arX

iv:1

611.

0880

5v1

[cs.

IT]

27 N

ov 2

016

W. Ahmad, G. Alyami, and I. N. Kostanic, “Multiuser separation and performance analysis of millimeter wave channels withlinear precoding,”acceptedin IEEE International Conference on Communication, Networks and Satellite (COMNETSAT)

(IEEE COMNETSAT 2016), Surabaya, Indonesia, Dec. 2016, pp.66-70.

Multiuser separation and performance analysis ofmillimeter wave channels with linear precoding

Waqas Ahmad∗, Geamel Alyami†, Ivica Kostanic†∗Huawei Technologies, Pakistan{waqas.ahmad1}@huawei.com

†Wireless Center of Excellence (WiCE) - Florida Institute ofTechnology, USA{galyami2007}@my.fit.edu

Abstract—In the conventional multiuser MIMO systems, userselection and scheduling has previously been used as an effectiveway to increase the sum rate performance of the system. However,the recent concepts of the massive MIMO systems (at centimeterwavelength frequencies) have shown that with higher spatialresolution of antenna arrays different users in the dense scenarioscan be spatially separated. This in turn significantly reduces thesignal processing efforts required for multiuser selection algo-rithms. On the other hand, recent measurements at millimeterwave frequencies show that multipath components only arrivefrom few angular directions leading to high spatial correlationbetween the paths and co-located users. This paper focus atthe investigation of spatial separation among the users at themillimeter wave frequencies with fully digital linear zero-forcingtransmit precoding considering various channel propagationparameters. Our analysis results convincingly give a proofthatmultiuser selection algorithms are still important for mil limeterwave communication systems. Results also show that increasednumber of antenna elements does not give a major benefit tosum rate improvements as compared to the selection of correctnumber of users to be selected/scheduled.

Keywords – mmWave channel model, Multipath clusters,large scale multiuser MIMO, user separation

I. I NTRODUCTION

Wireless communications at millimeter wave (mmwave)frequencies is one of the major proposals for fifth generationof mobile telephony. The major benefits coupled with mmwavefrequencies is the large unused band (30-300 GHz) whereUltra Wide Band (UWB) channel setups could easily berealized at different center frequencies. Additionally, highercarrier frequencies also allow design of compact antennaarrays with large number of antenna elements which increasethe directional resolution of the system. Both of the abovementioned features allow multi-gigabyte data rate communi-cations at wireless links.Very recently, realistic channel sounding campaign [1] at 2.4GHz band focused at the spatial separation of multiple usersin a densely populated scenario. Measurements were takenwith a circular shaped, dual polarized array with large numberof antenna elements at the base station (BS). Results in [1]concluded that under the considered massive antenna setupat the BS, users in the cell can indeed be separated. This isquite intuitive as the dual antenna polarization and circulararray geometry capture the Multi-Path Components (MPCs)from distinct Directions Of Arrivals (DOA) which are spatially

