Hybrid Automatic Repeat Request With Incremental Redundancy Research Articles

Performance Analysis and Optimal Design of HARQ-IR-Aided Terahertz Communications

Terahertz (THz) communications are envisioned to be a promising technology for 6G thanks to its broad bandwidth. However, the large path loss, antenna misalignment, and atmospheric influence of THz communications severely deteriorate its reliability. To address this, hybrid automatic repeat request (HARQ) is recognized as an effective technique to ensure reliable THz communications. This paper delves into the performance analysis of HARQ with incremental redundancy (HARQ-IR)-aided THz communications in the presence/absence of blockage. More specifically, the analytical expression of the outage probability of HARQ-IR-aided THz communications is derived, with which the asymptotic outage analysis is enabled to gain meaningful insights, including diversity order, power allocation gain, modulation and coding gain, etc. Then the long term average throughput (LTAT) is expressed in terms of the outage probability based on renewal theory. Moreover, to combat the blockage effects, a multi-hop HARQ-IR-aided THz communication scheme is proposed and its performance is examined. To demonstrate the superiority of the proposed scheme, the other two HARQ-aided schemes, i.e., Type-I HARQ and HARQ with chase combining (HARQ-CC), are used for benchmarking in the simulations. In addition, a deep neural network (DNN) based outage evaluation framework with low computational complexity is devised to reap the benefits of using both asymptotic and simulation results in low and high outage regimes, respectively. This novel outage evaluation framework is finally employed for the optimal rate selection, which outperforms the asymptotic based optimization.

On the Secure Performance of Intelligent Reflecting Surface-Assisted HARQ Systems

This paper analyzes the physical layer security performance of hybrid automatic repeat request (HARQ) systems with the assistance of an intelligent reflecting surface (IRS) and aims to reveal the primary factors that enhance PLS. First, closed-form expressions for the connection outage probability (COP) and secrecy outage probability (SOP) in HARQ with chase combining (HARQ-CC) are acquired using the generalized-K (KG) distribution. Then, these two critical metrics are derived while adopting HARQ with incremental redundancy (HARQ-IR), resorting to the mixture gamma (MG) distribution and the Mellin transform. Diversity and coding gain are also addressed through an asymptotic analysis of the COP and SOP. Finally, an evaluation of the numerical results demonstrates that a greater gain in the main channel and the wiretap channel can be produced by increasing the number of meta-surfaces rather than increasing the maximum transmission number, except for the higher signal-to-noise (SNR) region of HARQ-IR where the latter is preferred. This finding provides a significant guidance for the joint configuration of IRS and HARQ to achieve secure communication.

Outage Performance and AoI Minimization of HARQ-IR-RIS Aided IoT Networks

In this paper, reconfigurable intelligent surface (RIS) and hybrid automatic repeat request with incremental redundancy (HARQ-IR) are amalgamated to lower power expenditure, shorten latency and strengthen reliability of the internet of things (IoT) communications. By considering Rician fading channels and multiple RISs, the outage probability of single-input single-output (SISO) HARQ-IR-RIS aided IoT networks is derived in closed-form, with which the asymptotic outage analysis is carried out. The asymptotic results are further extended to single-input multiple-output (SIMO)/multiple-input multiple-output (MIMO) HARQ-IR-RIS aided IoT networks by using random matrix theory. Thereafter, the asymptotic expressions are invoked to reduce the design complexity of the phase shifts, transmit powers, and rate, which aims at minimizing the age of information (AoI) while ensuring the power and outage constraints. Particularly, the optimal phase shifts are firstly determined. The alternating optimization technique is then applied to solve the transmit rate and powers, which are iteratively updated based on majorization-minimization (MM) principle and geometric programming (GP) approximation, respectively. The numerical results consequently corroborate our theoretical analysis. More interestingly, the HARQ-IR-aided scheme with fixed power is found to provide a comparable performance as the proposed scheme with variable power especially for numerous reflecting elements at RIS.

