arXiv:1902.01943v1 [cs.NI] 23 Jan 2019 aaee n srqie ob sln spsil oensure to possible ce as the long for Secondly, key as services. a be long-lasting is and to continuous lifetime required operation is devices, and mobile parameter and dev WSN battery-powered the many crucial like and for important Firstly, extremely its scenarios. is in multiple metric (ITU) a indicate Such as Union [1]. requirements times, Telecommunications report 100 International 5G by the efficiency the energy metric by of the performance One increase to important systems. is effi- such an energy designing becoming the when is Consequently, environmental (EE) safety. from ciency ranging public diverse; to very monitoring be to expected are few. a only cite te to relaying niques, and (MIMO) multiple-output (OFDM and multiplexing multiple-input technologies frequency-division many orthogonal developing as in such o resulted focus SE The the channel. the wireless maximizing data a on over of transmitted based amount be maximum can throughput which the describes higher that obtain capacity Shannon spectral and the improve (SE) to made efficiency been effor have Hence, academia service. and content of industry quality reliable the enhance ensure to to and delivery is (WCS) systems communications pcrlefficiency. spectral steE ihn rd-f.Fnly epeetrlvn ope relevant present we Finally, the SE trade-off. that the no both show problems. with of research we EE increase results, the an numerical allows as Via scheme power design. i corresponding future its and 5G EE- technologies on the transmission about energy-effic various insights of on give performance we based particular, on highlight relationship In control. we EE-SE focused power metric, the as EE literature of othe relationship the the perspective introducing the EE-SE decreases after one article, the increasing in this that highlighted (meaning works and trade-off a EE many the limite reason, concer optimizing power environmental of this stringent and deployment devices, For massive attrac IoT per- the as is to design such (EE) WCS due main interest efficiency the huge energy been a Recently, has metric. 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NTRODUCTION e eainBetween Relation New A 1 ohi Rezki Zouheir , 1 cl eTcnlgeSpeiue( Sup´erieure Technologie de Ecole ´ 2 nvriyo dh,Mso,I,USA, ID, Moscow, Idaho, of University 2 he Sultan Ahmed , mpact new a based llular ) In r). sin ts ices ting ient ch- ns. in ), n n d d esuydfeetcssadseais single-input-sing scenarios; artic and this of cases rest the different In SE. study an the exhibits of we also function a EE tha as the shown EE been maximizes increasing has that it scheme [7], control in power particular, having In while SE. EE increasing maximizes th an that that scheme show control power we a addition, bot exists where In relationship increase. 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[4]. on control compromised power SE is was focus the EE the improve corresponding as the since to such fact, developed schemes, In were allocations power [3]. water-filling, many SE SE, the the the increase maximizing reduce to to order in need is, we that objectives, and conflicting analyzing are by applications EE. corresponding low-latency providers. the and maximizing service consump energy critical the the evaluate by to of important respected also is be it Finally, must that constraint oto h urn lcrcleeg sgnrtdvafossi via generated since is Thirdly, energy cost. to electrical CO related order the current processes, the in the reduce networks of cellular and most in EE describe used the [2] were improve in profit grids work the The smart enhance prices. and how same energy OPEX increasing the the the reduce conserving given to while important is re consumption QoS Consequently, energy (OPEX). importan the expenditure an ducing operating constitutes the of consumption part energy the operators, dslmkuteus,[email protected] [email protected], nti ae,adfrtefis ie eso httetrade- the that show we time, first the for and paper, this In SE and EE the maximizing that indicated works Previous T) otel Canada. Montreal, ETS), ´ 3 hwl akhPoic,SuiArabia. Saudi Province, Makkah Thuwal, , n oae-lmAlouini Mohamed-Slim and , 2 msini nte ocr n stringent a and concern another is emission 3 tion EE, ave ere tly, le- a t le, al. h s 1 - l t , 2 output (SISO), OFDM, and MIMO that cover the majority of current WCS. We also present some of the open research Mixer problems related to the EE of WCS. Power Encoder amplifier Filter

