Energy-Efficient OFDM Radio Resource Allocation Optimization With Computational Awareness: A Survey

In this paper, we review radio resource optimization methods for energy-efficient wireless communication in links and networks using the Orthogonal Frequency Division Multiplexing (OFDM) and Orthogonal Frequency Division Multiple Access (OFDMA) techniques. We first consider the energy-efficiency metrics and optimization goals. We discuss the increasingly complex systems, starting from (i) a single OFDM link, (ii) an OFDMA single-hop network to (iii) multi-hop relay OFDMA interference networks. In each case, we elaborate on the transmission rate estimation, power consumption modelling, existing optimization constraints and the optimization solutions. Specifically, in the power-consumption modelling, we include the signal-processing (and related computing) power. We discuss the practicality of the considered solutions. We also touch upon the problem of nonlinear power amplifier characteristics (causing distortions typical for OFDM signals) to be taken into account for energy-efficient resource allocation. We discuss trade-offs and provide recommendations for future energy-efficient OFDM networks design. We also discuss the future works and challenges in the context of energy efficiency resource allocation for OFDM/OFDMA and their derivative techniques. We conclude that the presented design practices should include computational awareness in the networks to trade-off between information communication, information processing and the required network management energy-efficiency.

global Internet users in 2022 and 28.5 billion networked 23 devices and connections [1]. Moreover, the mobile data traffic 24 will increase to 930 eksabytes in 2022. According to the 25 Ericsson Mobility Report [2], communication of 26, 9 bil-26 lions of machines and devices that are expected by 2026 to 27 The associate editor coordinating the review of this manuscript and approving it for publication was Kashif Saleem . comprise the Internet of Things (IoT) poses challenges, never 28 encountered before. One of these challenges is an increase of 29 energy consumption associated with the data-traffic growth 30 worldwide. That is why reduced-energy wireless communica-31 tion has been in the focus of research and industry interest for 32 the recent years, aiming at achieving 10 times the energy effi-33 ciency (EE) in the Fifth Generation (5G) radio systems com-34 pared with the Fourth Generation (4G) of these systems [3]. 35 Moreover, so-called zero-energy radios are envisioned for 36 future Sixth Generation (6G) systems as their technology 37 enablers [4]. According to this vision, drivers from soci-38 ety, including the United Nations sustainability goals, will 39 The paper is organized as follows. First, in Section II, 109 we overview other surveys and tutorials that might be related 110 to ours to show in what aspects our work is original and 111 more focused. Then, in Section III, we provide definition of 112 energy-efficency, and consider the main optimization goals 113 related to energy-efficient wireless OFDM/OFDMA commu-114 nication. We also review realistic power-consumption models 115 of an OFDM link. In Sections IV, V and VI, we overview 116 computationally-aware energy-efficiency optimization solu-117 tions for OFDM links, OFDMA single-hop and relay net-118 works respectively. Section VII presents example results of 119 energy-efficiency optimization for representative, carefully 120 selected use-cases. Then, in Section VIII, we discuss energy-121 efficiency optimization that takes non-linear PA characteristic 122 into account. In Section IX, we discuss practicality of the 123 considered solutions, taking their computational complexity, 124 and other related costs into account. We also provide rec- 125 ommendations for future energy-efficient OFDM networks 126 design. The discussion about future works and challenges 127 in the context of energy efficiency resource allocation for 128 other techniques based on OFDM/OFDMA is provided in 129 Section X. Finally, in Section XI, we summarize key findings 130 of our survey and considerations.
In [17], scenarios of multiple base stations co-existing 210 in the same area and sharing the available radio resources 211 are considered. The focus of the paper is on optimization 212 and game-theory-based (equilibrium) solutions for interfer-213 ence coordination between base stations in homogeneous, 214 heterogeneous and cooperative cellular networks. There, the 215 power related to base-band signal processing is not taken into 216 account, rather the power allocated to coexisting base sta-217 tions. Thus, this paper is different in the considered scenarios 218 (our aspect (a)) and energy-consumption model (aspect (b)) 219 from our survey. 220 In [18], Zappone et al. review optimization methods for 221 energy efficiency maximization in wireless networks and 222 provide example numerical results. They consider maxi-223 mization of network energy-efficiency metrics defined in 224 different ways (as global energy-efficiency, weighted min-225 imum energy efficiency, weighted sum energy efficiency 226 and weighted product energy efficiency). The paper is not 227 considering resource allocation for OFDM/OFDMA net-228 works, and assumes a different power model than our work 229 does. It presents optimization strategies (either monotonic 230 or sequential optimization merged with fractional program-231 ming) for power control in a network with multiple links, 232 each characterized by a specific circuit power independent 233 of a bit rate. Considering a different technique and a different 234 power model, this paper is different from our work in aspects 235 (a) and (b). 236 Finally, it is worth mentioning that high PAPR in 237 OFDM/OFDMA transmitters translates to inefficient power 238 utilization. In [19] and [20], PAPR minimization techniques 239 in OFDM systems are surveyed, however, these papers do 240 not touch upon the problem of link-or network energy-241 efficiency optimization, nor the global power-consumption 242 model. Thus, these surveys are narrowed with respect to our 243 aspect (a) and not addressing aspects (b)-(d). 244 To summarize, our survey presented below concerns 245 optimization methods of resource (subcarriers, resource-246 blocks, transmission power levels, modulation and coding 247 schemes, relays) allocation for energy-efficiency maxi-248 mization in OFDM/OFDMA links and networks. The 249 power-consumption model considered here encompasses 250 transmission (electromagnetic emission) power as well as 251 the circuit-and base-band signal processing (computa-252 tional) power dependent on the transmission bit-rate. This is 253 why we call such methods computationally aware. To the 254 best of our knowledge, no prior papers tackle systematic 255 overview of the problems of OFDM/OFDMA networks 256 global energy-efficiency optimization and dynamic resource 257 allocation with computational awareness. The major contri-258 butions of this paper are as follows: 259 • In this paper, the state of the art with the original 260 classification of the key aspects of energy-efficient 261 resource allocation in the context of OFDM is presented. 262 dations for energy efficiency as well as future works and 290 challenges are provided.

