Suboptimal Power Allocation Scheme Research Articles

Energy-Efficient Power Allocation for Multiuser Distributed MISO Systems With Beamforming and Imperfect CSI

In this article, we study the energy-efficient power allocation (PA) for multiuser distributed multiple-input-single-output (D-MISO) system with beamforming (BF) and imperfect channel state information (CSI). Given a target bit error rate, the system energy efficiency (EE) with imperfect CSI is deduced. Subject to the power budget constraints, a constrained optimization problem is first formulated to maximize EE of single-user D-MISO. The optimal BF is shown to be aligned with the channel direction that renders the joint optimization problem to be a PA problem. A near-optimal PA scheme is proposed to tackle this problem by using the concave–convex procedure method and fractional programming (FP) and block coordinate descent (BCD) method, and it can provide nearly optimal performance close to that of optimal exhaustive search scheme with less complexity. On this basis, a suboptimal PA scheme based on the FP and BCD method is developed to further decrease the complexity and maintain similar performance to near-optimal scheme, and it is suitable for the system with more distributed antennas. With these results, two PA schemes are, respectively, proposed for multiuser D-MISO with imperfect CSI to maximize EE. The first scheme can obtain better performance with relatively higher complexity, and the second scheme can gain the performance close to the first scheme with lower complexity, and only smaller performance loss is found. Interestingly, these two schemes have the same optimal performance for perfect CSI, and include the existing ones under perfect CSI as special cases. Simulation results verify the effectiveness of the developed schemes.

Power Allocation for Energy-Efficient Optimization in IoT-Based Distributed Antenna System With Imperfect Channel State Information

This article investigates energy efficiency (EE) maximization for an Internet of Things-based (IoT) distributed antenna system (DAS) with imperfect channel state information (CSI) subject to maximum transmit power and minimum data rate constraints. First, we derive achievable rates and corresponding EE expressions of the system for single and multiple IoT devices. Then, we formulate the EE maximization problem in the single-device IoT-DAS with imperfect CSI, and it has a special form of the difference of concave functions. To solve this problem, we develop a near-optimal power allocation (PA) scheme by using the concave–convex procedure (CCCP) and block coordinate descent (BCD) method. It can achieve an EE performance similar to that of the optimal exhaustive search scheme, but with lower complexity. Based on this result, we present a suboptimal PA scheme with a single-layer iteration to decrease the complexity and maintain a performance similar to that of the near-optimal scheme. Using the results above, the EE optimization for IoT-DAS with imperfect CSI for multiple devices is addressed. A near-optimal PA scheme based on the fractional programming (FP) theory as well as the CCCP and BCD methods for solving the optimization problem is presented. Also, a suboptimal PA scheme based on the FP theory and BCD method is developed to further decrease the complexity. Interestingly, these two schemes have the same performance for perfect CSI. Simulation results show the validity of the developed schemes and their superior performances over existing methods.

An energy-efficient power allocation scheme for Massive MIMO systems with imperfect CSI

As a design goal of green wireless communication, it is an important consideration to maximize energy efficiency of a Massive multiple-input multiple-output (MIMO) downlink system. By considering the case where the base station and all the users have the imperfect channel state information, a power allocation optimization problem is formulated to achieve the maximization of energy efficiency. Also, we derive the tractable closed-form expressions of lower bound on the achievable downlink rate utilizing maximum-ratio transmission (MRT) and zero-forcing precoding. Since the proposed optimization problem is non-convex, we strive to find a sub-optimal power allocation scheme. By decomposing the expression of the non-convex objective function, an energy-efficient power allocation algorithm that maximizes the energy efficiency is developed based on the difference of convex programming. Numerical results verify the tightness of the derived closed-form expressions, and show the performance improvement of the proposed energy-efficient power allocation scheme over the existing power allocation schemes.

