Optimal Decoding Order Research Articles

Optimal Decoding Order and Power Allocation for Sum Throughput Maximization in Downlink NOMA Systems.

In this paper, we consider a downlink non-orthogonal multiple access (NOMA) system over Nakagami-m channels. The single-antenna base station serves two single-antenna NOMA users based on statistical channel state information (CSI). We derive the closed-form expression of the exact outage probability under a given decoding order, and we also deduce the asymptotic outage probability and diversity order in a high-SNR regime. Then, we analyze all the possible power allocation ranges and theoretically prove the optimal power allocation range under the corresponding decoding order. The demarcation points of the optimal power allocation ranges are affected by target data rates and total power, without an effect from the CSI. In particular, the values of the demarcation points are proportional to the total power. Furthermore, we formulate a joint decoding order and power allocation optimization problem to maximize the sum throughput, which is solved by efficiently searching in our obtained optimal power allocation ranges. Finally, Monte Carlo simulations are conducted to confirm the accuracy of our derived exact outage probability. Numerical results show the accuracy of our deduced demarcation points of the optimal power allocation ranges. And the optimal decoding order is not constant at different total transmit power levels.

Secure Transmission in NOMA-Enabled Industrial IoT With Resource-Constrained Untrusted Devices

The security of confidential information associated with devices in the industrial Internet of Things (IIoT) network is a serious concern. This article focuses on achieving a non-orthogonal multiple access (NOMA)-enabled secure IIoT network in the presence of untrusted devices by jointly optimizing the resources, such as decoding order and power allocated to devices. Assuming that the devices are resource-constrained for performing perfect successive interference cancellation (SIC), we characterize the residual interference at receivers with the linear model. Firstly, considering all possible decoding orders in an untrusted scenario, we obtain secure decoding orders that are feasible to obtain a positive secrecy rate for each device. Then, under the secrecy fairness criterion, we formulate a joint optimization problem of maximizing the minimum secrecy rate among devices. Since the formulated problem is non-convex and combinatorial, we first obtain the optimal secure decoding order and then solve it for power allocation by analyzing Karush-Kuhn-Tucker points. Thus, we provide the closed-form global-optimal solution of the formulated optimization problem. Numerical results validate the analytical claims and demonstrate an interesting observation that the conventional decoding order and assigning more power allocation to the weak device, as presumed in many works on NOMA, is not an optimal strategy from the secrecy fairness viewpoint. Also, the average percentage gain of about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$22.75\%$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$50.58\%$</tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$94.59\%$</tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$98.16\%$</tex-math></inline-formula> , respectively, is achieved by jointly optimized solution over benchmarks ODEP (optimal decoding order, equal power allocation), ODFP (optimal decoding order, fixed power allocation), FDEP (fixed decoding order, equal power allocation), and FDFP (fixed decoding order, fixed power allocation).

K-Receiver Wiretap Channel: Optimal Encoding Order and Signaling Design

The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -receiver wiretap channel is a channel model where a transmitter broadcasts <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> independent messages to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> intended receivers while keeping them secret from an eavesdropper. The capacity region of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -receiver multiple-input multiple-output (MIMO) wiretap channel has been characterized by using dirty-paper coding and stochastic encoding. However, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> factorial encoding orders may need to be enumerated to evaluate the capacity region, which makes the problem intractable. In addition, even though the capacity region is known, the optimal signaling to achieve the capacity region is unknown. In this paper, we determine one optimal encoding order to achieve every point on the capacity region, and thus reduce the encoding complexity <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> factorial times. We prove that the optimal decoding order for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -receiver MIMO wiretap channel is the same as that for the MIMO broadcast channel without secrecy. To be specific, the descending weight ordering in the weighted sum-rate (WSR) maximization problem determines the optimal encoding order. Next, to reach the border of the secrecy capacity region, we form a WSR maximization problem and apply the block successive maximization method to solve this nonconvex problem and find the input covariance matrices corresponding to each message. Numerical results are used to verify the optimality of the encoding order and to demonstrate the efficacy of the proposed signaling design.