294
Energy-saving or energy-efficient operation of communica-295 tion and computing networks is typically evaluated using 296 metrics related to either a total energy-consumption figure or 297 the expected performance per energy unit. The later is called 298 energy-efficiency, and can be expressed in the number of 299 successfully transmitted bits per Joule or the number of com-300 putational operations (clock cycles) per Joule or the number 301 of transported and processed computational tasks per Joule. 302 In this paper, we concentrate on wireless networks exploiting 303 OFDM/OFDMA flexiblity for energy-efficient communica-304 tion. For such networks, the energy-efficiency metric η is 305 commonly defined as a benefit-cost ratio, where the achieved 306 data rate is divided over the associated power consumption: 307 η bit Joule = data rate [bit/s] power consumption [W] .
(1) 308 Thus, this EE metric determines the number of success-309 fully transmitted, received and processed bits per energy unit 310 and should be maximized. Here, processing of bits refers 311 to signal processing at the transmitter and at the receiver, 312 which is required for successful transmission and reception 313 of information. In Figure 1, the relation between the energy 314 efficiency and transmit power for different values of the 315 Signal to Noise Ratio (SNR) is presented. Let us observe 316 that there exist the optimal point for the transmit power that 317 maximizes EE. It means that there exists a trade-off between 318 the data rate and power consumption which allows for energy-319 efficient transmission. Moreover, for the higher SNR values, 320 the optimal point is reached for lower transmission power. 321 Thus, in order to maximize the energy efficiency of wireless 322 communications systems, one of three ways can be chosen: 323 (i) The maximization of the data rate, whilst minimizing 324 the total power consumption. This approach is practi-325 cally infeasible because the achievable data rate strictly 326 depends on the transmit power (and the overall power 327 consumption) and vice versa.

328
(ii) The maximization of the data rate with a minimum 329 possible increase in power consumption (e.g., minimum 330 increase of the transmit power can cause a significant 331 gain in the date rate, particularly for low SNR values). 332 (iii) The minimization of the power consumption with a min- 333 imum reduction of the data rate (e.g. by applying less 334 advanced coding decoding energy can be reduced, par-335 ticularly at short communication distances). 336 In the context of the energy-efficient resource allocation 337 exploiting OFDM/OFDMA techniques, the second and third 338 approaches are usually chosen because in OFDM/OFDMA 339 based networks, the total available bandwidth and power are 340 partitioned into a number of subcarriers (SC) or resource 341 blocks (RB). For each of them, the transmission parameters 342 can be determined and adopted, depending on the channel 343 conditions. Moreover, the short time-scale approach can be 344 applied to maximize the energy-efficiency metric. It means 345 that the resource allocation is realized in the frequency 346 domain for a given time slot. 347 Here, by resources we mean energy-related commu-348 nication means (such as transmit power, basic resource 349 blocks, modulation and coding schemes (MCS) and other 350 we concentrate on the system and network constraints and The crucial aspect of the energy-efficient resource allocation 383 is estimation of data rate and power consumption -the numer-384 ator and denominator of (1) respectively. In this subsection, 385 the main approaches to the transmission rate estimation are 386 described. Having in mind the diversity of wireless communi-387 cation systems, the transmission rate estimation is not a trivial 388 task. In the literature (not just that related to energy-efficient 389 resource allocation), three main approaches of transmission 390 rate estimation can be distinguished:

391
(i) based on the Shannon formula, 392 (ii) estimated by the Shannon formula with scaling factors, 393 (iii) based on the error-rate function and the spectral effi-394 ciency of the applied MCS.

395
The Shannon formula for transmission rate estimation is 396 the most commonly used approach. In general, the data rate 397 described by Shannon formula is given by: where W is the channel (and the signal) bandwidth, P R is 400 the average received signal power over that bandwidth, while 401 σ 2 N and σ 2 I are the average powers of the noise and interfer-402 ence respectively over bandwidth W . The Shannon formula 403 can be easily adapted to OFDM/OFDMA subcarrier-channels 404 as well as to different network scenarios e.g. multi-cell, 405 heterogeneous or cooperative network. Moreover, according 406 to (2), R for σ 2 I = 0 is the concave function of the signal 407 power P R , while when σ 2 I = 0, there exist techniques which 408 allow to transform it into the concave one. (Note that con-409 cavity of this function results in relative low computational 410 complexity of its optimization, as well as optimization of 411 the energy-efficiency, which is in the focus of this paper.) 412 The Shannon formula formulates the upper bound of the data 413 rate which is not achieved by any practical wireless system. 414 Therefore, using (2) for data rate estimation can be treated 415 as idealistic approach which does not take the limitations of 416 practical communication systems (e.g., such as a limited set 417 of the modulation and coding schemes) into account.

418
In order to account for practical limitations of a wireless 419 communication system, the data rate can be estimated by: where ξ and ν are the scaling factors fitting the Shannon 422 formula to a practical system. The scaling factors can fit 423 Shannon formula to the single MCS and spectral efficiency 424 or to the whole set of them. Such an approach for rate estima-425 tion has been first considered in [21] where scaling factor ν 426 depending on the bit error probability has been introduced. 427 Based on [21] and the assumed code rate, the coding gain 428 and bit error probability for various MCSs, the data rate has 429 been estimated in [22]. Similar approximations for a whole 430 range of the modulation and coding schemes can be found in 431 [23], [24]  to solve. In Figure 4, the trade-off between the accuracy 475 of data rate estimation and the complexity of the optimal, 476 FIGURE 4. Trade-off observed in the data rate estimation. energy-efficient resource allocation algorithm is illustrated. 477 Note that for the low accuracy of data rate estimation 478 (according to the Shannon formula), usually, the energy-479 efficient resource allocation algorithm with low complexity 480 can be designed. On the other hand, the estimation with high 481 accuracy causes high complexity of the energy-efficiency 482 optimization problem. Therefore, the Shannon formula with 483 scaling factor seems to be a good trade-off between mapping 484 practical system data rates and the complexity of solving the 485 considered optimization problem.

486
Finally, the pros and cons of data rate estimation for the 487 three described approaches are summarized in Table 1.  ing P RF (see Figure 5): In case of the OFDM/OFDMA technique, the transmission 501 power is equal to the sum of powers allocated to subcarriers 502 which are determined by the designed resource allocation 503 algorithm that responds to instantaneous channel conditions.

