on minimizing the mean squared error in the presence of

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CAPITALS

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On Minimizing the Mean Squared Error In the Presence Of Channel State Information Errors

Gabor Fodor Ericsson Research Royal Institute of Technology (Dept. of Automatic Control)

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Minimizing the MSE with CSI Errors | KTH Seminar | 2018-04-25 |

Mimo evolution

MU-MIMO SU-MIMO

Massive MU-MIMO Massive SU-MIMO Massive multi-layer

MU-MIMO

Multi-layer MU-MIMO

Mor

e an

tenn

as

LTE: Long Term Evolution SU MIMO: Single User Multiple Input Multiple Output MU MIMO: Multiuser Multiple Input Multiple Output

G.Fodor,N.Rajatheva,W.Zirwas,L.Thiele,M.Kurras,K.Guo,A.Tolli,J.H.Sorensen,E.deCarvalho,"AnOverviewofMassiveMIMOTechnologyComponentsinMETIS",IEEECommunicaLonsMagazine,Vol.55,Issue6,pp.155-161,June2017.

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Related Works (Pilot-to-Data Power Ratio)

›  T. Kim and J. G. Andrews, “Optimal Pilot-to-Data Power Ratio for MIMO-OFDM,” IEEE Globecom, St. Louis, MO, USA, Dec. 2005, pp. 1481–1485.

›  T. Marzetta, “How Much Training is Needed for Multiuser MIMO ?” IEEE Asilomar Conference on Signals, Systems and Computers (ACSSC) ,pp. 359–363, Jun. 2006.

›  C. P. Sukumar and R. M. M. Eltawil, “Joint Power Loading of Data and Pilots in OFDM Using Imperfect Channel State Information at the Transmitter,” in IEEE Global Communications Conference, Nov. 2008, pp. 1–5.

›  N. Jindal and A. Lozano, “A Unified Treatment of Optimum Pilot Overhead in Multipath Fading Channels,” IEEE Trans. on Communications, vol. 58, no. 10, pp. 2939–2948, October 2010.

›  K. Min, M. Jung, T. Kim, Y. Kim, J. Lee, and S. Choi, “Pilot Power Ratio for Uplink Sum-Rate Maximization in Zero-Forcing Based MU-MIMO Systems with Large Number of Antennas,” in IEEE Vehicular Technology Conference (VTC-Fall), Sep. 2013, pp. 1–5.

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Related Works (MMSE Receiver)

›  M. Wrulich, C. Mehlfuhrer, and M. Rupp, “Managing the interference structure of MIMO HSDPA: A multi-user interference aware MMSE receiver with moderate complexity,” IEEE Transactions on Wireless Communications, vol. 9, no. 4, pp. 1536–1276, April 2010.

›  J. T. Wang, “Joint MMSE equalization and power control for MIMO system under multi-user interference,”

IEEE Communications Letters, vol. 16, no. 1, pp. 54–56, January 2012. ›  B. Shim, J. W. Choi, and I. Kang, “Towards the performance of ML and the complexity of MMSE: A hybrid approach for multiuser detection,”

IEEE Transactions on Wireless Communications, vol. 11, no. 7, pp. 2508–2519, July 2012.

›  E. Eraslan, B. Daneshrad, and C.-Y. Lou, “Performance indicator for MIMO MMSE receivers in the presence of channel estimation error,” IEEE Wireless Communications Letters, vol. 2, no. 2, pp. 211–214, April 2013.

›  Y. Dong and L. Qiu, “Spectral efficiency of massive MIMO systems with low-resolution ADCs and MMSE receiver,” IEEE Communications Letters, vol. 21, no. 8, pp. 1771–1774, August 2017.

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Related Works (MMSE Receiver)

›  M. R. McKay, I. B. Collings, and A. M. Tulino, “Achievable sum rate of MIMO MMSE receivers: A general analytic framework,” IEEE Transactions on Information Theory, vol. 56, no. 1, pp. 396 – 410, January 2010.

›  Y. Wu and S. Verdu, “MMSE dimension,” IEEE Transactions on Information Theory, vol. 57, no. 8, pp. 4857 – 4879, August 2011.

›  C. Artigue and P. Loubaton, “On the precoder design of flat fading MIMO systems equipped with MMSE receivers: A large-system approach,” IEEE Transactions on Information Theory, vol. 57, no. 7, pp. 4138 – 4155, July 2011.

›  Y. Jiang, M. K. Varanasi, and J. Li, “Performance analysis of ZF and MMSE equalizers for MIMO systems: An in-depth study of the high SNR regime,” IEEE Transactions on Information Theory, vol. 57, no. 4, pp. 2008–2026, March 2011.

›  B. Wang, Y. Chang, and D. Yang, “On the SINR in massive MIMO networks with MMSE receivers,” IEEE Communications Letters, vol. 18, no. 11, pp. 1979 – 1982, September 2014.

›  G. Han and J. Song, “Extensions of the I-MMSE relationship to Gaussian channels with feedback and memory,” IEEE Transactions on Information Theory, vol. 62, no. 10, pp. 5422 – 5445, October 2016.