uncorrelated. These facts have been verified in [2] for cen-timeter wavelength frequencies. At the mmwave frequencies,measurement results in [3], [4] show that MPCs arrive at thereceiver from very few distinct directions known as spatiallobes. Hence, the users located very close to each other willalmost see the same channel which may lead to higher inter-user correlation. Therefore, at mmwaves the topic of inter-userchannel correlation is more interesting and needs thoroughinvestigations. It is important to understand the impact ofhighdirectional and bandwidth resolution at the spatial separationamong users. At the mmwave 60 GHz frequency band, authorsin [5] have discussed the mutual orthogonality between theusers as a function of inter user distance and the number of co-located users in an open square scenario. In another work [6],spatial separation of users has been discussed as a functionof users probability to be in Line of Sight (LOS) to the BS.Results have shown that user separation is difficult under thescenarios where the LOS probability is high.From system design perspective, it is well known that transmitprecoding and effects of different SNR levels also play avital role in defining the spatial separation among users. Fromauthors point of view, inter user orthogonality and the channelpropagation parameters that define the degree of separationamong the users yet needs to be extensively analyzed fordifferent transmit precoding schemes and SNR levels. In thispaper, we have provided a deep insight of the sum rate analysisby changing the channel propagation parameters e.g, numberof multipath clusters, number of BS antennas and BS antennasseparation for indoor (shopping mall) scenario. We have usedlinear zero forcing (ZF) precoder for the analysis of multi-usersystem. Although linear digital precoding is not yet realizedto be used at mmwave frequencies due to increased hardwarecomplexity in context of required number of RF chains.Therefore, hybrid (analog+digital) precoding techniqueshavereceived more attention among the wireless communicationsresearch community. These hybrid techniques have shownslight performance losses as compared to fully digital linearprocodings. Therefore, fully digital ZF precoding just give us aperformance upper bound and help to understand the behaviorof the channel in a simplistic manner. Additionally, we haveused the model in [4] for the number of multipath clusters inthe mmwave propagation channel. We have investigated thesum rate improvements if the count of multipath cluster is

more than the number defined in model [4] itself.

II. CHANNEL MODEL

Consider a downlink multiuser MIMO system withnBS

antennas mounted at the base station (BS) of heighthBS andnU be the number of mobile users (MU) each of heighthU. Allthe users are closely located in the XY plane of the Cartesiancoordinate system inside a ring of radiusR as shown in Fig. 1.The position of users in the ring follows uniform randomdistribution. The heights of the BS and MU correspond toz-axis of the coordinate system. LetNcl be the number ofmultipath clusters withNray subpaths in each cluster. Forsimplicity, we assume single bounce multipath clusters. Let θA

i,l

andθDi,l be azimuth angle of arrival and departure oflth ray of

theith cluster respectively. SimilarlyφAi,l andφD

i,l correspond tothe elevation angles of arrival and departure respectively. LetK be the number of antennas at each MU, then the channelmatrix Hi(τ) ∈ C

nBS×K of a single user MIMO link can bewritten as

Hi (τ) =∑Ncl

i=1

∑Nray

l=1αi,l

√

L (ri,l)ar

(

φAi,l, θ

Ai,l

)

×aHt

(

φDi,l, θ

Di,l

)

h (τ − τi,l) +HLOS (τ)

(1)where,

• HLOS (τ) is the channel impulse response matrix of theLOS component arriving at delayτ .

• at and ar are the transmit and receive antenna arraysteering vectors.

• h (τ − τi,l) is the impulse response at the delay tapτi,lof the lth ray of theith cluster.

• αi,l andL (ri,l) are the complex channel gain and atten-uation loss of thelth ray of theith cluster respectively.

Since each subpath may have different scattering conditions sothe subpath phases can be considered as independent identicaldistribution. We have assumed constant distance between theantenna array and all the scatterers which belong to the samecluster to simplify the model. Letri be the propagationdistance between BS and MU via the central ray of theith

cluster. The propagation distance of subpaths associated to theith cluster is geometrically computed as

ri,l = ri+√

(

hBS − hU + ri sin θDi,l

)2

+(

d− ri cos θDi,l cosφDi,l

)2 ·

(2)For the attenuation of the link, we have used the same modelproposed in [7]

L (ri,l) = −20 log10

(

4π

λ

)

− 10n

[

1− b+bc

λf0

]

log10 (ri,l)−Xσ

(3)

wheren is the path loss exponent,b is a system parameter,f0is the fixed reference frequency (the centroid of all frequenciesrepresented by the path loss model). Finally,Xσ is the shadowfading term with zero mean and varianceσ2. Parameters values

X

XX

X

XXXX

Cluster 1

Cluster 2

ring in which MS

are located

Fig. 1. Channel model and experiment description

of Eq. 3 for different indoor propagation scenarios have beendefined in [7].Millimeter wave frequencies are known for their quasi opticalnature [8], and similar like light multipath components couldbe blocked. Blockage modeling of LOS component is offundamental interest as it caries the highest energy. Therefore,channel model for LOS component is defined as