504
The issue is more difficult in the case of the estimation  Their pros and cons are presented in Table 2.

517
The high-level models can determine the power consump- In [22], [36], and [37], the power dissipation in a chip is 530 modelled as the sum of a static term and a dynamic term. 531 The latter depends on, among other parameters, the supply 532 voltage, the clock frequency and the circuit capacitance. It is 533 assumed that the dynamic term depending on the clock fre-534 quency is scaled with the data rate. Thus, the circuit power is 535 modelled as the linear function of the achieved data rate: where α is the static term, and β is the implementation-538 dependent factor determined in W/ (bit/s). These high-level 539 power consumption models are commonly used in the energy 540 efficient resource allocation optimization.

541
The second approach to estimate the power consumption of 542 wireless devices is based on measurements. Such an approach 543 guarantees high accuracy of power estimation but it highly 544  where P PA , P LNA , P LO , P RFF and P MIX describe the 584 power consumption of the power amplifier (PA), low noise 585 amplifier (LNA), local oscillators (LO), radio frequency (RF) 586 filter and mixer, respectively. The power consumed by base-587 band (BB) processing includes power consumption of the 588 analog-to-digital converter P ADC , the digital-to-analog con-589 verter P DAC , modulation P MOD and demodulation P DEMOD , 590 encoding P ENC and decoding P DEC , low-pass filter P LPF , 591 inverse fast Fourier transform P IFFT and fast Fourier trans-592 form P FFT . It can be observed that depending on the struc-593 ture of a transceiver, the power consumption model can be 594 different. Nevertheless, some elements are common for the 595 most digital transmission systems. The power consumption 596 models of these components consuming most considerable 597 amount of power can be found in [43], [44], [45], and [46]. 598 There, the total power spent in the communication link is 599 the sum of power consumed by the power amplifier, the 600 low noise amplifier, the analog-to-digital converter and the 601 error-correcting decoder. More system-level energy models 602 for the radio frequency front-end components of a wireless 603 transceiver with the exemplary power consumption values 604 from most commonly refereed publications can be found 605 in [47]. The components include ADC, DAC, the recon-606 struction and anti-aliasing filters, the mixers, the frequency 607 synthesizer, PA, LNA, and the baseband amplifier. In [48], 608 more exemplary power consumption values are listed in 609 the context of Long Term Evolution (LTE) technology. The 610 power consumption models from the papers cited above have 611 been adapted to multi-user massive MIMO (multiple-input 612 and multiple-output) scenario in [49] and [50]. In addition to 613 adapting existing models of energy consumption, the model 614 has been extended by elements specific to the presented sce-615 nario, such as energy consumption by the channel estimation 616 process, by the load-dependent backhaul or linear processing 617 at the base station.

618
In most of the papers cited above, the authors focus on 619 the power consumption of the RF front-end and channel 620 VOLUME 10, 2022 power consumption, in case of short links. In [51], [52], [53], 623 [54], and [55], more attention is put to this aspect. In [51]    in [54] and [55] where the more advanced scenarios are FPGAs by introducing a scaling factor has been introduced.

644
As overviewed above, diverse power consumption models 645 can be considered for distinct transmitter and receiver com-646 ponents. In Table 3, key parameters of the power consump- consumption model are presented [56]. The consumed power 652 was measured on the transmitting and receiving sides for dif-653 ferent values of pathloss. Moreover, all measured transceivers 654 work in IEEE 802.11g standard and were selected so that 655 the WiFi chipset was different. It can be observed that the 656 power consumption increases with the rate and the values of 657 the consumed power and curve slope highly depend on the 658 vendor. There is also a noticeable impact of pathloss on the 659 power consumed, particularly on the receiving side, which 660 is related to the increasing power of transmission. Moreover, 661 in Figure 8 the consumed power for high-level power con-662 sumption model and based on the estimation of the power 663 consumed by each transmitter and receiver components [25] 664 is presented. Note that in both approaches, the power con-665 sumed grows exponentially with the throughput, in contrast to 666 the measurement-based approach where the power increased 667 linearly. In addition, for a given system configuration, the 668 power consumed by the transmitter and receiver components 669 is in most cases constant. For the power consumption model 670 presented in [25], only the power consumed by channel 671 coding, the power amplifier and the transmit power change 672 dynamically depending on the channel conditions. Therefore, 673 both curves follow a similar course.

674
Finally, Figure 9 illustrates the trade-off between the accu-675 racy of the power consumption models and the difficulty 676 in defining them. It can be observed that if the power con-677 sumption model is easy to define, the representation of the 678 real system is low. On the other hand, if the accuracy of 679 the power consumption model is high, the model is really 680 difficult to determine, for example, due to the fact that all 681 transmitter/receiver components are integrated in a single 682 chip. Therefore, the power consumption based on the mea-683 surements and augmented with the interpolation or stochastic 684 modelling seems to be a good trade-off.

686
The maximization of energy efficiency metric as defined 687 by (1) without constraints is not practical for multiple rea-688 sons. 1 In the optimization, physical limitations of the network 689 1 One might achieve the maximum energy efficiency, if no transmission takes place.  such as the maximum transmit power, minimum guaranteed 690 throughput or particular standard requirements (e.g. the emis-691 sion spectrum mask) have to be taken into account. There-692 fore, the energy efficiency optimization problem is usually 693 defined as the objective function with constraints. Moreover, 694 some limitations of wireless communication systems can be 695 included in the objective function, e.g., grouping the sub-696 carriers into resource blocks. The most common constraints 697 known from the literature are listed below:

698
• the maximum transmission power constraint ensures 699 that the sum of the transmission power allocated to 700 the subcarriers is lower than or equal to the maximum 701 assumed value. In the case of downlink transmission, 702 this constraint typically limits the transmission power of 703 the base station while, for the uplink, the transmit power 704 of each end-user is limited. This constraint results from 705 practical aspect of designing wireless communication 706 systems where the total transmission power is limited 707 by standards.

708
• the requirement on the minimum data rate aims at pro-709 viding the end-user quality of service. In this case, the 710 achieved data rate has to be higher than or equal to 711 assumed threshold. In the literature, this constraint is 712 typically considered in the short-term context. It means 713 that in a given time slot, the resource allocation algo-714 rithm has to provide the required data rate. From the 715 energy efficiency point of view, the data rate for a user 716 with poor channel conditions can be extremely low, even 717 zero, if this constraint was not applied. Thus, such con-718 straint is necessary in the practical radio communication 719 networks.