Outage Performance of Cross-Packet HARQ

As opposed to hybrid automatic repeat request with incremental redundancy (HARQ-IR) that all the resources are occupied to resend the redundant information, cross-packet HARQ (XP-HARQ) allows the introduction of new information into retransmissions to substantially exploit the remaining resources. This letter provides a profound investigation into the outage performance of XP-HARQ. In particular, the exact outage expression of XP-HARQ is derived if the maximum number of transmissions is two, and tight outage bounds are obtained for more than two transmissions. Moreover, the asymptotic outage analysis of XP-HARQ in the high signal-to-noise ratio (SNR) regime is carried out not only to simplify the outage expression, but also to show that full time diversity is achievable by XP-HARQ. The simulation results are eventually presented for verifications.

Performance Analysis of MIMO-HARQ Assisted V2V Communications With Keyhole Effect

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 with incremental redundancy (HARQ-IR). With the results, meaningful insights are gained by conducting the asymptotic outage analysis. Specifically, it is revealed that full time diversity order can be achieved, while full spatial diversity order is unreachable as compared to MIMO-HARQ systems without keyhole effect. Moreover, we prove that the asymptotic outage probability is a monotonically increasing and convex function of the transmission rate. More importantly, although HARQ-IR performs better than HARQ-CC owing to its higher coding complexity, this advantage becomes negligible in the large-scale array regime. Finally, the numerical results are verified by Monte-Carlo simulations along with some in-depth discussions.

Statistical Delay and Error-Rate Bounded QoS Provisioning Over mmWave Cell-Free M-MIMO and FBC-HARQ-IR Based 6G Wireless Networks

As a new and dominating 6G mobile-networks’ service class for time-sensitive traffics, massive ultra-reliable and low latency communications (mURLLC) has received tremendous attention. One of key 6G enabling-techniques for achieving mURLLC lies in how to efficiently support statistical delay and error-rate bounded quality-of-services (QoS) provisioning for real-time data-transmissions over time-varying wireless networks. Towards this end, several emerging wireless techniques, including finite blocklength coding (FBC), hybrid automatic repeat request with incremental redundancy (HARQ-IR) protocol, millimeter wave (mmWave), cell-free (CF) massive multiple-input multiple-output (m-MIMO), etc., have been shown to be 6G promising enablers to significantly improve various QoS performances. However, integrating these techniques with the statistical delay and error-rate bounded QoS provisioning theory for mURLLC has imposed many new difficulties not encountered before. To overcome these challenges, in this paper we propose the statistical delay-and-error-rate-bounded QoS provisioning system architecture over mmWave user-centric CF m-MIMO and FBC-HARQ-IR based 6G wireless networks. First, we establish the comprehensive system models by accurately characterizing the integrations of above-described 6G promising techniques with statistical QoS provisioning theory. Then, we integrate FBC with HARQ-IR protocol to derive the channel capacity as a function of error probability. Finally, we obtain the closed-form expressions for effective capacities under our proposed schemes. We also conduct a set of simulations to validate and evaluate our proposed FBC-HARQ-IR based mmWave user-centric CF m-MIMO schemes.

Achievable Diversity Order of HARQ-Aided Downlink NOMA Systems

The combination between non-orthogonal multiple access (NOMA) and hybrid automatic repeat request (HARQ) is capable of realizing ultra-reliability, high throughput and many concurrent connections particularly for emerging communication systems. This paper focuses on characterizing the asymptotic scaling law of the outage probability of HARQ-aided NOMA systems with respect to the transmit power, i.e., diversity order. The analysis of diversity order is carried out for three basic types of HARQ-aided downlink NOMA systems, including Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR). The diversity orders of three HARQ-aided downlink NOMA systems are derived in closed-form, where an integration domain partition trick is developed to obtain the bounds of the outage probability specially for HARQ-CC and HARQ-IR-aided NOMA systems. The analytical results show that the diversity order is a decreasing step function of transmission rate, and full time diversity can only be achieved under a sufficiently low transmission rate. It is also revealed that HARQ-IR-aided NOMA systems have the largest diversity order, followed by HARQ-CC-aided and then Type I HARQ-aided NOMA systems. Additionally, the users’ diversity orders follow a descending order according to their respective average channel gains. Furthermore, we expand discussions on the cases of power-efficient transmissions and imperfect channel state information (CSI). Monte Carlo simulations finally confirm our analysis.

