Proportional Rate Constraints Research Articles

Energy-efficient power allocation algorithm based on the BFGS algorithm and the armijo criterion

In high-speed railway (HSR), the increasing demand for wireless communication and high-speed broadband leads to higher energy consumption by the system. To improve energy efficiency (EE) and fair allocation of resources in multi-user communication, an algorithm combining the BFGS algorithm and the Armijo criterion is used. Firstly, an EE optimisation model of the system is constructed by considering the constraints, such as the average transmitting power of the evolved Node B (eNB), the minimum transmission rate and fairness among users. Secondly, the objective function is transformed into a convex optimisation problem through equivalent transformation. Finally, an algorithm combining the BFGS algorithm and the Armijo criterion is used to solve the objective function and then determine the power allocation scheme for each moment of the system. The simulation results show that the proposed scheme shows a better performance in terms of EE than the traditional algorithm in the same scenario over time. Under different user numbers and proportional rate constraint conditions, the adopted scheme can optimise system EE while satisfying the user communication fairness threshold. In addition, compared with the traditional power allocation scheme, the proposed algorithm is significantly improved in terms of eNB transmit power, fairness and EE performance.

Resource Allocation for Layered Multicast Video Streaming in NOMA Systems

The application of non-orthogonal multiple access (NOMA) to multi-layer multicast video streaming is envisioned to address the explosively growing demand for capacity which is dominated mostly by multimedia content. In this paper, a joint power allocation and subgrouping scheme is developed to enhance the performance of NOMA-based multi-layer multicast systems. An optimization problem is formulated to maximize the overall sum multicast rate whilst satisfying the maximum transmission power and proportional rate constraints. Due to the complexity of the optimization problem, we first derive two power allocation techniques for the 2-layer case considering arbitrary subgrouping which are based on the iterative implementation and closed-form analysis, respectively. We then generalize the low-complexity closed-form solution for the general multi-layer case. This scheme successively allocates power to each layer stream while assuring that the minimum target rate and proportionality are guaranteed, particularly for the transmission rate of the high-priority base layer stream. A sub-optimal joint power allocation and subgrouping scheme is also designed by incorporating the power allocation scheme into the proposed iterative subgrouping techniques. Simulation results show the effectiveness of the power allocation and subgrouping schemes in enhancing the sum multicast rate performance. In addition, the proposed power allocation scheme ensures substantially higher rates for the base layer stream, which is crucial in robust delivery of standard quality video to all users.

QoS-Aware Resource Allocation with Pilot-Aided Channel Estimation for Heterogeneous Wireless Networks

The deployment of heterogeneous networks (HetNets) is a way to increase the network capacity and release part of the traffic generated by users inside a cell to small-scale wireless networks for service. In this context, the main problem is managing the interference due to the coexistence of small cells and macro cells. In this paper, a QoS-aware Resource Allocation (RA) algorithm jointly working with admission control (AC) over a two-tier HetNet scenario is investigated in the presence of both the pilot-symbols for channel estimation and the channel estimation error. The RA algorithm allows two users, the macro cell user (CU) and small cell user (SU), to simultaneously share the same resource block. Moreover, system performance and fairness are improved by including adaptive power allocation to users over resource blocks. In the framework of RA with proportional rate constraints, a novel algorithm is designed by including the effects of pilot-aided channel estimation. The algorithm is able to distribute the same proportional rate to all CUs and SUs, even in the presence of channel estimation error. Relevant numerical results for the downlink of a two-tier HetNet with pilot-aided channel estimation show that the rate dispersion is driven to zero while the sum-rate is maximized, and the average user rate penalty with respect to a perfect-CSI scenario may rise to 20%.

Proportional rate constrained resource allocation in multicarrier nonorthogonal multiple access systems