720
• the subcarrier/resource block allocation constraint 721 which guarantees that the same subcarriers can be 722 assigned to a certain, limited number of users. This 723 constraint is relevant in the case of a multi-user scenario 724 in order to avoid interference between users. In the 725 case of homogeneous network, it means that a subcar-726 rier can be assigned to at most one end-user. However, 727 there exist scenarios, e.g. heterogeneous or relay net-728 works, where the same subcarriers can be utilized by 729 more than one user, resulting in interference between 730 users. Note that a properly designed resource allocation 731 algorithm, in an interference network, can increase the 732 energy efficiency compared to the network without users 733 interference. From the optimization point of view, this 734 constraint requires the introduction of binary decision 735 variables (representing each subcarrier assignment or 736 no-assignment to a particular user) making the opti-737 mization problem a Mixed-Integer Nonlinear Fractional 738 programming problem which is very difficult to solve in 739 its original form.

740
• the fairness constraint is introduced to maintain the 741 transmission rate among users with a predetermined pro-742 portion. Thus, it is considered in the multi-user system 743 model.

745
The design of the energy-efficient resource allocation algo-746 rithm usually comes down to solving the optimization prob-747 lem defined as the maximization of the energy efficiency 748 VOLUME 10, 2022

752
subject to:  Since the objective function in (8) is in general non-760 concave, standard convex optimization algorithms are not 761 guaranteed to converge to global optimum and specific algo-762 rithms are required. In the literature, four approach to solve 763 the fractional programming problem can be found:  The Dinkelbach method and the Charnes-Cooper method can 769 be used if the numerator of the objective function is concave 770 while the denominator is convex or if the numerator is affine, 771 the denominator does not have to be restricted in sign. Oth-772 erwise, if the optimization problem can not be transformed 773 into concave one, the designing of the special algorithm or 774 heuristic to solve the optimization problem is required. In the 775 case of the Dinkelbach method the objective function is trans-776 formed into a new parameterized concave function which 777 can be solved by the iterative Dinkelbach algorithm with the 778 superlinear convergence. The generalized form of Dinkel-779 bach algorithm is presented in Figure 10. In the Charnes-780 Cooper method, the fractional problem is transformed into an 781 equivalent convex problem with one additional variable and 782 two constrains (if the numerator is affine only one constraint 783 is added). Finally, in Table 4, the comparison of the methods 784 to solve the fractional optimization problem is presented.

787
In this section, we focus on the energy-efficient resource 788 allocation in the context of a single OFDM link. Visualiza-789 tion of the example single link transmission with the related 790 power consumption is presented in Figure 11. It can be 791 observed that the user achieves some transmission rate as a 792 result of per-subcarrier power allocation in response to the 793 instantaneous channel conditions (visualized in Fig. 11 as 794 the magnitude of the instantaneous channel characteristic). 795 In the presented example, the resource allocation algorithms 796 come down to determine the values of transmission powers 797 T determines the power allocated on SC n ∈ N , the channel coefficient in the link is defined by h (u,n) while R (u) is the data rate achieved by user u. The variables related to the system constraints are denoted as P MAX and R  formula with a scaling factor related to an adopted modulation 820 and coding scheme and a target bit-error probability.

821
Most importantly, the data rate estimation methods can 822 have various complexity as a result of the number of degrees 823 of freedom available in a given system. In [22], the scal- to be preceded by the channel impulse response estimation, 842 typically using pilots, and feedback reporting quantized chan-843 nel quality reported by a UE to the BS. These two processes 844 need some time-frequency resources to accommodate pilots 845 or control messages, reducing available resources for user 846 data. The problem of finding the balance between the accu-847 rate channel estimation and the reduction in data rate has 848 been discussed in [60]. Thus, in many real-world OFDM-849 based systems, the available degrees of freedom in resource 850 allocation are limited and the data rate can be estimated per 851 block of several subcarriers. As shown in Figure 11 in the case of a single OFDM link 864 the total power consumption consists of the power consumed 865 by BB and RF signal processing on the transmitter and 866 receiver side as well as the transmit power being the sum 867 of powers allocated on subcarriers. Observe that, while the 868 wireless channel frequency response has an influence on the 869 VOLUME 10, 2022 the parameter related to the efficiency of the power amplifier 904 which is given by the Peak-to-Average Power Ratio (PAPR) 905 divided by the drain efficiency of the power amplifier. There 906 the maximum, rarely observed PAPR, equal to the number of 907 subcarriers for an OFDM system, is assumed. Although, the 908 authors have not provided the value of the power consump-909 tion model parameters, they have shown the impact of these 910 parameters on the energy efficiency metric.

911
In [22] the modulation and coding scheme-dependent cir-912 cuit power in the fast adaptive OFDM system has been con-913 sidered. It means that the power consumption model does 914 not depend only on the data rate and β parameter (as shows 915 equation (6)) but also on the coding rate of applied modu-916 lation and coding scheme. Moreover, the data rate achieved 917 per subcarrier has been estimated using Shannon formula 918 with scaling factor which depend on the modulation and 919 coding scheme as well. Therefore, the optimal transmit power 920 can vary among the modulation and coding schemes for the 921 same channel impulse response. The parameter describing 922 the constant circuit power is equal 0.1 W while parameter 923 β = 5 · 10 −5 W/ (Mbit/s).

924
Another high-level power consumption model consisting 925 of the fixed circuit power and the variable power increasing 926 with the number of utilized subcarriers has been presented 927 in [59]. 928 It can be observed that the above models present increasing 929 complexity in order to reflect rising number of relations 930 influencing an OFDM link power consumption. Though, the 931 models are rather high-level and general, independent of 932 specific transceivers architectures. This can be treated as an 933 advantage of these models, making the derived resource allo-934 cation algorithm independent from the hardware platform. 935 A set of transceiver-dependent parameters, e.g., β, can be 936 adjusted individually without a need for reformulation of the 937 optimization problem or its' solving algorithm.

