Closed-form Power Allocation Research Articles

Energy Efficient Resource Allocation for Uplink RIS-Aided Millimeter-Wave Networks With NOMA

In this paper, energy efficiency (EE) is maximized for the reconfigurable intelligent surface (RIS) aided millimeter-Wave (mmWave) networks with non-orthogonal multiple access (NOMA) and multiple mobile devices. To this end, we first propose the EE optimization, under the constraints of maximum power, minimal rate of devices and constant modulus of beamforming (BF) vectors. Then, the joint resource allocation scheme of power allocation (PA) and BF is designed. Specifically, given PA, an effective iterative algorithm based on the majorizationminimization, concave-convex procedure and block coordinate descent (BCD) is presented to obtain closed-form solutions of suboptimal passive BF (PBF) and analog BF (ABF) for each iteration. Then, given PBF and ABF, an effective iterative algorithm based on the successive convex approximation, BCD and Dinkelbach methods is derived to achieve suboptimal closedform PA for each iteration. By incorporating these two algorithms into the BCD method, a joint optimization algorithm for EE maximization is presented. As a result, joint resource allocation of PA, PBF and ABF is attained. Besides, the convergence and complexity of the algorithms are analyzed. For comparison, the benchmark scheme based on the multidimensional search method and artificial bee colony algorithm is also presented. Simulation results show that the proposed joint scheme is effective and higher EE can be obtained with lower complexity.

Full-Duplex SIC Design and Power Allocation for Dual-Functional Radar-Communication Systems

To meet the requirements for simultaneous sensing and communication, full-duplex operation is essential for dual-functional radar-communication (DFRC) systems. In this letter, both the full-duplex self-interference cancellation (SIC) and the corresponding power allocation problem is studied for a pulsed DFRC system. First, a full-duplex design is provided, and the radar signal to interference-plus-noise ratio (SINR) and the communication rate are derived considering imperfect full-duplex SIC. Then, a max-min-ratio problem is formulated to maximize the radar SINR under the constraint of the communication rate. For time-invariant channels, a closed-form power allocation solution is derived for both radar and communication pulses. For time-variant channels, we provide an iterative solution by adopting quadratic transform and successive convex approximation (SCA). Simulation results are further given to verify the effectiveness of the proposed designs.

Error Vector Magnitude-Based Low Complexity Adaptive Power Allocation in SM-MIMO System

In this article, we propose the error vector magnitude (EVM)-based adaptive power allocation (PA) for spatial modulation (SM) multiple-input-multiple-output (MIMO) system to optimize the minimum squared Euclidean distance and reduce the system complexity. We first investigate the typical Euclidean distance (ED)-based PA (ED-PA) algorithm. Second, an EVM-based ED-PA algorithm is proposed, where a simplified closed-form PA solution for the quadrature amplitude modulation is obtained in the case of two transmit antennas. For more transmit antennas, we further propose a low complexity-PA (LC-PA) algorithm, where all the transmit antennas are grouped with two antennas in each group and the proposed EVM-based ED-PA algorithm is utilized to assign the power within each group. Numerical results reveal that the proposed EVM-based ED-PA and LC-PA algorithms have considerably lower complexity and can achieve the optimal average bit error rate (ABER) and suboptimal ABER performance at low-and-moderate signal-to-noise ratio (SNR) region and high-SNR region, respectively, compared with the typical PA algorithms in SM-MIMO system.

