Shuangfeng Han，Chih-Lin I，Zhikun Xu，Qi Sun，and Haibin Li

（1.Green Communication Research Center，China Mobile Research Institute，Beijing 100053，China；2.Department of Planning and Construction，China Mobile，Beijing 100053，China）

Energy-Efficient Large-Scale Antenna Systems with Hybrid Digital-Analog Beamforming Structure

Shuangfeng Han1，Chih-Lin I1，Zhikun Xu1，Qi Sun1，and Haibin Li2

（1.Green Communication Research Center，China Mobile Research Institute，Beijing 100053，China；2.Department of Planning and Construction，China Mobile，Beijing 100053，China）

A large-scale antenna system（LSAS）with digital beamforming is expected to significantly increase energy efficiency（EE）and spectral efficiency（SE）in a wireless communication system.However，there are many challenging issues related to calibration，energy consumption，and cost in implementing a digital beamforming structure in an LSAS.In a practical LSAS deployment，hybrid digital-analog beamforming structures with active antennas can be used.In this paper，we investigate the optimal antenna configuration in anN×Mbeamforming structure，where N is the number of transceivers，Mis the number of active antennas per transceiver，where analog beamforming is introduced for individual transceivers and digital beamforming is introduced across allN transceivers.We analyze the green point，which is the point of maximum EE on the EE-SE curve，and show that the log-scale EE scales linearly with SE along a slope of-lg2/N.We investigate the effect ofMon EE for a given SE value in the case of fixed NM and independent N and M.In both cases，there is a unique optimal M that results in optimal EE.In the case of independentN andM，there is no optimal（N，M）combination for optimizing EE.The results of numerical simulations are provided，and these results support our analysis.

digital beamforming；analog beamforming；hybrid beamforming；energy efficiency；spectral efficiency

1 Introduction

Wireless communication systems have developed from first generation to fourth generation to accommodate ever-increasing and diversified mobile traffic.The anticipated thousandfold increase in wireless traffic by 2020 and the push for green communication worldwide create some very tough challenges for 5G system design［1］.Massive MIMO，also known as largescale antenna system（LSAS）［2］，［3］，is a promising green 5G communication scheme that improves both energy efficiency（EE）and spectral efficiency（SE）.With full digital beamforming（BF）LSAS can，in theory，perform optimally.When many antennas are implemented to increase beamforming gain，it may not be feasible to implement the same number of transceivers because of excessive demand on real-time signal processing when there is large BF gain［4］and also because of cost and power consumption，especially for mixed-signal devices in a millimeter-wave system.A beamforming structure with a much smaller number of digital transceivers than antennas is therefore more practical and cost-effective.

To reduce complexity in a LSAS，analog beamforming with active antennas can be considered［5］，［6］.With analog beamforming，the signal phase on each antenna is controlled by a network of analog phase shifters.In［7］-［9］，hybrid analog-digital beamforming strategies were investigated for pre-coding multiple data streams and increasing beamforming gain.In［7］，the transmitted signal on each of N digital transceivers travels along all NM RF paths（mixer，PA，and phase shifter），where M is the number of active antennas per transceiver.The signal is summed up before being connected with each antenna element（Fig.1a）.Analog beamforming is then introduced over NM RF paths per transceiver，and digital beamforming is introduced over N digital transceivers.The complexity of this structure is high.

In Fig.1b，the N×M hybrid beamforming structure has N transceivers connected to M antennas.This structure is more practical for base station antenna deployment in 3G and 4G LTE systems，where each transceiver is connected to a column of antennas.With active antennas on each RF path，elevation beamforming can be introduced by applying different phases to each antenna in each column.

▲Figure 1.Hybrid beamforming structure

Recently，there has been growing interest in hybrid beamforming design.The structure in Fig.1a features a precoding solution where only some aspects of the channel（e.g.，angle of arrival and departure）are known at the base station and mobile station［7］.The spatial structure of millimeter-wave channels has been further exploited to formulate the single user precoding/combining problem as a sparse reconstruction problem［8］.In［4］，the authors propose an angle-of-arrival estimation algorithm and beamforming algorithm.In［9］，the authors propose a beam-domain RS design that results in better performance than a design based on pure analog beamforming.An outdoor trial of the N×M beamforming structure has been carried out in South Korea［10］，but the optimal configuration of M remains an open and very important issue.An improper M may reduce EE even if the SE is satisfactory.