HLOS (τ) = ILOS (d)√KnBSe

jη√

L (d)×ar

(

φAi,l, θ

Ai,l

)

aHt

(

φDi,l, θ

Di,l

)

h (τ − τi,l)

(4)where,η ∼ U (0, 2π) corresponds to the phase of the LOScomponent andILOS (d) is a random variable indicating if aLOS link is present between the transmitter and receiver ata distanced. Regarding the probabilityp of a LOS link, weused the same model defined in [7], [9] for the evaluationof considered shopping mall scenario. Some other selectedstatistical features and model distributions are summarizedin Table. I whereby other detailed description are availablein [10].We have placed different number of users in a ring of radiusR. Inside the ring, location of the users and their antennaorientations changes following a uniform random distributionin each channel snapshot. All users are assumed to be static fora particular channel realization, hence the channel stays timeinvariant. Multiuser MIMO channel matrix is now defined as

H = [H1 H2 · · ·HnU] ∈ C

nBS×nUK (5)

III. SUM RATE CALCULATION WITH ZERO FORCING

PRECODER

Considering equal power allocation per user, the zero-forcing precoding matrix is defined asW = H

+, whereH+

is the pseudo inverse ofH andwi ∈ W . The post processingSNR of theith user is defined as

SNRZFi =

P

N0LU

[

(HHH)−1

]

i,i

(6)

WhereLU corresponds to the number of selected users. Theoverall sum rateRZF of the selected users using zero-forcing

TABLE ITABLE OF STATISTICAL DISTRIBUTIONS AND THEIR PARAMETERS ALONG

WITH SOME OTHER MISCELLANEOUS PARAMETERS

Parameter Distribution Mean & St. dev.Azi. AOA per clusteri Laplacian θA

i∼ U [0, 2π] & 5◦

Azi. AOD per clusteri Laplacian θDi

∼ U [−π

2, π

2] & 5◦

Ele. AOA per clusteri Laplacian φAi

∼ U [−π

2, π

2] & 5◦

Ele. AOD per clusteri Laplacian φDi

∼ U [−π

2, π

2] & 5◦

# Clusters(Ncl) max {Poisson(Λ), 1} ,Λ = 1.9 [4]# Rays per clusteri U [1, 30] [11]Miscellaneous parametersParameter ValueScenario Indoor Shopping MallCarrier frequency 73 GHznBS (5× 8,20× 8) UPA →(40,160) antnU 2,5,10Antenna spacingda 0.5λ, 4λ, 6λ# antennas per userK 1hBS 7 mhMU 1.68 mAverage BS-MU distance 20 mRadius of the ring(R) 5 mBS orientation ArbitraryMS orientation Arbitrary

beamforming is defined in [12] and it can be written as

RZF =

K∑

i=1

log2(

SNRZFi

)

· (7)

IV. SIMULATION RESULTS

In the following, we evaluate the impact of three channelparameters: number of clusters, number of BS antennas in theuniform patch array (UPA) and inter element distance (IED)of BS antennas on sum rate ofn users at different SNR setups.In Fig. 2, we compare the impact of multipath clusters at lowSNR i.e. at 0 dB. It can be seen that the sum rate increasesby increasing the number of clusters for ten and five users butincrease in sum rate is negligible for two users. It can also beobserved that increase in the sum rate is more significant for10 users. Fig. 2 also shows that even if the number of clustersare increased, the sum rate of ten users setup is still lowerthan two users setup at low SNR regime.

