Sustainable Green Networking: Exploiting Degrees of Freedom towards Energy-Efficient 5G Systems

Sustaina ble Green Networking: Explo iting Degrees of F reedom towards Energy-Efficien t 5G System s Miao Yao, Munawwar Sohul, Xiaofu Ma, Vuk Ma rojevic, Jeffrey H. R eed Bradley Dept. Electrical a nd Computer Engineering, W ireless@Virginia Tech miaoyao@vt.edu Abstract The carbon fo otprint concern in the development and deplo yment of 5G new radio systems has drawn the attention to s everal stakeholders. In this article, w e analyze the critical p ower con suming component of all candidate 5G s ystem architectures—the p ower amplifier (P A)—and prop ose PA-centric resource management s olutions f or green 5G communications. We d iscuss the impa ct of ongoing trends in cellular communications on sustainable green networking and analyze two c ommunications architectures that allow exploiting the extr a degrees-of-freedom (DoF) fro m multi-antenna and massive antenn a deployments: small cells/di stributed antenna network and m assive MIMO. F or s mall cell syst ems with a moderate number of antennas, we propose a peak to average power ratio-aware resource allocation scheme for j oint or thogonal frequenc y and sp ace di vision multiple access. For massive MI MO systems, we develop a highly parallel re c urrent neural network for energ y -efficient prec oding. Simulation results for representative 5G deployment scenarios demonstrate an energy efficiency improvement of one order of magnitude or higher with respect to current state-of-the-art solutions. Key Word: 5G New Radio, Green Co m munications, PA, C-RAN, Massive MIMO 1. Introducti on The global climate chan ge has e merged as a cri tical issue over the last de cades. The incr eas ing popularity of w ireless commun ication networks, has resulted in info rmation and communication te chnology (ICT) becoming a non-negligible contributor to the overall carbon footprint [1]. With the assumption o f relatively constant energy efficiency, the increasing number of base stations (BSs) and remote radio heads (RRHs) leads to higher ope rating expenditure (OPEX) m ainly because of the higher energy consumption [2]. This growth can be attrib uted not only to the inc rease in the number of smar t devices in emerging economies, but also to the growth o f shared multimed ia data an d online games. The wireless industry needs significant improvements in the en ergy efficiency of BSs and o ther network infrastructure t o compensate for the increas ed energy demands from the network gr owth [3] [4] [5]. Therefore, designing energy-efficient c ommunication s ystems h as become a critical issue for 5G, which pro mises massiv e deployment of smart devices served new infrastructure elements. The International Mobile Telecommunications’ (IMT) view of the next generation cellular s ystem indicates th e expectation of 100x improvement in network energy efficiency by 2020 [1]. Concepts such as “sustainable green communications” have recen tly emerged an d desc ribe the c ommon trend toward ene rgy-efficient wireless communications systems. It is most likely the shift from 4G long term evolution (LTE) to 5G new radio ( NR) will be the first wireless standard m igration wi thout waveform change [6], although alternative multicar rier waveforms such as filter bank multicarrier (FBMC) and universal filtered multi carrier (UFMC) have also been proposed as promising 5G w aveform candidates. As a typic al multicarrier air interface, orthogonal frequency division multiplexing ( OFDM) has been widely adopted as the air interface o f various wireless comm unication systems such as 4G LTE and IEEE 802.11 family. Its success is asso ciated with m any advantages including robustness against multipath fading, high spectral efficiency, and the support f or MIMO a nd orthogonal frequency div ision multiple access (OFDMA). All the aforementioned multicarrier waveforms suffer from a high peak to average power rati o (PAPR) to different extents at the transmitter as a result of the constructive addition of modulation symbols that are simultaneously carried over several narrowband subcarriers. The high peaks lead to signal excursions into no nlinear region of the h igh power amplifier (PA) and, thereby, to nonlinear signal distortion and spectral spreading. High input power back-off is required at the PA to keep the peaks of a multicarrier sign al within the amplifier’s linear region. In cellular networks, the high back-off r equirement causes low energy efficiency at the BS, higher c ost P As, and increases the utility and cooling costs for the operator. As a result, app roximately 60% of the total power consumption of a 4G macrocell BS is attribu ted to the PAs [ 7]. Hence, the PA is the most critica l component to c o nsider when targeting energy-efficient cellular network design and operation. One of th e most promising features of 5G th at can b ridge th e net work energy efficiency gap is large-scale antenna deployment, both as distributed antenna networks (DANs) and massive MIMO systems. We identify and examine the following key challenges in building PA-centric green and sustainable 5G communications and networking s ystems:  Can a cloud radio access network (C-RAN) provide additional probability for energy efficiency improvement of PA-centric multiple antenna system ?  