In this paper，we focus on the N×M hybrid beamforming structure.In particular，we investigate the optimization of both EE and SE in the cases of fixed NM and independent N and M. In section 2，we discuss the relationship between EE and SE. Then，we investigate this relationship at the“green”points，i.e.，the points of maximum EE on the EE-SE curve.We discuss the effect of M on EE for a given SE.We investigate the optimal（N，M）combination that results in the highest EE in the case of independent N and M.In particular，we discuss the optimal M when there is severe inter-user interference.In section 3，we present and discuss numerical simulation results.In section 4，we draw some conclusions from our analyses.

2 Energy Efficiency and Spectral Efficiency

2.1 Relationship

In the N×M structure in Fig.1b，perfect analog beamforming is assumed within M antennas per transceiver，which points to one user（there are N users in total）.Assuming there is no inter-user interference，i.e.，there is proper user scheduling（the BS schedules users with orthogonal channels），then the sum capacity of this structure for N users is:

where W is the bandwidth，P is transmit power of each transceiver（the total power of M antenna PAs），ηPAis the PA efficiency，and N0is the thermal noise density.Without loss of generality，the channel gain is assumed to be the unity.The SE of this structure is

Because the accurate power model is non-trivial，the following simple power model is used:

where Ptotalis the total power；NP is the RF power of N transceivers；Pstaticis the static power of the BS，including NP0，which scales with N；Pcommon，which is common for any number of transceivers；and NMPrf_circuit，which scales with NM.The relationship between EE and SE is

Therefore，for a required SE，the hybrid LSAS beamforming should be designed to maximize EE through joint design of N，M，P0，Pcommon，Prf_circuitandηPA..This paper focuses on the design for an optimal number of active antennas per transceiver M* that ensures the best EE for a given SE.

2.2 Relationship at Green Points

When we take the circuit power into consideration，there is a“green”point on the EE-SE curve where EE is at its maximum and is denotedη*EE［11］.Here，we discuss two cases for the N×M hybrid beamforming structure:NM=L（i.e.，the total number of antennas is fixed asL，but N and M are variable），and 2）NandMare independent.In the former case，we allow the first-order derivative of EE over SE to be zero:

Combining（5）with（4），the relationship between theη*EEand corresponding SEη*SEis

The relationship betweenη*EEandη*SEis further given as

which indicates that lg（η*EE）scales linearly withη*SEand has a slope of-lg2/N.Similar to the EE-SE relationship in classic Shannon theory，higherη*SEalways leads to lowerη*EE.The relationship betweenη*EEandη*SEdoes not depend on P0，Pcommon，Prf_circuitand W，although from（4），we see thatη*SEandη*EEare based on all the other parameters.

It is expected，therefore，that the system operates at the green point.Also，it is important thatη*SEsatisfies the system SE requirement，andη*EEshould be high enough.This requires careful design of P0，Pcommon，Prf_circuit，W，ηPA，N and M.For example，when other parameters are given，M can be designed to maximize EE.

2.3 Optimal M for Maximizing EE for a Given SE

2.3.1 When N and M are Independent

It is of practical importance to know how M affects EE for a given SE.If there is one optimal M that results in the highest EE，it is not necessary to deploy too many antennas per transceiver.In the following，we derive the optimal M to maximize EE.We denote the denominator of（4）as f（M）:

The first-and second-order derivatives of f（M）are

and

Then f（M）is a quasi-convex function of M.The M*that gives the minimum f（M）is derived by making f'（M）=0:

Because of the definition ofηEEin（4），EE is a quasi-concave function of M，and the EE is at its maximum when M=M*.When M≤M*，EE monotonically increases with M. When M＞M*，EE monotonically decreases with M.In practical system design，for a given SE there is one M*that results in the highest EE.As in（11），M*increases with SE and bandwidth，but decreases with PA power efficiency and Prf_circuit.For a given number of transceivers N，more antennas per transceiver are needed for higher SE.If W increases，the noise power increases correspondingly，and a larger M is needed to achieve the SE.A larger Prf_circuit，however，reduces M*because the increased circuit power may reduce EE.

