User Assisted Cooperative Relaying in Beamspace Massive MIMO NOMA Based Systems for Millimeter Wave Communications

Jaipreet Kaur＊,Maninder Lal Singh

Department of Electronics Technology,Guru Nanak Dev University,Amritsar-143005,India

Abstract: A novel scheme ‘user assisted cooperative relaying in beamspace massive multiple input multiple output (M-MIMO)non-orthogonal multiple access (NOMA) system' has been proposed to improve coverage area,spectrum and energy efficiency for millimeter wave (mmWave) communications.A downlink system for M users,where base station (BS) is equipped with beamforming lens antenna structure having NRF radio frequency(RF) chains,has been considered.A dynamic cluster of users is formed within a beam and the intermediate users (in that cluster) between beam source and destination (user) act as relaying stations.By the use of successive interference cancellation (SIC) technique of NOMA within a cluster,the relaying stations relay the symbols with improved power to the destination.For maximizing achievable sum rate,transmit precoding and dynamic power allocation for both intra and inter beam power optimization are implemented.Simulations for performance evaluation are carried out to validate that the proposed system outperforms the conventional beamspace M-MIMO NOMA system for mmWave communications in terms of spectrum and energy efficiency.

Keywords: cooperative relaying system(CRS); millimeter wave (mmWave); massive multiple input multiple output (M-MIMO);non-orthogonal multiple access (NOMA);power allocation; sum rate

I.INTRODUCTION

Globalization demands such a fast pace connectivity today which could increase the present communication level to a large extent.One such advancement is the fifth generation (5G).The 5G mobile and wireless communication systems constitute integration of leading technological advancements,such as massive multiple input multiple output (M-MIMO),cooperative relaying system (CRS),millimeter wave (mmWave) and non-orthogonal multiple access (NOMA).In order to satisfy the exploding capacity demand of 5G [1],a productive exploitation of massive MIMO in mmWave communications needs to be carried out.

In the prevailing beamspace MIMO system,each base station (BS) antenna utilizes one reserved radio frequency (RF) chain to support single user at similar allocation of time-frequency resources.However,in a beamspace M-MIMO system,large number of antennas are deployed at the BS,and the required number of RF chains are increased in proportion to the number of antennas at the BS.This results in higher energy consumption and greater complexity in transceiver circuitry of the system,which is a problem in itself.To tackle this problem,the number of RF chains are reduced by using lens antenna array [2,3]which incorporates the sparse structure of mmWave channel [4].But it also decreases number of supported users in the system.So,the remedy to this problem lies in the integration of beamspace M-MIMO with NOMA,which helps in serving multiple users within a beam simultaneously [2,5].In NOMA,the users are differentiated by different power levels at identical allocation of time-frequency resources [6].It employs intra beam superposition coding at transmitter end and successive interference cancellation (SIC) at receiver end to eliminate multiuser interferences [5].Moreover,mmWave communication assists implementation of NOMA,as it has directional features of making channels highly correlated for users [4].

The mmWave is otherwise suitable for indoor short distance communications.But in order to enhance coverage area and system performance,physical length between destination and the BS can be covered by engaging intermediate users as cooperative relays for destination within that beam [6].The intermediate users in NOMA due to SIC act as cooperative relays for distant user as they beforehand have,the information of distant user's messages,thus it is known as user assisted CRS [7].Whereas in relay assisted CRS,a committed relay is engaged to support distant users.

A novel scheme ‘user assisted cooperative relaying in beamspace massive multiple input multiple output(M-MIMO) non-orthogonal multiple access (NOMA) system'has been proposed to improve coverage area,spectrum and energy efficiency for millimeter wave(mmWave) communications.

1.1 Related work

In existing analog beamforming systems,low channel rank of mmWave channel is attained by discrete lens array with continuous aperture phased MIMO,or phase shifting networks [1,8].The sparsity of beamspace channel matrix can be exploited by using beam selection techniques.The earlier beam selection schemes depended upon magnitude maximization [1],where stronger beams were chosen for each user by overlooking multiuser interferences.The present paper explores the prevailing interference aware (IA) beam selection technique [2,3],that supresses multiuser interferences.Enhancement of spectrum efficiency in MIMO NOMA for two users was proved in[9]whereas for multiple users was investigated in [10].A multicell beamspace M-MIMO NOMA downlink system is tackled in [11].Another work of multi-cluster beamforming MIMO NOMA system for downlink [3,9]implemented intra beam power allocation with optimization for two users and inter beam power allocation without optimization.

