Energy efficiency of three common hybrid automatic repeat request (HARQ) schemes including Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR), is analyzed and joint power allocation and rate selection to maximize the energy efficiency is investigated in this paper. Unlike prior literature, time-correlated fading channels is considered and two widely concerned quality of service (QoS) constraints, i.e., outage and goodput constraints, are also considered in the optimization, which further differentiates this work from prior ones. Using a unified expression of asymptotic outage probabilities, optimal transmission powers and optimal rate are derived in closed-forms to maximize the energy efficiency while satisfying the QoS constraints. These closed-form solutions then enable a thorough analysis of the maximal energy efficiencies of various HARQ schemes. It is revealed that with low outage constraint, the maximal energy efficiency achieved by Type I HARQ is $\frac{1}{4\ln2}$ bits/J, while HARQ-CC and HARQ-IR can achieve the same maximal energy efficiency as $\frac{κ_\infty}{4\ln2}$ bits/J where $κ_\infty = 1.6617$. Moreover, time correlation in the fading channels has a negative impact on the energy efficiency, while large maximal allowable number of transmissions is favorable for the improvement of energy efficiency. The effectiveness of the energy-efficient optimization is verified by extensive simulations and the results also show that HARQ-CC can achieve the best tradeoff between energy efficiency and spectral efficiency among the three HARQ schemes.
This paper investigates the problem of power allocation for hybrid automatic repeat request (HARQ) schemes over time-correlated Nakagami-m fading channels under outage constraint. The presence of time correlation complicates the power allocation problem due to the involvement of multiple correlated fading channels. Under a general time-correlated Nakagami-m fading channel with exponential correlation, outage probabilities for three widely adopted HARQ schemes, including Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR), are first derived. With thes…
This paper proposes a general analytical approach to derive the outage probability of hybrid automatic repeat request with incremental redundancy (HARQ-IR) over correlated fading channels in closed-form. Unlike prior analyses, the consideration of channel correlation is one of the key reasons making the outage analysis involved. Using conditional Mellin transform, the outage probability of HARQ-IR over correlated Rayleigh fading channels is exactly expressed as a mixture of outage probabilities of HARQ-IR over independent Nakagami fading channels, where the weights are negative multinomial pro…
This paper analyzes the performance of cooperative hybrid automatic repeat request with incremental redundancy (HARQ-IR) and proposes a new approach of outage probability approximation for performance analysis. A general time-correlated Nakagami fading channel covering fast fading and Rayleigh fading as special cases is considered here. An efficient inverse moment matching method is proposed to approximate the outage probability in closed-form. The effect of approximation degree is theoretically analyzed to ease its selection. Moreover, diversity order of cooperative HARQ-IR is analyzed. It is…
In this paper, we investigate the effectiveness of the hybrid automatic repeat request (HARQ) technique in providing high-reliability and low-latency in the finite blocklength (FBL) regime in a single user uplink scenario. We characterize the packet error rate (PER), throughput, and delay performance of chase combining HARQ (CC-HARQ) and incremental redundancy HARQ (IR-HARQ) in AWGN and Rayleigh fading channel with $m$ retransmissions. Furthermore, we consider a quasi-static fading channel model, which is more accurate than the over-simplified i.i.d. block fading or same channel assumption ove…
In this paper, performance of hybrid automatic repeat request with incremental redundancy (HARQ-IR) over Rayleigh fading channels is investigated. Different from prior analysis, time correlation in the channels is considered. Under time-correlated fading channels, the mutual information in multiple HARQ transmissions is correlated, making the analysis challenging. By using polynomial fitting technique, probability distribution function of the accumulated mutual information is derived. Three meaningful performance metrics including outage probability, average number of transmissions and long te…
This paper analyzes Type I hybrid automatic repeat request (HARQ) over time-correlated Rayleigh fading channels. Due to the presence of channel time correlation, the analysis is more challenging than the prior analysis in the literature. Outage probability is first derived as a weighted sum of joint CDF of multiple independent Gamma random variables based on an infinite series representation. A truncation method is proposed for efficient computation of the outage probability and it is proved that the truncation error decreases exponentially with the truncation order. Asymptotic outage probabil…
