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Energy Efficient Power Allocation in Massive MIMO Systems based on Standard Interference Function
Abstract
In this paper, energy efficient power allocation for downlink massive MIMO systems is investigated. A constrained non-convex optimization problem is formulated to maximize the energy efficiency (EE), which takes into account the quality of service (QoS) requirements. By exploiting the properties of fractional programming and the lower bound of the user data rate, the non-convex optimization problem is transformed into a convex optimization problem. The Lagrangian dual function method is utilized to convert the constrained convex problem into an unconstrained convex one. Due to the multi-variable coupling problem caused by the intra-user interference, it is intractable to derive an explicit solution to the above optimization problem. Exploiting the standard interference function, we propose an implicit iterative algorithm to solve the unconstrained convex optimization problem and obtain the optimal power allocation scheme. Simulation results show that the proposed iterative algorithm converges in just a few iterations, and demonstrate the impact of the number of users and the number of antennas on the EE.
... The authors in [13] proposed the use of circuit power and channel conditions in a closed form to maximize EE. The authors in [14] analyzed quality of service issues to maximize EE in a single-cell massive MIMO system. They analyzed total power transmission from users and data rate constraints based on a constrained nonconvex optimization problem to maximize EE. ...
... The proposed algorithms are evaluated based on different benchmark metrics. These metrics are commonly used to evaluate the performance of the conventional approaches in massive MIMO systems [4], [9], [11], [13], [14], [21], [22], [24], [38]. A. CONSTRAINED ENERGY EFFICIENCY RESULTS Figure 1 shows the EE versus the maximum transmitted power for different values of p c . The proposed lowcomplexity algorithm increased EE with total transmitted power allocation p t . ...
... The optimal EE can be achieved based on the optimal transmit power * k . The EE was concave according to the numerator in (14) and when the transmitted power was more than the circuit power consumption according to (C 2 ) in (10). The study analyzed a massive MIMO system with M = 200 transmit antennas and p c = 400mW in Fig. 1; from the proposed low-complexity algorithm, with maximum EE because of the large number of antennas at the BS, and generally, nonlinear schemes outperformed linear schemes. ...
Singular value decomposition is highly essential to achieve a higher performance in signal processing using massive multiple-input multiple-output (MIMO) systems. This paper aims to provide a solution to control power allocation problem identified as an essential metric in a massive MIMO system that maximizes energy efficiency (EE). The network performance was evaluated by measuring circuit power consumption to maximize EE. The computational efficiency to maximize EE power allocation is very important to fifth generation networks (5G). The study aims to maximize the non-convex EE in a downlink (DL) massive MIMO system using a proposed energy-efficient low-complexity algorithm (EELCA) that guarantees optimal power allocation solution based on Newton’s methods and joint user’s association based on the Lagrange’s decomposition method. An optimal power allocation solution in closed form to decrease the complexity of the power subject to both the maximum power and minimum data rate constrained systems was derived. Then, the unconstrained EE power allocation to solve the unconstrained optimal power was used to select the optimal power allocation by computing a root of the first derivative of the EE based on differentiating the instantaneous power allocation to maximize EE was formulated. Simulation results showed that the proposed EELCA with a total transmitted power allocation provided maximum EE for a large number of antennas at the base station (BS), Generally, non-linear schemes outperformed linear schemes. Finally, the large cost of circuit power consumption increased at the BS due to the large loss of radio frequency (RF) chains at every antenna when the signals were transmitted to all users. The maximum EE = 5.9 Mbits/joule when the number of distributed users, K=33, with (pc,M)=(1000mW,200). The proposed low complexity algorithm provides the better result EE based on a training channel for a number of distributed users.
... Power control in a single-cell massive MIMO system has been considered in [20], and the spectral efficiency (SE) has been used as the main metric to develop algorithms based on the weighted minimum SE among the users and the weighted sum SE. Another approach has been taken in [21] where the main metric for optimization is the energy efficiency in the downlink (DL), with QoS constraints. A more recent work [22] extended the max-min SE and max-product SE strategies in [2] by proposing the use of a deep learning approach to predict the optimal power allocation policies from the UE positions. ...