Should we apply different P A-centric green communication strategies for m oderate and large scale antenna systems?  Is the application of statistical o r instantaneous P APR-aware scheme related with the num ber of antennas? Multiuser resource allocation for OFDMA systems has drawn the attention of many researchers. The authors of [8] introduce algorithms that allocate power to each subcarrier as a fun ction of the channel state information (CS I) to provide optimal resource allocation. Growing economic pressures and environmental awareness have shifted the attention of designers towards energy effic iency. The fundamental tradeoffs between spectral efficiency and energy efficiency in resource alloc ation ar e discussed in [9 ]. On the other hand, there has been recent research to e nhance the system energy efficiency by using m ultiple collocated or distributed antennas [2] [10] [11]. He et al. [2] pro poses a suboptimal resource allocation algorithm to m aximize the energy effic iency while considering the proportional fairness for different mo bile stations (MSs) and discusses t he tradeoff between energy efficiency and spectral efficien cy for DAN. Ng e t al. [11] propose an ene rgy-efficient r esource allocation algorithm with a large number of c ollocated antennas. However, these methods neglect the effect of power allocation on the PAPR but, rather, assume constant and equally efficient PAs. In other words, the interrelation among PAPR, drain efficiency and sub carrier resource allocation is negl ected. DAN is considered a promising tec hnology for future wireless systems [2]. In a traditional DAN architecture, the remote radio heads (RRHs) are geographically distributed and connected to the c entral unit of the system. The mul ti-antenna su bcarrier allocation pro v ides n umerous degrees-o f-freedom (DoF) for jointly optimizing channel capacity and PAPR at each RRH. For this r eason, the sc heme proposed in the Case Study 1 provides cap acity impro vement using DAN over a single antenna OFDMA system. Massive MIMO is also widely perceived as a leading candidate technology for 5G [12]. The high number of BS antennas requires a large number of PAs, one per an te nna. Noticed th e tradeoff between linearity and efficiency in Figure 1 , highly linear and low efficie ncy P As in a 5G B S would drive the CAPEX cost to infeasible figu res. It is therefore critical for 5G cellular networks to us e inexpensive PAs . Massive MIMO systems have the potential t o reduce the in stantaneous PAPR by means of the pr ecoding ma trix, which is used fo r suppressing multiuser inte rference (MUI ). The m ain idea behind the Case Study 2 is to jointly perform multiuser MIMO (MU-MIMO) precoding and PAPR reduction with a recurrent neural netwo rk (RNN). This network exploits the numerous Do F in a m assive MIMO systems. The analogy between a neural network and massive MIMO syst em is used to inspire a PAPR redu ction technique that lends itself to parallel implementation. The rest of this paper is organized as follows. Section 2 introduces the definition of energy effic iency and the impact of PA efficiency to energy -efficient communication systems. Section 3 disc usses the trends of small cell and m assive antenna in energy-efficient communication systems. Section 4 presents a case study o f the architecture, analysis, and simulation results o f distributed antenna network in C-RAN. Section 5 pre sents a c ase st udy of energy-efficient massive MIMO s y stem. Sect ion 6 c onc ludes the paper. 