User Scheduling Problem Research Articles

Access strategies in mmWave cell-free network: A matching and auction theory based approach

The mmWave cell-free network is viewed as an energy-efficient and emerging architecture for beyond 5G systems. However, many practical issues should be solved for this system before the benefits are enjoyed, whereof feasible implementation of access strategy is one of the most vital. To this end, the access strategy including user scheduling and bandwidth allocation is investigated in this paper. Firstly, to maximize the defined utility function, the joint optimization problem of user scheduling and bandwidth allocation is formulated as a mixed integer nonlinear programming problem, which is intractable to search for an optimal solution in polynomial time. Secondly, a two-stage matching and sealed-auction-based access strategy is proposed to obtain a sub-optimal solution, where UEs with high-quality channel conditions are scheduled in the first-stage matching as much as possible, and the rest unmatched UEs are scheduled in the second-stage matching with the sealed-auction based bandwidth allocation. Thirdly, a simplified full-matching based access strategy with lower complexity is proposed for the high-dynamic scenario caused by the high-speed movement of UEs, and the complexities and convergence of the two proposed strategies are quantitatively analyzed. Finally, the performance of proposed strategies is evaluated through abundant simulations in different scenarios, and the superiorities of the proposed strategies are demonstrated through the comparison with reference strategies.

Neighbor-based joint spatial division and multiplexing in massive MIMO: user scheduling and dynamic beam allocation

AbstractTwo-stage precoding schemes have been developed to reduce the channel estimation overhead in FDD systems. By integrating user scheduling into these schemes, it becomes possible to meet the quality-of-service requirements of high-density wireless communication systems, despite the limitations on spatial resources and transmit power budget. In this paper, we propose a user scheduling and dynamic beam allocation method for neighbor-based joint spatial division multiplexing (N-JSDM) transmission. The user scheduling problem is formulated as a 0–1 quadratic programming problem to maximize effective spectral efficiency (ESE) using directional channel properties. To address the complexity issue, convex relaxation and linearization methods are employed to transform the problem into a 0–1 mixed integer linear programming, and a dimensionality reduction method is introduced. The proposed user scheduling-aided N-JSDM scheme reduces downlink training length and feedback of channel state information. Additionally, a dynamic configuration form is used for pre-beamforming matrix design based on user distribution, outperforming conventional approaches. Simulation results demonstrate higher ESE achieved by the proposed scheme compared to previous methods.

Spectrum Allocation and User Scheduling Based on Combinatorial Multi-Armed Bandit for 5G Massive MIMO.

As a key 5G technology, massive multiple-input multiple-output (MIMO) can effectively improve system capacity and reduce latency. This paper proposes a user scheduling and spectrum allocation method based on combinatorial multi-armed bandit (CMAB) for a massive MIMO system. Compared with traditional methods, the proposed CMAB-based method can avoid channel estimation for all users, significantly reduce pilot overhead, and improve spectral efficiency. Specifically, the proposed method is a two-stage method; in the first stage, we transform the user scheduling problem into a CMAB problem, with each user being referred to as a base arm and the energy of the channel being considered a reward. A linear upper confidence bound (UCB) arm selection algorithm is proposed. It is proved that the proposed user scheduling algorithm experiences logarithmic regret over time. In the second stage, by grouping the statistical channel state information (CSI), such that the statistical CSI of the users in the angular domain in different groups is approximately orthogonal, we are able to select one user in each group and allocate a subcarrier to the selected users, so that the channels of users on each subcarrier are approximately orthogonal, which can reduce the inter-user interference and improve the spectral efficiency. The simulation results validate that the proposed method has a high spectral efficiency.