Joint Design of Power Allocation, Beamforming, and Positioning for Energy-Efficient UAV-Aided Multiuser Millimeter-Wave Systems

In this paper, the joint design of power allocation (PA), beamforming (BF) and positioning is studied for unmanned-aerial-vehicle (UAV) aided millimeter-Wave (UAV-mmWave) systems, with the objective of maximizing the energy efficiency (EE), under the constraints of maximum transmitting power, minimum data rate from the ground users and positioning range of the UAV. To address the above problem, we first obtain the positioning of the UAV, with the help of approximate beam pattern. Then, near-optimal BF and closed-form PA are derived given the obtained position, with the help of block coordinate descent method. To reduce the complexity, two suboptimal BF schemes with one-loop iteration and closed-form solutions are respectively derived. Furthermore, we propose the simplified algorithms for two special cases, i.e., only line-of-sight (LoS) path and Non-LoS (NLoS) path exist between the users and the UAV. Simulation results verify the effectiveness of the developed joint schemes and show the superior EE performance. Moreover, they can obtain almost the same performance as the existing benchmark schemes but with lower complexity.

Improving Quality of Service for Cell-Edge Users in D2D-Relay Networks

In this paper, we build a D2D-relay communications model where the D2D user is selected as a relay to forward data for the users at the edge of the networks. We aim at maximizing the achievable data rates of the cell-edge users, a resource allocation problem is formulated and an iterative power allocation algorithm is proposed. We derive the optimal closed-form power allocation expressions by the Lagrange dual method. Simulation results show that our communication scheme can achieve greater spectral efficiency than the traditional cellular-relay communication scheme.

Effective Throughput Maximization of NOMA With Practical Modulations

Non-orthogonal multiple access (NOMA) has been considered as a promising technology for future wireless communications. In most of the existing NOMA schemes, the ideal information rate based on Shannon capacity is used as the performance metric, assuming perfect successive interference cancellation (SIC) and Gaussian transmit signals without considering practical modulations. The implicit assumptions and the resulting schemes may lead to suboptimal performance in practical NOMA systems. In this paper, we consider multi-user multi-channel NOMA systems using practical quadrature amplitude modulation (QAM) with imperfect SIC. We aim to maximize a more practical performance metric, namely the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">effective throughput</i> , which takes into account the data rate and error performance. To achieve this goal, we derive both the exact and approximate expressions of the effective throughput. We also formulate a joint resource optimization problem of the power allocation, channel assignment, and modulation selection to maximize the effective throughput. We develop an efficient power allocation solution by proposing a closed-form power allocation within channels and a waterfilling-form power budget allocation among channels. We also develop efficient channel assignment and modulation selection methods with the aid of matching theory and machine learning, respectively. Consequently, we provide an efficient joint resource allocation algorithm via iterative optimization to maximize the effective throughput. Numerical results are presented to verify the superiority of the proposed NOMA scheme over orthogonal multiple access (OMA) and other NOMA schemes.

Joint Power Allocation and Beamforming for Energy-Efficient Design in Multiuser Distributed MIMO Systems

Energy efficiency (EE) optimization of joint power allocation (PA) and beamforming (BF) is studied for multiuser distributed multiple-input multiple-output (D-MIMO) systems with maximum ratio combining. Subject to power budget constraints, a non-convex constrained optimization problem is firstly formulated to maximize EE of single-user D-MIMO. We propose a near-optimal joint design scheme with the block coordinate descent method, which has an effective iterative algorithm to find optimal BF for fixed PA, and an iterative algorithm based on the Dinkelbach methods to find optimal PA for fixed BF. We also develop a low-complexity suboptimal joint scheme, which has closed-form BF and PA by maximizing an effective signal-to-noise ratio for fixed PA and a derived EE upper bound for fixed BF, respectively. It has lower complexity than the near-optimal scheme with slight performance loss. With these results, two joint design schemes are developed for multiuser D-MIMO. The first scheme can achieve the best performance, while the second one based on closed-form PA and BF has slight performance loss in comparing to that of the former, but with lower complexity. Simulation results verify the effectiveness of the developed schemes over some existing schemes.