2. Energy Eff iciency a nd the Eff ect of PA Ef ficiency The cellular network is composed of a variety o f components in which the BS is the hig hest power consumer. Energy-efficient wideband wireless communications systems are very sensitive to nonlinear distortions c aused by the radio frequency (RF) c hain and the high power amplifier ( HPA), in particular. Energy e fficiency metrics have been proposed to evaluate the performance of the wireless network at different levels [13]. The energy efficiency at the BS level r eflects the a chievable data rate scaled by the system power consumption and can be expressed as   =  () ∑    ∑  ,     , (1) where  () represents the sum data rate and  the power allocation m atrix,  = [ , ] × . Th e first part in the denominator represents the p ow er consumption of t he P As, whe re   captures the PA efficiency (PAE) of the HPA at t he th antenna, which is a function the power all ocation and the PAPR as illustrated in Figure 1(a) and captured by   =   +    ∆  ( , ∑    , ( ∑  , )  )  ,  . (2) Symbols   and   are constants, ∆ is the subcarrier s pacing and  ,  the transm it power constraint o f  th antenna. Note that there are two fractions in (1) for energy effic iency calculation (one for data rate over power consumption, on e f or allocated power ov er PA efficiency), a simple expansion of traditional fractional pr ogramming [14] is necessary to find the optimal ene rgy efficiency. The power consumption of the remaining part of th e trans mission s ystem   in (1) includes the p o wer supply, baseband unit (BBU ) for analog and digital signal processing and air conditionin g. (a) (b) Figure 1: PA efficiency (PAE) vs Pout for LTE power amplifier; (a) PA gain vs Pout for LTE power amplifier at different operating frequencies (b) (Graph s obtained from r eal measurements for 20 MHz bandwidth). The worst-case P APR is proportional to the number of active s ubcarriers in the OFDM signal because the peak power is obtained as t he constructive add ition of the subcarriers’ modulation symbols. The PA mus t be capable of accommodating the dynamic range o f the sign al determined by the PAPR. There fore, the input power back-off in dB is defined for a PA by the differe nce between the operating point, which is usually the signal average p ower, and the peak power, which correspond s to the PAPR. As shown in our measurement of Figure 1 (b), th e g ain of a PA corresponds to the ratio between its output and input powers and remains relatively constant in the linear region, beyond which the gain starts to decrease due to the saturation. According to o ur measurement in Figure 1(a), the PA efficiency (PAE) increases wi th the transmitted power, where th e s aturation point o f th e PA delivers t he highest operating efficiency. The o perating p o int of a PA must be shifted to the lower p o wer region to reduce the nonlinear distortion that occurs wh en reaching saturation. T y pically, the PAE is reduced when reducing the averag e output power as deter mined by the ap propriate input back- off value. F or input signals with a large PA PR, 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 PAE (%) Pout (dBm) PAE @2.535 GHz PAE @ 2.593 GHz PAE @ 2.68 GHz PAE @ 2.31 GHz PAE @ 2.39 GHz 22 23 24 25 26 27 28 29 30 31 0 5 10 15 20 25 30 35 Gain (dB) Pout (dBm) Gain @2.535 GHz Gain @ 2.593 GHz Gain @ 2.68 GHz Gain @ 2.31 GHz Gain @ 2.39 GHz the inpu t b ack-off must be accordingly large to ke ep t he peak po wer bel ow the saturation level and make the PA w orking in its l i near region. A signal with a higher PAPR also calls for m ore expensive PA with wider linear to m aintain a reasonable average output power. The substantial power consumptio n of the PA leads to low e nergy effici ency o f the entire BS [15]. Conversely, if the PAPR could be reduced, less ex pensive PAs would be needed while operating at higher efficiency. As a result, PAPR-aw are resource allocation helps opera tors r educing capital and operatio nal expenditu res (CAPEX and OPEX) of netwo rk de ployment and operation. 3. Improving Ener gy Eff iciency by S mall Cell a nd Increa sing the Number of Antenn as As o ne of the most promising effo rts towards sustainable green networking, the small ce lls provides a higher av erage data rate and bette r ene rgy effic iency than a mac rocell by reducing the cell size and, hence, the propagation loss [16] [17]. In t his manner , a group of small ce lls which ar e e nabled and managed b y a C-RAN provide an energy eff iciency gain in several ways [18] [19]:  Lower CAPEX because of less overprovisioning d ue to infrastructure sharing;  Lower OPEX because of more e fficient maintenance (e.g. coo ling), management, integration and upgrades;  Lower transmission powers on d o wnlink and uplink;  Higher data to signalin g/control ratio due to increased granu larity for resource management an d less diversified user/traffic profile and  Comparatively higher achievable data rat es due to spatial frequ ency reuse. The RRH/C-RAN arch itecture lend s itself to more effecti ve resource usage a nd natu rally provides a better energy effic iency [20]. The research question arises how to further leverage the centralized baseband processing and distribu ted antenna syst em to impro ve the energy e fficiency of th e RF fr ont end, largely determined by signal statis tics and PA performance figures. The diversity of t he wireless ch annel can be l everaged by a multiple antennas system using MIMO technology to increase the system capac ity a n d reliab ility of one or several wireless c ommunications links [21]. It is well kno wn that the DoFs increase wi th the nu mber of antennas. A higher DoF, m oreover, allo ws selecting a larger signal space for resource alloca tion o r precoding to achieve a comparati vely l ower PAPR in eac h RF chain. I n addition, the power consumption of each antenna’s PA is significantly reduced since the power is spread across various separate amplifiers in each radio anten na. The evolution of MIMO, m assive MIMO, us es orders of magnitude more antennas (e.g., 100 or more) at each BS, enabling even higher gains in terms o f energy efficiency. Bec ause of the large number of P As to support massive MIMO in next generation cellular c ommunication systems, inexpensive PAs need t o be deployed. As the number o f antennas at a B S g rows, the fast fading effects o f the c hannels can be neglected, and t he PAPR reduce to almost 0 dB. Massive MIMO, moreover, h elps reducing the complexity of single-antenna receivers, where even si mple linear signal process ing, such as max imal ratio combing (MRC), can provide the des ired performance. 4. Case Study 1: Distributed Antenna Network in a C -R AN Arch itectu re A) Communications Architecture In the c ontext of a small cell, we a s sume that  distributed antennas/RRHs are connected to the centralized baseband processing units o f a C-RAN [2]. Figure 2 show s  users that are served by a set of distributed antennas, sharing N subcarriers. The subcarriers are allocated on SDMA group basis, which means that each subcarrier is exclusive to one group. Furthermore, all RRHs are involved in t he transmission to the m obile stations (MSs) and any sub carrier carries the same inf o rmation symbol across all t he RRHs involved in the transmission. The power is dynamically allocated to the subcarriers of the different RRHs according to the channel c onditions [10] [22]. Statistical PAPR-aware approach is applied in this case study since we take care of statistical characteristic o f transmit signal. B) Problem Formulation We use the energy efficiency ( 3) as the objective function of our o ptimization framework to jointly account for data rate and PAPR. As shown in Figure 1(a), it is n ot practical to assume that the P A e fficiencies are equal ac ross all R RHs and independent of the power allocation sche me. We rather consider that the PA efficiency depends on the PAPR whic h determines the po wer back-off and, he nce, the subcarrier p ower allocation. The optimal solution for subcarrier and power allocation can be obtained by solving Maximize   , (3) Subject to ∑  ,  ≤  ,  , ∀  ,  , ≥ 0, ∀  , , ∑  , ∈  = 1 , ∀ ,  , ∑  , ∈  ∈ 󰇝 0,1 󰇞 , ∀  ,  ,  . Parameter  , indicates whether the th subcarrier is allocated to the t h MS,   represents the set of MSs in th SDMA group, and   , represents the power const raints of the th RRH. Figure 2: Structure of OFDMA/SDMA based DAN for small cell depl oyment with multiple distrib uted users (greedy based SDMA grou p is applied to allocate the MSs to different groups, subcarriers which represented by color blocks are assigned t o different MSs within each group ). C) Joint Channel Capacity a nd PAPR Optimization By combining OFDMA with s pace div ision m ultiple access (SDMA) the sys tem can exploit the rich spatial diversity of DAN f or further im proving t he sp ectral effic iency. The ban dwidth of SDMA is reused by letting multiple users which are sufficiently spatially separated share t he s ame subcarriers. A joint OFDMA/SDMA method with greedy grouping is proposed in this case study. The multi-antenna subcarrier allocation technique exploits the DoF at each RRH. In order to address this joint optimization problem, we derive the complementary cumulat ive distributi on function ( CCDF) and hence the PA efficiency for the O FDM waveforms with unequal power allocation (UPA ) in (2), which generalizes the closed-form solution for the PAPR distribution of OFDM that has been developed for equal power allocation [23]. The closed-form expression for the PAPR distribution o f an OFDM signal allows analyzing the interdependenc y between the PA efficiency and the resource allocation. D) Solution The joint OFDMA/SDMA communications system allocates subcarriers to MSs