Research on Resource Allocation Algorithm for Satellite Uplink to Provide Differentiated QoS Support

Broadband satellite systems are built to serve different user groups ranging from enterprise and military users to common personal users, with various kinds of services calling for dissimilar quality of service (QoS). Obviously, the satellite systems are expected to distinguish the specific type of an incoming service request as well as the importance of its owner in order to perform an efficient assignment of valuable resources. In this article, the uplink resource management challenge in a multifrequency-time-division multiple access satellite system is addressed where provisioning the discriminated QoS is of vital importance. Having taken both user priority and service type into account, a differentiated QoS support principle conforming to the digital video broadcast - second generation DVB interactive satellite system (DVB-RCS2) standard is put forward, based on which the uplink timeslot assignment problem is formulated.The NP-hardness of the problem is proved, and a differentiated QoS resource allocation scheme is designed, decoupling the problem into the coarse-level of resource allocation and fine-level of timeslot assignment. The former stage involves the constant rate assignment, bandwidth adjustment, QoS degradation and user scheduling, among which the subproblem of user scheduling is an integer nonlinear program. To tackle the issue, the problem is first innovatively converted to an integer linear program, and is then modeled as the multiple-choice multiple knapsack (MCMK) problem. Furthermore, an MCMK algorithm is presented to give the optimal solution to the user scheduling problem, after which the timeslot assignment is investigated in the second phase to generate the terminal burst time plan table for return channel satellite terminals.

User Scheduling and Power Allocation for Precoded Multi-Beam High Throughput Satellite Systems With Individual Quality of Service Constraints

For extensive coverage areas, multi-beam high throughput satellite (HTS) communication is a promising technology that plays a crucial role in delivering broadband services to many users with diverse Quality of Service (QoS) requirements. This article focuses on multi-beam HTS systems where all beams reuse the same spectrum. In particular, we propose a novel user scheduling and power allocation design capable of providing guarantees in terms of the individual QoS requirements while maximizing the system throughput under a limited power budget. Precoding is employed in the forward link to mitigate mutual interference among the users in multiple-access scenarios over different coherence time intervals. The combinatorial optimization structure from user scheduling requires an extremely high cost to obtain the global optimum even when a reduced number of users fit into a time slot. Therefore, we propose a heuristic algorithm yielding a good trade-off between performance and computational complexity, applicable to a static operation framework of geostationary (GEO) satellite networks. Although the power allocation optimization is signomial programming, non-convex on a standard form, the solution can be lower bounded by the global optimum of a geometric program with a hidden convex structure. A local solution to the joint user scheduling and power allocation problem is consequently obtained by a successive optimization approach. Numerical results demonstrate the effectiveness of our algorithms on GEO satellite networks by providing better QoS satisfaction combined with outstanding overall system throughput.

A DRL-Based Automated Algorithm Selection Framework for Cross-Layer QoS-Aware Scheduling and Antenna Allocation in Massive MIMO Systems

The rapid development of mobile networks proliferates the demands of high data rate, low latency, and high-reliability applications for the fifth-generation (5G) and beyond (B5G) mobile networks. Concurrently, the massive multiple-input-multiple-output (MIMO) technology is essential to realize the vision and requires coordination with resource management functions for high user experiences. Though conventional cross-layer adaptation algorithms have been developed to schedule and allocate network resources, the complexity of resulting rules is high with diverse quality of service (QoS) requirements and B5G features. In this work, we consider a joint user scheduling, antenna allocation, and precoding problem in a massive MIMO system. Instead of directly assigning resources, such as the number of antennas, the allocation process is transformed into a deep reinforcement learning (DRL) based dynamic algorithm selection problem for efficient Markov decision process (MDP) modeling and policy training. Specifically, the proposed utility function integrates QoS requirements and constraints toward a long-term system-wide objective that matches the MDP return. The componentized action structure with action embedding further incorporates the resource management process into the model. Simulations show 7.2% and 12.5% more satisfied users against static algorithm selection and related works under demanding scenarios.

Near Interference-Free Space-Time User Scheduling for mmWave Cellular Network

The highly directional beams applied in millimeter wave (mmWave) cellular networks make it possible to achieve near interference-free (NIF) transmission under judiciously designed space-time user scheduling, where the power of intra-/ inter-cell interference between any two users is below a predefined threshold. In this paper, we investigate two aspects of the NIF space-time user scheduling in a multi-cell mmWave network with multi-RF-chain base stations. Firstly, given that each user has a requirement on the number of space-time resource elements, we study the NIF user scheduling problem to minimize the unfulfilled user requirements, so that the space-time resources can be utilized most efficiently and meanwhile all strong interferences are avoided. A near-optimal scheduling algorithm is proposed with performance close to the lower bound of unfulfilled requirements. Furthermore, we study the joint NIF user scheduling and power allocation problem to minimize the total transmit power under the constraint of rate requirements. Based on our proposed NIF scheduling, an energy-efficient joint scheduling and power allocation scheme is designed with limited channel state information, which outperforms the existing independent set based schemes, and has near-optimal performance as well.