At high SNR dynamics i.e. at 20 dB, Fig. 3 shows that thesum rate of ten users is significantly higher as compared totwo and five users. This is due to higher multiplexing gains athigh SNR regime. The analysis of channel condition numberσmin

σmax

from Fig. 4 shows that the CDF of two users is morecloser to′1′ which shows singular value spread is lower for 2users as compared to 5 and 10 users where it is high enough.It indicates that the channel correlation among users increasesby increasing the number of users so the spatial separationamong the users becomes increasingly difficult. Hence, thechannel hardeningassumption is increasingly violated withincreasing number of users in the ring. Channel hardeningrefers to the phenomenon where the off-diagonal terms ofthe H

HH matrix become increasingly weaker compared to

the diagonal terms as the size of the channel gain matrixH

increases [13].

−100 −80 −60 −40 −20 0 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum Rate (Bits/Sec/Hz)

CD

F

N

cl(Model based)

Ncl=4

Ncl=6

Ncl=10

10 Users

2 Users

5 Users

Fig. 2. Sum rate by changing the number of clusters (SNR= 0 dB,da = 0.5λ,nBS = 20× 8 UPA)

−20 −10 0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum Rate (Bits/Sec/Hz)

CD

F

N

cl(Model based)

Ncl=4

Ncl=6

Ncl=10

5 Users

2 Users

10 Users

Fig. 3. Sum rate by changing the number of clusters (SNR= 20 dB, da =0.5λ, nBS = 20× 8 UPA)

It is generally assumed that with large number of antenna ele-ments at the BS increases the channel hardening factor so thatthe low complexity match filtering precoder i.e.W = H

H

becomes optimal. Mathematically, it means thatWH is anidentity matrix. However, high correlation in Fig. 4 showsthat W = H

H may not result in identity matrix that makesmatch filtering sub-optimal. So, one can use other linear butrelatively more computationally complex precoding schemessuch as zero forcing (ZF) or minimum mean square error(MMSE) techniques in conjunction with multiuser selection.User selection techniques are well understood to be an effec-tive way to reduce the computational complexity of the system.While optimal user selection is a NP-hard [14] problem andrequires exhaustive search over all possible user combinations.Therefore, sub-optimal greedy incremental and decrementalselection strategies are widely used.The linear gain in channel capacity by increasing the number

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

σmin

/σmax

CD

F

nU=2

nU=5

nU=10

Fig. 4. Channel condition number by changing the number of users,Ncl−Model based,da = 0.5λ, nBS = 20× 8 UPA

of antennas depends upon the SNR scaling and the number ofscattering points in the channel. Increased number of scatterersgive rise to the higher number of multipath components.Therefore, leading towards multipath diversity which in turnresults in increased channel capacity. In general, at lowerfrequencies (< 6 GHz), the famous 3GPP channel modelse.g. WINNER/SCM [15] assume that resolvable multipathcomponents are composed of 20 sub-paths so that central limittheorem holds and the amplitude fading of the resolvable pathsfollows the Rayleigh distribution. If the number of multipathcomponents are such high then off-course the high spatialresolution associated with large number of antenna elementsin the array may explore more scattering points in the channeland hence may increase the channel capacity. However, on theother hand mmWave channels could be sparse due to higherpropagation and penetration losses from the different objectsin the channel. Therefore, it is quite likely that under certainscenarios the number of antenna elements in the MIMO arrayis larger than the number of resolvable multipath components.In such scenarios, further increase in the antenna elementsmaynot result in linear gain in the channel capacity and in the worstcase it could be bottlenecked. Fig. 5 shows the CDF analysisof the sum rate by changing the number of BS antennas from5×8 UPA (40 antennas) to20×8 UPA (160 antennas) for two,five and ten users at 0 dB SNR. The sum rate of two users ishigher than five and ten users because the multiplexing gainis negligible at 0 dB. However, the change in sum rate issignificant for ten users as compared to five and two usersby increasing the BS antennas due to exploration of moremultipath for more users. The results from Fig. 6 at 20 dBSNR shows that the sum rate of ten users is higher than fiveand two users. At high SNR, increasing BS antennas givesrise to multiplexing gain.The separation between the antenna elements explains thechannel correlation properties and the exploration of thenumber of scatterers. When antenna elements are very close