II. BACKGROUNDONTHE EE METRIC Oscillator The concept of EE for WCS was first studied from an information-theoretical perspective in [8] by defining a metric (a) called minimum energy per bit. Then, the authors in [9] defined the energy-per-bit as the ratio of the consumed power to the achieved throughput expressed in J/bit. Recently, the EE 1 metric, defined as the ratio of the channel capacity C to the power consumed to achieve this rate, was introduced in [3], 0.8 Massive (P =0.1 W) C c that is, EE = + , where Pc is the system’s circuit power, Customer (P =1 W) Pc PTx c and PTx is the transmit power. Note that the spectral efficiency, 0.6 Critical (P =10 W) C c SE is defined as SE = B , where B is the system bandwidth, meaning that EE = B SE . In the rest of this paper, we Pc+PTx adopt a unit bandwidth analysis where the EE is expressed 0.4 as EE = SE in bits/J. EE (bits/J) Pc+PTx Considering this relationship, it is clear that when SE is 0.2 maximized for high values of PTx, EE is reduced, thus the existence of a trade-off between SE and EE. 0 -15 -10 -5 0 5 10 Power budget (dB) A. Circuit Power Model (b) When defining the EE, the consumed power, which includes both the transmit power, PTx, and the circuit power, Pc, is required. The circuit power includes the power consumed by GEEWSEE WPEE WMEE Global the communication chain (amplifiers, mixers, ADCs, DACs, Fairness Performance filters, oscillators, etc) excluding the antenna as shown in Fig. 1.a. Note that the EE does not consider the overall power consumption of the WCS as it may be related to services (c) other than the communication such as data processing and data storing for WSN, cooling for BSs, transportation for drones, Figure 1: (a) Circuit components involved in the circuit etc. In Fig. 1.b, we highlight the impact of Pc on the EE in power; (b) various power profiles based on application type various applications, that is, massive, consumer, and critical and circuit power value; (c) fairness degree of various applications, as a function of the available transmit power different EE definitions [10]. budget. We show, clearly that Pc has a negative impact on EE since as Pc increases, the EE is degrading. 1) Global EE (GEE): The GEE is defined as the ratio of global achievable rate to the B. Energy Efficiency of Multi-Dimension WCS Pi SEi total consumed power, that is, GEE = + . The GEE Pi Pc,i PTx,i In the case of multi-dimension WCS (MD-WCS) such is simple to compute and characterizes the global performance as multiple antennas, multiple subcarriers or multiple users of the WCS but does not allow sufficient fairness in MD-WCS. systems, the EE can have multiple expressions, depending on The GEE is wildly used in MIMO and OFDM applications the target criteria. For example, in OFDM communications, where the fairness is not required among the antennas and the if all subcarriers are equivalent, the employed EE expression subcarriers, respectively. is defined as the ratio of the total SE to the total power. In 2) Weighted Sum EE (WSEE): the case of an uplink cellular network, if the fairness is to be The WSEE is defined as the weighted sum of the partial EE’s, SEi considered, EE could be defined as the product of partial EE that is, WSEE = ωi where ωi is the weight as- i Pc,i+PTx,i achieved by each user. This way, we avoid situations where sociated to the i-th dimension.P The WSEE can ensure a priority some users with bad channels may never communicate. to a subset of the system. While the weights in the WSEE are In the rest of this paper, N denotes the dimension of the chosen to highlight the importance of some parts of the MD- MD-WCS and i denotes the index of a given sub-system of it. WCS, it does not guarantee total fairness. The WSEE can be As indicated in [10], there are mainly four different ways to considered for heterogeneous networks (HetNets) applications define the EE: where small cells have different weights than the macro cell 3 when maximizing the EE. realization when an EEPA is employed and the corresponding 3) Weighted Product EE (WPEE): EE-SE variation. The WPEE is defined as the weighted product of the partial In Fig. 2.a, the EEPA, i.e., PEE(γ) is compared to the SEi EE’s, that is, WPEE = ωi . The WPEE aims to WPA, i.e., PWPA(γ). It is shown that both schemes behave Qi Pc,i+PTx,i ensure higher fairness among all system’s subsets. The WPEE oppositely as γ increases. In fact, the WPA scheme is well- can be employed for cases of multiple users with no priority known to transmit when the channel is good and remains silent and with high fairness. The WPEE might be used in cellular for bad channels in order to reach a high overall spectrum applications, where the power and resource allocation at the efficiency. However, when the EE is maximized the EEPA cell maximize the EE, considering all users’ EE. Otherwise, scheme transmits with low power for good channels as the if one user is not connected the overall WPEE is reduced to resulting SE divided by a low power corresponds to a high EE. zero. In Fig. 2.b, the EE and SE are presented for both EEPA 4) Weighted minimum of the energy efficiencies (WMEE): and WPA schemes to have an idea of the resulting tradeoffs The WMEE is defined as the minimum of the weighted partial between maximizing the EE or SE. Interestingly, the SE of the SEi EE’s, that is, WMEE = mini ωi . The WMEE can Pc,i+PTx,i EEPA is higher than the SE of the WPA for bad channels, in ensure higher fairness by focusing on maximizing the lowest this case for γ < 0.2. However, the SE of the WPA overcomes partial EE among all system’s subsets. This EE is employed the one of the EEPA which, gives in average, a maximum SE. for cases of multiple users with a certain minimal EE per each This EEPA scheme is the essence of the new EE-SE rela- user. An application of the WMEE is the case of WSN where tionship highlighted in Fig. 2.c. In this figure, we notice that a failure of one node may cause an outage of the network the variation of the transmit power shows a pseudo concave performance. EE function that has global maxima at a certain value of In Fig. 1.c, we present the different types of the EE and P . This value matches the optimal power maximizing the their corresponding degree of fairness. Note that the fairness is EE, i.e., PEE(γ) as γ varies given by the red circles in the formally defined according to the Max-Min fairness. In other figure. Interestingly, the SE is increasing with the EE when words, as this fairness increases, the distribution of the EE the transmit power exceeds this value, the EE decreases and among the multiple communications links is more balanced. reaches zero. Interestingly, the set of the EE-SE red circles, resulting from picking the PEE (γ) as γ varies, presents a III. ENERGY EFFICIENCY OF SISO SYSTEMS strictly increasing curve of the SE with respect to the EE. In SISO communications cover a wide range of applications other words, when the power is designed in a way to maximize such as WSN, mobile systems and public safety commu- the EE, the resulting SE is increasing with EE as shown by nications. Usually, the transmit power of SISO systems is the blue curve in Fig. 2.c for Pc =1W designed to maximize the SE under a certain power budget. In Fig. 2.d, we analyze the impact of the circuit power The resulting power control is called the water-filling power Pc on the SISO performance. As shown in Fig. 2.c, the SE allocation (WPA). While the WPA ensures obtaining the computed using the power resulting from the EE maximization maximum SE, the corresponding EE is compromised which is increasing with the EE. However, the EE is decreasing by urges the need to develop a new power allocation scheme around 50% as the Pc doubles while conserving the same focusing on maximizing the EE. value of the SE. This observation shows the high influence of Pc on the overall EE. In fact, one of the ways to considerably A. SISO EE Power Control enhance the EE, while conserving the same data rate, is to