SVD-Precoded Faster-Than-Nyquist Signaling With Optimal and Truncated Power Allocation

This study proposes a precoded faster-than-Nyquist (FTN) signaling scheme based on singular-value decomposition (SVD) with optimal power allocation. An information-theoretic analysis is conducted on the conventional and proposed SVD-precoded FTN signaling architectures. The associated information rate bound is derived in a closed-form by extending the classic Shannon capacity to support the SVD-precoded FTN signaling schemes. Our analytical performance results demonstrate that the proposed scheme outperforms its conventional Nyquist-criterion-based counterpart and the conventional SVD-precoded FTN signaling scheme, which does not use power allocation. Several important implementation issues, such as inter-block interference, the use of a frequency-selective (dispersive) channel, truncation, and sampling rate, are also considered. Finally, a suboptimal power allocation scheme that overcomes the truncation issue is presented.

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.

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.

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.

Energy‐efficient power allocation scheme for distributed antenna system over spatially correlated Rayleigh channels

The energy-efficient power allocation (PA) of distributed antenna system using multiple receive antennas is studied over spatially correlated Rayleigh channels. A new energy efficiency (EE) defined as the ratio of the average transmission rate to the consumed total power is presented. According to this definition, subject to the maximum power constraint, an optimal PA scheme is developed by maximising the EE. It is shown that the solution of PA in the constrained EE optimisation does exist and is unique. A Newton method with iterative algorithm is proposed to attain the PA. To avoid iterative calculation of the optimal scheme, a suboptimal PA scheme is derived by means of the Lambert function. As a result, closed-form PA is obtained. The developed schemes only need the statistical channel information and large scale information, and thus they have lower overhead and better robustness. Moreover, they may include the ones over spatially independent channel as special cases. The theoretical EE is further derived for performance evaluation, and the resultant closed-form expression is obtained. Computer simulation indicates that the theoretical EE agrees well the simulation result, and the suboptimal PA scheme can achieve the EE value near to the optimal one with lower complexity.

Cooperative Interference and Power Allocation in a Bidirectional Untrusted Relay Network With Channel Estimation Errors

The secure communication of a two-way untrusted amplify-and-forward relay network under the imperfect channel state information is investigated. To improve the secrecy of the relay wiretap system, artificial noise is introduced into each source signal. The total and the individual power constraint conditions are considered. To maximize the attainable secrecy rate, an iterative power allocation algorithm is designed under the total power constraint. As a more practical system design, a suboptimal power allocation scheme is proposed. For the sake of comparison, the security performances of the noncooperative interference strategy and the one-way cooperative interference strategy are also investigated. Simulation results demonstrate that the proposed bidirectional cooperative interference schemes perform better in the secrecy rate of communication system.

Power Allocation and Performance Analysis of Cooperative Spatial Modulation in Wireless Relay Networks

In this paper, the error performance analysis of an amplify-and-forward (AF) relay-aided cooperative multi-antenna system using spatial modulation (SM) over Rayleigh channels is presented. The SM is a simple and spectral efficient modulation technique that can increase the data rate by using input data bits to select a transmit antenna to send a constellation point. The relay transmission deploying SM not only can enhance the coverage and but also can improve the spectral efficiency. In the performance analysis, the overall average bit error rate (BER), which is related to the error probability of an antenna index detection ( $P_{a}$ ) and the error probability of symbol detection ( $P_{d}$ ) given transmit antenna index, is analyzed. With the derivation of the probability density function and the moment generating function of output signal-to-noise ratio (SNR), closed-form expressions of $P_{a}$ and $P_{d}$ are obtained to compute the overall BER. With the obtained BER expression, asymptotical BER expressions are derived to reveal the BER performance of the system at high SNR. By minimizing the asymptotical BER, a suboptimal power allocation (PA) scheme is developed. The diversity gain is analyzed at high SNR. The results indicate that the cooperative AF-SM can achieve full diversity order. Simulation results verify the effectiveness of the theoretical BER analysis, and the cooperative AF-SM with PA scheme outperforms upon the equal PA scheme.