The simple amplify and forward MIMO cooperative wireless networks was implemented in [12].NOMA based cooperative relay assisted system was first projected in [7]and later on,NOMA based decode and forward relaying system was studied with Rayleigh fading channel [7,13],Nakagami-m fading channel[14]and Rician fading channel [6,15].Relay assisted CRS-NOMA with multiple antennas has been considered in [16].One of the works[17]compared the performance of near users working as relays at half duplex or full duplex for far users.

1.2 Contributions and outcomes

The present paper explores the novel technique ‘user assisted cooperative relaying beamspace M-MIMO NOMA in mmWave communications',that combines the benefits of cooperative relaying,beamspace M-MIMO and NOMA together.Also,dynamic user clustering problem has been investigated from perspective of each user's fairness.In this system,the number of users is grouped dynamically into clusters,where number of clusters is equal to number of reduced beams.A single beamforming channel vector (beam) is shared by all users within a cluster.The message intended for each user in a particular cluster is divided into number of symbols equal to number of intermediate users and is sent to destination via these intermediate users,known as relaying with multiple hops.In proposed system,a dynamic power allocation is implemented by optimizing of both intra and inter beam power allocation coefficients.

The rest of the paper is structured as follows.The detailed system model of beamspace M-MIMO NOMA and analysis of achievable sum rate of system are given in section II.Section III explains proposed CRS in existing beamspace M-MIMO NOMA.Section IV presents simulation results.Finally,section V concludes with a summary.

II.SYSTEM MODEL

A single cell downlink mmWave beamspace M-MIMO system employingNantennas at the BS and servingMusers simultaneously has been considered in this work.In conventional beamspace M-MIMO system,as illustrated in figure 1(a),the required number of RF chainsNRFis equal to the number of antenna elementsN,servingMusers such that(M≤NRF=N).

The Saleh-Valenzuela channel model [2,8]has been adopted for mmWave communications in this work.The mmWave spatial channel matrixH= [h1,h2,…,hM]with dimensions(N×M),whose vectors between themth user(m= 1,2,… ,M) and the BS can be represented byhm(N×1)[1,2].

a(θ) is (N×1) array steering vector forNelement uniform linear array and also denotes the directional sine vector at BS and is given by represents line-of-sight

Fig.1.System models of M-MIMO architecture: (a) Conventional beamspace M-MIMO [2]; (b) Beamspace M-MIMO using lens antenna array [2]; (c) Beamspace M-MIMO NOMA [2]; (d) Proposed system

whereθis spatial angle given bysinφ,φis physical angle covering one sided spatial horizon satisfyingλis signal wavelength anddis spacing between antennas,satisfyingat mmWave frequencies [1].The amplitudes of NLoS componentsare quite feebler than the amplitude of LoS componentmaking mmWave channel sparse.

2.1 Beam selection

The conventional spatial channel matrixHin figure 1(a) can be transformed into beamspace channel matrixby employing discrete lens antenna array at the BS as in figure 1(b),which reduces RF chains (NRF＜N).The lens antenna array can be realized mathematically by spatial discrete Fourier transform matrixUwith size (N×N),covering whole space withNarray steering vectors as given by

In (4),the discrete Fourier transformation of channelHis represented byto capture the sparsity of mmWave channel [2].

The influential scatters are very scarce in beamspace channel vectorfor mmWave frequencies [4].The dominant beams are selected fromto reduce the number of RF chains [1,18].

The present work adopts IA beam selection scheme [2].Letbe the strongest beam index within a vectorfor themth user [3].There is a strong probability that some users are assigned the same strongest beam.TheMusers are then classified into two categories as per their strongest beam index.One is non-interference users (NIUs),i.e.where user's does not share the same strongest beam index of any other user.Another is interference users (IUs),i.e.where user's strongest beam index is the same as that of other users [3].A dimension reduced beamspace channel matrixis thus obtained by selecting only those row beam vectors having strongest beam index.For NIUs,the row beam vectors are unique and for every set of IUs havingUusers,a common row beam vector is shared among a set and these users are positioned in decreasing order of theirTheis further reduced to equivalent channel matrixof size (NRF×NRF),by considering all NIUs columns as such and the maxima column from each IU set.The transmit precoding matrix(NRF×NRF) fromcan be given as

The(NM×) is obtained fromW~ by substituting the selected maxima column from a set of IUs,to all elements of that IU set.Theis the dimension reduced precoding matrix of size (NRF×M),which is obtained by normalizing