Note that the EE function with respect to PTx is not a convex design systems with low circuit power. Hence, efforts need to but a pseudo-concave function, which is known to admit a be made in the direction of reducing the circuit power while unique maximizer [10]. Therefore, many works in the literature designing future wireless devices and equipments (sensors, used numerical methods to find the PTx maximizing the mobile stations and base stations, etc.) EE [11]. The most used method is the fraction programming method based on the Dinkelbach’s algorithm [10]. However, IV. ENERGY EFFICIENCY OF OFDM SYSTEMS the reached solution is not entirely satisfactory as the lackofa closed-form solution does not allow to build sufficient insights A. About the OFDM Technology into the problem. Recently, an explicit expression of the The OFDM technique was introduced to avoid the channel corresponding energy-efficient power allocation (EEPA) has −1 1 1+W γPc variation and enhance the QoS by dividing the total bandwidth been presented in [7] as P (γ) = e ( e ) − 1 , EE γ   into N subcarriers. This technique is based on transforming where γ is the channel realization modulus squared and W a serial wideband stream to narrowband parallel streams. The is the main branch of W-Lambert function. Interestingly, the resulting signals are then transmitted on multiple orthogonal EE expression, in [7], presented new insights on the EE subcarriers that have different channel gains as shown in performance and particularly on the EE-SE relationship. Fig. 3.a. The main advantage of OFDM is to overcome fading variations resulting in a robust and enhanced overall B. The SISO EE-SE Relationship transmission used the correction codes [3]. The OFDM is In order to capture the mentioned new EE insights, we currently part of many wireless communications protocols present in Fig. 2 the variation of the EE with the channel such as WiFi and WiMAX. 4