This paper thoroughly investigates the performance of variable-rate hybrid automatic repeat request with incremental redundancy (HARQ-IR) over Beckmann fading channels, where Beckmann channel model is used to characterize the impacts of line-of-sight (LOS) path, time correlation between fading channels and unequal means & variances between the in-phase and the quadrature components. The intricate channel model and variable-rate transmission strategy significantly complicate the performance analysis. The complex form of the joint distribution of channel coefficients makes the exact analysis rat…
In this work, we consider transmissions over block fading channels and assume that adaptive modulation and coding (AMC) and hybrid automatic repeat request (HARQ) are implemented. Knowing that in high signal-to-noise ratio, the conventional combination of HARQ with AMC is counterproductive from the throughput point of view, we adopt the so-called layer-coded HARQ (L-HARQ). L-HARQ allows consecutive packets to share the channel and preserves a great degree of separation between AMC and HARQ; this makes the encoding and decoding very simple and allows us to use the available/optimized codes. Num…
In this study, a cross-layer design which combines adaptive modulation and coding (AMC) and hybrid automatic repeat request (HARQ) techniques for a cooperative wireless network is investigated analytically. Previous analyses of such systems in the literature are confined to the case where the fading channel is independent at each retransmission, which can be unrealistic unless the channel is varying very fast. On the other hand, temporal channel correlation can have a significant impact on the performance of HARQ systems. In this study, utilizing a Markov channel model which accounts for the t…
Vehicle-to-vehicle (V2V) communications under dense urban environments usually experience severe keyhole fading effect especially for multi-input multi-output (MIMO) channels, which degrades the capacity and outage performance due to the rank deficiency. To avoid these, the integration of MIMO and hybrid automatic repeat request (HARQ) is proposed to assist V2V communications in this paper. By using the methods of integral transforms, the outage probabilities are derived in closed-form for different HARQ-assisted schemes, including Type I-HARQ, HARQ with chase combining (HARQ-CC), and HARQ wit…
This paper studies the performance of delay-constrained hybrid automatic repeat request HARQ protocols. Particularly, we propose a fast HARQ protocol where, to increase the end-to-end throughput, some HARQ feedback signals and successive message decodings are omitted. Considering quasi-static channels and a bursty communication model, we derive closed-form expressions for the message decoding probabilities as well as the throughput, the expected delay and the error probability of the HARQ setups. The analysis is based on recent results on the achievable rates of finite-length codes and shows t…
In response to a comment on one of our manuscript, this work studies the posterior channel and noise distributions conditioned on the NACKs and ACKs of all previous transmissions in HARQ system with statistical approaches. Our main result is that, unless the coherence interval (time or frequency) is large as in block-fading assumption, the posterior distribution of the channel and noise either remains almost identical to the prior distribution, or it mostly follows the same class of distribution as the prior one. In the latter case, the difference between the posterior and prior distribution c…
Reconfigurable intelligent surface (RIS) has recently attracted a spurt of interest due to its innate advantages over Massive MIMO on power consumption. In this paper, we study the outage performance of multi-RIS system with the help of hybrid automatic repeat request (HARQ) to improve the RIS system reliability, where the destination received channels are modeled by Rician fading and the phase shift setting only depends on the line-of-sight (LoS) component. Both the exact and asymptotic outage probabilities under Type-I HARQ and HARQ with chase combining (HARQ-CC) schemes are derived. Particu…
In this paper, we first propose an universal polar coding scheme for parallel Gaussian channels with non-binary inputs. It is assumed that the encoder knows only the sum capacity of M parallel channels instead of the capacity of any single channel. By decomposing each parallel channel into T = [log2r] sub channels, we therefore obtain MT binary sub-channels. A super polar coding scheme that across all sub-channels is then proposed. This scheme can achieve the sum capacity when the block length is sufficiently large. We have also discussed the applications of parallel polar coding design for bo…
This paper investigates the incremental-redundancy hybrid-automatic repeat request (IR-HARQ) transmission over independent block-fading channels in the presence of an eavesdropper, where the secrecy of the transmission is ensured via introduction of dummy-messages. Since the encoder only knows the statistics of the channel state, the secrecy and the reliability are defined in a probabilistic framework. Unlike previous works on this subject, we design a coding strategy tailored to IR-HARQ by splitting the dummy-message rate over several rate parameters. These additional degrees of freedom impro…
Although terahertz (THz) communications can provide mobile broadband services, it usually has a large path loss and is vulnerable to antenna misalignment. This significantly degrades the reception reliability. To address this issue, the hybrid automatic repeat request (HARQ) is proposed to further enhance the reliability of THz communications. This paper provides an in-depth investigation on the outage performance of two different types of HARQ-aided THz communications, including Type-I HARQ and HARQ with chase combining (HARQ-CC). Moreover, the effects of both fading and stochastic antenna mi…