938
The above-cited papers use the high-level power consump-939 tion models to optimize the energy efficiency. Sample results 940 for maximization of EE have been generated in the single link 941 scenario with the linearly rate-dependent circuit power con-942 sumption model (described by equation (6)) are presented in 943 Figure 12. The energy efficiency, data rate and transmit power 944 in a function of the static part of circuit power consumption 945 model are plotted. Let us observe that the data rate and trans-946 mit power are the same for different value of the parameter 947 related to the dynamic part of the circuit power consumption 948 (β). It means that the dynamic part does not affect transmit 949 powers allocated on subcarriers but only energy efficiency 950 value. Moreover, the transmit power increases with the static 951 part of the circuit power (α) in order to eliminate the domi-952 nation of static power over the transmission power.

953
However, there are some more detailed power consumption 954 models considered in the literature as well. A single link 955 transmission where the BB power consumption is modelled 956 as the power consumed by each component is presented 957 in [54]. The authors do not consider EE optimization. In [53]  ing the data rate requirement the energy efficiency decreases 991 in both schemes above some point. However, for relatively 992 low throughput requirements and the EE maximization, the 993 energy efficiency takes constant value because the through-994 put resulting from optimization is higher than the data rate 995 requirement.

997
The complexity of the energy-efficient resource alloca-998 tion algorithm depends on the degrees of freedom of the 999 considered system and on the utilized model of the data 1000 rate and power consumption as well as the system limita-1001 tions/requirements. In the literature, two sets of the optimiza-1002 tion variables are considered in the context of a single-link 1003 scenario: (i) the transmit powers allocated on the resource 1004 unit or related to them data rates achieved on the resource 1005 unit, (ii) the transmit powers/data rates on the resource unit 1006 and applied modulation and coding scheme. It means that in 1007 the first approach the data rate is estimated by the Shannon 1008 formula, thus only transmission power can be determined 1009 and the modulation and coding schemes are not selected. 1010 In contrast, in the second approach the data rate is esteemed 1011 by different methods where the transmit power and the mod-1012 ulation and coding scheme have be to determined. The first 1013 set of the optimization variables has been considered in [36], 1014 [37], and [58]. In [58] the authors have optimized the energy 1015 efficiency by selecting optimal transmission power using 1016 Dinkelbach method with superlinear convergence. Due to the 1017 rate-dependent circuit power consumption model, in [36] and 1018 [37] the energy efficiency has been maximized by obtaining 1019 the optimal value of the data rate achieved on each subcar-1020 rier. Moreover, in [58] the Charnes-Cooper and Dinkelbach 1021 methods have been used to solve the energy-efficient resource 1022 allocation optimization problem. The authors have shown that 1023 both methods give the same optimal result. In [34] and [35] 1024 the energy efficiency is optimized for an uncoded M-QAM 1025 modulated OFDM link. The modulation order is expressed 1026 as the function of the data rate, thus, in fact, the data rate 1027 achieved per subcarrier is optimized. The authors has proven 1028 that the defined optimization problem is quasiconcave, thus 1029 if a local maximum exists, it is also globally optimal. In order 1030 to find the optimal data rate for the single subchannel trans-1031 mission Gradient Assisted Binary Search (GABS) method 1032 has been proposed which then is used in the Binary Search 1033 Assisted Ascent (BSAA) algorithm to find the optimal solu-1034 tion in the multi-subchannel scenario.

1035
The second set of optimization variables is considered 1036 in [22]. The transmit power and modulation and coding 1037 scheme are determined per each subcarrier in order to max-1038 imize the energy efficiency. In the first step of proposed 1039 algorithm the Dinkelbach method has been used to transform 1040 the objective function. Next, the transmit power for each MCS 1041 has been obtained. Finally, based on the cost-benefit function 1042 the modulation and coding scheme is selected per subcarrier. 1043 In Table 5 the summary of the energy-efficient resource 1044 allocation methods in a single-link scenario is presented. 1045 VOLUME 10, 2022  T determines the power allocated on SC n, (u,n) the binary variable determining if the subcarrier n is assigned to user u or not while the channel coefficients in the link between BS and users u and u are defined by h (u,n) and h u ,n , respectively. The data rate achived by user u and u are denoted as R (u) and R u respectively. The variables related to the system constraints are denoted as P MAX ,  In Figure 14 and 15 the example of the downlink and 1072 uplink transmissions in the multi-user OFDMA network is 1073 presented, respectively. It can be observed that (in the con-1074 trast to the single link scenario) the available bandwidth is 1075 shared among many users in the network. It means that not 1076 only transmit power but the subcarrier assignment has to be 1077 determined as well. Moreover, for some systems, the modu-1078 lation and coding schemes have to be determined for each 1079 user. Thus, more degrees of freedom can be distinguished 1080 compared to the single link scenario. T determines the power allocated on SC n ∈ N , (u,n) the binary variable determining if the subcarrier n is assigned to user u or not while the channel coefficients in the link between BS and users u and u are defined by h (u,n) and h u ,n , respectively. The data rate achived by user u and u are denoted as R (u) and R u respectively. The variables related to the system constraints are denoted as P  in [62], [63], [64], [65], [66], [67], [68], and [69]. In [61],

1091
[62], [63], [64], [65], [66], [67], and [70] the subcarri-  In the multi-user OFDMA network the total power consump-1126 tion power (similar to the single link scenario) consists of the 1127 transmit power and the power consumption of BB and RF 1128 processing at the transmitter and receiver. The total transmit 1129 power is equal to the sum of the users' transmission power. 1130 The users' transmission power is usually determined as the 1131 sum of the transmit power allocated on the resources assigned 1132 to them. This definition works both for uplink and downlink 1133 scenario. As shown in the Figures 14 and 15 the transmit 1134 power can be potentially allocated per subcarrier. While this 1135 is an additional degree of freedom, able to increase achivable 1136 data rate, it comes at a cost. The receiver has to know the 1137 power allocated on each subcarrier to enable channel esti-1138 mation and decoding, thus the signalling overhead is much 1139 bigger than in a more practical scenario, e.g., in LTE where 1140 the transmit power is the same among all resource blocks 1141 assigned to the user [29]. In the case of the BB and RF 1142 processing the power consumption model can be determined 1143 for each user differently that can result, e.g., from different 1144 end-user devices. Thus, the receiver circuit power is the 1145 sum of power consumed by the BB and RF processing at 1146 the end-users in the downlink scenario. For example in [64], 1147 the power of the circuit is divided into the power consumed 1148 at the base station and the user equipment which is scaled 1149 with the number of subcarriers assigned in the base station to 1150 VOLUME 10, 2022 users. In the rest of the cited papers the power consumed by 1151 circuits remains constant or is modeled as the linear function 1152 of achieved data rate. Therefore, in Table 6  been considered in [61], [62], [63], [64], [65], [66], [67],  Whereas, for the uplink transmission [62], [67] the max-1186 imum transmission power constraint concerns each user 1187 in the network. It means that the sum of transmit powers 1188 allocated on subcarriers for a given user has to be less 1189 than or equal to the maximum transmit power of its 1190 device. It is obvious that the maximum transmit power 1191 can vary among users as shown in Figures 14 and 15. 1192 Moreover, in [61] the authors constrain the maximal 1193 transmit power per subcarrier in order to avoid inter-cell 1194 interference.