1.2 1.2 6 P( )=P ( ) EEPA 1 P( )=P ( ) 1

) 5 WPA

0.8 0.8 4 SE EE 3 0.6 0.6

2 0.4 0.4 Power profile, P( Energy Efficiency (bits/J)

P( )=P ( ) Spectral Efficiency(bps/Hz) 1 EEPA 0.2 0.2 P( )=P ( ) WPA 0 0 0.2 0.4 0.6 0.8 1 1.2 0 0 0 0.2 0.4 0.6 0.8 1 1.2 Channel realization, Channel realization, (a) (b)

2 4 P =1 W P varies in [0, [ P =0.25W c c P=P ( ) EEPA P =0.5W c New SE-EE relationship P =1W 1.5 3 c [-5:.25:1.5] P =2W =10 c P =4W c 1 2

0.5 1 Energy Efficiency (bits/J/Hz) Energy Efficiency (bits/J)

0 0 0 2 4 6 8 0 0.5 1 1.5 2 2.5 3 3.5 4 Spectral Efficiency (bps/Hz) Spectral Efficiency (bps/Hz) (c) (d)

Figure 2: (a) EE and SE based power profile [12]; (b) SE and the EE of both EE and SE based power control [12]; (c) The new EE and SE relationship in SISO communications [7]; (d) The EE-SE relationship with different Pc.

B. OFDM EE Maximization that the EE enhancement, when increasing the number of Improving the EE of OFDM systems was performed, in subcarriers, is highly predictable independently of the circuit previous works, based on minimizing the power consumption. power of the system. Then, the EE of the OFDM systems based on maximizing the A more interesting result related to the EE-SE relationship EE metric was studied in [14] and an explicit expression of the is presented in Fig. 3.c. We show that, for a fixed Pc, having power was presented in [13] where the authors present analyti- more subcarriers enhances both the SE and the EE, which cal power allocation expressions in OFDMA cellular networks results again in an increasing SE with respect to the EE. Hence, under unconstrained and constrained conditions regarding the the new EE-SE proportional relationship is also preserved in power and rate requirements. These EEPA expressions, follow- OFDM when EEPA schemes are adopted. ing the same insights of the SISO EEPA, present interesting results in terms of the EE of subcarriers scalability and the V. ENERGY EFFICIENCY OF MIMO SYSTEMS EE-SE relationship. A. About the MIMO Technology To improve the spectral efficiency, the MIMO concept was C. OFDM EE-SE relationship introduced in [15] as an alternative to reach higher data rate In Fig. 3.b, we show that, for a given Pc, having more using the same bandwidth and power resources. The MIMO subcarriers, enhances the EE, meaning that considering an is a promising technology to remarkably increase the wireless energy efficient transmission reduces the OPEX of cellular channel capacity and allow to reach higher throughput. The operators as the consumption is reduced for the same data rate. MIMO is based on using multiple antennas at the transmitter In addition, we notice that even if the circuit power increases, and receiver as shown in Fig. 4.a. The corresponding the- the slope of the EE curve is almost the same. This fact shows oretical limit of the maximum data rate is proportional to 5