Vehicle-to-vehicle (V2V) communications under dense urban environments usually experience severe keyhole fading effect, especially for multi-input multi-output (MIMO) channels, which degrades the capacity and outage performance due to the rank deficiency. To avoid these, the integration of MIMO and Type-I hybrid automatic repeat request (HARQ) is proposed to assist V2V communications in this paper. By using the Meijer G-function, the outage probability of the proposed V2V communications system is derived in closed form. With the result, meaningful insights are gained by conducting the asymptot…
Hybrid automatic repeat 1 request (HARQ) is a key enabler for ultrareliable communications. This paper optimizes transmit power for the initial transmission and the subsequent retransmissions of HARQ with either incremental redundancy or Chase combining, aiming to minimize the expected energy consumption given the target outage probability and the target latency. The main challenge is due to the fact that the outage probability is a complicated function of the power variables which are nested in successive convolutions. The existing works mostly use a classic upper bound to approximate the out…
In many wireless systems, the signal-to-interference-and-noise ratio that is applicable to a certain transmission, referred to as channel state information (CSI), can only be learned after the transmission has taken place and is thereby delayed (outdated). In such systems, hybrid automatic repeat request (HARQ) protocols are often used to achieve high throughput with low latency. This paper put forth the family of expandable message space (EMS) protocols that generalize the HARQ protocol and allow for rate adaptation based on delayed CSI at the transmitter (CSIT). Assuming a block-fading chann…
This paper investigates the usage of hybrid automatic repeat request (HARQ) protocols for power-efficient and reliable communications over free space optical (FSO) links. By exploiting the large coherence time of the FSO channel, the proposed transmission schemes combat turbulence-induced fading by retransmitting the failed packets in the same coherence interval. To assess the performance of the presented HARQ technique, we extract a theoretical framework for the outage performance. In more detail, a closed-form expression for the outage probability (OP) is reported and an approximation for th…
Inspired by several delay-bounded mission-critical applications, optimizing the end-to-end reliability of multi-hop networks is an important problem subject to end-to-end delay constraints on the packets. Towards that direction, Automatic Repeat Request (ARQ) based strategies have been recently proposed wherein the problem statement is to distribute a certain total number of ARQs (that capture end-to-end delay) across the nodes such that the end-to-end reliability is optimized. Although such strategies provide a fine control to trade end-to-end delay with end-to-end reliability, their performa…
In a heterogeneous unreliable multiaccess network, wherein terminals share a common wireless channel with distinctive error probabilities, existing works have showed that a persistent round-robin (RR-P) scheduling policy (i.e., greedy policy) can be arbitrarily worse than the optimum in terms of Age of Information (AoI) under standard Automatic Repeat reQuest (ARQ), and one must resort to Whittle's index approach for optimal AoI. In this paper, practical Hybrid ARQ (HARQ) schemes which are widely-used in today's wireless networks are considered. We show that RR-P is very close to optimum with …
In this paper, we investigate the impact of side information (SI) on the performance of physical layer security (PLS) under correlated fading channels. By considering non-causally known SI at the transmitter and exploiting the copula technique to describe the fading correlation, we derive closed-from expressions for the average secrecy capacity (ASC) and secrecy outage probability (SOP) under positive/negative dependence conditions. We indicate that considering such knowledge at the transmitter is beneficial for system performance and ensures reliable communication with higher rates, as it imp…
This paper considers the uplink (UL) of a multi-cell Massive MIMO (multiple-input multiple-output) system with spatially correlated Rician fading channels. The channel model is composed of a deterministic line-of-sight (LoS) path and a stochastic non-line-of-sight (NLoS) component describing a spatially correlated multipath environment. We derive the statistical properties of the minimum mean squared error (MMSE) and least-square (LS) channel estimates for this model. Using these estimates for maximum ratio (MR) combining, rigorous closed-form UL spectral efficiency (SE) expressions are derive…
VLSF Decoding with Reliability Guarantees over Correlated Noncoherent Fading Channels
Inria（法国国家信息与自动化研究所）；Université de la Polynésie française（法属波利尼西亚大学）；Princeton University（普林斯顿大学）；Univ. Rennes, INSA, CNRS, IETR UMR 6164（雷恩大学、国立应用科学学院、法国国家科学研究中心、信息电子工程研究所）；Inria, INSA Lyon, CITI Laboratory（法国国家信息与自动化研究所、里昂国立应用科学学院、信息与通信技术创新实验室）