1195
• the minimum data rate constraint considered in [61], 1196 [62], [63], [64], [65], [  Bender's decomposition method. The drawbacks of these 1264 methods are their poor scalability, i.e., these are efficient 1265 only for small size problems. For example, in branch-and-1266 bound method the complexity increases exponentially as the 1267 problem size increases. Therefore, the suboptimal solutions 1268 which give the near-optimal results have been proposed in 1269 the literature. In this paper, we focus on the most common 1270 method which can be applied to different system models. and-bound method has been applied to find optimal RB allo-1296 cation. In [69] and [73] the brute force search has been applied 1297 to find optimal subcarrier assignment, but due to extremely 1298 high complexity near-optimal and suboptimal solution have 1299 been proposed as well. The suboptimal methods which are 1300 based on the energy efficiency transmit power estimation 1301 and subcarrier assignment resulting from spectral-efficient 1302 maximization have been designed in [66] and [67]. Another 1303 suboptimal methods have been proposed in [61], [63], [64] The use of relay nodes in the network is a promising technique 1310 for increasing the energy efficiency of the system. In the 1311 literature, different scenarios of transmission with help of 1312 relay nodes can be distinguished. Figure 17 illustrates four 1313 transmission modes in the multi-user OFDMA relay network 1314 which can be found in the literature:     complex data encoding and decoding. On the other hand, the 1342 cooperative transmission required two time slots to deliver 1343 data to end-user whereas the direct transmission only one. 1344 Moreover, similar to the base stations and end-user devices 1345 the relay nodes consume the power related to receiving, 1346 processing and transmitting data, as well. Thus, there are 1347 a few aspects which can increase as well as decrease the 1348 energy efficiency in the case of relay networks. These are 1349 summarized in Table 7 in contrast to the direct transmission. 1350 Therefore, adaptive resource allocation methods are required 1351 to maximize the energy efficiency metric.

1352
As one may have guessed, in the context of the multi-user 1353 OFDMA relay network more degrees of freedom than for 1354 multi-user OFDMA network can be distinguished. In the 1355 literature the following degrees of freedom can be found:

1356
• the transmission mode selection -if more than one of 1357 modes presented in Figure 17 are considered in the 1358 system, the transmission mode can be selected.    case is when the relay node is located very close to 1410 the base station or the end-user. In such cases, the 1411 distance to the end-user is divided into a very short 1412 and long path with a length comparable to that of the 1413 direct link. Figure 20 illustrates the energy efficiency 1414 versus distance to the relay node from the base station 1415 for the Amplify and Forward (AF) and the Decode and 1416 Forward (DF) relaying protocols which are elaborated 1417 in the next subsection. The relay is placed in between 1418 source and destination nodes of fixed positions. It can 1419 be observed that for both relaying protocols the highest 1420 energy efficiency is achieved when the relay divides the 1421 distance between the base station and end-user in half. 1422 • the transmit power and subcarrier/resource block alloca-1423 tion -in this case, the transmission powers allocated on 1424 subcarriers and subcarriers assignment to the users are 1425 determined (similar to the multi-user OFDMA network 1426 or the single link).   The data rate of user u while using subcarrier pair (n, k), 1465 i.e., subcarrier n for transmission from BS and subcarrier 1466 k for transmission from the relay, and MRC reception 1467 can be estimated by [94], [95]:  The factor of 1 2 in (12), similarly as in (11), accounts 1490 for the fact that two time slots are required. Moreover, 1491 in [91], [92], and [93] the data rate estimation of the 1492 DF relaying protocol in the interference networks can 1493 be found.

1494
Sometimes, the authors have consider AF relaying pro-1495 tocol instead of DF protocol because they think that 1496 DF relaying protocol requires more than two time slots 1497 due to the time-consuming signal processing. Finally, 1498 in Table 8 the pros and cons of the described relaying 1499 protocols are summarized.