A Minimum Error Probability NOMA Design

Non-orthogonal multiple access (NOMA) enables massive connectivity and achieves high spectral efficiency. The vast majority of the NOMA literature has adopted the ideal information rate as performance metric assuming perfect successive interference cancellation (SIC) without any error propagation, which, however, may lead to NOMA designs adverse to SIC. In this paper, we take into account imperfect SIC and practical modulation schemes for power-domain NOMA design. To characterize the error propagation, we derive the bit error rates (BERs) of the users for arbitrary-order quadrature amplitude modulation (QAM) schemes. Then, we propose a minimum error probability NOMA (MEP-NOMA) design, minimizing the average BER of the users via power allocation. Considering the complicated error probability expressions of the MEP-NOMA design, we derive lower and upper bounds on the average BER, based on which a simple closed-form power allocation is obtained. We show that the proposed power allocation minimizes both the lower and upper bounds on the average BER for a sufficiently large power budget and provides near-optimal error performance. On this basis, we theoretically prove the superiority of MEP-NOMA over existing OMA and NOMA schemes in terms of error performance. Comprehensive numerical results are provided to verify the accuracy of the error probability analysis of the considered practical NOMA scheme with imperfect SIC and to demonstrate the efficacy of the proposed MEP-NOMA design.

Queue-Aware Dynamic Resource Allocation for the Joint Communication-Radar System

The joint communication-radar system (JCRS) is promising in the future wireless network which can provide great advantages, such as structure simplification, interference mitigation and less resource occupation, compared with the traditional separate deployment of communication and radar systems. However, with the large number of users accessing the network both for communication and radar purposes, massive user data packets may arrive at the base station equipped with the JCRS in a short period of time, which can easily cause the backlog of user data packets and affect network stability. To solve this problem, we introduce orthogonal frequency division multiple access (OFDMA) technique into the JCRS to support communication function for massive users. Then, we design a queue scheduling model of user data packets to perceive the status of current queue backlog and schedule the queue dynamically. Different from the existing works, we formulate a transmit power minimization problem, while taking network stability and radar detection performance into account. Since the problem is a non-convex problem, we transform it into the upper-bound minimization of drift-plus-function by using the Lyapunov optimization technique. Further, the successive convex approximation method and parameter transformation method are exploited to convert this problem into a convex problem. Finally, we derive an optimal closed-form power allocation expression by using the Lagrangian dual decomposition method and propose a dynamic subcarrier and power allocation algorithm. Simulation results show that the proposed algorithm can achieve an $[{\rm {O}}(1/\eta),{\rm {O}}(\eta)]$ power-backlog tradeoff and demonstrate the efficacy of the proposed algorithm in reducing transmit power while significantly enhancing network stability.

Low‐complexity energy‐efficient power allocation scheme for distributed MISO system with beamforming

This letter investigates the energy efficiency (EE) optimisation of a distributed multiple-input single-output (D-MISO) system, and a suboptimal power allocation (PA) scheme with low complexity is developed for D-MISO system with beamforming. Different from the existing optimal PA scheme that needs iterative calculation, the developed scheme can provide closed-form PA and no iteration is required. Using the Cauchy-Schwarz inequality, the upper bound of EE is first obtained, and then the optimised objective function is formulated subject to a set of power budget constraints. By maximising this upper bound, a suboptimal PA scheme for the system is derived, and closed-form PA coefficients are attained. Interestingly, it is found that the proposed scheme has the same general form of PA as the optimal scheme. Numerical results verify the effectiveness of the proposed scheme, it can achieve the EE performance very close to that of the existing optimal scheme due to better approximation, but it has lower complexity than the latter.