A CA and ML approach for M-MIMO optical non-orthogonal multiple access power efficiency

Abstract The non-orthogonal multiple access (NOMA) multiple access approach can be used in future wireless communication systems to support massive connections and increase spectrum efficiency. Because user signal intensities and interference levels vary, precise channel assessment is essential in NOMA. Optimal power allocation and decoding order are made possible by precise algorithms, increasing system effectiveness and performance. However, NOMA can be adversely impacted by high peak-to-average power ratio (PAPR) values, leading to worsened system performance and more complex power amplifiers. In order to solve this issue, this paper recommends PAPR reduction in NOMA using companding methods for 512, 256, and 64 sub-carriers. Nonlinear companding techniques, such as MA and A-law companding, can efficiently reduce the high peak power of NOMA signals while reducing distortion and enhancing overall system dependability. The effectiveness of the proposed companding methods is evaluated using simulations, and the results demonstrate a significant decrease in PAPR, ensuring higher bit error rate (BER) effectiveness and transmission resilience in NOMA-based communication systems. The proposed approach is compared to the traditional Ml (C- Ml) and A-Law (C- A-Law).

Optimization of STAR-RIS-Assisted Hybrid NOMA mmWave Communication

Simultaneously reflecting and transmitting reconfigurable intelligent surfaces (STAR-RIS) has recently emerged out as prominent technology that exploits the transmissive property of RIS to mitigate the half-space coverage limitation of conventional RIS operating on millimeter-wave (mmWave). In this paper, we study a downlink STAR-RIS-based multi-user multiple-input single-output (MU-MISO) mmWave hybrid non-orthogonal multiple access (H-NOMA) wireless network, where a sum-rate maximization problem has been formulated. The design of active and passive beamforming vectors, time and power allocation for H-NOMA is a highly coupled non-convex problem. To handle the problem, we propose an optimization framework based on alternating optimization (AO) that iteratively solves active and passive beamforming sub-problems. Channel correlations and channel strength-based techniques have been proposed for a specific case of two-user optimal clustering and decoding order assignment, respectively, for which analytical solutions to joint power and time allocation for H-NOMA have also been derived. Simulation results show that: 1) the proposed framework leveraging H-NOMA outperforms conventional OMA and NOMA to maximize the achievable sum-rate; 2) using the proposed framework, the supported number of clusters for the given design constraints can be increased considerably; 3) through STAR-RIS, the number of elements can be significantly reduced as compared to conventional RIS to ensure a similar quality-of-service (QoS).

Impact of Decoding Order on User Pairing in NOMA-CoMP Joint Transmission

This correspondence investigates the optimal decoding order and its impact on user pairing in non-orthogonal multiple access (NOMA)-enabled coordinated multipoint (CoMP) joint transmission (JT) to maximize the sum rate of users. First, the optimal solution of power control for a user pair is obtained under different decoding orders, where closed-form expressions and a low-complexity algorithm are given by monotonic optimization. Then, a criterion for finding the optimal decoding order is derived for any given user pair in the considered scenario. Results show that the optimal decoding order is distinct for different user pairs, which can be achieved separately. This indicates that the decoding order is not a necessary prerequisite for user pairing in NOMA-enabled CoMP systems. Moreover, the optimal decoding order is shown to depend on the differentials of channel gains between the user served by JT and coordinated base stations.

Joint Computation Offloading and Resource Allocation for MIMO-NOMA Assisted Multi-User MEC Systems

This paper investigates the resource allocation and computation offloading problem for multi-access edge computing (MEC) systems, where multiple mobile users (MUs) equipped with multiple antennas access the base station in a non-orthogonal multiple access manner. We jointly optimize the offloading ratio, computational frequency and transmit precoding matrix of each MU to minimize the total energy consumption of all MUs while satisfying the latency constraints. The problem is formulated as a non-convex optimization problem and a two-layer iterative method is proposed to solve the problem efficiently with low complexity. Specifically, we first decompose the original problem into several subproblems, and then sequentially solve these subproblems in an alternative fashion. Furthermore, we also discuss the optimal decoding order of MUs under two different scenarios. Firstly, when the MUs’ channel conditions are similar, by deriving closed-form expressions for energy consumptions of all MUs, we prove that the optimal decoding order is only determined by the latency requirements. On the other hand, when the MUs’ channel conditions are different, we show that the optimal decoding order is determined by both the channel conditions and the latency requirements. As such, we propose a metric aiming to balance the effects of channel conditions and latency requirements on the MUs’ decoding order. Simulation results validate the convergence of the proposed method and demonstrate its superiority over benchmark algorithms.

