Harmonized Multiuser Transmission Scheme forCellular Systems

Wei Xi, Hua ZhouFujitsu Research & Development Center Co., LTD., Beijing, PRC, 100027

Email: {xiwei, zhouhua}@cn.fujitsu.com

Abstract—Besides multiuser multi-input multi-output (MU-MIMO), non-orthogonal multiple access (NOMA) has been pro-posed as another promising alternative for multiuser multiplexingin cellular systems targetting for efficient spectrum utilization,and consequently has been attracting the attention of an in-creasing number of universities and institutes in both academicand industrial areas. In this paper, we focus on the azimuthaldifference between the paired users, and investigate its influenceon the system performance for both MU-MIMO and NOMA,respectively. The investigation reveals the different preference ofthe both schemes in respect of the inter-user azimuthal difference.Accordingly, a harmonized transmission framework for multiusermultiplexing has been proposed whereby the better transmissionscheme of the both is always selected. Theoretical analysis justifiesits effectiveness.

Index Terms—Azimuthal difference, deviation, multiuser mul-tiplexing, MU-MIMO, NOMA.

I. INTRODUCTION

Over the last decade, with the new service types emergingand wireless traffic soaring, high speed data rate access isbecoming increasingly necessary and important. To this end,spectral efficiency needs to be improved further or widerspectrum should be used. However, radio spectrum has alwaysbeen the most valuable and scarcest resource in wirelesscommunication. Besides the exploration of wider and higherfrequency bands, one of the biggest challenges is how to utilizethe existing spectrum in an extremely efficient way.

In a cellular system, a base station (BS) needs to provideservice to its associated users. Clearly, scheduling multipleusers in a frequency division multiplexing (FDM) or timedivision multiplexing (TDM) manner cannot contribute tospectral efficiency enhancement. Instead, a BS can only resortto the technologies whereby multiple users can be sched-uled for co-transmission on the same frequency resourcesimultaneously. Regarding the technologies, multiuser multi-input multi-output (MU-MIMO) [1]–[3] and non-orthogonalmultiple access (NOMA) [4]–[6] are two typical candidates.

MU-MIMO transmission is widely used in cellular sys-tems to deal with the restriction of the conventional singleuser MIMO (SU-MIMO) scheme that the link capacity isconstrained to the number of the antennas equipped at oneuser. In MU-MIMO, the antennas of the co-scheduled users,probably geographically separated, can be equivalently treatedas one virtual antenna array. Therefore, MU-MIMO is alsotermed virtual MIMO. Since it was proposed, a variety ofMU-MIMO specific beamforming schemes have emerged, e.g.

zero forcing (ZF), block diagonization (BD), and etc. What isinteresting, in the presence of a large number of candidatesusers, remarkable multiuser diversity gain can be obtained dueto the opportunistic user scheduling and pairing. Moreover,a carefully dedicated ZF-based beamforming scheme can beasymptotically optimal and the achievable throughput canapproach that of dirty paper coding (DPC) [1], [7], i.e. thetheoretical upper bound of MIMO broadcast channels [8].Hence, the capacity of cellular systems can be significantlyenhanced by the technology.

The concept of NOMA was proposed as a new multi-ple access strategy towards future wireless systems, and iscompletely different from the orthogonal manner adopted inexisting systems. According to the knowledge in informationtheory, NOMA has a larger capacity region than orthogonalmultiple access (OMA) schemes. Therefore, it has alreadygiven rise to a series of research activities in the industry,e.g. a new study item termed “study on downlink multiusersuperposition transmission for LTE” was approved by 3rdgeneration partnership project (3GPP) in March, 2015 [9],and further it has already been identified as one of themost remarkable features of long term evoluation advancedprofessional (LTE-AdvancedPro) release 13.

In essence, both MU-MIMO and NOMA are multiusermultiplexing methods or equivalently multiple access schemeswithout time domain or frequency domain separation. Liter-ally, the former multiplexes users in spatial domain, while thelatter performs multiplexing in one or more non-orthogonaldimensions, e.g. power dimension. Obviously, NOMA has avery large scope. Moreover, in strict sense, MU-MIMO isalso a kind of NOMA, since the spatial domain is not afully orthogonal dimension due to the existence of inter-userinterference. But in this paper, as in the majority of the existingliteratures, NOMA means the power domain multiplexing withno separation but complete superposition in spatial domain.