Learning Based User Scheduling in Reconfigurable Intelligent Surface Assisted Multiuser Downlink

Reconfigurable intelligent surface (RIS) is capable of intelligently manipulating the phases of the incident electromagnetic wave to improve the wireless propagation environment between the base-station (BS) and the users. This paper addresses the joint user scheduling, RIS configuration, and BS beamforming problem in an RIS-assisted downlink network with limited pilot overhead. We show that graph neural networks (GNN) with permutation invariant and equivariant properties can be used to appropriately schedule users and to design RIS configurations to achieve high overall throughput while accounting for fairness among the users. As compared to the conventional methodology of first estimating the channels then optimizing the user schedule, RIS configuration and the beamformers, this paper shows that an optimized user schedule can be obtained directly from a very short set of pilots using a GNN, then the RIS configuration can be optimized using a second GNN, and finally the BS beamformers can be designed based on the overall effective channel. Numerical results show that the proposed approach can utilize the received pilots more efficiently than the conventional channel estimation based approach, and can generalize to systems with an arbitrary number of users.

Joint Video Packet Assignment, Power Control and User Scheduling Over Cognitive Multi-Homing Heterogeneous NOMA Networks

Non-orthogonal multiple access (NOMA)-based cognitive heterogeneous multi-homing networks is a very important scenario in the future wireless networks. In this work, we formulate a joint video packet assignment, power control and user scheduling problem as a mixed integer non-linear programming (MINLP) to maximize the total video transmission quality for cognitive multi-homing heterogeneous NOMA networks, which is subject to the maximum accessed number of secondary users at each subchannel, video encoding characteristics, maximum interference power constraint and total available power constraint. For the joint video packet assignment, power control and user scheduling problem, we divide it into a video packet assignment subproblem, a power control subproblem and a secondary user scheduling subproblem for cognitive multi-homing heterogeneous NOMA networks. Firstly, the secondary user scheduling algorithm is proposed using the greedy method. Then, we utilize successive convex approximation (SCA) method to transform the power control subproblem into a convex programming problem, and an approximated optimal power control algorithm is proposed with the dual decomposition method. Finally, a heuristic video packet assignment algorithm is designed, which utilizes the auction theory. Numerical simulation results demonstrate that the proposed algorithms not only improve the video transmission quality, but also enhance the total throughput of cognitive multi-homing heterogeneous NOMA networks.

Joint User Scheduling and Resource Allocation in Distributed MIMO Systems with Multi-Carriers

Compared with the traditional collocated multi-input multi-output system (C-MIMO), distributed MIMO (D-MIMO) systems have the advantage of higher throughput and coverage, making them strong candidates for next-generation communication architecture. As a practical implementation of a D-MIMO cooperative network, the multi-TRP (multiple transmission/reception point) system becomes a hotspot in the research of advanced 5G. Different from previous research on a cooperative D-MIMO network with single narrowband transmission, this paper proposes a joint optimization scheme to address the user scheduling problem along with carrier allocation to maximize the total spectral efficiency (SE) in the downlink of coherent multi-TRP systems with multi-carriers. We establish a joint optimization model of user scheduling and resource allocation to maximize the system spectral efficiency under the constraints of power consumption and the backhaul capacity limits at each RAU (remote antenna unit), as well as the QoS (quality of service) requirement at each user. Since the optimization model is both non-covex and non-smooth, a joint optimization algorithm is proposed to solve this non-convex combinatorial optimization problem. We first smooth the mixed-integer problem by employing penalty functions, and after decoupling the coupled variables by introducing auxiliary variables, the original problem is transformed into a series of tractable convex optimization problems by using successive convex approximation (SCA). Numerical results demonstrate that the proposed joint optimization algorithm for user scheduling and resource allocation can reliably converge and achieve a higher system SE than the general multi-TRP system without carrier allocation, and this advantage is more pronounced under a higher backhaul capacity or higher power consumption constraints.