2.3.2 When NM is Fixed

Assume NM=L，the denominator of（4）is written as

For simplicity of derivation，f（M）is rewritten as

The first-order derivative of f（M）is

Respectively，the first-and second-order derivatives of g（M）are

and

Therefore，g'（M）monotonically increases with M.In addition，

Thus，there is unique positive M0so thatg'（M0）=0.When M＜M0，g'（M）＜0，g（M）monotonically decreases with M. When M＞M0，g'（M）＞0，g（M）monotonically increases with M.Because g（0）=0 andg（∞）=∞，there is a unique positive M1that is larger than M0and satisfies g（M1）=0.From（14），g（M）determines monotonicity of f（M）；therefore，when M＜M1，g（M）＜0，f'（M）＜0.When M＞M1，g（M）＞0，f'（M）＞0. Also，

Therefore，whenM≤M1，EE monotonically increases with M.When M＞M1，EE monotonically decreases with M.In the case of fixed MN，EE is maximum at M=M1，where M1can be obtained by solvingg（M1）=0.

2.3.3 Optimal（N，M）Combination

An important issue is finding the N and M that results in the highest EE for a given SE when N and M are not fixed.Combining（11）and（4）the maximum EE for a given SE and N is

The optimal N can then be calculated:

We denote the denominator in（4）f（N，M）:

There is no extreme point for f（N，M）.The partial derivative of f（N，M）over M is

which leads to

The partial derivative of f（N，M）over N is

which leads to

The optimal M and N should satisfy（24）and（26）.Combining（24）and（26），we get

This is equivalent to

However，M in（28）cannot not exist because when 2N-ηSEln2＞0，M＜0，and when2N-ηSEln2＜0， M＜0. This is not feasible because M must be positive.

2.3.4 When Inter-User Interference is Taken into Account

In subsection 2.3.3，it is assumed there is no inter-user interference.However，in practical systems，inter-user interference may exist.For simplicity，we assume that interference from the kth beam to the nth beam isMηPAPαk，n.Then，EE can be expressed as

Note that αk，ncan be a function of N and M.For example，consider a linear antenna array with NM elements，where the antenna spacing is half a wavelength.The main beam direction（azimuth）of the analog beamforming for the nth transceiver is ?n=nΔ/N，n=0，…，N-1，and N users are located on the N different main beam directions with same channel gain.We approximate αk，n:

It seems difficult to determine how M affects EE in the cases that fixed NM and independent N and M are used.In some special cases，for example，in the interference-limited region，increasing the transmit power P does not improve spectral efficiency and actually reduces energy efficiency.When inter-us-er interference is negligible，the analysis in previous subsections holds.

3 Simulation Results

3.1Mvs EE When There is No Inter-User Interference

▲Figure 2.Mvs EE with different SE values（N=2）.

Assume Pcommon=50 W，Prf_circuit=1 W，P0=1 W，W=2×107Hz，N0=10-17dBm/Hz，ηPA=0.375 and the channel gain is-100 dB.Fig.2 shows the effect of M on EE for N=2 and where M is variable.Five spectral efficiencies between 4 bps/Hz to 20 bps/Hz are simulated.On each M versus EE curve，there is a unique M that results in the highest EE.For example，when SE is 20 bps/Hz，the M*is 33.When SE is 12bps/Hz，M*is 8.When M is smaller than optimal，more antennas per transceiver improve EE by providing beamforming gain.When M is greater than optimal，the extra power in the circuit needed by more antennas per transceiver negates any reduction in transmit power so that EE is reduced.

Fig.3 shows the effect of M on EE when NM is fixed，e.g.，NM=128，and other parameters are the same as those in Fig. 2.Actually，M can only be 1，2，4，8，16，32，64 and 128（not shown），because N and M are both integers.As in the case of independent N and M，there is a unique M on each curve that results in the highest EE.For example，when SE is 48 bps/Hz，the optimal M is 8.In Fig.2，the optimal M increases as SE increases；however，in Fig.3，the optimal M increases as SE decreases.The reason for this is:as SE increases，more transceivers are needed to make the system more energy efficient，and a smaller M（M=L/N）is required.

▲Figure 3.Mvs EE for different SE values（NM=128）.

The above analysis can be referred to when designing an optimal LSAS.In a practical system，the required SE may vary according to the traffic load and service types.For example，in Fig.2，the M*for a maximum required SE of 20 bps/Hz is 33. However，when the required SE is reduced to 12 bps/Hz，M*is 8.Therefore，it is important that，in the case of independent N and M，the system is designed with the largest M*for the possible SE range，and the best M is chosen according to the SE requirement via antenna on/off.This can help increase EE according to system traffic load.