1500
It can be observed that the equations (11) and (12) describe 1501 the data rate achieved by user u using a given subcarrier 1502 pair. Thus, in general, the total throughput in the multi-user 1503 OFDMA relay network within two time slots is equal to 1504 the sum of the data rate for all users links using subcarriers 1505 assigned to them, in one of the selected transmission modes or relaying protocols if they can be adaptively selected accord-1507 ing to channel conditions. It means that the total throughput 1508 can contain the throughput of relayed transmission as well 1509 as the throughput of direct transmission. In order to avoid 1510 inter-user interference, typically it is assumed that the subcar-  Depending on the considered past work, some elements of 1551 the models presented above are taken into account and some 1552 are omitted. Therefore, similarly as in the previous section 1553 in the case of multi-user OFDMA network, the values of the 1554 power consumption parameters used by various authors are 1555 collected in Table 9. It is obvious that due to the diversity of 1556 the relay nodes and end-user devices in the network the circuit 1557 power consumption can be different. Nevertheless, in all cited 1558 papers it is assumed that the circuit power consumption is the 1559 same among the end-user devices and relay nodes. Moreover, 1560 in some papers [87], [89] the circuit power has not been 1561 divided into power consumed by BS, relay node and end-user 1562 but has been summed in one value. Furthermore, it can be 1563 observed that in Table 9 the direction of transmission (down-1564 link or uplink) is not specified for some papers. These authors 1565 consider transmission between pairs of users with help of the 1566 relay node as shown in Figure 18. If some value in Table 9 1567 is not specified, it means that such an parameter has not been 1568 considered. If there is more than one value provided, it means 1569 that the authors have analyzed different scenarios. There is high number of potential degrees of freedom in the 1573 multi-user OFDMA relay network. Below we summarize the 1574 constraints considered in the related papers:  [92], [93], [96], and [98]. In the context of practical 1578 wireless communication systems, the transmit power 1579 should be limited in each transmitter. Nevertheless, the 1580 common approach in the literature is to ensure that the 1581 sum of the power allocated in all transmitters does not 1582 exceed the maximum power budget of the whole system. 1583 In the contrast to the common approach in [ [98]. 1587 Due to two time slots that are required to deliver the 1588 data to the end-user in the relayed transmission mode, 1589 two approaches are considered in the context of the data 1590 rate constraints. In the first approach, the data rate is 1591 considered over two time slots. It means that in the 1592 direct transmission the data rate achieved by the user 1593 is summed over two time slots [86], [98] or scaled by 1594 factor 1 2 [82]. If the sum of the data rate achieved in 1595 the direct transmission mode is not scaled the factor 1 2 is 1596 neglected for relayed transmission. Whereas, in the sec-1597 ond approach the minimum data rate constraint ensures 1598 that the data rate achieved in the one time slot has 1599 to gather or equal to the assumed threshold, thus for 1600 the relayed transmission the data rate is scaled by the 1601 factor 1 2 [84], [90], [96].

1602
• the subcarrier assignment constraints which restrict each 1603 subcarrier to be used at most once in each time slot 1604 in order to avoid interference. In the contrast to the 1605 multi-user OFDMA network this constraint has two 1606 meanings in the context of relay network. On the one 1607  in [95], [100], and [102] ensures that the outage proba-1634 bility of the link is lower than the given threshold value. increases with the number of the degree of freedom. More-1642 over, usually the originally defined optimization problem can 1643 not be solve by the standard optimization techniques and 1644 some transformations may be required.  [92], [93], [94], [97]. Therefore, by applying , [92], [93], [96], [97], [101]. In the lit- [91], [92], [93], [96].

1709
The more universal method, based on the Difference    distribute known transmit power among subcarriers. Finally, 1799 a single MCS is selected for each allocated UE in order to 1800 maximize rate. The second reference algorithm, called Shan-1801 non EE, maximizes EE but considering Shannon formula as 1802 an estimator of data rate.

1803
It is visible that for both considered cell radiuses (0.75 km 1804 and 3 km) the proposed solution outperforms the reference 1805 solutions in terms of EE. The difference is the higher the 1806 higher number of users, as visible in Fig. 25, and the higher 1807 the number of available resource blocks, as visible in Fig. 26. 1808 The most important outcome is significantly improved EE of 1809 the proposed method against Shannon EE method, showing 1810 that simplified, Shannon-based rate estimation is not accurate 1811  without parallel transmission, 3) without relay, with parallel 1832 transmission, 4) without relay, without parallel transmission. 1833 While the proposed solution is able to leverage all these pos-1834 sibilities, the Reference method considers only options with-1835 out parallel transmission, i.e., without intra-cell interference. 1836 Fig. 27 shows that for an OFDM system of 16 subcarriers 1837 with 8 relays located in a cell both considered algorithms have 1838 increasing EE and data rate with number of users. The gap 1839 between both solutions is the greater the more users are in the 1840 cell. For higher number of users the proposed algorithm can 1841 easier find a pair of them with such a channel gain relations 1842 that allows the parallel transmission to be scheduled as more 1843 efficient. 1846 An important topic that is typically overlooked while opti-1847 mizing resources allocation for OFDM-based networks is 1848 the nonlinearity of OFDM transceivers. All above mentioned 1849 works consider OFDM transceivers as linear systems result-1850 ing in, e.g., linear increase of the consumed power with the 1851 allocated power and no influence of power allocation on 1852 interference power for this link. However, while this model 1853 can be used for high-throughput systems it cannot be used 1854 when the transceiver is optimized for low energy consump-1855 tion. This is mainly caused by nonlinear characteristic of 1856 any practical power amplifier [105]. The operating point of a 1857 power amplifier, called ''back-off'' is the difference between 1858 the PA clipping power and the mean transmit power (in 1859 logarithmic scale). When high back-off is used the nonlinear 1860 distortion can be negligible at the cost of low power amplifier 1861 efficiency. When trying to maximize the PA efficiency, thus, 1862 emitting the maximal part of the PA input power as a useful 1863 waveform, low back-off has to be used and high nonlinear 1864 distortion is expected. Note that the power amplifier effi-1865 ciency is not a fixed value [47]. It depends not only on the 1866 power back-off but also on the amplifier architecture (defined 1867 VOLUME 10, 2022

ENERGY-EFFICIENCY
One of the heavily investigated scheme that can allow for the 1869 amplifier increased energy efficiency is envelope tracking, 1870 whose aim is to adjust PA supply voltage according to the envelope of the transmitted signal [107]. Even if the PA energy consumption is reliably modeled, the nonlinearity of 1873 the supply voltage should be considered while powering a 1874 transceiver from batteries. The battery capacity decreases 1875 nonlinearly with the energy consumption of PA [108].  1905 As there may be tens or hundreds of subcarriers, central limit 1906 theorem applies, resulting in OFDM signal samples being 1907 approximated by the complex Gaussian distribution [113]. there is no frequency-selectivity of the utilized distortion 1949 model, neither the number of utilized subcarriers influences 1950 the results. The optimization variable is the total allocated 1951 power, and equal power is allocated to each subcarrier.

1952
The above discussion shows that there are still unsolved 1953 problems in resources allocation for energy efficient OFDM-1954 based transmission. One of these is the front-end nonlinearity 1955 aware optimization.

1958
As discussed in the previous sections, the role of computa-1959 tional awareness in OFDM/OFDMA resource allocation opti-1960 mization for the expected energy-efficiency of future radio 1961 communication systems cannot be overestimated, and has 1962 been emphasized in a number of recent papers. However, 1963 there are some limitations of the wireless systems or costs 1964 related to EE maximization, that can prevent the optimal 1965 solution to be achieved or makes it not profitable.