Proportional Fair Scheduling for Downlink mmWave Multi-User MISO-NOMA Systems

In this paper, we study non-orthogonal multiple access (NOMA) user scheduling and resource allocation problem for a generic downlink single-cell multiple input and single output (MISO) millimeter wave (mmWave) system. The larger number of packed antennas and the highly directional property of mmWave communications enable directional beamforming to achieve spatial diversity. Toward this end, we consider two different hybrid precoding schemes which are based on orthogonal matching pursuit (OMP). Users are assigned into different clusters and the base station (BS) transmits superposed signals that share the same precoding vector. Moreover, both fixed number of users per cluster and dynamic number of users per cluster are investigated. We aim to jointly optimize the user clustering, service scheduling, and power allocation strategy, in maximizing the proportional fairness (PF) among the users and exploring the multiuser diversity and multiplexing gain. Since the formulated joint user clustering, scheduling and power allocation problem is a mixed integer non-convex optimization problem, we propose a two-fold methodology. First, we apply a hybrid precoding and user clustering scheme, where the hybrid precoder is constructed by singular vector division (SVD) or minimum mean square error (MMSE). Then, with the obtained result, we approximate the proportional fairness power allocation problem by a sequence of Geometric Programming (GP) problems which are solved iteratively. The proposed scheme strikes a balance between the spectral efficiency and service fairness. Results show that the proposed MISO-NOMA scheme which is based on MMSE hybrid precoder and the proposed user scheduling and power allocation strategy under proportional fairness metric can outperform various conventional MISO schemes. Furthermore, our proposed dynamic number of users per cluster scheme outperforms the fixed scheme and can be considered as an upper bound in several aspects, including spectral efficiency and fairness.

Energy and Delay Guaranteed Joint Beam and User Scheduling Policy in 5G CoMP Networks

Massive Multi-Input Multi-Output (MIMO) and Coordinated MultiPoint (CoMP) technologies in Cloud-RAN (C-RAN) architecture become inevitable trend due to the advent of next-generation mobile applications, which are traffic-intensive, such as ultra high definition (UHD) video. In this paper, we study a joint beam activation and user scheduling problem in a 5G cellular network with massive MIMO and CoMP utilizing orthogonal random beamforming technique. This paper aims to minimize total Remote Radio Heads’ (RRHs’) energy expenditure in a dynamic C-RAN architecture while ensuring finite service time for all user traffic arrivals in the communication coverage. We leverage Lyapunov drift-plus-penalty framework to transform an original long-term average problem into a series of per-slot modified problems. Since the provided per-slot problem is combinatorial and nonlinear optimization problem, we are inspired by a greedy algorithm to design energy and delay guaranteed joint beam activation and user scheduling policy, namely BEANS. We prove that the proposed BEANS ensures finite upper bounds of average RRH energy consumption and average queue backlogs for all traffic arrival rates within constant ratio of capacity region and all energy-delay tradeoff parameters. These proofs are the first attempt to theoretically demonstrate guarantees of energy and queue bounds in a framework consisting of possibly negative submodular objective function and non-matriod constraints. Finally, via extensive simulations, we compare the capacity region and energy-queue backlog tradeoff of BEANS with optimal and existing algorithms, and show that BEANS attains up to 65% of energy saving for the same average queue backlog compared to the algorithms which do not take traffic dynamics and energy consumption into considerations.

Resource Allocation and Hybrid OMA/NOMA Mode Selection for Non-Coherent Joint Transmission

Supporting non-orthogonal multiple access (NOMA) in non-coherent joint transmission (NCJT) systems is beneficial for improving spectral efficiency (SE), but the interference coordination, user scheduling, and resource allocation problems in this new scenario have not been well studied. In this paper, a NOMA-enabled NCJT system is considered in which the connected users are jointly served by two multi-antenna transmitting-receiving points (TRPs) with non-ideal backhauls. Each user has two independent receiving (RX) chains that can work with orthogonal multiple access (OMA) or NOMA mode. A joint resource allocation and hybrid OMA/NOMA mode selection is proposed to maximize the throughput. The primal non-convex and NP-hard problem is decomposed into the following three subproblems, i.e., power allocation (PA) of a single TRP, hybrid mode selection (HMS) of a single TRP, and cross-TRP interference optimization (CIO). Firstly, a successive convex approximation (SCA) method is proposed to solve the non-convex PA subproblem, which achieves a local maximum solution. Secondly, the combinatorial HMS subproblem is transformed into finding the maximum matching of bipartite graphs. By constructing two weighted bipartite graphs for the OMA/near UEs and far UEs, a suboptimal solution is found. Thirdly, an alternating optimization is proposed to solve the CIO subproblem by iteratively performing PA and HMS of the two TRPs. Finally, simulation results demonstrate the superiority of throughput improvement of the proposed method, and the sum rate of the NOMA-enabled NCJT system can approach the sum rate of individual TRPs without interference.