−140 −120 −100 −80 −60 −40 −20 0 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum Rate (Bits/Sec/Hz)

CD

F

nU=2, n

BS=5×8 UPA

nU=2, n

BS=20×8 UPA

nU=5, n

BS=5×8 UPA

nU=5, n

BS=20×8 UPA

nU=10, n

BS=5×8 UPA

nU=10, n

BS=20×8 UPA

Fig. 5. Sum rate by changing the number of BS antennasNcl− Modelbased, SNR=0 dB,da = 0.5λ

−60 −40 −20 0 20 40 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum Rate (Bits/Sec/Hz)

CD

F

nU=2, n

BS=5×8 UPA

nU=2, n

BS=20×8 UPA

nU=5, n

BS=5×8 UPA

nU=5, n

BS=20×8 UPA

nU=10, n

BS=5×8 UPA

nU=10, n

BS=20×8 UPA

Fig. 6. Sum rate by changing the number of BS antennasNcl− Modelbased, SNR=20 dB,da = 0.5λ

to each other, the channel correlation will be very high andthe interference among the users will increase. From Fig. 7,we can see that increasing inter element distance (IED) atBS results more change in sum rate for ten users because ofreduction in channel correlation. However, from Fig. 7 at 0dB SNR, one can see that the even by increasing the IED thesum rate of ten users is significantly lower than five and twousers because the diversity gain is high in case of two andfive users as compared to ten users. From Fig. 8 at 20 dBSNR, by changingda = 0.5λ to da = 6λ gives minor gain insum rate foe two and five users setups. Whereas, the weakereigen mode are scaled up by high SNR so the sum rate often users significantly increase by increasing the IED due tomultiplexing gain. The gain in sum rate by increasing the IEDis limited up to the extent where the number of scatterers canbe fully exploited and further increase in IED of BS antennascould not provide the gain in sum rate of mmWave multiuser

−100 −80 −60 −40 −20 0 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum Rate (Bits/Sec/Hz)

CD

F

da=0.5λ

da=2λ

da=6λ

10 Users

5 Users

2 Users

Fig. 7. Sum rate by changing the BS antenna spacingNcl− Model based,SNR=0 dB,da = 0.5λ, nBS = 20× 8 UPA

−20 −10 0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sum Rate (Bits/Sec/Hz)

CD

F

da=0.5λ

da=2λ

da=6λ

5 Users

2 Users

10 Users

Fig. 8. Sum rate by changing the BS antenna spacingNcl− Model based,SNR=20 dB,da = 0.5λ, nBS = 20× 8 UPA

system.

V. CONCLUSION AND FUTURE WORK

In this paper, we have conducted several experiments, wherewe have increased the number of multipath clusters in thechannel and additionally at the base station antenna arraywe increased inter-antenna element distance and the numberof antenna elements. Our experiments used the statisticalchannel models derived from the realistic state of the artmmwave channel models. Results show that the mmwavefrequencies channels are correlated in space and it is hardto spatially separate users in the dense cellular networks.Incontrast to centimeter wavelength frequencies, the results ofour experiments show that the channel hardening assumptiondoes not remain valid at the mmwave channels. We haveprovided evidence in terms of channel conditions and sumrate performance. Hence, for the sum rate maximization we

recommend to use multiusers selection and scheduling algo-rithms.

REFERENCES

[1] J. Flordelis, X. Gao, G. Dahman, F. Rusek, O. Edfors, and F. Tufvesson,“Spatial separation of closely-spaced users in measured massive multi-user mimo channels,” inIEEE International Conference on Communi-cations (ICC), June 2015, pp. 1441–1446.

[2] C. Schneider, N. Iqbal, and R. S. Thomae, “Impact of angular spreadand number of multipath clusters on mimo channels,” inIEEE 26thAnnual International Symposium on Personal, Indoor, and Mobile RadioCommunications (PIMRC), Aug 2015, pp. 512–516.