considering their spatial diversity. The MSs are therefore divided into several SDMA groups, the MSs with spatially c orrelated channels are placed in the same group and m ultiplexed on different resources, e.g. on different subcarriers. MSs are multiplexed by employing the SDMA scheme, e.g., with a transmit ZF filter, while reusing the same resources in frequenc y and time. Th e power is allocated to subc arriers of d ifferent RR Hs afterwards. Suboptimal subcarrier allo cation is carried out by considering only the sum capacity (without considering energy efficiency). Notice that there are two fractions in the ener gy efficiency (1) , namely data rate over t o tal power consumption and power allocation over PA efficiency. The subcarrier allocation is followed by the dual fractional programming to deal with the two fractions in (1) with a two-step approach [24]. The energy efficiency problem after application of two-ste p dual fractional programming is reduced to a simple wate r filling problem. Therefore, we introduce an iterative power allocation algorithm where the power is allocated to o nly one antenna in each iteration while the powers of the remaining antennas are assumed constant. Al t hough the PAPR is consid e red during t he resource all oc ation, the co m puting complexity of our DAN power allocation solution i ncreases linea rly wit h the number of distributed antennas  and is thus suitable for massive deployments of RRHs. E) Numerical Results The simulations assume small cells within the service area of 2 kilometer radius. The distributed antenna network consists of 5-40 RRHs, serv ing 50 MSs using 128 subcarriers and QPSK. A l ower number of RRHs helps to ev aluate the performance o f the PAPR reduct ion with limited degradation on channel capacity, whereas a high number of RRHs are considere d to evaluate the performance of the energy efficiency optimization wi th practically unlimited DoF. The MSs are randomly distributed within the range of the small cell. T he C-RAN’s BB Us are located in the center of the service area. The RRHs are uniformly distributed. The channels between RRH and u sers are modeled as in dependen t f requency selective channels. Figure 3: Performance com parison of different PAPR red uction schemes. Figure 3 sho ws the performance in terms of PAPR reduction o f the proposed approach along with state- of-the-art PAPR reduc tion schemes . The cli pping rate (CR) is chosen to be 0.8 and 1.6 in the simulations for cli pping and filtering scheme [25]. The number of subblocks, which determine the granularity of optimization, in partial transmit sequence (PTS) [26]are chosen to be 2, 4 and 8, respectively, and each partitioned subblock is multiplied by a corresponding c omplex phase factor. The graph shows that the proposed PAPR-aware energy efficiency optimization approach c an provide consisten t improvement when compared with traditional clippin g and filtering or PTS approaches. Figure 4: Energy efficiency over the number of RRHs for PAPR-aware energy effic ienc y optimization. Figure 4 p lots the energy ef fic iency over the number of RRHs for the p roposed sol ution and the approach from [2], whic h treats the PA e fficiency of different RRHs as e qual and constant numbers irr espective of power allocation results. The energy efficiency gain of the proposed solution is almo st one o rder of magnitude higher. The general trend shows that the en ergy efficiency of the proposed method increases with the number of RRHs, more steeply when t he number of RRHs is relatively low. The PAPR-aware energy-efficient algorithm increases w ith the number of RRHs because of the higher DoF, which provides more space for optimization . These results show that the maximu m energy efficiency is achieved for as many as 30 RRHs. We al so observe that the energ y efficiency o f the approach proposed in [2] increases when the number of RRH is low, but decreases when increasing t he number of RRHs beyond the optimal point of 10 RRHs in this case. F) Conclusions This cas e stud y has considered the overall data rate as well as the PAPR influence on the PA and, thus, the energy consumption for resource allocation to a DAN enabled by RRH/C-RA N infrastructure. Dual fractional programming is applied to derive the optimal power al location method fo r DANs and an iterative solution is proposed to reduce the c omputational complexity. Simulation results have shown that both PAPR reduction and energy efficiency are improved significantly when compared with traditional energy-efficient resource allo cation schemes. The expectation of PAPR-aware energy-efficient DAN structure is ve ry pro mising in two