User scheduling and power allocation for downlink multi-cell multi-carrier NOMA systems

In Non-Orthogonal Multiple Access (NOMA), the best way to fully exploit the benefits of the system is the efficient resource allocation. For the NOMA power domain, the allocation of power and spectrum require solving the mixed-integer nonlinear programming NP-hard problem. In this paper, we investigate user scheduling and power allocation in Multi-Cell Multi-Carrier NOMA (MCMC-NOMA) networks. To achieve that, we consider Weighted Sum Rate Maximization (WSRM) and Weighted Sum Energy Efficiency Maximization (WSEEM) problems. First, we tackle the problem of user scheduling for fixed power using Fractional Programming (FP), the Lagrange dual method, and the decomposition method. Then, we consider Successive Pseudo-Convex Approximation (SPCA) to deal with the WSRM problem. Finally, for the WSEEM problem, SPCA is utilized to convert the problem into separable scalar problems, which can be parallelly solved. Thus, the Dinkelbach algorithm and constraints relaxation are used to characterize the closed-form solution for power allocation. Extensive simulations have been implemented to show the efficiency of the proposed framework and its superiority over other existing schemes.

Novel Design of User Scheduling and Analog Beam Selection in Downlink Millimeter-Wave Communications

In this article, the joint design for user scheduling and analog beam selection in a downlink multiuser millimeter-wave (mmWave) system is studied. Our objective is to maximize the achievable sum rate under the user scheduling constraint, the analog beam selection constraint, and the resource capacity constraint. This problem is nonconvex and NP hard. We first propose a whale optimization algorithm (WOA)-based scheme to obtain a near-global-optimal solution with fast convergence and low complexity. Since the joint optimization user scheduling and beam selection problem is a constrained integer programming problem, the binary version of WOA is applied to deal with integer variables and the penalty method is used to handle the constraints. Besides, a nonlinear convergence factor is introduced to enhance the optimal solutions. For real-time use, we also propose a low-complexity machine-learning (ML)-based scheme. In the ML-based scheme, we decompose the original optimization problem into two subproblems: 1) user classification subproblem and 2) the analog beam selection subproblem. The user classification subproblem is solved based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -means algorithm, where the users are clustered according to channel correlation. To solve the analog beam selection subproblem, we reformulate this subproblem as a multiclass classification problem. Considering the imbalance nature of the data set of the subproblem, we train the multiclass classifiers via the biased-SVM algorithm. Finally, the simulation results of the WOA-based scheme and the proposed ML-based scheme against the state-of-the-art schemes have shown the advantages of our proposed schemes.

Throughput Maximization in Cloud-Radio Access Networks Using Cross-Layer Network Coding

Cloud radio access networks (C-RANs) are promising paradigms for the fifth-generation (5G) networks due to their interference management capabilities. In a C-RAN, a central processor (CP) is responsible for coordinating multiple Remote Radio Heads (RRHs) and scheduling users to their radio resource blocks (RRBs). In this paper, we develop a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cross-layer network coding (CLNC)</i> approach that proposes to optimize RRH’s transmit powers and user’s rates in making the coding decisions. As such, cross-layer throughput of the network is maximized. The joint user scheduling, file encoding, and power adaptation problem is solved by designing a subgraph for each RRB, in which each vertex represents potential user-RRH associations, encoded files, transmission rates, and power levels (PLs) for one RRB. It is then shown that the C-RAN throughput maximization problem is equivalent to a maximum-weight clique problem over the union of all such subgraphs, called herein the CRAN-CLNC graph. Numerical results revealed that the proposed joint and iterative schemes offer improved throughput performances as compared to the existing algorithms in the literature. Compared to our proposed joint scheme, our proposed iterative scheme has a certain degradation, roughly in the range of 9%–14%. This small degradation in the throughput performance of the iterative scheme comes at the achieved low computational complexity as compared to the high complexity of the joint scheme.