Energy-Efficient Power Allocation Scheme for Distributed MISO System With OFDM Over Frequency-Selective Fading Channels

Considering multiple transmit antennas in each distributed antenna unit (DAU), two power allocation (PA) schemes are proposed for energy efficiency (EE) maximization for downlink distributed multiple-input single-output (DMISO) systems with orthogonal frequency-division multiplexing (OFDM) over frequency-selective fading channels, where the power constraints for individual antenna units are addressed. The optimization problem for the maximization of the EE subject to per-antenna maximum power constraints is formulated. By means of linear programming, the optimization is simplified to as if for a DMISO system whose DAUs use a single antenna corresponding to the largest channel-gain-to-noise ratio (CGNR) for transmission. Using the block coordinate descent (BCD) method, an iterative optimal PA scheme to the simplified optimization problem is derived, where an efficient procedure for determining the number of effective subcarriers and the optimized PA is developed. Since the optimal scheme needs iterative calculations, a closed-form suboptimal PA scheme is also derived by sorting the total CGNR and using the principle of the BCD method. Interestingly, this suboptimal scheme has small performance loss in comparing with the optimal scheme, and its relative EE loss is decreased with the number of subcarriers. Moreover, these two schemes include the ones with single transmit antenna for distributed antenna systems as special cases. Computer simulations verify the effectiveness of the two proposed schemes, and the proposed optimal one can obtain the same performance as the existing optimal scheme for DMISO-OFDM but with lower complexity.

Spectrum efficient power allocation schemes for OFDM cognitive radio with statistical interference constraints

In this paper, we study the power allocation problem for an orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) system. In a departure from the conventional power allocation schemes available in the literature for OFDM-based CR, we propose power allocation schemes that are augmented with spectral shaping. Active interference cancellation (AIC) is an effective spectral shaping technique for OFDM-based systems. Therefore, in particular, we propose AIC-based optimal and suboptimal power allocation schemes that aim to maximize the downlink transmission capacity of an OFDM-based CR system operating opportunistically within the licensed primary users (PUs) radio spectrum in an overlay approach. Since the CR transmitter may not have the perfect knowledge about the instantaneous channel quality between itself and the active PUs, the interference constraints imposed by each of the PUs are met in a statistical sense. We also study an optimal power allocation scheme that is augmented with raised cosine (RC) windowing-based spectral shaping. For a given power budget at the CR transmitter and the prescribed statistical interference constraints by the PUs, we demonstrate that although the on-the-run computational complexity of the proposed AIC-based optimal power allocation scheme is relatively higher, it may yield better transmission rate for the CR user compared to the RC windowing-based power allocation scheme. Further, the AIC-based suboptimal scheme has the least on-the-run computational complexity, and still may deliver performance that is comparable to that of the RC windowing-based power allocation scheme. The presented simulation results also show that both the AIC-based as well as the RC windowing-based power allocation schemes lead to significantly higher transmission rates for the CR user compared to the conventional (without any spectral shaping) optimal power allocation scheme.

Multiuser Two-Way Relaying with Large-Scale Antenna Arrays and Energy Harvesting

This paper considers an energy-harvesting multiuser cellular two-way relay channel (EH-cTWRC), where multiple energy-harvesting users exchange information with a base station (BS) via a relay station (RS). Both the BS and the RS are powerful infrastructures equipped with a very large antenna array, while the energy-constrained users are equipped with a single antenna and harvest energy from the RS. We propose a three-phase harvest-decode-and-forward (HDF) relaying protocol for the considered EH-cTWRC. In the first phase, the RS transfers energy to the mobile users. With the harvested power and their inherent power supply, the users exchange information with the BS via the RS in the second and third phases using a low-complexity antenna-selection based decode-and-forward relaying scheme. We analyze performance of the proposed HDF scheme, and derive closed-form asymptotic expressions for the signal-to-interference-plus-noise ratio and the achievable sum-rate when the numbers of antennas at the BS and the RS become large. We investigate the optimal power allocation at the RS to maximize the achievable sum-rate. A low-complexity suboptimal power allocation scheme with closed-form expression is also proposed. Both analytical and numerical results show that large antenna arrays can improve the spectral efficiency and wireless power transfer efficiency significantly.