Power Allocation for Energy Efficient Optimization of Distributed MIMO System With Beamforming

This paper presents three energy-efficient power allocation (PA) schemes for the downlink of a distributed multiple-input multiple-output (D-MIMO) system with beamforming at distributed antenna ports and antenna selection (AS) at a mobile station over composite Rayleigh channels. Subject to maximum power constraints, a constrained maximization problem on energy efficiency (EE) is formulated. Based on theoretical analysis, the optimal beamforming is shown to be aligned with the channel direction that renders the joint design problem to be a PA optimization one. It is shown that the optimization problem is strictly pseudo-concave with a unique maximum. Thus, an optimal PA scheme based on a gradient projection method is proposed to obtain the global solution. To speed up the gradient projection method, a closed-form initialization is derived. Furthermore, a low-complexity optimal PA schemes based on the Karush–Kuhn–Tucker conditions is proposed. This optimal scheme has a closed-form PA expression for a certain condition or else computes the PA by the Lambert function or the bisection method, and gives the same EE performance as that of the optimal gradient-based scheme. The performances of these two optimal schemes are optimal and verified to be valid in contrast to the inaccurate optimal scheme in the literature. For large maximum power, the closed-form initial PA will become the optimal solution and can be considered as a suboptimal solution with no iterative computation. Making use of the tight upper and lower bounds of the Lambert function, a very low-complexity suboptimal PA scheme is developed. Simulation results show that the proposed suboptimal scheme can achieve nearly optimal performance. Maximum EE and maximum channel power, which are optimal and suboptimal criteria, are adopted for antenna selection. The simple suboptimal criterion can provide EE performance very close to that of the optimal one. The D-MIMO with AS is shown to give considerable EE gain over the single receive antenna system. Moreover, the proposed three PA schemes can be used for multiuser diversity D-MIMO systems to achieve superior EE performance.

Joint Transmitter-Receiver Spatial Modulation Design via Minimum Euclidean Distance Maximization

Joint transmitter-receiver spatial modulation (JSM) is an appealing transmission scheme in the spatial modulation family, where transmit diversity, receive diversity, and multiplexing gain are achieved simultaneously. However, the conventional JSM technique is neither spectrum efficient nor antenna efficient due to its limited candidates of bit-to-antenna mapping. In this paper, we propose a novel JSM approach that involves more mapping candidates to relax the implementation constraint and achieve better reliability. The proposed JSM scheme maximizes the minimum Euclidean distance (MED) between the received signals of different antenna mappings by optimizing the antenna selection and the power allocation over the transmit antennas, named MED-JSM. In particular, an optimal closed-form power allocation solution is derived when there are two receive antennas. For more receive antennas, a lower bound of the minimum Euclidean distance is derived, and a corresponding lower bound-approaching power allocation algorithm is proposed accordingly. Then, the proposed power allocation algorithm and antenna selection are used in a hybrid manner to further enhance the system reliability. Since the optimal MED-JSM requires an exhaustive search over all the received signals, we propose a suboptimal scheme with reduced computational complexity, which shrinks the search space via the Rayleigh-Ritz theorem. Numerical results show that the proposed MED-JSM outperforms the conventional JSM schemes in system's reliability.

Optimal Energy Efficient Power Allocation With User Fairness for Uplink MC-NOMA Systems

The optimal energy efficient power allocation is investigated for the uplink multi-carrier non-orthogonal multiple access (MC-NOMA) system. Considering the user fairness, the power allocation is formulated as a maximization problem of the system weighted energy efficiency, which is defined as a ratio of the weighted sum rate to the total power consumption. By utilizing Dinkelbach algorithm and Lagrange dual decomposition approach, the optimal closed-form power allocation expressions are derived. The convergence and optimality of the proposed scheme can be proved. The simulation results demonstrate performance enhancement of the proposed algorithm compared to the existing works, i.e., the enhance water-filling scheme and orthogonal multiple access (OMA) system.