2.2 Beamspace M-MIMO NOMA

As discussed in previous section,Musers are allocated to theNRFbeams according to the channel matrixLetCnrepresents the set of users served bynth beam,forn=[1,2,…,NRF],such thatCi∩Cj=0∀i≠jandas illustrated in figure 1(c).Cnmay comprise a single user or a set of users,depending upon the beam having an NIU or a set ofUIUs respectively.The dimension reduced beamspace channel vector between BS andmth useratuth position withinnth beam is denoted by(NRF×1).The power allocation coef ficients formth useratuth position withinnth beam is symbolized aspu,n.The dimension reduced precoding vectorwrm,is same for alluusers withinnth beam and is denoted bywn(NRF×1).

The order of channel gains and power allocation coefficients of users [5,19]for eachCnhaving a set of IUs are given by (8) and (9)respectively

The received signalru n,atuth user innth beam can be given by [2]wherezi j,is transmitted signal forith user injth beam andvu n,～ 0,Nc(σ2) is AWGN.

The inter beam interference can be restrained by designed transmit precoding vectorThe intra beam interference is nullified by SIC detection used in NOMA i.e.uth user innth beam can suppress the interference from alliusers,for alli＞u.So,third term gets cancelled in (11) and the remaining terms form the received signal.

The signal to interference and noise ratio(SINR)δu,natuth user innth beam,according to (11) can be expressed as

where

The realizable rate atuth user innth beamRu n,is given in (14) and the achievable sum rateRsumfor beamspace M-MIMO NOMA system is summation ofRu n,for all users,giv-en in (15).

To raiseRsum,joint power optimization is implemented for reduction of intra and inter beam interferences in an objective functionRsumwith the following constraints

whereC1constraint ensures positive power allocation to each user,C2constraint limits the summation of power allocation of all users to maximum powerPttransmitted by the BS andC3is the data rate constraint for each user,which bounds to minimum data rateRmin.By substituting value ofδu n,from (12) into (14),the constraintC3can be given as

The nonlinear constraint in (17) has been transformed into linear constraint in (18).

whereη= 2Rmin-1 andω=ησ2.

The minimum mean squared error (MMSE)detection is used,whose mean square error(MSE)eu,ncan be formulated as

wherecu,nis the channel equalization coefficient

The optimal value of channel equalization coefficient is represented byand can be found by differentiatingeu,nw.r.t.cu,nto find its minima [2].

The optimal solution of mean square error(MSE)[2]is obtained by substitutingfrom (20) intocu,nin (19) and is given by

TheRu,nin (14) is proved to be equal to( - l og2eu,n) [2]and by using proposition 1 in [2],Rsum(16) can be re-expressed as

where

Indth iteration ofRsum,solution offu n,is obtained by (23),(21) and solution ofeu n,is from (19) usingpu n,of ( 1)d- th iteration.The iterative updating ofpu n,with bounding con-straints will rise or retainRsumin (22).

III.PROPOSED COOPERATIVE RELAYING BEAMSPACE M-MIMO NOMA

The proposed cooperative relaying beamspace M-MIMO NOMA system is implemented in the beams having more than one user as shown in figure 1(d).The representation of one of the beams is illustrated in figure 2.Transmitted powerpbof each beam is equal to algebraic sum of optimized powersof all users within that beam.Message to be sent to destinationDis divided intousymbols[z1,z2,… ,zu],whereuis the number of relaying stations between sourceBS/R0and destinationD,and is received inutime slots.

As shown in TableI,during first time slot,source BS/R0broadcast symbols [z1,z2,…,zu]to first relayR1and destinationD.The first relayR1removes symbolz1from the received signals and acquire the remaining set of symbols [z2,z3…,zu]using SIC.The destinationDacquires the symbolz1as it has highest power allocation coefficienta10and treating remaining set of symbols as noise.The same scenario develops in each time slot until remaining symbols [z2,z3,…,zu]are acquired by the destinationD.The subscript in the power allocation coef ficient represents the symbol index and the superscript represents the time slot,i.e.aux-1power allocation coef ficient is foruth symbol atxth time slot,such thatin each time slot.

Inxth time slot,the following three steps are performed:

Step 1.RelayRx-1broadcasts the set of symbolsto next relayRxand destinationD.Superposition of the set of broadcasted symbols by relayRx-1at time slotxis given by

Fig.2.System model of proposed CRS-NOMA for a beam with u users.

TableI.Symbols received at various relays at different time slots.

Step 2.RelayRxremoves symbolzxfrom thereceived signal and cquire the remaining set of symbolsusing SIC.