Time‐Efficient Power Allocation Scheme for Two‐Way Multi‐relay Cognitive Radio Networks

Cooperative relaying has been emerging as a key technology in Cognitive radio (CR) networks. A two-way Amplify-and-forward (AF) based multi-relay CR network is considered, where a primary user coexists with a pair of secondary users and multiple relays. A Timeefficient sub-optimal power allocation scheme (TESOPA) based on Cauchy-Schwarz inequality is provided to maximize the total end-to-end transmission rate of the secondary system. TESOPA is proposed under maximal transmission power constraints, while ensuring the quality of service of the primary user during the whole communication process. The computational complexity is sharply decreased by using the Cauchy-Schwarz inequality. Simulation results show that the proposed TESOPA scheme performs very close to the near-optimal Interior point method based power allocation (IPMPA), especially in interference dominant networks where interference constraints play a key role in determining power allocation results instead of maximal transmission power constraints.

On the Ergodic Capacity and Energy Efficiency for Fading MIMO NOMA Systems

Non-orthogonal multiple access (NOMA) is expected to be a promising multiple access techniques for 5G networks due to its superior spectral efficiency (SE). Previous research mainly focus on the design to improve the SE performance with instantaneous channel state information (CSI). In this paper, we consider the fading MIMO channels with only statistical CSI at the transmitter, and explore the potential gains of MIMO NOMA scheme in terms of both ergodic capacity and energy efficiency (EE). The ergodic capacity maximization problem is first studied for the fading multiple-input multiple-output (MIMO) NOMA systems. We derive the optimal input covariance structure and propose both optimal and low complexity suboptimal power allocation schemes to maximize the ergodic capacity of MIMO NOMA system. For the EE maximization, the optimization problem is formulated to maximize the system EE (defined by ergodic capacity under unit power consumption) under the total transmit power constraint and the minimum rate constraint of the weak user. By transforming the EE maximization problem into an equivalent one-dimensional optimization problem, the optimal power allocation for EE design is proposed. To further reduce the computation complexity, a near-optimal solution based on golden section search and suboptimal closed form solution are proposed as well. Numerical results show that the proposed NOMA schemes significantly outperform the traditional orthogonal multiple access scheme with traditional orthogonal multiple access transmission in terms of both SE and EE.

Capacity Analysis of Cooperative Relaying Systems Using Non-Orthogonal Multiple Access

In this letter, we propose the cooperative relaying system using non-orthogonal multiple access (NOMA) to improve the spectral efficiency. The achievable average rate of the proposed system is analyzed for independent Rayleigh fading channels, and also its asymptotic expression is provided. In addition, a suboptimal power allocation scheme for NOMA used at the source is proposed.

On the Ergodic Capacity of MIMO NOMA Systems

Non-orthogonal multiple access (NOMA) is expected to be a promising multiple access technique for 5G networks due to its superior spectral efficiency. In this letter, the ergodic capacity maximization problem is first studied for the Rayleigh fading multiple-input multiple-output (MIMO) NOMA systems with statistical channel state information at the transmitter (CSIT). We propose both optimal and low complexity suboptimal power allocation schemes to maximize the ergodic capacity of MIMO NOMA system with total transmit power constraint and minimum rate constraint of the weak user. Numerical results show that the proposed NOMA schemes significantly outperform the traditional orthogonal multiple access scheme.

Power allocation in OFDM cognitive radio relay networks with outdated channel state information

SummaryIn this paper, we study power allocation in OFDM cognitive radio (CR) relay networks. The objective of power allocation is to maximize the instantaneous capacity of the CR network. It is assumed that the available channel state information between the secondary and primary users is an outdated but correlated version of the actual instantaneous channel state information. Optimal power allocation schemes are developed for both decode‐and‐forward and amplify‐and‐forward relay assisted CR transmission, assuming that the primary users are subject to average interference constraints and the CR transmitters are subject to maximum transmit power constraint. In addition, suboptimal power allocation schemes with reduced complexity are also proposed. Performance of the proposed schemes is compared with uniform power allocation and numerical results confirm that the proposed power allocation schemes achieve significant capacity improvement in comparison to uniform power loading. Furthermore, the proposed suboptimal power allocation schemes can be used as less complex alternatives for optimal power allocation with some capacity degradation. Copyright © 2014 John Wiley & Sons, Ltd.