[3] T. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar, K. Wang,G. Wong,J. Schulz, M. Samimi, and F. Gutierrez, “Millimeter wave mobilecommunications for 5g cellular: It will work!”Access, IEEE, vol. 1,pp. 335–349, 2013.

[4] M. R. Akdeniz, Y. Liu, M. K. Samimi, S. Sun, S. Rangan, T. S.Rappaport, and E. Erkip, “Millimeter wave channel modelingandcellular capacity evaluation,”IEEE Journal on Selected Areas in Com-munications, vol. 32, no. 6, pp. 1164–1179, June 2014.

[5] S. L. H. Nguyen, K. Haneda, J. Jarvelainen, A. Karttunen,and J. Putko-nen, “On the mutual orthogonality of millimeter-wave massive mimochannels,” inIEEE 81st Vehicular Technology Conference (VTC Spring),May 2015, pp. 1–5.

[6] G. Alyami and I. N. Kostanic, “On the spatial separation of multi-user channels using 73 GHz statistical channel models,” inIEEEInternational Conference on Communication, Networks and Satellite(IEEE COMNETSAT 2016), Surabaya, Indonesia, Dec. 2016.

[7] ”5G Channel Model for bands up to 100 GHz”,http://www.5gworkshops.com/5GCM.html/.

[8] A. Maltsev, R. Maslennikov, A. Sevastyanov, A. Lomayev,and A. Kho-ryaev, “Statistical channel model for 60 ghz wlan systems inconferenceroom environment,” inProceedings of the Fourth European Conferenceon Antennas and Propagation, April 2010, pp. 1–5.

[9] K. Haneda, L. Tian, Y. Zheng, H. Asplund, J. Li, Y. Wang, D.Steer,C. Li, T. Balercia, S. Lee, Y. Kim, A. Ghosh, T. A. Thomas,T. Nakamura, Y. Kakishima, T. Imai, H. C. Papadopoulos, T. S.Rappaport, G. R. M. Jr., M. K. Samimi, S. Sun, O. H. Koymen, S. Hur,J. Park, J. C. Zhang, E. Mellios, A. F. Molisch, S. S. Ghassamzadah, andA. Ghosh, “5g 3gpp-like channel models for outdoor urban microcellularand macrocellular environments,”CoRR, vol. abs/1602.07533, 2016.[Online]. Available: http://arxiv.org/abs/1602.07533

[10] S. Buzzi and C. D’Andrea, “On clustered statistical mimo millimeterwave channel simulation,”CoRR, vol. abs/1604.00648, 2016. [Online].Available: http://arxiv.org/abs/1604.00648

[11] M. K. Samimi and T. S. Rappaport, “Statistical channel model withmulti-frequency and arbitrary antenna beamwidth for millimeter-waveoutdoor communications,” in2015 IEEE Globecom Workshops (GCWkshps), Dec 2015, pp. 1–7.

[12] G. Caire and S. Shamai, “On the achievable throughput ofa multiantennagaussian broadcast channel,”Information Theory, IEEE Transactions on,vol. 49, no. 7, pp. 1691–1706, July 2003.

[13] T. L. Narasimhan and A. Chockalingam, “Channel hardening-exploitingmessage passing (chemp) receiver in large-scale mimo systems,” IEEEJournal of Selected Topics in Signal Processing, vol. 8, no. 5, pp. 847–860, Oct 2014.

[14] A. Civril and M. Magdon-Ismail, “On selecting a maximum volumesub-matrix of a matrix and related problems,”Theor. Comput. Sci., vol.410, no. 47-49, pp. 4801–4811, 2009.

[15] “WINNER II interim channel models,,” Tech. Rep. IST-4-027756WINNER D1.1.1. [Online]. Available: https://www.ist-winner.org