Effective Capacity for Renewal Service Processes With Applications to HARQ Systems

Considering the widespread use of effective capacity in cross-layer design and the extensive existence of renewal service processes in communication networks, this paper thoroughly investigates the effective capacity for renewal processes. Based on Z-transform, we derive exact analytical expressions for the effective capacity at a given quality of service (QoS) exponent for both the renewal processes with constant reward and with variable rewards. Unlike prior literature that the effective capacity is approximated with no many insightful discussions, our expression is simple and reveals further meaningful results, such as the monotonicity and bounds of effective capacity. The analytical results are then applied to evaluate the cross-layer throughput for diverse hybrid automatic repeat request (HARQ) systems, including fixed-rate HARQ (FR-HARQ, e.g., Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR)), variable-rate HARQ (VR-HARQ) and cross-packet HARQ (XP-HARQ). Numerical results corroborate the analytical ones and prove the superiority of our proposed approach. Furthermore, targeting at maximizing the effective capacity via the optimal rate selection, it is revealed that VR-HARQ and XP-HARQ attain almost the same performance, and both of them perform better than FR-HARQ.

On the Impact of Time-Correlated Fading for Downlink NOMA

This paper investigates the performance of non-orthogonal multiple access (NOMA) systems over time-correlated Rayleigh fading channels, where the users have heterogeneous quality of service requirements, e.g., a latency-critical user with a low target rate and a delay-tolerant user with a large target rate. In order to meet the different requirements of the users, two partial hybrid automatic repeat request (HARQ) schemes, including partial HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR), are proposed. The closed-form expressions of outage probabilities for NOMA with and without re-transmission are derived. With the developed outage probabilities, a condition on the superiority of NOMA to orthogonal multiple access (OMA) is obtained. In particular, the condition is characterized by the transmit powers for NOMA without re-transmission and is obtained by using the bisection method in the case with re-transmission. To further improve the performance of the HARQ enabled NOMA schemes, we consider an average transmit power minimization problem by optimizing the transmit power among different transmission rounds with outage constraints. However, due to the complexity of the developed outage probabilities, the formulated problem is non-convex and challenging to solve. Then we approximate the original problem by deriving the upper-bound approximations of the outage probabilities and solve it by using the geometric programming method. Simulation results demonstrate the accuracy of the developed analytical results. It is shown that the performance of NOMA is superior to OMA, only when the obtained condition is satisfied. HARQ-CC and HARQ-IR can enhance the outage performance of NOMA over time-correlated fading channels and the HARQ-IR has excellent performance in terms of energy efficiency.

Energy-Efficient HARQ-IR for Massive MIMO Systems

In this paper, an optimization problem to maximize the energy efficiency of a hybrid automatic repeat request with incremental redundancy (HARQ-IR) is considered for massive multiple-input multiple-output (MIMO) systems. Because a sum rate for multiple HARQ-IR rounds is approximated by a Gaussian distribution, a problem maximizing energy efficiency becomes tractable. In particular, a simplified form of energy efficiency for massive MIMO transmissions with an HARQ-IR protocol is derived using an outage probability, which is given by a tail probability of the Gaussian distribution. By exploiting the proposed simplified form, we show that the energy efficiency of the system is approximated by a piecewise quasi-concave function. Using these properties, an algorithm finding the optimal transmission power and number of transmission rounds for maximizing energy efficiency is proposed. Moreover, we show that the optimal number of HARQ transmission rounds can be less than the maximum allowable retransmissions when considering the constant power consumption of the massive MIMO system with an HARQ-IR protocol. Simulation results verify the theoretical analysis and show the performance of the proposed algorithm.