1966
Let us now summarize these design trade-offs which 1967 are graphically presented in Figure 28 and provide 1968 recommendations.    Even if the EE optimization algorithm results in globally 2023 optimal solution, it is optimal only for the considered system 2024 model, being inherently imperfect. The most common source 2025 will be delayed or quantized channel-and network-state 2026 information required by the optimization algorithm. Find-2027 ing the proper balance between EE maximization and pro-2028 visioning of accurate input knowledge is one of the main 2029 trade-offs for the deployment of EE OFDM networks. First, 2030 this information can be inaccurate or outdated at source since 2031 it is based on (inevitably imperfect) estimation of the channel 2032 coefficients in the presence of noise using, typically, pilot 2033 signals from past symbol periods. Moreover, this informa-2034 tion is typically quantized in order to reduce the required 2035 throughput of the control channel, e.g., to send it periodically 2036 from a UE performing channel estimation to a BS allocat-2037 ing resources. Last but not least, it may not be available in 2038 full at all network nodes, i.e., transmission of all channel 2039 coefficients of a given link to all other network nodes or to 2040 a central resource management unit, in order to coordinate 2041 inter-BS interference, would be associated with impractically 2042 high signalling overhead and potentially significant delay. 2043 Even if the optimal solution is calculated on time in the central 2044 resource management unit, the decision should be distributed 2045 among all controlled BSs within very tight latency budget. 2046 Therefore, an optimization using reduced (but represen-2047 tative) information of links qualities should be considered, 2048 accepting reduced EE. The second option is to use hierar-2049 chical or distributed optimization, that performs delay and 2050 control link-demanding optimization locally at a single base 2051 station. This allows for prompt reaction to mobile radio 2052 channel changes, limiting control messages between BSs. 2053 The hierarchical optimization means that local decisions are 2054 supported by global, but slowly-varying coordination among 2055 BSs. A limitation in achieving high energy-efficiency may be a 2059 particular radio communication standard or a radio architec-2060 ture with a limited number of degrees of freedom. For exam-2061 ple, only one MCS might be available (allowed by system 2062 recommendations) for a given OFDM symbol or resource 2063 block (as in LTE or 5G system standard) or a fixed power 2064 per RB will be emitted. Moreover, the power-consumption 2065 of the wireless transceiver may be invariant of the resources 2066 allocation, e.g., the power consumed by a class A power 2067 amplifier may be independent of the transmitted signal or 2068 base-band power consumption may not scale linearly with 2069 the transmission rate. In such cases the potential EE gain by 2070 optimization can be limited, making the total signaling and 2071 computing overhead not justified. In the practical design of  Another technique to consider is Non-Orthogonal Multi-2120 ple Access (NOMA) [125], [126], [127], [128] which can 2121 achieve higher spectral efficiency than OMA (Orthogonal 2122 Multiple Access). However, it should be remembered that 2123 higher spectral efficiency does not always result in higher 2124 energy efficiency. In the case of Non-Orthogonal Multiple 2125 Access more than one user uses the same frequency resource 2126 causing interference to each other. Therefore, NOMA 2127 requires an advanced interference cancellation algorithm. 2128 From the energy efficiency point of view, the additional 2129 power consumed by the interference cancellation algorithm 2130 has to be estimated and may be dominant over the gain result-2131 ing from increased spectral efficiency. Moreover, interfer-2132 ence between users causes the energy efficiency optimization 2133 problem to be non-concave and can not be solved by standard 2134 optimization techniques as we have shown in Section VI-D. 2135 Nevertheless, the optimization techniques described in this 2136 paper can be applied in such case. Finally, it can be observed 2137 that Non-Orthogonal Multiple Access can be a promising 2138 technique for increasing the spectral as well as energy effi-2139 ciency but all its aspects have to be taken into account 2140 in designing energy efficient resource allocation algorithm. 2141 Nonetheless, our analysis can be the baseline to investigate 2142 the energy efficient resource allocation in NOMA systems. 2143 Another interesting problem is the concept of Age of 2144 Information (AoI) which was introduced in 2011 by [129] to 2145 quantify the freshness of the knowledge we have about the 2146 status of a remote system. More specifically, AoI is the time 2147 elapsed since the generation of the last successfully received 2148 message containing update information about its source sys-2149 tem. In practice, it describes how often the data are updated, 2150 so it is completely different from the delay or latency. The 2151 frequent updating of information ensures its high timeless 2152 and accuracy but also consumes a lot of energy which is 2153 undesirable in the case of battery powered IoT devices. In the 2154 literature, the AoI concept has been investigated for many 2155 different aspects.  [137], and [138]. In [133] the authors has dealt with the 2163 age of information for a sensor network with wireless power 2164 transfer capabilities. The considered sensor node harvests 2165 energy from radio frequency signals, generates an update 2166 when its capacitor/battery becomes fully charged and trans-2167 mits by using all the available energy without further energy 2168 management. The average AoI performance of the considered 2169 greedy policy is derived in closed form and is a function of 2170 the size of the capacitor. The optimal value of the capacitor 2171 that maximizes the freshness of the information, corresponds 2172 to a simple optimization problem requiring a 1-D search. 2173 The AoI minimization problem for a network with gen-2174 eral interference constraints, and time varying channels have 2175 been considered in [135]. The authors have proposed two 2176 methods which demonstrates significant improvement in age 2177 due to the availability of channel state information. Simi-2178 lar optimization problem has been investigated in [137] but 2179 with minimum throughput constraints. They have developed 2180 four low-complexity transmission scheduling policies that 2181 minimize AoI and evaluate their performance against the 2182 optimal policy. The simulation results show that two proposed methods outperform the other policies, both in terms of AoI 2184 and throughput, in every network configuration simulated, 2185 and achieve near-optimal performance. The wireless sensors 2186 networks (WSN) in the context of the information freshness 2187 has been considered in [133] and [139], but only in the 2188 second paper the energy efficiency aspect has been taken 2189 into account. In [140] the upload scheduling scheme which 2190 minimize the update energy consumption subject to informa-2191 tion freshness constraints has been proposed. Nevertheless, 2192 in both paper and others viewed by authors of this project quency (RF) System Scenarios, document ETSI, TR 136 942 V.14.0.0,