aspects: 1) the perfo rmance of PAPR reduction enables the operator to equip the R R Hs with low-cost PAs, which helps the operator to r educe the CA PEX of th e DAN deployment and; 2) the OPEX of DAN in te rms of energy consumption can be r educ ed b y up to 9 0% esp ecially with t he large scale DAN. 5. Case Study 2 : Ma ssive MIMO i n 5G A) Communications Architecture and System Model The second case s tudy proposes a novel PAP R reduction method for energy-efficient massive MIMO operation. The pre mise is t o exploit th e DoF of the large number of antennas w ith minimal effect on data rate and multi-user interfer ence (MUI). Our solution mimics an ar tific ial neural n etwork (ANN) t o find th e minimal dynamic range of the signal with an optimal prec oding m atrix. Consider a downlink massive MIMO-OFDM system which has   single antenna users and one BS equipped with   antennas, the number o f subcarrier is   . The num ber of B S antenn as is sig nificantly larger than number of users, i.e.   ≫   [27]. It has been proven that fo r the single carrier case, the large scale M IMO system yields signals wit h unit PAPR across the antennas as the number o f antennas   approaches infinity for a finite number o f us er   [27]. Wh en considering an OFDM waveform, the problem becomes mo re complicated since the constraints of the PAPR and precoding are in differe nt domains: The PAPR depends on the spectral content of the signal at each individual antenna, whereas the precoding mechanism depends on the signal ac ross multiple antennas. There fore, t he overall signal representatio n ac ross different antennas and subcarriers can be formulated b y the single equation  =  󰇯  , ⋯  ,  ⋮ ⋱ ⋮    , ⋯    ,  󰇰 󰆄 󰆈 󰆈 󰆈 󰆈 󰆈 󰆅 󰆈 󰆈 󰆈 󰆈 󰆈 󰆆   󰇭    ⋮     󰇮 󰆄 󰆅 󰆆   . (4) Symbol  is the in formation symbol and  the channel state. The per m utation matrix is comprised by the   ×   matrix  , whose entries are 1 for 1 ≤  ≤   and 1 ≤  ≤   , all other entries being 0.   represents the signals transmitted fr om the   antennas. Instantaneous PAPR-a ware approach is applied in this case study since we deal with transmit signal on symbol basis. B) Problem Formulation The PAPR-aware d o wnlink massive MIMO system is f ormulated as an opti mization p roblem to d etermine the o ptimal signal and maximum allowed dynamic range of the transmitted signal. Assum ing that the channel state information is available at the transmitter (CSIT), certain signal preprocessing algorithms such as linea r precoding are applied at the BS to eliminate the M UI at the receivers. Zero forcing (ZF) precoding is commonly applied in massive MIMO because of its simplicity and good performance. The user info rmation symbols at the BS are mapped to the appropriate transmit antenna so that the information received by each user has minimal interference from the o ther users’ signals. In order to derive the PAPR of the transmit signal, the fr equency domain signal   needs to be transformed into the time domain signal   . Th erefore, the constraint of perfect MUI remover across different antennas and subcarriers is derived as (5 a) and the overall massive MI MO-OFDM downlink pro blem formulated as    [   ⨀  −   ]  +  , ( 5) Subj ect to  = ℋ   , (5a)  ≥ 0 (5b) Operator ⨀ denotes element-wise multiplication, [ ]  = m ax (, 0) , and  = [ 1,1, ⋯ ,1 ] is a     -vector. The maximum dynamic ran ge is de fined as the RNN activation variable  , which also represents th e crest factor of the PA. The solution space (  , )  ∈   is the convex set where the solution exists. It is clear that the R NN activation variable  in represents the minimum PA efficiency among all th e transmit antennas. For the given optimal RNN variable, the proposed structure guarantees t hat the signal   at all transmit antennas will not be distorted. Th e similarity between the nonlinear function [ ]  in (5) and th e activation function in a neural network as shown in Figure 5(a) allow us to adopt neural network to solve the problem. (a) (b) Figure 5: Analogy between p recoding & nonlinear PA s tructure and weighted sum an d activation function neural network stru cture (a); Block diagram of the proposed recurren t neural network (b). C) Solution It has been demo nstrated that the RNN is suitable fo r real-time impleme ntation with finite and exponential convergence in v arious applications. In order to formulate the dynamic equation to derive the optimal prec oding vector and RNN activation v ariable, we hav e to rest ate the optim ization in (5) in Lagrangian form. First of al l, let us relax the precoding constraint  = ℋ   in ( 5a) to the Frobenius n o rm form |  − ℋ   |   ≤  , noting that t he relaxation