In this paper, we focus on the azimuthal difference betweenthe co-scheduled users, and investigate its influence on thesystem performance for both MU-MIMO and NOMA, respec-tively. In the light of the investigation, the both schemes havedifferent preference in respect of the inter-user azimuthal dif-ference. Targetting for better performance, a harmonized andunified framework for multiuser multiplexing and transmissionhas been proposed whereby the better transmission scheme ofthe both is always selected. In other words, a feasible criteriafor dynamic switching between MU-MIMO and NOMA is

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proposed. Its effectiveness is justified by theoretical analysis.The remainder of this paper is structured as follows. The

system model is briefly introduced in Section II. In SectionIII, the proposed scheme is presented in detail. Finally, con-clusions are drawn in Section IV.

Throughout this paper, we adopt the following notationalconvention: Scalars are denoted by upper-case or lower-caseplain letters, and their absolute values can be obtained by | · |.Vectors and matrices are expressed by lower-case boldface andupper-case boldface letters, respectively. ‖ · ‖2F returns theirFrobenius norms. Cm×n stands for the complex matrix spaceof dimension m×n. Particularly, Cm×1 and C1×n denote thecomplex column and row vector spaces of dimension m andn, respectively. CN (0, σ2) represents the zero mean circularlysymmetric complex Gaussian (ZMCSCG) distribution withvariance σ2. E(·) is the expectation operator for randomvariables.

II. SYSTEM MODEL

Without loss of generality, we consider a simple scenariothat a BS equipped with N antennas selects a couple ofsingle antenna users, user-1 and user-2, for NOMA or MU-MIMO transmission. A birdview of the system model can beillustrated in Fig. 1. For user-i, xi is its constellation symbolwith a unit power, i.e. E(|xi|2) = 1; its polar coordinate isdenoted by (ri, θi); the downlink channel from the BS can becharacterized by a large scale distance-dependent fading L(ri)and a small scale fading hi ∈ C1×N ; i = 1, 2. The total powerconstraint at the BS is Pt, a fraction α of which is allocatedto user-1 and the rest 1 − α of which is assigned to user-2,α ∈ [0, 1].

BS

H user-1

(r1, θ1)

H user-2

(r2, θ2)

h1

h2

Fig. 1. System model

A. NOMA

Generally speaking, for NOMA transmission, the channelstate information (CSI) of the paired users, e.g. user-1 anduser-2, should meet two requirements: approximate or thesame precoding matrix index (PMI) and different enoughchannel quality indicator (CQI). The former guarantees the

azimuthal concentration of the co-scheduled users for largebeamforming gain and high power efficiency; while the latterutilizes large propagation difference for easy distinction andseparation in power dimension. Accordingly, a BS allocates amajority of its power to the far user (e.g. user-2) to conquethe severe path loss, and assign less power to the near user(e.g. user-1). The received signals at user-1 and user-2 can bewritten as

y1 =√PtL(r1)h1w(

√αx1 +

√1− αx2) + n1, (1)

y2 =√PtL(r2)h2w(

√αx1 +

√1− αx2) + n2, (2)

where w ∈ CN×1 is the power normalized beamformingvector shared by the both users, ‖w‖2F = 1; ni is the additiveGaussian noise at the user-i, ni ∼ CN (0, σ2

i ), i = 1, 2.In this case, after experiencing the serious attenuation, the

interference user-2 suffers from user-1 becomes very weak andtolerable. Thus, the user-2 can still detect its own data success-fully. However, this is not the case for user-1. In the presenceof the strong interference, i.e. the data intended for user-2,user-1 has to first detect and cancel the interference beforeobtaining its own data. To this end, the BS usually needs tosignal user-1 the necessary configurations and parameters ofthe transmission to user-2. With the information available, theinterference user-1 suffers can be cancelled precisely. Owingto the smaller propagation attenuation, even though less poweris allocated to it, user-1 is still able to detect its own datacorrectly.

B. MU-MIMO

For MU-MIMO transmission, what is different fromNOMA, two different beamforming vectors can be adoptedfor the two users. Accordingly, the received signals at the bothusers can be expressed as[

y1y2

]=√Pt

[h1

h2

] [w1 w2

] [ √αx1√1− αx2

]+

[n1n2

], (3)

where wi ∈ CN×1 is the power normalized beamformingvector for user-i, ‖wi‖2F = 1, i = 1, 2.