... This induces a trade-off, between how much power should be allocated to devices experiencing a weak channel, at the expense of a performance degradation of the network sum SE and of devices with stronger channels. To this extent, several power allocation strategies have been proposed in the literature [2], [22], [20], [21]. The most simple solution is equal power allocation, i.e., ρ i = P max /K with P max being the maximum DL transmit power. ...
Massive MIMO is seen as a main enabler for low latency communications, thanks to its high spatial degrees of freedom. The channel hardening and favorable propagation properties of Massive MIMO are particularly important for multiplexing several URLLC devices. However, the actual utility of channel hardening and spatial multiplexing is dependent critically on the accuracy of channel knowledge. When several low latency devices are multiplexed, the cost for acquiring accurate knowledge becomes critical, and it is not evident how many devices can be served with a latency-reliability requirement and how many pilot symbols should be allocated. This paper investigates the trade-off between achieving high spectral efficiency and high reliability in the downlink, by employing various power allocation strategies, for maximum ratio and minimum mean square error precoders. The results show that using max-min SINR power allocation achieves the best reliability, at the expense of lower sum spectral efficiency.
... Since the interference varies over the UTs, power allocation at the access point (AP) is an efficient way to mitigate such interference. Power allocation schemes for interference channels have been extensively studied, such as the geometric programming (GP) [20] [22], the fractional programming (FP) [23] [24], the successive convex approximation (SCA) [25] [27], and the iterative water-filling (IWF) [28]. However, the existing approaches for traditional systems are not suitable for the considered systems. ...
... However, the existing approaches for traditional systems are not suitable for the considered systems. For example, the GP in [20] and the SCA in [26] approximate the power allocation problem as a convex optimization problem but cause approximation error, which means these approaches are not optimizing the power for the original problem, the FP in [23] [24] maximizes the power efficiency, which means that the ratio of the spectral efficiency to the power rather than the spectral efficiency is maximized, the IWF in [28] allocates the power at each UT rather than at the AP. For mm-wave beamspace MIMO systems, there are also several existing power allocation approaches. ...
This paper investigates the power allocation in millimeter-wave multiple-input multiple-output systems. The asymptotic concavity of the sum rate of the system is utilized to form the proposed power allocation approach. In contrast to the traditional approaches, the proposed approach utilizes a channel asymptotic orthogonality based approximation which is more suitable, thus achieves higher spectral efficiency. The analysis demonstrates that the sum rate of the system increases as the number of antennas increases. Numerical results verify the analysis and show that the proposed approach can perform better than those traditional approaches.
Energy efficiency (EE) is one of the most important challenges in fifth generation telecommunication systems. One of the ways to solve this challenge is to allocate the suitable power to users. The goal of the authors in this paper is to solve the challenge of EE in massive MIMO systems. The objective function in the EE optimization problem is a non-convex function and also has two constrained: maximum transmission power and minimum data rate. To convert the objective function into a convex function, maximum ratio transmission (MRT) precoding and the lower bound of the data rate are used. In order to obtain the lower bound of the data rate, the inequality of the lower bound is used. Lagrange dual function is also used to eliminate existing constrained. Since the power of the users is obtained by optimizing a lower bound, the successive convex approximation method (SCAM) can obtain a good result. According to this method, an iterative algorithm is introduced that solves the optimization problem numerically. One of the features of the proposed algorithm is that it has low computational complexity and can reach the optimal value faster than existing algorithms. The simulation results show that the proposed method performs better than the existing methods and has good results in the field of EE of massive MIMO systems.
The energy consumption of massive multiple-input multiple-output (MIMO) systems increases with the number of antennas. Optimizing the energy efficiency (EE) of massive MIMO systems is one of the ways to achieve green communication. This paper proposes an EE optimization method that genetic algorithm-based antenna selection and power allocation (GA-AS+PA) for the downlink of a multicell massive MIMO system under the restriction of the users’ sum-rate. First, we use the genetic algorithm to determine the active transmitting antenna of each base station (BS). Then, the transmission power for each user is allocated using the convex optimization method. Finally, the EE of system is optimized under the achieved optimum BS’s transmit power and the number of active antennas. From the simulation results, the GA-AS+PA method can improve the EE of the system while meeting user sum-rate requirements, which achieves better performance compared with random antenna selection+equal power allocation method (RAS+EPA), random antenna selection+power allocation method (RAS+PA), the antenna selection method based on genetic algorithm+equal power allocation method (GA-AS+EPA), and equal power allocation (EPA) these four methods. The EE of the proposed GA-AS+PA method is improved by 33.3% compared to the EPA method.