Joint Receive and Passive Beamforming Optimization for RIS-Assisted Uplink RSMA Systems

In this letter, we investigate the joint optimization of transmit power allocation and receive/passive beamforming in a reconfigurable intelligent surface (RIS)-assisted uplink two-user rate-splitting multiple access (RSMA) system. Aiming at maximizing the achievable rate of one user subject to another user’s quality of service (QoS) requirements, RIS is deployed to assist the uplink transmissions from both users to a multi-antenna base station (BS). We decouple the non-convex rate maximization problem into three sub-problems and propose an alternating optimization (AO) algorithm to optimize the receive/passive beamforming and transmit power allocation. A closed-form expression is derived for the sub-problem of transmit power allocation by using the optimal decoding order and the concave-convex fractional programming beamforming problems are converted to convex ones by using the Charnes-Cooper transform. Then, a penalty term approach is applied to effectively solve the rank-1 constrained beamforming subproblems. Simulation results verify that the proposed AO algorithm attains a higher achievable rate than the existing benchmark schemes.

Rate Splitting Multiple Access for Sum-Rate Maximization in IRS Aided Uplink Communications

In this paper, an intelligent reflecting surface (IRS) aided uplink (UL) rate-splitting multiple access (RSMA) system is investigated for dead-zone users where the direct link between the users and the base station (BS) is unavailable and the UL transmission is carried out only through IRS. In the considered RSMA system, a message of each user is split into several sub-messages and each part contributes to the rate of that user and depending upon split proportions BS decodes them using appropriate decoding order. The problem of sum-rate maximization is formulated to jointly design the optimal power allocation at each UL user, passive beamforming at the IRS under optimal decoding order of sub-messages. Due to non-convexity and discrete non-linear programming of the formulated problem, the original problem is intractable and hence, we decouple the problem into different sub-problems in which the problems of power allocation and passive beamforming are alternatively solved under using successive convex approximation and Riemaniann conjugate gradient algorithms, respectively. Moreover, the decoding order strategy is analytically derived which confirm that the optimal decoding order strategy depend upon decreasing order of channel gain of users and increasing order of split proportions of sub-messages. Later, the unified solution based on block-coordinate descent (BCD) algorithm is proposed. Simulation results validate that the proposed decoding order scheme attains performance closer to the optimal solution with low computational complexity. Moreover, the proposed IRS aided RMSA system outperforms the system with non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA) schemes in terms of achievable sum-rate throughput.

Cross-Layer Resource Allocation in HetNet NOMA Systems With Dynamic Traffic Arrivals

Non-orthogonal multiple access (NOMA) has become a promising candidate aiming to enhance the system performance in the fifth generation of wireless communication. However, most existing studies on the resource allocation of NOMA systems only consider the short-term performance improvement but ignore the problems caused by the imperfect time-varying channels and the dynamic traffic arrivals, which will result in unsuccessful transmission issues. Different from the existing approaches, we propose a long-term cross-layer resource allocation model with dynamic traffic arrivals and limited channel information. With the low-overhead one-bit feedback, the optimal decoding order, user scheduling, and power allocation are analyzed. Specifically, the problem is formulated as a stochastic optimization framework to minimize long-term power consumption. By applying the Lyapunov optimization framework, the problem can be transformed into a joint traffic rate control and mixed-integer programming resource allocation problem. This NP-hard problem is difficult to be solved directly. Therefore, we devise an efficient sub-optimal algorithm with the dynamic penalty factor. In our theoretical analysis, we prove that the delay-power tradeoff can be achieved by tuning a control parameter. The simulation results confirm that our proposed algorithms can efficiently reduce the power consumption compared with the baseline algorithms while satisfying the QoS requirements.

Joint Queue-Aware and Channel-Aware Scheduling for Non-Orthogonal Multiple Access

Non-orthogonal multiple access (NOMA) has received considerable attention as a promising candidate for future mobile networks. How to reduce traffic delay through cross-layer scheduling in NOMA systems is a challenging issue. In this paper, a cross-layer approach for NOMA systems is designed to fulfill the delay requirements. In particular, scheduling decisions should adapt to the system dynamics. With the distribution information of the system dynamics, the constrained Markov decision process (CMDP) is employed to characterize the scheduling decision. The optimal scheduling policy can be obtained by converting the scheduling problem to linear programming. A computational approach based on the Kronecker product is conceived to formulate the linear programming when the dimension of the CMDP is high. Then the optimal delay-power tradeoff can be achieved. Moreover, the optimal decoding order is demonstrated that it can be obtained directly based on the channel states. The threshold-based structure of the optimal scheduling decisions is revealed. Without the distribution information, the Lyapunov approach is exploited to propose an online scheduling policy, where the virtual power queue is used to tackle the power constraint. In NOMA systems, our CMDP-based approach achieves a better performance over the Lyapunov approach by taking advantage of the distribution information.