III. PROPOSED SCHEME

In this section, the influence of the azimuthal difference onthe system performance is first investigated for both NOMAand MU-MIMO, respectively. Then, the proposed scheme ispresented in detail.

A. NOMA

From its principle, we understand that NOMA transmissionfavors user pairs with very similar, ideally the same azimuths,i.e. θ1 u θ2. In this case, the BS can concentrate its power onthe azimuth of the user pair. Considerable beamforming gainand excellent performance can be obtained. On the contrary,if the inter-user azimuthal difference, e.g. |θ1 − θ2|, is large,no matter how the BS tunes its beam, at least one user suffersreduced beamforming gain. If the BS steers its beam towardsone user, then the other user will suffer degraded beamforming

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performance. Therefore, the performance of NOMA transmis-sion is very sensitive to the inter-user azimuthal difference.

According to (1) and (2), the signal-to-interference-plus-noise-power-ratios (SINR’s) of the both users can be obtainedas

ΓNOMA1 (w) =

αPtL(r1)|h1w|2

σ21

= αγ1|h1w|2 (4)

ΓNOMA2 (w) =

(1− α)PtL(r2)|h2w|2

αPtL(r2)|h2w|2 + σ22

=(1− α)|h2w|2

α|h2w|2 +1

γ2

, (5)

where γi =PtL(ri)

σ2i

is the geometry SINR of user-i, which

can be measured based on the downlink pilots or referencesignals, i = 1, 2.

For clear description, we use a function g(ξ) to quantita-tively characterize the extent to which the beamforming vectorw matches the channel to a user, where ξ is the azimuthaldeviation of the user from the beam axis. Then, we have

|h1w|2 = A(θ1)g(φ− θ1)

|h2w|2 = A(θ2)g(φ− θ2),

where A(·) is the pattern of each antenna and φ is the azimuthof the formed beam, which corresponds to beamforming vectorw and varies between θ1 and θ2. Accordingly, the SINR’s ofthe both users can be rewritten as

ΓNOMA1 (φ) = αγ1A(θ1)g(φ− θ1) (6)

ΓNOMA2 (φ) =

(1− α)A(θ2)g(φ− θ2)

αA(θ2)g(φ− θ2) +1

γ2

. (7)

Specially, if the BS steers its beam towards user-1, i.e. φ =θ1, the SINR’s of the both users become

ΓNOMA1 (θ1) = αγ1A(θ1)g(0)

ΓNOMA2 (θ1) =

(1− α)A(θ2)g(δ1,2)

αA(θ2)g(δ1,2) +1

γ2

,

where δ1,2 = |θ1−θ2| is the azimuthal difference between theboth users. If the BS tunes its beam pointing to user-2, i.e.φ = θ2, their SINR’s turn to be

ΓNOMA1 (θ2) = αγ1A(θ1)g(δ1,2)

ΓNOMA2 (θ2) =

(1− α)A(θ2)g(0)

αA(θ2)g(0) +1

γ2

.

As a compromise, the BS can adjust its beam to the middle

of the azimuths of the both users, i.e. φ =θ1 + θ2

2. In this

case, their SINR’s can be given by

ΓNOMA1

(θ1 + θ2

2

)= αγ1A(θ1)g

(δ1,22

)

ΓNOMA2

(θ1 + θ2

2

)=

(1− α)A(θ2)g

(δ1,22

)αA(θ2)g

(δ1,22

)+

1

γ2

.

B. MU-MIMO

Similarly, according to (3), the SINR’s of the both users canbe calculated by

ΓMU-MIMO1 (φ1, φ2) =

αPtL(r1)|h1w1|2

(1− α)PtL(r1)|h1w2|2 + σ21

=αA(θ1)g(φ1 − θ1)

(1− α)A(θ1)g(φ2 − θ1) +1

γ1

(8)

ΓMU-MIMO2 (φ1, φ2) =

(1− α)PtL(r2)|h2w2|2

αPtL(r2)|h2w1|2 + σ22

=(1− α)A(θ2)g(φ2 − θ2)

αA(θ2)g(φ1 − θ2) +1

γ2

, (9)

where φi is the azimuth of the beam dedicated for user-i,corresponding to beamforming vector wi, i = 1, 2.