Energy-Efficient Optimization for HARQ Schemes Over Time-Correlated Fading Channels

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 are 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 paper 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 $\frac{1}{4\ln 2}$ b/J, while HARQ-CC and HARQ-IR can achieve the same maximal energy efficiency as $\frac{\kappa _\infty }{4\ln 2}$ b/J, where $\kappa _\infty = 1.6617$ . Moreover, time correlation in the fading channels has a negative impact on the energy efficiency, whereas 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.

Goodput Maximization of HARQ-IR Over Arbitrarily Correlated Rician Fading Channels

This paper investigates the optimal design of hybrid automatic repeat request with incremental redundancy (HARQ-IR) over arbitrarily correlated Rician fading channels for goodput maximization. With practical consideration of both the channel time correlation and line-of-sight (LOS) links, theoretical analysis and optimal design of HARQ-IR become very challenging. To address them, asymptotic outage analysis is first carried out to not only gain meaningful insights but also facilitate the optimal design. With simple forms of asymptotic expressions derived, joint optimization of the transmission powers and rate aiming at goodput maximization under average total transmission power constraint is enabled and solved analytically. The optimal goodput is also derived in closed form, with which meaningful insights can then be extracted. Particularly, the scaling law of the optimal goodput with respect to the transmit signal-to-noise ratio is found, and the harmfulness of time correlation and the benefit of LOS links are revealed. Finally, the analytical results are validated through extensive simulations.

Asymptotic Outage Analysis of HARQ-IR Over Time-Correlated Nakagami- $m$ Fading Channels

In this paper, outage performance of hybrid automatic repeat request with incremental redundancy (HARQ-IR) is analyzed. Unlike prior analyses, time-correlated Nakagami- $m$ fading channel is considered. The outage analysis thus involves the probability distribution analysis of a product of multiple correlated shifted Gamma random variables and is more challenging than prior analyses. Based on the findings of the conditional independence of the received signal-to-noise ratios, the outage probability is exactly derived by using conditional Mellin transform. Specifically, the outage probability of HARQ-IR under time-correlated Nakagami- $m$ fading channels can be written as a weighted sum of outage probabilities of HARQ-IR over independent Nakagami fading channels, where the weightings are determined by a negative multinomial distribution. This result enables not only an efficient truncation approximation of the outage probability with uniform convergence but also asymptotic outage analysis to further extract clear insights, which have never been discovered for HARQ-IR even under fast fading channels. The asymptotic outage probability is then derived in a simple form, which clearly quantifies the impacts of transmit powers, channel time correlation, and information transmission rate. It is proved that the asymptotic outage probability is an inverse power function of the product of transmission powers in all HARQ rounds, an increasing function of the channel time correlation coefficients, and a monotonically increasing and convex function of information transmission rate. The simple expression of the asymptotic result enables optimal power allocation and optimal rate selection of HARQ-IR with low complexity. Finally, numerical results are provided to verify our analytical results and justify the application of the asymptotic result for optimal system design.

Inverse Moment Matching Based Analysis of Cooperative HARQ-IR over Time-Correlated Nakagami Fading Channels

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 a 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 proved that the diversity order is irrelevant to the time correlation coefficient $\rho$ , as long as $\rho , and full diversity from both spatial and time domains can be achieved by cooperative HARQ-IR under time-correlated fading channels. The accuracy of the analytical results is verified by computer simulations, and the results reveal that cooperative HARQ-IR scheme can benefit from high fading order and low channel time correlation. Optimal rate selection to maximize the long-term average throughput given a maximum allowable outage probability is finally discussed as one application of the analytical results.