AbstractIn multicarrier nonorthogonal multiple access (MC‐NOMA) systems, resource allocation for user rate fairness is an inherent challenge due to the huge difference in channel conditions among different users. As the general case of proportional fairness, proportional rate constraint is usually adopted in resource allocation optimization problems to ensure that achievable rates of users are distributed proportionally according to a set of arbitrarily predefined portion. In this article, we investigate joint subcarrier and power allocation in MC‐NOMA systems under proportional rate constraints. The formulated resource allocation optimization problem belongs to a mixed integer nonlinear programming (MINLP) problem due to its binary subcarrier allocation variables and nonaffine equality constraints. By introducing an auxiliary variable in proportional rate constraints and substituting power variable with rate variable, we convert this nonconvex problem into a convex optimization problem and solve it by using Karush‐Kuhn‐Tucker (KKT) conditions and the dual decomposition method. Based on the optimal solutions, we divide the resource allocation process into two phases, that is, subcarrier allocation and power allocation, and develop an optimal subcarrier allocation solution based resource allocation algorithm (OSSRA). Furthermore, we also propose a heuristic algorithm, referred to as proportional rate constrained subcarrier allocation algorithm (PCSAA), as a benchmark. Numerical results show that, substantial gains can be achieved by OSSRA over the existing work and the traditional orthogonal multiple access (OMA) schemes in terms of both sum rate and user fairness. Besides, PCSAA has better user fairness performance than OSSRA.

Cross-Layer Scheduling and Beamforming in Smart-Grid Powered Cellular Networks With Heterogeneous Energy Coordination

User scheduling, beamforming and energy coordination are investigated in smart-grid powered cellular networks (SGPCNs), where the base stations are powered by a smart grid and natural renewable energy sources. Heterogeneous energy coordination is considered in SGPCNs, namely energy merchandizing with the smart grid and energy exchanging among the base stations. A long-term grid-energy expenditure minimization problem with proportional-rate constraints is formulated for SGPCNs. Since user scheduling is coupled with the beamforming vectors, the formulated problem is challenging to handle via standard convex optimization methods. In practice, the beamforming vectors need to be updated over each slot according to the channel variations. User scheduling needs to be updated over several slots (frame) since the frequent scheduling of user equipment can cause reliability issues. Therefore, the Lyapunov optimization method is used to decouple the problem. A practical two-scale algorithm is proposed to schedule users at each frame, and obtain the beamforming vectors and amount of exchanged natural renewable energy at each slot. We prove that the proposed two-scale algorithm can asymptotically achieve the optimal solutions via tuning a control parameter. Numerical results verify the performance of the proposed two-scale algorithm.

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.

Power Allocation Schemes for Uplink Massive MIMO System in the Presence of Imperfect CSI

In this paper, spectrum efficiency (SE) and energy efficiency (EE) performances of uplink massive multiple-input multiple-output (MIMO) systems with continuous-rate adaptive modulation and imperfect channel state information (CSI) are investigated over Rayleigh fading channels. Given a target BER, closed-form SE and EE expressions are derived. With these results, a constrained non-concave optimization problem of power allocation (PA) to maximize the SE is firstly formulated subject to the maximum transmit power per user. A near-optimal PA scheme with the concave-convex procedure (CCCP) method is then developed, and it can offer nearly optimal performance close to that of the optimal scheme with exhaustive search, but require lower complexity. Since this scheme needs more iterations, we propose a suboptimal scheme with reduced complexity and slight performance loss, which utilizes the property of a large number of receive antennas to approximate the objective function as a concave one, thereby reducing the number of iterations. Secondly, the PA problem for EE maximization under the same constraints is addressed. Based on the CCCP method and fractional programming theory, we propose a near-optimal PA scheme to solve this problem, and it has the EE performance very close to the optimal exhaustive search scheme. However, multi-layer iterations make this scheme have relatively higher complexity. For this reason, we propose a low-complexity suboptimal scheme with small EE loss by using variable transformation and a large number of antennas. Based on the above results, we simultaneously optimize both EE and SE. A multi-objective optimization problem (MOP) subject to the maximum power constraint and proportional data rate constraint is formulated. By means of the weighted sum method, the complicated MOP is transformed into a simple single-objective optimization problem. Then a PA scheme is proposed by using the Lagrange multiplier method to balance the EE and SE effectively. Simulation results validate the effectiveness of the proposed PA schemes in term of high SE and EE, and illustrate the fundamental tradeoff between EE and SE for different parameter settings.