Taking the popular ZF-based scheme for instance, the inter-user interference can be completely mitigated by zero-forcingprojection. Alternatively, it can be realized by φ1 = θ2 −θnull, φ2 = θ1+θnull, where θnull is a null azimuth, i.e. g(θnull) =0, which is an inherent attribute of the antenna array at theBS. The SINR’s of the both users in (8) and (9) can be furthersimplified as

ΓZF-MU-MIMO1 (δ1,2) = αγ1A(θ1)g(θnull − δ1,2) (10)

ΓZF-MU-MIMO2 (δ1,2) = (1− α)γ2A(θ2)g(θnull − δ1,2). (11)

C. Proposed scheme

Based on the SINR’s of the both users in (6), (7), (10) and(11), the SINR region of the both users can be shown in Fig.2.

Given an inter-user azimuthal difference δ1,2, the achievableSINR performance of the NOMA scheme varies as the beamazimuth goes from the azimuth of user-1 (φ = θ1) to thatof user-2 (φ = θ2). As expected, when φ = θ1, user-1 canobtain the maximal beamforming gain, while user-2 suffers theminimal beamforming gain; when φ = θ2, user-2 can enjoythe largest beamforming gain, while user-1 suffers the mostsevere loss due to the large azimuthal deviation from the beamaxis. In other words, there is always a tradeoff between thebeamforming gains of the both users.

However, this is not the case for the ZF-based MU-MIMOcase. Instead, the SINR’s of the two users fully depend on theazimuthal difference between the both users δ1,2 and the null

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azimuth θnull. As illustrated in Fig. 2, the SINR performancecan be represented by a cluster of parallel lines. Particularly,in the case of δ1,2 = θnull, when the BS steers a beam to oneuser, fortunately there is completely no interference leakedto the other user, and it outperforms the NOMA scheme. Ifδ1,2 = θnull/2, remarkable beamforming gain is sacrificed inthe zero forcing processing, and ZF-based scheme performsworse than the NOMA scheme.

Γ2

0 Γ1

γ2A(θ2)g(δ1,2)

γ2A(θ2)g(0)

γ1A(θ1)g(δ1,2) γ1A(θ1)g(0)

δ1,2 =

θnullδ1,2 =

θnull /2

φ=θ2

φ = θ1

Fig. 2. Achievable SINR region of user-1 and user-2.

In a word, irrespective of NOMA or MU-MIMO, the mostdecisive factor is the azimuthal difference between the pairedusers1. In the light of the different preference of the bothschemes in respect of the inter-user azimuthal difference, aharmonized multiuser transmission scheme can be proposed,whereby transmission mode can be flexibly switched betweenNOMA and MU-MIMO. Given a pair of users, e.g. user-i anduser-j, the favorable multiuser transmission mode for themcan be determined as follows.

1) Compute the azimuthal difference between user-i anduser-j, δi,j .

2) Compare δi,j with the null azimuth of the antenna arrayat the BS, θnull.

• If δi,j ≤ θnull/2, adopt NOMA scheme. In thiscase, the paired users cannot be well separatedin spatial domain, and this will definitely degradethe performance of MU-MIMO. But the azimuthalconcentration is prefered by NOMA scheme.

• If δi,j ≥ θnull, use MU-MIMO scheme. In thiscase, good separation in the spatial domain yieldsnegligible inter-user interference. Hence, comparedto NOMA, MU-MIMO can provide better perfor-mance.

• If θnull/2 < δi,j < θnull, evaluate the achievable per-formance metrics of both NOMA and MU-MIMOand thereby make the final decision for transmissionmode. The performance metric can be weightedsum of SINR or throughput of the co-scheduledusers2. Essentially, this case corresponds to the

1The CQI gap between the paired users is assumed to be sufficiently largefor NOMA transmission herein.

2In fact, for the popular proportional fairness (PF) scheduling, the perfor-mance metric is a weighted sum of user’s throughput.

region between the two red parallel lines (a solid anda dashed) in Fig. 2, and the SINR cures of the bothschemes have intersection points. Which scheme isbetter depends on the target performance metric.Thus, it is indispensable for the BS to compare theachievable performance of the both schemes.

Clearly, the proposed scheme provides a feasible criteria fordynamic switching between NOMA and MU-MIMO, wherebyfor each potential user pair, a better choice can always beguaranteed. Consequently, it can provide a better performancethan either the pure NOMA or the pure MU-MIMO schemes.