3.2Mvs EE When There is Inter-User Interference

We assume Pcommon=50W，Prf_circuit=1 W，P0=10 W，W=2× 107Hz，N0=10-17dBm/Hz，ηPA=0.375，and channel gain is 10-10.A linear antenna array with N=10 and half-wavelength antenna spacing is considered.The effect of M on EE is shown in Fig.4，and the inter-user interference is calculated according to（30）（whereΔ=π/3）.Ten power levels between P=10 W to P=100 W are simulated.One power level corresponds to one SE value.At each power（and corresponding SE）level，increasing M from 1 to 25 increases EE，but if M goes beyond 25，EE decreases.This is quite different from when there is no inter-user interference and M*is generally different for different SE values.The possible reason for this is that the coverage of N（N=10）beams is onlyΔ（π/3），and there is too much inter-beam interference.Therefore，M has to be large enough to reduce this interference and increase EE.

▲Figure 4.Mvs EE with different power levels.

▲Figure 5.Mvs EE for different power levels.

WhenΔ increases to π，the beam spacing increases from π 30toπ 10，resulting in less inter-beam（inter-user）interference.Fig.5 shows the effect of M on EE.The trend is similar to that in the case of no inter-user interference:at each power level，there is one M*that results in the highest EE.Interuser interference can be mitigated via digital precoders whose design is based on certain channel assumptions and that result in increased EE.One straightforward method is to use beam domain downlink reference signals via analog beamforming to estimate 1）the angle of departure of each user，2）the effective channel with analog beamforming，and 3）the inter-beam（interuser）interference.Then，digital precoding can further increase the multiuser beamforming gain.EE-SE optimization depends on different multiuser beamforming algorithms and is more complicated，especially in the case of fixed NM.

4 Conclusions

In this paper，an N×M hybrid analog-digital LSAS beamforming structure is investigated.In this structure，the number of transceivers can be much smaller than the number of antennas.We analyzed the relationship between EE and SE to determine the optimal design of the N×M beamforming structure. In particular，we analyzed two cases:fixed NM and independent N and M.We analyzed the EE-SE relationship at the green point and showed that the log-scale EE scales linearly with SE along a slope-lg2/N.In both cases，a unique number of antennas M per transceiver results in the optimal EE for a given SE.In the case of independent N and M，there is no optimal（N，M）combination that results in optimal EE.When interuser interference is negligible，the above results hold；when there is severe inter-user interference，the optimal M can be quite similar for each SE value.The findings in this paper can be used as guidelines for optimizing an LSAS design.

Acknowledgement

The authors would like to thank the editors and the reviewers for their very helpful comments and review.The authors are also grateful to the team members in the Green Communication Research Center of China Mobile Research Institute.

［1］C.-L.I，C.Rowell，S.Han，Z.Xu，G.Li，and Z.Pan，“Towards green&soft:a 5G perspective，”IEEE Communication Magazine，vol.52，no.2，pp.66-73，F(xiàn)eb. 2014.doi:10.1109/MCOM.2014.6736745.

［2］F.Rusek，D.Persson，B.K.Lau，E.Larsson，T.Marzetta，O.Edfors，and F. Tufvesson，“Scaling up MIMO:opportunities and challenges with very large arrays，”IEEE Signal Processing Magazine，vol.30，no.1，pp.40-60，Jan.2013. doi:10.1109/MSP.2011.2178495.

［3］T.L.Marzetta，“Noncooperative cellular wireless with unlimited numbers of base station antennas，”IEEE Transactions on Wireless Communications，vol.9，no.11，pp.3590-3600，Nov.2010.doi:10.1109/TWC.2010.092810.091092.

［4］X.Huang，Y.J.Guo，and J.D.Bunton，“A hybrid adaptive antenna array，”IEEE Transactions on Wireless Communications，vol.9，no.5，pp.1770-1779，May 2010.doi:10.1109/TWC.2010.05.091020.

［5］J.Wang，Z.Lan，C.Pyo，T.Baykas，C.Sum，M.Rahman，J.Gao，R.Funada，F(xiàn). Kojima，H.Harada，and S.Kato，“Beam codebook based beamforming protocol for multi-Gbps millimeter-wave WPAN systems，”IEEE Journal on Selected Areas in Communications，vol.27，no.8，pp.1390-1399，2009.doi:10.1109/ JSAC.2009.091009.

［6］V.Venkateswaran and A.-J.van der Veen，“Analog beamforming in MIMO communications with phase shift networks and online channel estimation，”IEEE Transactions on Signal Processing，vol.58，no.8，pp.4131-4143，2010.doi: 10.1109/TSP.2010.2048321.