Resource Allocation in Non-Orthogonal and Hybrid Multiple Access System With Proportional Rate Constraint

Non-orthogonal multiple access (NOMA), which has attracted a lot of attention recently due to its superior spectral efficiency, could play a vital role in improving the capacity of future networks. In this paper, a resource allocation scheme is developed for a downlink multi-user NOMA system. An optimization problem is formulated to maximize the sum rate under the total power and proportional rate constraints. Due to the complexity of computing the optimal solution, we develop a low complexity sub-optimal solution for a two-user scenario and then extend it to the multi-user case by proposing a user-pairing approach as well as a number of power allocation techniques that facilitate dealing with a large number of users in NOMA system. Simulation results support the effectiveness of the proposed approaches and show the close performance to the optimal one. In addition, we propose a new hybrid multiple access technique that combines the properties of NOMA and the orthogonal frequency division multiple access. Simulation results show that the proposed hybrid method provides better performance than NOMA in terms of the overall achievable sum rate and the coverage probability.

Energy-Efficient Power Allocation for Distributed Antenna Systems With Proportional Fairness

In this paper, we propose an energy-efficient power allocation scheme for the downlink multiuser distributed antenna systems. The objective is to maximize the energy efficiency (EE) under the constraints on per-antenna transmit power and proportional data rates among users. Since EE function is typically defined in fractional form, it is computationally complex to optimize the EE directly. We first convert the nonlinear fractional problem into an equivalent but better tractable problem, based on which we derive an iterative algorithm to obtain the global optimum of the considered problem. On top of being optimal, the solution is also lightweight since only a single-variable nonlinear equation needs to be solved. Furthermore, we can flexibly switch to another mode of operation which delivers relatively higher spectral efficiency (SE) at the expense of losing EE. Numerical simulations and complexity analysis validate that the proposed scheme achieves much higher SE and EE performance with stricter satisfaction of the proportional rate constraints and lower complexity, compared to the state-of-the-art scheme in literature.

Energy‐efficient resource allocation in multiuser OFDM systems with proportional rate constraints

An efficient resource allocation scheme is presented to maximise energy efficiency for multiuser orthogonal frequency division multiple systems with proportional rate constraints. For a determined subchannel assignment, an optimal energy-efficient power allocation algorithm has been derived through a bisection search method.

Differential evolution aided adaptive resource allocation in OFDMA systems with proportional rate constraints

Orthogonal frequency division multiple access (OFDMA) is a promising technique, which can provide high downlink capacity for the future wireless systems. The total capacity of OFDMA systems can be maximized by adaptively assigning subcarriers to the user with the best gain for that subcarrier, with power subsequently distributed by water-filling. In this paper, we propose the use of a differential evolution combined with multi-objective optimization (CMODE) algorithm to allocate the resources to the users in a downlink OFDMA system. Specifically, we propose two approaches for resource allocation in downlink OFDMA systems using CMODE algorithm. In the first approach, CMODE algorithm is used only for subcarrier allocation (OSA), while in the second approach, the CMODE algorithm is used for joint subcarrier and power allocation (JSPA). The CMODE algorithm is population-based where a set of potential solutions evolves to arrive at a near-optimal solution for the problem under study. During the past decade, solving constrained optimization problems with evolutionary algorithms has received considerable attention among researchers and practitioners. CMODE combines multi-objective optimization with differential evolution (DE) to deal with constrained optimization problems. The comparison of individuals in CMODE is based on multi-objective optimization, while DE serves as the search engine. In addition, infeasible solution replacement mechanism based on multi-objective optimization is used in CMODE, with the purpose of guiding the population towards the promising solutions and the feasible region simultaneously. It is shown that both the proposed approaches obtain higher sum capacities as compared to that obtained by previous works, with comparable computational complexity. It is also shown that the JSPA approach provides near optimal results at the slightly higher computational cost.

On Ergodic Sum Capacity of Fading Channels in OFDMA-Based Cognitive Radio Networks

An orthogonal frequency-division multiple access (OFDMA)-based cognitive radio network (CRN) is considered where cognitive radio users (CRUs) can only access the frequency bands not being occupied by primary users (PUs) while keeping the cross-channel interference to each PU under a specified threshold. In this paper, we investigate the ergodic sum capacity of all CRUs in OFDMA-based networks and consider the constraints on the long-term transmit power of all CRUs, the long-term interference thresholds of PUs, and the statistical proportional fairness of all CRUs. In OFDMA-based CRNs, the number of available subchannels is smaller than that of CRUs in some OFDM symbol durations. To deal with this time-varying nature of available spectrum resource and achieve the ergodic sum capacity of all CRUs, we propose an optimal resource-allocation algorithm under the given constraints. Simulation results show that the proposed algorithm can achieve substantial capacity gains for CRUs over the traditional resource-allocation algorithm and maintain the statistical proportional rate constraints of all CRUs.