IV. CONCLUSIONS

In this paper, from the perspective of azimuthal differencebetween the co-scheduled users, the performance of NOMAand MU-MIMO were investigated in detail. Moreover, basedon the different preference of the both schemes in respect ofthe inter-user azimuthal difference, a harmonized multiusermultiplexing framework was proposed. In other words, afeasible criteria for dynamic switching between NOMA andMU-MIMO was provided. Its effectiveness was verified bytheoretical analysis.

Moreover, it should be noticed that even though the beam-forming was restricted only in azimuthal dimension in thispaper, it can be directly extended to the elevention domain,especially when 2-dimension antenna arrays are equipped atBS’s, i.e. full-dimension MIMO (FD-MIMO) or 3-dimensionMIMO (3D-MIMO) systems. Additionally, more general MU-MIMO schemes beyond ZF will be explored in the futurework.

REFERENCES

[1] T. Yoo and A. Goldsmith, “On the optimality of multiantenna broadcastscheduling using zero-forcing beamforming,” Selected Areas in Commu-nications, IEEE Journal on, vol. 24, no. 3, pp. 528–541, March 2006.

[2] V. Stankovic and M. Haardt, “Generalized design of multi-user mimoprecoding matrices,” Wireless Communications, IEEE Transactions on,vol. 7, no. 3, pp. 953–961, March 2008.

[3] X. Xia, S. Fang, G. Wu, and S. Li, “Joint user pairing and precodingin mu-mimo broadcast channel with limited feedback,” CommunicationsLetters, IEEE, vol. 14, no. 11, pp. 1032–1034, November 2010.

[4] M.-R. Hojeij, J. Farah, C. Nour, and C. Douillard, “Resource allocation indownlink non-orthogonal multiple access (noma) for future radio access,”in Vehicular Technology Conference (VTC Spring), 2015 IEEE 81st, May2015, pp. 1–6.

[5] K. Saito, A. Benjebbour, Y. Kishiyama, Y. Okumura, and T. Nakamura,“Performance and design of sic receiver for downlink noma with open-loop su-mimo,” in Communication Workshop (ICCW), 2015 IEEE Inter-national Conference on, June 2015, pp. 1161–1165.

[6] C. Yan, A. Harada, A. Benjebbour, Y. Lan, A. Li, and H. Jiang, “Receiverdesign for downlink non-orthogonal multiple access (noma),” in VehicularTechnology Conference (VTC Spring), 2015 IEEE 81st, May 2015, pp.1–6.

[7] M. Costa, “Writing on dirty paper (corresp.),” vol. 29, no. 3, pp. 439–441,1983.

[8] H. Weingarten, Y. Steinberg, and S. Shamai, “The capacity region of theGaussian MIMO broadcast channel,” in Information Theory, 2004. ISIT2004. Proceedings. International Symposium on, 2004.

[9] 3GPP, “New SI proposal: study on downlink multiuser superpositiontransmission for LTE,” 3rd Generation Partnership Project (3GPP), RP150496, March 2015.

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Wei Xi obtained M.S. and Ph.D. in communicationand information system from School of Informationand Communication Engineering, Beijing Universityof Posts and Telecommunications (BUPT), Beijing,China in 2007 and 2010, respectively.

He worked as a researcher in DOCOMO BeijingLaboratories, Beijing, China from 2011 to 2015.Now, he is with Fujitsu Research and DevelopmentCenter, Beijing, China.

Dr. Xi’s research interests mainly focus on sig-nal processing and radio resource management in

wireless communications, e.g. OFDM/OFDMA, MIMO, NOMA. Now, heis engaged in the research work towards 3GPP standardization and keytechnologies of 5G wireless communication.

Hua Zhou obtained M.S. and Ph.D. in communication and informationsystem from School of Information and Communication Engineering, BeijingUniversity of Posts and Telecommunications (BUPT), Beijing, China in 2001and 2004, respectively.

He worked as a researcher in Bell Labs shortly after getting his Ph.D., andthen joined Fujitsu Research and Development Center, Beijing, China. Sincethen, Dr. Zhou has been deeply involved in IEEE 802.16e/16m standardiza-tion, and 3GPP LTE/LTE-Advanced/LTE-AdvancedPro release 10/11/12/13standardization. And currently he is working towards standardization of 5Gwireless communication.

Dr. Zhou’s research interests mainly focus on a variety of physicallayer technologies in wireless communications, such as MIMO, NOMA, andOFDM/OFDMA.

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