Energy-Efficient Power Allocation for Millimeter-Wave System With Non-Orthogonal Multiple Access and Beamforming

In this paper, two power allocation (PA) and beamforming (BF) schemes of a downlink millimeter-wave communication system with non-orthogonal multiple access (mmWave-NOMA) over mmWave fading channels is presented. The proposed scheme is developed based on the maximization of the energy efficiency (EE) of the mmWave-NOMA system. First, with the EE analysis under the simplified channel model, the optimization of the PA and BF design for maximizing EE of the mmWave-NOMA system subject to minimum rate and maximum total power constraints is formulated. Since this optimization problem cannot be solved directly, it is decomposed into sub-problems that can be solved efficiently. An optimal PA scheme for ideal BF is developed, and a suboptimal BF with one dimensional search is derived, which has lower complexity than an existing suboptimal BF scheme. With this suboptimal BF scheme, a closed-form PA procedure is obtained. Second, based on the block coordinate descent method, a suboptimal joint PA and BF scheme is proposed for the system over practical channels. Simulation results verify that the proposed suboptimal schemes are valid, they have almost the same EE performance as the ideal scheme for the simplified channel model and superior performance over the latter for the practical channel model.

Power allocation for AF relaying aided spatial modulation in the presence of imperfect channel state information

ABSTRACTBy combining Spatial modulation (SM) with cooperative communication, the diversity gain brought by cooperative relaying and high rate of SM can be obtained. In this paper, considering amplify-and-forward (AF) protocol, the performance of cooperative SM system with imperfect channel state information (CSI) over Rayleigh channel is analyzed. According to the performance analysis, the moment generating functions (MGFs) of effective signal-to-noise ratios (SNRs) are derived. With the MGFs, closed-form expressions of the error probability of antenna index detection and the error probability of symbol detection for imperfect CSI are achieved. Thereby, the approximate overall average bit error ratio (BER) is obtained, and these theoretical expressions include those under perfect CSI as special cases. Besides, the asymptotically approximate BER for large SNR is also derived. Based on this, a suboptimal power allocation (PA) scheme is developed, and the corresponding PA coefficients are attained by minimizing the asymptotical BER. As a result, closed-form PA can be attained for the system with multiple receive antennas. Computer simulations show that the theoretical BERs are close to the corresponding simulated results, which illustrates the effectiveness of the derived theoretical expressions. Compared with the conventional equal PA scheme, the proposed PA scheme enhances the BER performance efficiently.

Energy Efficiency Optimization for D2D Communication Underlaying Distributed Antenna System

In this paper, the energy efficiency (EE) performance of a downlink distributed antenna system with device-to-device (D2D) underlay communication is investigated over a composite Nakagami fading channel. The optimal power allocation (PA) schemes are developed for improving the EE performance. Under the minimum rate constraint of cellular user (CU), the maximum power constraints of CU and D2D pair, an optimization problem for maximizing the system EE is formulated. The Karush–Kuhn–Tucker conditions are used to solve the optimization problem. Based on the 1-D search method and the bisection method, two schemes and corresponding algorithms are, respectively, proposed to obtain the optimal solutions of PA. For a given transmit power of D2D pair, the closed-form PA of remote antennas (RAs) and the number of active RAs are derived, which greatly simplifies the optimization. It is shown that the proposed two schemes can obtain the same EE performance, and the scheme with the bisection method has lower complexity than that with the 1-D search method. Computer simulation verifies the effectiveness of these two schemes, and superior EE performance can be achieved.

Joint Energy Efficient Subchannel and Power Optimization for a Downlink NOMA Heterogeneous Network

Non-orthogonal multiple access (NOMA) has been considered as a key technology in the fifth-generation mobile communication networks due to its superior spectrum efficiency. Since the heterogeneous network has been emerged to satisfy users' explosive data rate requirements and large connectivity of mobile Internet, implementing NOMA policy in heterogeneous networks (HetNets) has become an inevitable trend to enhance the 5G system throughput and spectrum efficiency. In this paper, we aim to maximize the entire system energy efficiency, including the macrocell and small cells, in a NOMA HetNet via subchannel allocation and power allocation. By considering the co-channel interference and cross-tier interference, the energy efficient resource allocation problem is formulated as a mixed integer nonconvex optimization problem. It is challenging to obtain the optimal solution; therefore, a suboptimal algorithm is proposed to alternatively optimize the macrocell and the small cells resource allocation. Specifically, convex relaxation and dual-decomposition techniques are exploited to optimize the subchannel allocation and power allocation. Moreover, optimal closed-form power allocation expressions are derived for small cell and macrocell user equipments by the Lagrangian approach. Simulations results show that the proposed algorithms can converge within ten iterations and can also attain higher system energy efficiency than the reference schemes.