Composite differential evolution aided channel allocation in OFDMA systems with proportional rate constraints

Orthogonal frequency division multiple access (OFDMA) is a promising technique, which can provide high downlink capacity for the future wireless systems. The total capacity of OFDMA can be maximized by adaptively assigning subchannels to the user with the best gain for that subchannel, with power subsequently distributed by water-filling. In this paper, we propose the use of composite differential evolution (CoDE) algorithm to allocate the subchannels. The CoDE algorithm is population-based where a set of potential solutions evolves to approach a near-optimal solution for the problem under study. CoDE uses three trial vector generation strategies and three control parameter settings. It randomly combines them to generate trial vectors. In CoDE, three trial vectors are generated for each target vector unlike other differential evolution (DE) techniques where only a single trial vector is generated. Then the best one enters the next generation if it is better than its target vector. It is shown that the proposed method obtains higher sum capacities as compared to that obtained by previous works, with comparable computational complexity.

Proportional Fair Resource Allocation Based on Chance-Constrained Programming for Cognitive OFDM Network

Proportional fair resource allocation plays a critical role to balance the spectrum efficiency and fairness for cognitive orthogonal frequency division multiplexing (OFDM) network. However, due to the lack of cooperation between cognitive radio (CR) network and primary network, channel state information between CR base station (CRBS) and primary user (PU) could not be estimated precisely. Therefore, the interference of CRBS---PU couldn't be computed precisely and chance-constrained programming is adopted to formulate the resource allocation problem. In this work, we study the proportional fair resource allocation problem based on chance-constrained programming for cognitive OFDM network. The objective function maximizes the spectral efficiency of cognitive OFDM network over subcarrier and power allocation. The constraint conditions include the interference constraint of PU with the target probability requirement and the proportional fair rate requirement of CR users. In order to solve the above optimization problem, two steps are taken to develop hybrid immune optimization algorithm (HIOA). In the first step, the probabilistic interference constraint condition is transformed as an uncertain function which is computed by a generalized regression neural network (GRNN). In the second step, we combine immune optimization algorithm and GRNN to develop HIOA. Simulation results demonstrate that HIOA yields higher spectral efficiency while the probabilistic interference constraint condition and the proportional fair rate constraint condition could be satisfied very well.

Adaptive Resource Allocation With Proportional Rate Constraints for Uplink SC-FDMA Systems

In this letter, we address the problem of ergodic sum-rate maximization under proportional rate constraints for the uplink of single-carrier frequency-division multiple-access (SC-FDMA) systems. Finding optimal solution generally requires high computational complexity, because SC-FDMA imposes the contiguous allocation of the available frequency resources. To reduce complexity, we propose a novel suboptimal algorithmic solution, based on Lagrangian relaxation of the rate constraints, which exploits a simple but effective estimation of the average number of the resources to allocate in order to reduce the search space. The complexity of the resulting algorithm increases only linearly with the number of users and the number of resources, whereas the performance gap to optimal solution is limited to the 10% of the sum-rate.

Frequency and Power Allocation for Energy Efficient OFDMA Systems with Proportional Rate Constraints

A two-step solution to the problem of finding the subchannel and power allocation that maximizes the energy efficiency of the OFDMA based transmissions from a base station, under proportional rate and total power constraints, is presented. A low complexity subchannel assignment is followed by an optimal power allocation that is obtained via a single non-linear equation. The proposed algorithm has the same computational complexity as the best algorithm in the literature for the same problem but with minimum rate constraints. While the convergence of the algorithm in the literature is not guaranteed, the algorithm in this paper is proven to converge. Simulation results show that the proposed algorithm out-performs the one in the literature when the rate constraints are ignored.