does not significantly degrade t he BER performance for small values of  . With an auxiliary para m eter  , the scalar valued objective function of the R NN system is defined as the nonnegati ve Lagrangian function of the overall system  (   ,  ) =  ( [    ⨀  −    ]  +  ) + |  − ℋ   |   . (6) With the no nnegative L agran gian function defined in (6), the dynamic equations for solving ( 5) can be derived by taking the negati ve gradient   = −  (  ) , (7 ) where  = (  , )  ∈   , the nonnegative Lagrangian function  () being defined in (6), ∇  () be ing the gradient of the objective function, and  a positive scalar constant that is used to scale the convergence rate of the RNN. The block diagra m of the proposed RNN is sho wn in Figure 5( b). The PAPR block represents the PAPR level of (   ⨀  −   ) , and the MU I block the amount of MU I given by Re(ℋ  (ℋ   −)) . Each layer in Figure 5(b) represent the RNN f or each antenna. The nonlinear activation f unction   (  ) and d eactivation f unction    (  ) are intr oduced to emulate the ideal cut-off characteristic beyond the 1-dB compression point in (8) an d (9)   (  ) =  1,   ≥ 0 0,   < 0 (8)    (  ) =  1,   < 0 0,   ≥ 0 (9) The residual part of the signal after cut-off is back-propagated, and   is trained b y the signal residue to satisfy the precoding constraint in the meantime. D) Results The RNN-based large scale MU -MIMO-OFDM downlink system with 128 subcarriers, up to 250 antennas at the BS and 12 single-antenna MSs is chosen to ev aluate the perfo rmance o f the proposed PAPR- reduction scheme. The modulation is 16 -QAM and the MSs are r andomly distributed within the range of the small cell. The channels between each antenna an d user are modeled as frequency selective channels and are in dependent from one another. The R NN-based scheme is simulated to derive the optimal transmitted signal and activation variable. The least sq uares (LS) method is used as a baseline, because i t is one of the most prominent precoding m ethods for MIMO system. It generates the trans mitted signal with minimum L2 norm while perfectly re moving all the MUI. The PAPR reduction p erformance o f different PA PR-aware algorithm in t ime do main is shown in Figu re 6. It is revealed in Figure 6 that the LS algorithm gives a solution with less power but the P APR reduction performance is clearly wo rse than the other approaches. The fast iterative trun cation algorith m (FITRA) [27] and the pro posed RNN approach have similar performance in te rms of PAPR reduction, while the proposed RNN approach h as hardware-friendly parallel structur e with less complexity. Figure 6: Transmit signal w aveforms for different PAPR-aware precodin g approaches in time domain The relation between antenna configuration and energy efficiency performance is illustrated in Figure 7. The increasin g n umber of antennas at the BS yields to better p erformance for the proposed RNN method, but to worse performance for the LS scheme. Figure 7: Energy efficiency of propos ed RNN and least square precoding schemes as a function of the number of transmit antenn as E) Conclusions The second case study has introduced a PAPR-aware massive M IMO-OFD M downlink system that is inspired by RNNs. It draws the analogy between the linear precoding with nonlinear PAs and massive- MIMO and the linear wei ghtin g of n euro ns with n onlinear activation functions o f artificial neural networks. The proposed RNN provides a sc alable, parall el processing solution which i s especially suitable for tackling large-scale problems such as massive M U-MIMO. The n ear-constant envelop e of th e input sig nal is achieved by exploiting the extra DoF of the antenna array. The simulation resu lts indicate that the DoF in PAPR-aware massive MIMO system can be ex ploited to improve the energy effic iency of the communications system. The proposed RNN scheme presents a simple processing structure, which is especially suitable for very-large scale integration (VLSI) implementati o n. 6. Conclusion The high i nput power b ack-off p ower require ment for PAs causes low PA effi ciency and hence low energy efficiency a t the BS. Sustainable green ne t working systems nee d to b e P APR-aware. The trends for 5G NR, deploying RRH /CRAN or massive MIMO BSs, naturally provide more DoF tha t can be exploited t o increas e the net energy effic iency and reduc e OPEX for the operator. This article has ex amined two c andidate architectures for nex t generation cellular netwo rks c haracterized by median-scale and large-scale antenna systems and developed the suitable resource allocation schemes. 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