Optimal Power Allocations for Non-Orthogonal Multiple Access Over 5G Full/Half-Duplex Relaying Mobile Wireless Networks

This paper investigates the power allocation problems for non-orthogonal multiple access with coordinated direct and relay transmission (CDRT-NOMA), where a base station (BS) communicates with its nearby user directly, while communicating with its far user only through a dedicated relay node (RN). The RN is assumed to operate in either half-duplex relaying (HDR) mode or full-duplex relaying (FDR) mode. Based on instantaneous channel state information (CSI), the dynamic power allocation problems under HDR and FDR schemes are formulated respectively, with the objective of maximizing the minimum user achievable rate. After demonstrating the quasi-concavity of the considered problems, we derive the optimal closed-form power allocation policies under the HDR scheme and the FDR scheme. Then, a hybrid relaying scheme dynamically switching between HDR and FDR schemes is further designed. Moreover, we also study the fixed power allocation problems for the considered CDRT-NOMA systems based on statistical CSI so as to optimize the long-term system performance. The simulations show that our proposed power allocation policies can significantly enhance the performance of CDRT-NOMA systems.

Performance Analysis for Spatial Modulation With AF Relaying Over Spatially Correlated Rayleigh Channels

As a low-complexity and energy-efficient multiple input multiple output (MIMO) technique, spatial modulation (SM) has received much interest recently. Combining SM with cooperative relaying, the performance of SM systems can be significantly improved. Considering joint transmit-receive-correlated Rayleigh channels, the error performance and power allocation (PA) of the amplify-and-forward (AF) relaying aided cooperative SM system are presented in this paper. Based on the moment generating function (MGF), the probability density function (PDF) of effective signal-to-noise ratio (SNR) is derived. With this PDF, a closed-form expression of the pairwise error probability (PEP) is obtained. Utilizing the obtained PEP and the union bound of bit error rate (BER), the approximate average BER expression is further derived, which will benefit the performance analysis of the system in spatially correlated channels. According to the asymptotical performance analysis at high SNR, an asymptotic BER expression is also derived. By minimizing this asymptotic BER, a suboptimal power allocation scheme is developed, and the closed-form PA coefficients are attained. Besides, the diversity order of system is also analyzed and derived for the performance evaluation. Numerical results show that our theoretical analysis is valid, and can match the corresponding simulation well. Moreover, the proposed PA scheme can achieve superior BER performance over the conventional equal PA scheme since the powers are well allocated in terms of channel information.

Power Allocation Schemes for DAS With OFDM Under Per-Antenna Power Constraint

In this paper, three power allocation (PA) schemes for distributed antenna (DA) systems with orthogonal frequency division multiplexing over multipath fading channels are presented. Unlike the conventional total power constraint, power constraints for individual antenna ports are considered. By maximizing the channel capacity of the system subject to per-antenna maximum power constraints, the optimization problem for the PA design is formulated. Based on the block coordinate descent method, an optimal PA scheme to the optimization problem is derived. Considering that the optimal scheme is an iterative algorithm, a suboptimal PA scheme is derived by maximizing an upper bound of the channel capacity, which provides a closed-form PA procedure. Interestingly, this suboptimal scheme can obtain almost the same performance as the optimal one for large number of subcarriers, low maximum power, and/or small number of DA ports. To reduce the performance loss, a modified suboptimal scheme with closed-form PA is developed, and it has the capacity performance very close to the optimal scheme. Computer simulations verify the effectiveness of the three proposed schemes.