［7］A.Alkhateeb，O.El Ayach，G.Leus，and R.W.Heath，“Hybrid precoding for millimeter wave cellular systems with partial channel knowledge，”in Information Theory and Applications Workshop，San Diego，USA，F(xiàn)eb.2013，pp.1-5. doi:10.1109/ITA.2013.6522603.

［8］O.El Ayach，S.Rajagopal，S.Abu-Surra，Z.Pi，and R.W.Heath，“Spatially sparse precoding in millimeter wave MIMO systems，”IEEE Transactions on Wireless Communications，vol.13，no.3，pp.1499-1513，Mar.2014.doi: 10.1109/TWC.2014.011714.130846.

［9］S.Han，C.-L.I，Z.Xu，and S.Wang“Reference signals design for hybrid analog and digital beamforming，”IEEE Communications Letters，vol.18，no.7，pp. 1191-1193，Jul.2014.doi:10.1109/LCOMM.2014.2317747.

［10］W.Roh，J.-Y.Seol，J.Park，B.Lee，J.Lee，Y.Kim，J.Cho，K.Cheun，and F. Aryanfar，“Millimeter-wave beamforming as an enabling technology for 5G cellular communications:theoretical feasibility and prototype results，”IEEE Communication Magazine，vol.52，no.2，pp.106-113，F(xiàn)eb.2014.doi:10.1109/ MCOM.2014.6736750.

［11］G.Y.Li，Z.Xu，C.Xiong，C.Yang，S.Zhang，Y.Chen，and S.Xu，“Energy-efficient wireless communications:tutorial，survey，and open issues，”IEEE Wireless Communications，vol.18，no.6，pp.28-35，Dec.2011.doi:10.1109/ MWC.2011.6108331.

Manuscript received:2014-09-15

Biographiesphies

Shuangfeng Han（hanshuangfeng@chinamobile.com）received his MS and PhD degrees in electrical engineering from Tsinghua University in 2002 and 2006.He joined Samsung Electronics as a senior engineer in 2006 and worked on MIMO and MultiBS MIMO.Since 2012，he has been a senior project manager in the Green Communication Research Center of China Mobile Research Institute.His research interests include green 5G，massive MIMO，full-duplex，non-orthogonal multiple access，energy efficiency，and spectral efficiency co-design.

Chih-Lin I（icl@chinamobile.com）received her PhD degree in electrical engineering from Stanford University.She has worked for numerous world-class companies and research institutes，including AT&T Bell Labs，AT&T HQ，ITRI Taiwan，and ASTRI Hong Kong.She was awarded the Stephen Rice Best Paper Award from IEEE Tranactions on Communications and is a winner of the CCCP National 1000 Talent program.Currently，she is China Mobile's chief scientist of wireless technologies and has established the Green Communications Research Center，spearheading major initiatives including key 5G technology R&D；high EE system architectures，technologies and devices；green energy；and C-RAN and soft base stations.She was an elected Board Member of IEEE ComSoc，Chair of the ComSoc Meetings and Conferences Board，and Founding Chair of the IEEE WCNC Steering Committee.She is currently an Executive Board Member of GreenTouch and a Network Operator Council Member of ETSI NFV.Her research interests are green communications，C-RAN，network convergence，bandwidth refarming，EE-SE co-design，massive MIMO，and active antenna arrays.

Zhikun Xu（xuzhikun@chinamobile.com）received his BSE and PhD degrees in signal and information processing from Beihang University（BUAA），China in 2007 and 2013. After graduation，he joined the Green Communication Research Center of China Mobile Research Institute as a project manager.His current interests include green technologies，cross-layer resource allocation，advanced signal processing，and transmission techniques

Qi Sun（sunqiyjy@chinamobile.com）received her BSE and PhD degrees in information and communication engineering from Beijing University of Posts and Telecommunications in 2009 and 2014.After graduation，she joined the Green Communication Research Center of China Mobile Research Institute.Her research interests include MIMO，cooperative communication，and green communications.

Haibin Li（lihaibin@chinamobile.com）received her MS degree in project management from Beijing University of Posts and Telecommunications，China.She is currently the director of Division of Energy Conservation and Emission Reduction，Department of Planning and Construction，China Mobile Communications Corporation.She has been in charge of energy saving and emission reduction from April 2011 and has 19 years experience in the field of communications planning and construction.She is also the director of Resource Sharing Plan for CMCC and deputy head of the CCSA ST2 and ST4 group.

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