Step 3.DestinationDacquires the symbolzxas it has highest power allocation coefficient,treating remaining set of symbols as noise.

The received signalsrRx-1RxandrRx-1Dat relay and destination inxth time slot are expressed asxu1,2,,.

At theuth time slot the received signal at the destination is given as

The received SINR atDforzxsymbol inxth time slot using (24) is obtained as

Atuth time slot the received SINR atDis obtained using (25) as

whereρis transmit SNR.For ef ficient decoding of symbols [zx+1,…,zu]at relay and symbolzxat destination,the rates of these symbols should be lesser than the rate given by Shannon formula.The achievable rateCzxatxth time slot forzxsymbol is given as

The overall achievable rate forzxinxtime slotsis given by (31)

The achievable sum rateCprofor the destination inutime slots is given by

The achievable sum rate of the first relay/destination within the beam is given by (22),whereas for remaining relays/destinations which undergo CRS,achievable sum rate is given by their respectiveCpro(32).

IV.SIMULATION RESULTS

A distinctive downlink system where 256 antennas are equipped at the BS,servingMusers simultaneously,is considered.The total transmitted powerPtis assumed to be 32 mW(15 dBm) and minimum data rateRminis 10-2for each user [2].The considered assumptions for spatial channelhmof each user are: 1)An LoS component and two NLoS components; 2)andforl=1,2 that satisfies uniform distribution withinTheλi(i∈ {R0D,R0Rx,RxD}) denotes millimeter power channel gain of source - destination,source -xth relay andxth relay - destination.Theλi(i∈ {Rx-1Rx,Rx-1D}) are obtained by finding the means of respective adjacent power channel gains.

In the simulations,we compare and analyse three typical mmWave M-MIMO schemes in terms of spectrum ef ficiency and energy ef ficiency,

1.“Fully digital M-MIMO”,where each antenna is connected to one RF chain with(M≤NRF=N),represented by dot curves.

2.“Beamspace M-MIMO NOMA” with(M≤NRF＜N) which integrates beamspace M-MIMO with NOMA,represented by dash curves.

3.“Proposed CRS beamspace M-MIMO NOMA” with (M≤NRF＜N),that integrates beamspace M-MIMO with NOMA and cooperative relaying system,represented by solid curves.

The performance of “Beamspace M-MIMO NOMA” [2],is taken as benchmark for the comparison.Figure 3 represents the spectrum efficiency against transmit SNR of above mentioned three schemes,where number of users taken areM= 32.This figure demonstrates improvement of the spectrum efficiency,as compared with the existing scheme [2]of about 1dB SNR gain and the proposed system outperforms at the higher values of SNR.

Fig.3.Spectrum efficiency v/s SNR,with number of users M= 32.

Fig.4.Energy efficiency v/s SNR,with number of users M= 32.

Fig.5.Spectrum efficiency v/s number of users M,where SNR=20 dB.

Fig.6.Energy efficiency v/s number of users M,where SNR = 20 dB.

The energy efficiency∈is expressed as the ratio of achievable sum rateRsumand total power consumption.wherePtis maximum transmitted power,PRFis power consumption for each RF chain,PSWis power consumed by beam switch andPBBis baseband power consumption.The assumed values areP= 32 mW,PRF= 300 mW,PSW= 5 mW andPBB= 200 mW [20].

The energy efficiency of the proposed system forM= 32users is represented in figure 4.From this figure,it can be deduced that the energy efficiency of the proposed system is relatively higher than the conventional system by about 1dB SNR gain.Moreover,the energy efficiency at the higher SNR values shows asignificant rise from the conventional system.

TableII.A comparative study between the proposed work and relevant latest research.

The performance comparison of spectrum efficiency against the number of users is shown in figure 5,where SNR is fixed to 20 dB.From this figure,it depicts that with increase in the number of usersM,the performance gap between existing and proposed system becomes wider and after approximately 32 users,the gap remains constant of about 2 bps/Hz/W.Because the probability of selecting same beam for different users is increased with increase in the number of users.

V.CONCLUSIONS

In this paper ‘cooperative relaying system of beamspace M-MIMO NOMA' scheme has been proposed which presented the achievable sum rate of the system forMusers in mmWave communications.It becomes clear from the simulation results that the proposed system provides a significant enhancement in signal performance in terms of spectrum and energy efficiency as compared to existing system.This system could be employed for enhancing the coverage of the mmWave channel by improving the throughput of the system simultaneously.