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.
This paper exploits variations in the average channel gains in multi-cell multi-user massive multiple input multiple output (MIMO) systems. An average transmit power-control-based sum-rate optimization scheme is presented for the uplink of the system. The matched filtering (MF) and the zero forcing (ZF) processors are considered with perfect and imperfect channel state information at receiver (CSIR) under frequency flat Rayleigh fading channel. An average power-control-based system model is constructed for analyzing the sum-rate and formulating an optimization problem. A discrete level combinatorial optimization is performed for MF and ZF sum-rate under perfect and imperfect CSIR. The numerical results show a significant improvement in the sum-rate and power consumption. A low complexity algorithm for numerical optimization of the sum-rate is proposed. The performance of algorithm is quantified with different scenarios including different number of users, macro cells, and micro cells with low and high inter-cell interference powers. The evaluation results show that the improvement in sum-rate and energy efficiency increases with inter-cell interference power and the number of MTs.
This brief mainly investigates energy efficiency (EE) and spectrum efficiency (SE) for the uplink massive multiple-input–multiple-output orthogonal frequency-division multiplexing system in a single-cell environment. An approximate SE expression is first derived by employing the maximum ratio combination or zero-forcing detection at the base station. Then, the theoretical tradeoff between EE and SE is established after introducing a realistic power consumption model in consideration of both the radiated power and the circuit power. Based on the tradeoff, the optimal EE with respect to SE is derived using the convex optimization theory. Results show that the optimal EE increases by deploying a suitable number of antennas, multiplexing a reasonable number of users, expanding the system bandwidth, or shrinking the cell radius. Partly different from the EE, the SE corresponding to the optimal EE can be improved by increasing the number of antennas, multiplexing a rational number of users, narrowing the system bandwidth, or shrinking the cell radius.
This paper addresses the problem of energy-efficient resource allocation in
the downlink of a cellular OFDMA system. Three definitions of the energy
efficiency are considered for system design, accounting for both the radiated
and the circuit power. User scheduling and power allocation are optimized
across a cluster of coordinated base stations with a constraint on the maximum
transmit power (either per subcarrier or per base station). The asymptotic
noise-limited regime is discussed as a special case. %The performance of both
an isolated and a non-isolated cluster of coordinated base stations is examined
in the numerical experiments. Results show that the maximization of the energy
efficiency is approximately equivalent to the maximization of the spectral
efficiency for small values of the maximum transmit power, while there is a
wide range of values of the maximum transmit power for which a moderate
reduction of the data rate provides a large saving in terms of dissipated
energy. Also, the performance gap among the considered resource allocation
strategies reduces as the out-of-cluster interference increases.
Massive multiple-input multiple-output (MIMO) has been seen as a promising technology to improve the spectrum efficiency (SE), reliability and energy efficiency (EE) for the next generation wireless communication systems. Excessive energy consumption of wireless communication networks induces both the increasing carbon emission and unaffordable operational expenditure in recent years. In this paper, energy efficient power allocation scheme is investigated for the massive MIMO system with the maximum ratio transmission (MRT) precoding, since MRT precoding can balance the system performance and complexity. As of the intractable expression of the received SINR at user terminal (UT), an approximate expression is deduced by proper simplification. Based on the simplified expression, a power allocation algorithm is proposed to achieve the optimal EE according to convex optimization theory. Compared with the power allocation scheme ignoring the inter user interference, the proposed power allocation algorithm can enhance EE and decrease transmission power, and does not impair the SE. Simulation results also show that both the EE and SE are improved by increasing the number of antennas at BS and the number of multiple UTs.