Federated Learning Over Energy Harvesting Wireless Networks

In this article, the deployment of federated learning (FL) is investigated in an energy harvesting wireless network in which the base stations (BSs) employs massive multiple-input–multiple-output (MIMO) to serve a set of users powered by independent energy harvesting sources. Since a certain number of users may not be able to participate in FL due to interference and energy constraints, a joint energy management and user scheduling problem in FL over wireless systems is formulated. This problem is formulated as an optimization problem whose goal is to minimize the FL training loss via optimizing user scheduling. To find how the transmit power, the number of scheduled users and user association, affect the training loss, the FL convergence rate is first analyzed. Given this analytical result, the original optimization problem can be decomposed, simplified, and solved. Simulation results show that the proposed user scheduling and user association algorithm can reduce training loss compared to a standard FL algorithm.

Joint User Scheduling and Resource Allocation for Millimeter Wave Systems Relying on Adaptive-Resolution ADCs

Millimeter wave (mmWave) communication systems using adaptive-resolution analog-to-digital converters (RADCs) have recently drawn considerable interests from the research community as benefit of their high energy efficiency and low implementation cost. In this paper, we focus on the mmWave uplink using RADCs and investigate the joint user scheduling and resource allocation problem. Specifically, we seek to maximize the system throughput of the scheduled users by jointly optimizing their transmit power level and hybrid combiners as well as the number of quantization bits, subject to practical constraints. By relying on fractional programming (FP) techniques, we first covert this problem into a form amenable to optimization and exploit the specific structures in its solutions with the aid of the so-called Ky Fan <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -norm.Then, the resultant optimization problem is solved using a penalty block successive concave approximation (P-BSCA) algorithm. Our numerical results reveal that the proposed algorithm substantially enhances the throughput of the scheduled users compared to the state-of-the-art benchmark schemes and provides more flexible and efficient resource allocation control.

Throughput Maximization of Network-Coded and Multi-Level Cache-Enabled Heterogeneous Network

One of the paramount advantages of multi-level cache-enabled (MLCE) networks is pushing contents proximity to the network edge and proactively caching them at multiple transmitters (i.e., small base-stations (SBSs), unmanned aerial vehicles (UAVs), and cache-enabled device-to-device (CE-D2D) users). As such, the fronthaul congestion between a core network and a large number of transmitters is alleviated. We consider the throughput maximization problem that optimizes jointly the network-coded user scheduling and power allocation, subject to fronthaul capacity, transmit power, and NC constraints. Given the intractability of the problem, we decouple it into two separate subproblems. In the first subproblem, we consider the network-coded user scheduling problem for the given power allocation, while in the second subproblem, we use the NC resulting user schedule to optimize the power levels. We design an innovative two-layered rate-aware NC (RA-IDNC) graph to solve the first subproblem and solve the second subproblem using an iterative function evaluation (IFE) approach. Simulation results are presented to depict the throughput gain of the proposed approach over the existing solutions.

Joint Resource Allocation and Trajectory Optimization With QoS in UAV-Based NOMA Wireless Networks

Replacing base stations with unmanned aerial vehicles (UAVs) to serve the communication of ground users has attracted a lot of attention recently. In this paper, we study the joint resource allocation and UAV trajectory optimization for maximizing the total energy efficiency in UAV-based non-orthogonal multiple access (NOMA) downlink wireless networks with the quality of service (QoS) requirements. To handle the user scheduling problem, a heuristic algorithm based on matching and swapping theory is proposed first to allocate users that access UAV in each subperiod, then the transmit power allocation problem which considers the maximum transmit power and minimum user date rate is transformed to a convex optimization problem using logarithmic approximation. Meanwhile, the successive convex optimization is used in UAV trajectory optimization problem and a joint optimization algorithm is presented with the algorithm’s convergence and computational complexity. Finally, numerical results are provided to support the rationality of the proposed algorithm.