Serial to Parallel Modulation Encoder parallel IFFT to serial Filter DAC RF Mapping converter converter

OFDM Transmitter

Parallel Serial to Modulation Decoder to serial FFT parallel Filter ADC RF De-Mapping converter converter

OFDM Receiver

(a)

3.5 3.5 P =0.25W n=1 c n=2 3 3 P =0.5W n=4 c n=8 2.5 2.5 P =1W c n=16 P =2W n=32 2 2 c n=64 P =0.25W 1.5 c 1.5 P =0.5W EE(bits/J) EE(bits/J) P =4W c c 1 P =1W 1 c P =2W 0.5 c 0.5 P =4W c 0 0 1,24 8 16 32 64 0 5 10 15 20 Number of subcarriers Spectral Efficiency (bps/Hz) (b) (c)

Figure 3: (a) The OFDM communication chain; (b) EE variation with the number of subcarriers [13]; (c) The new EE and SE relationship in OFDM communications. the minimum between the transmit and receive antennas [15] methods were presented as in [10], where the nonconvex which presents a huge gain compared to SISO. problem is transformed into a subtractive one. Note that the MIMO communications are based on two main techniques: EEPA of MIMO systems with the WSEE objective function multiplexing and beamforming. In multiplexing, the transmit- is a natural extension of the SISO EEPA since each SVD ter sends parallel streams of data at the same time in order to parallel channel can be considered as a SISO system. However, increase the overall data rate. In beamforming, the transmitter in the case of the MIMO GEE objective function, a new sends a narrow signals beam to the receiver and enhance the scheme was presented in [12] with the closed-form expression reliability. MIMO technology is currently deployed in multiple of the optimal power derived under certain conditions. As IEEE 802.11n and the 3GPP LTE in the 4G. we mentioned before, the WPEE and WMEE are not widely used for MIMO systems since there is no fairness requirement B. MIMO EE Maximization among the different antennas. When the CSI is perfectly known, the singular value decom- position (SVD) of the channel matrix is employed in order to C. MIMO EE-SE relationship maximize the SE via leveraging parallel SISO channels. The We first start, in Fig. 4.b, by exploring the effect of MIMO-SVD is widely employed as it simplifies the power increasing the number of antennas N on the EE with an EEPA allocation procedure and results in high SE. Similarly, the EE scheme. We show that the EE increase is logarithmic with N of MIMO system can be maximized using the SVD [10]. which gives a general insight about the EE gain of MIMO The challenge of MIMO systems is again related to the systems compared to the SISO systems. In particular, as the non-convexity of the EE. Numerical fractional programming circuit power is lower, the gain in EE is higher as N increases. 6

RF RF

RF RF DSP DSP

RF RF MIMO Channel

(a)

6 6 P =0.25 P =0.25W N=1 c c P =0.5W N=2 c 5 5 P =1W N=4 c N=8 P =2W c N=16 4 P =4W 4 P =0.5W c c N=32

3 3 P =1W c EE(bits/J)

2 EE(bits/J/Hz) 2 P =2W c 1 1 P =4W c 0 0 1 2 4 8 16 32 0 50 100 150 Number of antennas N Spectral Efficiency (bps/Hz) (b) (c)

Figure 4: (a) The MIMO communication chain; (b) EE variation with the number of antennas; (c) The new EE and SE relationship in MIMO communications.

