Hardware Impairments (1311.2634v2)

Abstract: Physical transceivers have hardware impairments that create distortions which degrade the performance of communication systems. The vast majority of technical contributions in the area of relaying neglect hardware impairments and, thus, assumes ideal hardware. Such approximations make sense in low-rate systems, but can lead to very misleading results when analyzing future high-rate systems. This paper quantifies the impact of hardware impairments on dual-hop relaying, for both amplify-and-forward and decode-and-forward protocols. The outage probability (OP) in these practical scenarios is a function of the effective end-to-end signal-to-noise-and-distortion ratio (SNDR). This paper derives new closed-form expressions for the exact and asymptotic OPs, accounting for hardware impairments at the source, relay, and destination. A similar analysis for the ergodic capacity is also pursued, resulting in new upper bounds. We assume that both hops are subject to independent but non-identically distributed Nakagami-m fading. This paper validates that the performance loss is small at low rates, but otherwise can be very substantial. In particular, it is proved that for high signal-to-noise ratio (SNR), the end-to-end SNDR converges to a deterministic constant, coined the SNDR ceiling, which is inversely proportional to the level of impairments. This stands in contrast to the ideal hardware case in which the end-to-end SNDR grows without bound in the high-SNR regime. Finally, we provide fundamental design guidelines for selecting hardware that satisfies the requirements of a practical relaying system.

• The paper introduces a generalized impairment model that captures composite distortions, including phase noise and amplifier nonlinearities, in dual-hop networks.
• It derives closed-form outage probability expressions and ergodic capacity bounds for both amplify-and-forward and decode-and-forward protocols under Nakagami-m fading.
• The study reveals a high-SNR SNDR ceiling phenomenon and offers practical design guidelines to mitigate hardware impairments in future wireless systems.

Comprehensive Analysis of Dual-hop Relaying under Hardware Impairments

This paper, titled "A New Look at Dual-Hop Relaying: Performance Limits with Hardware Impairments" by Emil Bjornson, Michail Matthaiou, and Merouane Debbah, investigates the ramifications of hardware impairments on dual-hop relay networks, specifically focusing on amplify-and-forward (AF) and decode-and-forward (DF) protocols. While the majority of existing research assumes ideal transceivers, this work addresses the significant impact that practical, non-ideal hardware has on communication systems, particularly in high-rate scenarios likely to characterize future standards.

Main Contributions

• Generalized Impairment Model: A general model is proposed to account for the composite effect of hardware impairments in dual-hop relaying systems. This captures the joint effect of distortions such as phase noise, I/Q imbalance, and high power amplifier nonlinearities as a single impairment measure at both the transmitter and receiver.
• Closed-form Expressions for Outage Probability (OP): The paper derives new closed-form expressions that quantify OP under hardware impairments for both AF and DF relaying protocols. This analysis addresses the impact across arbitrary signal-to-noise ratio (SNR) values, with a focus on Nakagami-m fading distributions.
• Ergodic Capacity Analysis: Expressions for upper bounds on the ergodic capacity are presented, illustrating how hardware impairments lead to performance degradation under different channel conditions.
• High-SNR Regime and SNDR Ceilings: The paper identifies a significant effect termed the "SNDR ceiling," where the end-to-end signal-to-noise-plus-distortion ratio (SNDR) converges to a deterministic constant at high SNR, fundamentally differing from ideal scenarios where SNDR grows indefinitely. The ceiling is inversely proportional to the level of impairments and establishes fundamental performance limits.
• Design Guidelines: The authors provide design insights for selecting transceiver hardware that meets practical system requirements, guided by the maximum permissible level of hardware impairments derived from their analysis.

Numerical and Theoretical Implications

The numerical results reinforce the theoretical claims, demonstrating only minor performance loss at low data rates due to hardware impairments, but substantial degradation as data rates increase. The paper emphasizes that while hardware impairments are often negligible in single-hop systems, they are crucial in dual-hop systems, especially at high SNRs. The identification of the SNDR ceiling is particularly impactful, as it offers a quantifiable basis for communications engineers to consider when designing relaying systems.

Future Perspectives

The implications of this research underscore the necessity of adapting current relay node designs to account for aggregate hardware impairments. The insights on SNDR and capacity ceilings suggest a need for new compensation algorithms or alternative architectures that can mitigate the practical limitations imposed by real-world transceiver imperfections. Future AI developments could focus on optimizing these strategies dynamically, leading to more robust and efficient communication systems.

In essence, this paper significantly advances our understanding of the constraints imposed by non-ideal hardware in dual-hop relaying, providing both theoretical foundations and practical guidelines for future wireless network designs. The findings have substantial implications for the development of communication systems that can reliably support high data rate demands in the presence of unavoidable hardware imperfections. The strategies and tools offered herein lay critical groundwork for further exploration and refinement of relay communication systems in the ever-evolving landscape of wireless technology.