Analysis of HARQ-IR Over Time-Correlated Rayleigh Fading Channels

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 term average throughput (LTAT) are then derived in closed-forms. Moreover, diversity order of HARQ-IR is also investigated. It is proved that full diversity can be achieved by HARQ-IR, i.e., the diversity order is equal to the number of transmissions, even under time-correlated fading channels. These analytical results are verified by simulations and enable the evaluation of the impact of various system parameters on the performance. Particularly, the results unveil the negative impact of time correlation on the outage and throughput performance. The results also show that although more transmissions would improve the outage performance, they may not be beneficial to the LTAT when time correlation is high. Optimal rate design to maximize the LTAT is finally discussed and significant LTAT improvement is demonstrated.

On the Energy–Delay Tradeoff and Relay Positioning of Wireless Butterfly Networks

This paper considers energy–delay tradeoff (EDT) of data transmission in wireless-network-coded butterfly networks (WNCBNs) where two sources convey their data to two destinations with the assistance of a relay employing either physical-layer network coding (PNC) or analog network coding (ANC). Hybrid automatic repeat request with incremental redundancy (HARQ-IR) is applied for reliable communication. In particular, we first investigate the EDT of both PNC and ANC schemes in WNCBNs to evaluate their energy efficiency. It is found that there is no advantage to using a relay in a high-power regime. However, in a low-power regime, the PNC scheme is shown to be more energy efficient than both the ANC and direct transmission (DT) schemes if the relay is located far from the sources, whereas both the PNC and ANC schemes are less energy efficient than the DT scheme when the relay is located near the sources. Additionally, algorithms that optimize relay positioning (RP) are developed based on two criteria: minimizing total transmission delays and minimizing total energy consumption subject to node location and power allocation constraints. This optimization can be considered a benchmark for RP in either a low-latency or low-energy-consumption WNCBN.

On the Energy Efficiency of AMC and HARQ-IR With QoS Constraints

In this paper, we compare the energy efficiencies of two well-known transmission schemes that can adapt to fading channels for reliable transmissions, namely, adaptive modulation and coding (AMC) and hybrid automatic repeat request (HARQ) schemes, with limited channel state information (CSI) feedback. Since they exploit CSI differently, they have different characteristics, which make the comparison study (in terms of energy efficiency) challenging. Using the notion of energy-delay tradeoff (EDT), we derive approaches to compare them with given equivalent quality-of-service (QoS) constraints. The derived approaches are important as they allow us to choose energy-efficient transmission schemes under certain conditions. It is shown that AMC is more energy efficient than HARQ with incremental redundancy (HARQ-IR) in the low-power regime. However, in the high-power regime, HARQ-IR has better energy efficiency than AMC.

On the Energy Delay Tradeoff of HARQ-IR in Wireless Multiuser Systems

Energy delay tradeoff (EDT) is a fundamental tradeoff that plays a crucial role in understanding the energy efficiency of various transmission schemes. In particular, for hybrid automatic repeat request (HARQ) protocols, the EDT can be well defined. In this paper, in order to understand the EDT for a wireless multiuser system, we consider various downlink transmission schemes where the HARQ with incremental redundancy (HARQ-IR) protocol is employed for reliable transmissions to users. For a given total power, the impact of different transmission schemes in conjunction with power allocation on EDT is extensively studied. Among the transmission schemes, it is shown that the threshold-based transmission (TBT) scheme efficiently lowers the minimum energy per bit (EB) in spite of limited prior channel state information (CSI) feedback. The study is further extended to a more plausible scenario where users have different channel statistics. In doing so, we consider a proportional fairness scheduling based on relative channel gain that can be easily accommodated in the proposed TBT scheme, and study its EDT behaviors. Performance evaluations show that the schemes incorporating proportional fairness achieve good EDT performances while guaranteeing the fairness among users.