From another side, in Fig. 4.c, we analyze the EE-SE and similarities in SISO, OFDM, and MIMO, we present in relationship when the number of antennas N increases. We Table I a summary of the EE and SE performance results. confirm again, in MIMO, that the EE-SE relationship is pro- In particular, in MD-WCS, as we increase the dimension N, portional, since an increasing N results in higher EE and SE. the system becomes more energy efficient in addition to In addition, we highlight the effect of the circuit power Pc on providing higher spectral efficiency. As a result, when OFDM the EE-SE relationship. For the same SE, as Pc decreases, EE is combined with MIMO, we expect to have even higher EE is increasing remarkably. For instance, for N =4, the MIMO and SE. For example, for Pc =1W, the OFDM EE increases system is twice more energy efficient with Pc =0.25W than by more than three folds from 1 to 16 subcarriers (with one when Pc = 1W . Which means, in this case, that mobile antenna) where as the MIMO EE is more than the double devices will have a double lifetime, or that mobile operators for 4 antennas compared to SISO (with on subcarrier). As a will pay half the electricity bill. conclusion, the MIMO-OFDM EE, with 16 subcarriers and 4 antennas, is expected to reach more than six times the SISO VI. RESULTS DISCUSSION AND RELATED RESEARCH EE. This observation reflects a high synergy between OFDM PROBLEMS and MIMO in WCS which is already observed in terms of SE We present in this part a discussion about the afore- in high speed technologies such as WiMAX LTE, LTE-A, and mentioned results as well as suggestion of related research IEEE 802.11n/ac/ax. As a result, the new EE-SE relationship problems. has an important impact on the design of 5G systems from two perspectives. First, the transmit power profile is expected to be radically changed from the traditional WPA to the EEPA A. Results Discussion described in Fig. 2.a. Second, the EE is expected to be the After our analysis of the EE-SE relationship, we clearly primary performance metric instead of the SE. In fact, EE show that the EE is an increasing function of SE for all considerations are mandatory for energy-sensitive applications technologies. In addition, in order to highlight the differences 7

Table I: Analysis summary for SISO, OFDM, and MIMO. of the EE metric and studied the corresponding performance Detailed EE gain SE gain for SISO, OFDM, and MIMO communications. Our study is EE shape in EE-SE WCS power compared compared MD-WCS shape ∗ ∗ based on a new power control scheme maximizing the EE profile to SISO to SISO rather than the SE. We highlighted that not only does the increasing, proposed scheme improve the EE, but it shows a new EE- SISO [7] - - - parabolic SE proportional relationship. In addition, we highlighted the increasing, 3x (N=16) 4x (N=16) impact of this new relationship on the design of the future OFDM [13] increasing, logarithmic linear 5x (N=64) 7x (N=64) 5G systems. Finally, we presented some interesting research increasing, increasing, 2x (N=4) 6x (N=4) topics related to the EE. MIMO [12] logarithmic logarithmic 5x (N=32) 84x (N=32) ∗ REFERENCES : for Pc = 1W. in order to extend operation time, and is recommended in other [1] ITU-R Rec. M.2083, “IMT vision framework and overall objectives of applications to reduce operation costs. the future development of IMT for 2020 and beyond,” Tech. Rep. 4, Oct. 2015. [2] J. Xu, L. Duan, and R. Zhang, “Cost-aware green cellular networks B. Related Research Problems with energy and communication cooperation,” IEEE Communications Magazine, vol. 53, no. 5, pp. 257–263, May 2015. We present some interesting research problems related to [3] G. Li, Z. Xu, C. Xiong, C. Yang, S. Zhang, Y. Chen, and S. Xu, “Energy- the EE requiring future investigations. efficient wireless communications: Tutorial, survey, and open issues,” IEEE Wireless Communications Magazine, vol. 18, no. 6, pp. 28–35, • MIMO with CSI Unavailability: In some practical Dec. 2011. MIMO scenarios, the CSI is not available or imperfect. [4] T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Hence, the EEPA is hard to obtain and further algorithms Wiley-Interscience, 2006. [5] C. Han, T. Harrold, S. 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VII. CONCLUSION In this paper, we presented a novel perspective regarding the EE-SE relationship. This new relationship is based on an increasing EE with SE. We presented multiple varieties