Assume that a multi-user multiple-input multiple-output (MIMO) system is designed from scratch to uniformly cover a given area with maximal energy efficiency (EE). What are the optimal number of antennas, active users, and transmit power? The aim of this paper is to answer this fundamental question. We consider jointly the uplink and downlink with different processing schemes at the base station and propose a new realistic power consumption model that reveals how the above parameters affect the EE. Closed-form expressions for the EE-optimal value of each parameter, when the other two are fixed, are provided for zero-forcing (ZF) processing in single-cell scenarios. These expressions prove how the parameters interact. For example, in sharp contrast to common belief, the transmit power is found to increase (not to decrease) with the number of antennas. This implies that energy-efficient systems can operate in high signal-to-noise ratio regimes in which interference-suppressing signal processing is mandatory. Numerical and analytical results show that the maximal EE is achieved by a massive MIMO setup wherein hundreds of antennas are deployed to serve a relatively large number of users using ZF processing. The numerical results show the same behavior under imperfect channel state information and in symmetric multi-cell scenarios.
Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth.
A joint PRB management and power control in LTE self-optimizing networks is proposed using the non-cooperative game with resource consuming pricing into consideration. We derive the closed-form of optimal PRB and power control strategies, based on which we develop the joint PRB and power control algorithms for the down-link LTE. Simulation results verify the performance of the presented scheme with the benchmark schemes.
A multiplicity of autonomous terminals simultaneously transmits data streams to a compact array of antennas. The array uses imperfect channel-state information derived from transmitted pilots to extract the individual data streams. The power radiated by the terminals can be made inversely proportional to the square-root of the number of base station antennas with no reduction in performance. In contrast if perfect channel-state information were available the power could be made inversely proportional to the number of antennas. Lower capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) detection are derived. An MRC receiver normally performs worse than ZF and MMSE. However as power levels are reduced, the cross-talk introduced by the inferior maximum-ratio receiver eventually falls below the noise level and this simple receiver becomes a viable option. The tradeoff between the energy efficiency (as measured in bits/J) and spectral efficiency (as measured in bits/channel use/terminal) is quantified for a channel model that includes small-scale fading but not large-scale fading. It is shown that the use of moderately large antenna arrays can improve the spectral and energy efficiency with orders of magnitude compared to a single-antenna system.
In this paper, resource allocation for energy-efficient communication in an orthogonal frequency division multiple access (OFDMA) downlink network with a large number of transmit antennas is studied. The considered problem is modeled as a non-convex optimization problem which takes into account the circuit power consumption, imperfect channel state information at the transmitter (CSIT), and different quality of service (QoS) requirements including a minimum required data rate and a maximum tolerable channel outage probability. The power allocation, data rate adaptation, antenna allocation, and subcarrier allocation policies are optimized for maximization of the energy efficiency of data transmission (bit/Joule delivered to the users). By exploiting the properties of fractional programming, the resulting non-convex optimization problem in fractional form is transformed into an equivalent optimization problem in subtractive form, which leads to an efficient iterative resource allocation algorithm. In each iteration, the objective function is lower bounded by a concave function which can be maximized by using dual decomposition. Simulation results illustrate that the proposed iterative resource allocation algorithm converges in a small number of iterations and demonstrate the trade-off between energy efficiency and the number of transmit antennas.
The main purpose of this paper is to delineate an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator. The algorithm presented is based on a theorem by Jagannathan (Jagannathan, R. 1966. On some properties of programming problems in parametric form pertaining to fractional programming. Management Sci. 12 609-615.) concerning the relationship between fractional and parametric programming. This theorem is restated and proved in a somewhat simpler way. Finally, it is shown how the given algorithm can be related to the method of Isbell and Marlow (Isbell, J. R., W. H. Marlow. 1956. Attrition games. Naval Res. Logist. Quart. 3 71-93.) for linear fractional programming and to the quadratic parametric approach by Ritter (Ritter, K. 1962. Ein Verfahren zur Lösung parameterabhängiger, nichtlinearer Maximum- Probleme. Unternehmensforschung, Band 6, S. 149-166.). The Appendix contains a numerical example.
A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.
Fast algorithms and performance bounds for sum rate maximization in wireless networks
- C W Tan
- M Chiang
- R Srikant
C. W. Tan, M. Chiang, and R. Srikant, "Fast algorithms and performance
bounds for sum rate maximization in wireless networks," IEEE Trans.
Networking, vol. 21, no. 3, pp. 706-719, June 2013.