Ergodic Performance of Downlink Untrusted NOMA System With Imperfect SIC

In this letter, the ergodic performance of a non-orthogonal multiple access (NOMA) system with untrusted users and imperfect successive interference cancellation based decoding is manifested. Closed-form expressions of the ergodic rate and the ergodic secrecy rate of each user have been derived for all possible decoding orders. In addition, Taylor series expansion based approximation has been proposed to gain analytical insights and obtain optimal decoding order. Numerical simulations endorse the analytical findings, and highlight impact of various key parameters on the ergodic performance of the system.

User Clustering and Resource Allocation in Hybrid NOMA-OMA Systems Under Nakagami-m Fading

In this paper, we tackle the problem of optimizing user clustering, power, and resource (time slot or bandwidth) allocation in the downlink of a hybrid non-orthogonal multiple access (NOMA)-orthogonal multiple access (OMA) system. In such a system, users are organized into several clusters under one of the following scenarios: (1) fixed cluster size, (2) fixed number of clusters, and (3) variable number of clusters and variable cluster size. A power domain NOMA (PD-NOMA) scheme is used in each cluster, while OMA is employed for allocating resources to different clusters. The goal is to maximize the minimum success probability (which is equivalent to minimizing the maximum outage probability) among all users to guarantee fairness. We prove that at the optimal solution, all users have the same success probability, which is called the common success probability (CSP). Then, we propose an efficient algorithm for finding the optimal CSP and cluster resource allocation factors simultaneously. The optimal power allocation factors and the optimal decoding order of users in each cluster are then derived in closed-form expressions based on the obtained optimal CSP. Simulation results show considerable performance gains by the proposed scheme, compared to existing schemes in terms of fairness, the minimum success probability of users, and the sum throughput.

Outage Balancing in Downlink NOMA Over Nakagami-m Fading Channels

In this paper, we investigate joint optimization of power allocation factors (PAFs) and decoding order of users in the downlink of a non-orthogonal multiple access (NOMA) system over Nakagami- m fading channels. The objective is to guarantee fairness among the users in terms of outage probability (or its complement success probability). To this end, we maximize the minimum success probability (Max-MSP) among the users when only statistical channel state information (CSI) is available at the transmitter side. We solve such a problem by first proving that at the optimal solution, all the users have a common success probability (CSP), and then proposing an efficient algorithm for finding CSP of the users. The optimal PAFs and optimal decoding order are derived in closed form based on the CSP and statistical CSI of the users. It is proved that the proposed algorithm always converges to a unique optimal solution. Furthermore, we show that in contrast to Rayleigh fading channels, in Nakagami- m fading channels, the optimal decoding order not only depends on the average signal-to-noise ratio (SNR) of each user but also depends on the variance of the SNR and data rate of that user.

Performance Analysis of Distributed Uplink NOMA

We propose an optimal joint user association and decoding order selection scheme for distributed uplink non-orthogonal multiple access (DU-NOMA) with fixed transmission rates. It is considered that the remote radio heads can either perform decoding independently from each other or exchange information via a dedicated feedback link with limited capacity. The outage probability is derived in closed-from and useful insights for the high signal-to-noise ratio regime are provided. Finally, it is illustrated that DU-NOMA with feedback together with the proposed coordination scheme achieves substantial gain compared to DU-NOMA without feedback. Also, in most of the practical cases it outperforms orthogonal multiple access schemes, even if the feedback link is not error-free.

Joint Energy-Efficient Power Allocation and Beamforming for Uplink mmWave-NOMA System

In this paper, we study the joint power allocation (PA) and beamforming (BF) design problem to maximize the energy efficiency (EE) for an uplink millimeter-wave (mmWave) system with non-orthogonal multiple access (NOMA). To track this non-convex optimization problem, we decompose it into the PA problem and BF design problem. For any feasible fixed BF, the condition of the optimal decoding order is firstly presented to reduce the decoding complexity, and then the optimal and suboptimal PA solutions with closed-form expressions are derived, respectively. On this basis, two suboptimal joint design schemes of PA and BF are proposed based on the one-dimensional search method. Furthermore, the extensions of the proposed schemes to mmWave-NOMA system with imperfect channel information and more users are also presented. Simulation results verify the effectiveness of the proposed two joint schemes, and they can achieve superior EE performance over the existing schemes and the conventional time division multiple access scheme.