Energy-Efficient Resource Allocation in Downlink OFDM Wireless Systems With Proportional Rate Constraints

Orthogonal frequency-division multiplexing (OFDM), with its own advantages of spectral efficiency (SE) enhancement and flexible resource allocation, is a promising basic technique for fulfilling the ever increasing demand for high-data-rate transmission and various service type support for mobile multimedia communications. In the meantime, energy efficiency (EE) has now become a critical metric for green system design. In this paper, energy-efficient and fair resource allocation is investigated in a downlink OFDM-based mobile communication system. Given a subcarrier assignment, the bisection-based optimal power allocation (BOPA) is proposed at first, which achieves the maximum EE and guarantees proportional data rates for users. Then, a two-step subcarrier assignment is designed to avoid unaffordable computational complexity of exhaustive search. In the first step, the estimated energy-efficient transmit power is found via the assumptions on flat fading and subcarrier sharing. In the second step, the traditional spectral-efficient subcarrier assignment (SESA) is introduced to complete the bandwidth resource allocation among users. Although the two-step subcarrier assignment is suboptimal due to the fact that the optimization is done independently in two separate steps, numerical results demonstrate that its performance is very close to the optimum. This paper also studies the difference between the energy-efficient solution and the traditional spectral-efficient policy and observes that they are similar with each other in the low channel-gain-to-noise ratio (CNR) regime. This observation is helpful and could enable that the energy-efficient design can be turned into the relatively simpler spectral-efficient policy when the CNR is low.

Bee colony optimization aided adaptive resource allocation in OFDMA systems with proportional rate constraints

Orthogonal frequency division multiple access (OFDMA) is a promising technique, which can provide high downlink capacity for the emerging wireless systems. The total capacity of OFDMA can be maximized by adaptively assigning subcarriers to the users with the best gains for those subcarriers, with power subsequently distributed by water-filling. In this paper, we propose the use of artificial bee colony (ABC) algorithm combined with Deb's selection mechanism to handle the constraints. In this scheme, a probabilistic selection scheme assigns probability values to feasible solutions based on their fitness values and to infeasible individuals based on their violations, to allocate the resources to the users in downlink OFDMA system. Specifically we propose two approaches for resource allocation in downlink OFDMA systems using ABC algorithm. In the first approach, ABC algorithm is used for subcarrier allocation only, while in second approach the ABC algorithm is used for joint subcarrier and power allocation. It is shown that both these approaches obtain higher sum capacities as compared to that obtained by previous works, with comparable computational complexity. It is also shown that the joint subcarrier and power allocation approach provides near optimal results at the cost of slightly higher computational cost.

On the Power Allocation Problem in the Gaussian Interference Channel with Proportional Rate Constraints

This paper takes an analytical approach to solving the optimization problem of finding the power allocation that maximizes the sum-rate of the Gaussian interference channel with any linear power (interference) constraint and proportional rate constraints. It is proved that the sum-rate of the Gaussian interference channel restricted to proportional rate constraints does not have a critical point and the maximum sum-rate subject to said constraints occurs at the boundary of the domain formed by the plane representing the linear power constraint. This is accomplished by using analytic geometry in higher dimensions to show that the curve of intersection of the sum-rate and the proportional rate constraints is always increasing, and intersects the boundary plane representing the linear power constraint at a unique point. A polynomial time (in the number of users) centralized algorithm that finds this point of optimal power allocation is proposed. This is a significant improvement over existing algorithms for related power allocation problems which have exponential time complexity in the number of users. Two distributed algorithms with linear and constant complexities are also presented. Simulation results supporting the analysis and demonstrating the performances of the algorithms are presented.

Optimal Resource Management with Delay Differentiated Traffic and Proportional Rate Constraint in Heterogeneous Networks

In this paper, we focus on the radio resource management (RRM) in heterogeneous networks with orthogonal frequency division multiple access (OFDMA), and aim to maximize the system sum-rate and meet quality of service (QoS) requirements under the proportional fairness constraint of user rates. The previously proposed resource allocation schemes, which do not differentiate the traffic types or consider the fairness performance, may result in inefficient allocation of radio resources. To tackle this problem, we present an analytical model which takes consideration of two types of the traffic including the Delay-Constraint (DC) traffic and the Best-Effort (BE) traffic, and then formulate the RRM problem as a linear programming (LP) problem. We propose an efficient iterative algorithm to find the optimal solutions by converting this combinatorial problem with exponential complexity into a convex problem or showing that it can be solved in the dual domain. Numerical studies are conducted to evaluate the performance of the proposed algorithm in terms of achievable transmission rate for the DC traffic and fairness for the BE traffic, multiuser diversity, and system throughout. Index Terms—Heterogeneous networks; optimal resource manangement; convex optimization; multi-radio access; power control