Slotted ALOHA With NOMA for the Next Generation IoT

Random access (RA) has recently been revisited and considered as a key technology for the medium access control layer of the Internet of Things applications. Compared to other RA protocols, slotted ALOHA (SA) has the advantages of low complexity and elimination of partially overlapping transmissions, reducing the number of collisions, however it may suffer from congestion as the traffic load and the number of devices increase. To this end, two RA protocols based on SA and uplink non-orthogonal multiple access are proposed and applied to wireless sensor networks and wireless powered sensor networks. More specifically, to reduce the number of collisions and increase the throughput of SA, while maintaining low complexity, two detection techniques are used to mitigate the interference, when two sources transmit information in the same time slot, namely successive interference cancellation (SIC) with optimal decoding order policy and joint decoding (JD). To evaluate the performance of the proposed protocols, the outage probability of SIC and JD is derived, which is used to express the average throughput attained by each protocol in closed-form. Finally, both the analytical results and the simulations verify that the proposed protocols substantially increase the throughput and the number of connected devices compared to SA.

Sum-Rate Maximization of Uplink Rate Splitting Multiple Access (RSMA) Communication

In this paper, the problem of maximizing the wireless users’ sum-rate for uplink rate splitting multiple access (RSMA) communications is studied. In the considered model, the message intended for a single user is split into two sub-messages with separate transmit power and the base station (BS) uses a successive decoding technique to decode the received messages. To maximize each user’s transmission rate, the users must adjust their transmit power and the BS must determine the decoding order of the messages transmitted from the users to the BS. This problem is formulated as a sum-rate maximization problem with proportional rate constraints by adjusting the users’ transmit power and the BS’s decoding order. However, since the decoding order variable in the optimization problem is discrete, the original maximization problem with transmit power and decoding order variables can be transformed into a problem with only the rate splitting variable. Then, the optimal rate splitting of each user is determined. Given the optimal rate splitting of each user and a decoding order, the optimal transmit power of each user is calculated. Next, the optimal decoding order is determined by an exhaustive search method. To further reduce the complexity of the optimization algorithm used for sum-rate maximization in RSMA, a user pairing based algorithm is introduced, which enables two users to use RSMA in each pair and also enables the users in different pairs to be allocated with orthogonal frequency. For comparisons, the optimal sum-rate maximizing solutions with proportional rate constraints are obtained for non-orthogonal multiple access (NOMA), frequency division multiple access (FDMA), and time division multiple access (TDMA). Simulation results show that RSMA can achieve up to 10.0, 22.2, and 81.2 percent gains in terms of sum-rate compared to NOMA, FDMA, and TDMA.

Outage Performance of Pairwise NOMA Allowing a Dynamic Decoding Order and Optimal Pairs of Power Levels

In this article, we evaluate the overall outage probability (OOP) of pairwise Non-orthogonal Multiple Access (NOMA) for both uplink and downlink. We also propose a dynamic decoding order (DDO) together with a fixed pairwise power allocation (FPPA) scheme, in which the optimal decoding order is decided based on the instantaneous channel gains, and thereafter, a pair of power levels is assigned in accordance with the selected decoding order. Exact closed-form expressions of the OOPs for both uplink and downlink pairwise NOMA considering all proposed decoding orders over Nakagami-m fading are derived. Further, we find the optimal fixed power levels for different power allocation strategies so that the OOPs are minimized. Moreover, we investigate the influence of the distances between the source nodes and the access point (AP), the target transfer rates and the path-loss exponents on the OOPs for all cases of decoding orders. In addition, we benchmark our proposed DDO against other decoding orders in terms of the OOP. The results show that assigning optimal fixed power levels which takes the instantaneous decoding order into account not only improves the communication reliability, but also reduces the complexity and computational load at the AP.

User Association and Power Allocation for Multi-Cell Non-Orthogonal Multiple Access Networks

In this paper, user association and power allocation are investigated in a non-orthogonal multiple access (NOMA)-based multi-cell network. In order to perform successive interference cancellation (SIC) techniques for removing the intra-base station (BS) interference, the optimal decoding order is derived for all users associated with the same BS. In an effort to improve the system, a sum rate maximization problem is formulated by jointly designing user association and power allocation. Two game theory based algorithms are proposed to obtain the stable user structure by dividing users into different BSs’ clusters, where the sub-optimal and global optimal solutions can be achieved. The properties of the proposed algorithms, including complexity, convergence, stability and optimality, are analyzed. Based on the quality-of-service (QoS) constraint, the closed-from solutions for power allocation are derived, and thus the expressions for the sum rate of all users in each cluster is obtained. Moreover, the case that the QoS threshold cannot be achieved by all users in each cluster is considered. Simulation results demonstrate that: i) the proposed user association algorithms and the closed-form solutions for power allocation can significantly enhance the sum rate and outage probability; and ii) the proposed NOMA-based system is capable of achieving promising gains over the conventional orthogonal multiple access (OMA)-based framework in the multi-cell scenario.