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› Channel Estimation – Toy Model

› Channel Estimation and Receiver Design for Multiuser Systems

Outline

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Channeles)ma)onatthereceiverfromthereceivedsignal:

Channel Estimation – Toy Model

Tagged User

(path loss)

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LinearcombinaLonofGaussianvariables

arejointlyGaussian(mul$variatenormal)!andh h^

Channel Estimation – Toy Model

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›  DeterminingtheCondi)onalChannelDistribu)on

›  DeterminingtheMeanSquaredError(MSE)

›  DeterminingtheaverageMSEasafunc)onofthepilotanddatapower

1

2

3

Three Steps to determine the Mean Squared Error of the Received Data Symbols

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Multivariate Normal Distribution

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Recall:

Multivariate Normal Distribution

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What is the distribution of ?

›  ApplyingtheTheoremofMVGaussian[seee.g.Kay’93]:

›  ApplyingtheBayesianLinearModelof[seee.g.Kay’93]:

1

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Pilotpower

Datapower

”perfect”CSI

Minimumpilot

SNR1SNR2

Feasibleregionundersumpower

constraint

SNRtargetfordata

›  Intui)vetradeoffbetweenthepilotandthedatapowerwhensustainingagivenSNR(nointerference!):

The Pilot Power – Data Power Trade-off

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MSE – 20 un-correlated / correlated antennas

AgivenMSEoftheequalizeddatasymbolscanbereachedbydifferentpilotanddatapowerse\ng.

Uncorrelated Correlated

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› Channel Estimation – Toy Model

› Channel Estimation and Receiver Design for Multiuser Systems

Outline

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Pilot-Based Channel Estimation

Trade-offs:

Higherpilotpower

BeWerchanneles)mate

SNRdegrada)onfordata+increasedpilotcontamina)on

Morepilotsymbols

BeWerchanneles)mateLessaggressivepilotreuseMoreusersforMUmul)plexing

Lessdatasymbols

MU: Multi user SNR: Signal-to-Noise-Ratio

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MU MIMO Signal Model

ThenaïveGminimizestheMSEofthereceiveddatasymbolswhenperfectchanneles)ma)onisavailableatthereceiver.

Tagged User

Data signal model:

G.Fodor,P.DiMarco,M.Telek“OnMinimizingtheMSEinMulLpleAntennaSystemsinthePresenceofChannelStateInformaLonErrors”,IEEECommunicaLonsLebers,Vol.19,No.9,pp.1604-1607,September2015.

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Preliminaries I

Pilot signal model:

Estimated channel:

Pilot sequence:

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Preliminaries II

Data signal model:

MU MIMO Receiver at the BS:

N.Rajatheva,S.Suyama,W.Zirwas,L.Thiele,G.Fodor,A.Tölli,E.Carvalho,J.H.Sorensen,"MassiveMulLpleInputMulLpleOutput(MIMO)Systems",Chapter8in:A.Osseiran,J.F.Monserrat,P.Marsch,"5GMobileandWirelessCommunicaLonsTechnology",CambridgeUniversityPress,June2016.ISBN:9781107130098

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How to find the (true) MMSE Receiver ?

›  Tofindtheop=malreceiverinthepresenceofchanneles)ma)onerrors:

›  Step1:DeterminetheMSEofataggedUserasafunc)onofGinthecaseofperfectCSI

›  Step3:Determinethatminimizes

›  Step2:DeterminetheMSEofataggedUserasafunc)onofGandthees)matedchannel

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Results

› ClosedformexpressionfortheMMSEreceiverinthepresenceofCSIerrors

› ClosedformexpressionfortheMSEwhenusingthenaïveandtheMMSEreceiver

› Closedformexpressionsfortheop)mumpilot-to-datapowerra)owhenusingtheMMSEreceiver

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How to find the (true) MMSE Receiver ?

Elementsofproof: Quadra)cForm:

G.Fodor,P.DiMarcoandM.Telek,"OntheImpactofAntennaCorrelaLonandCSIErrorsonthePilot-to-DataPowerRaLo",IEEETransacLonsonCommunicaLons,Volume64,Issue6,pp.2622-2633,April2016.

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PL=50 dB

PL=45 dB PL=40 dB

PL=40 dB PL=45 dB

PL=50 dB MMSE

Naïve

Gain of using the (true) MMSE Detector

over Naïve ~8 dB

The optimal receiver yields significant gains over the whole CDF, including the 10 and 90 percentiles and for various levels of the path loss.

Sq.Error

G.Fodor,P.DiMarcoandM.Telek,"OntheImpactofAntennaCorrelaLonandCSIErrorsonthePilot-to-DataPowerRaLo",IEEETransacLonsonCommunicaLons,Volume64,Issue6,pp.2622-2633,April2016.

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Naïve

MMSE

Naïve

MMSE

Minimum value

Gain

The gain increases as the number of antennas increases.

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Naïve MMSE

Optimal MMSE

How does the Gain depend on the Number of Antennas ?

Gain increases

This plot shows the minimum MSE, that is the MSE that is achieved when using the optimal pilot power.

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Comparison With Perfect CSI

Nr=4

Nr=20

Nr=100

naive

opt

perfect

Data transmit power decreases

With large number of antennas, the MSE performance of the optimal receiver remains close to the perfect CSI performance, whereas the performance of the naïve receiver is far from the perfect CSI case. Therefore, with larger number of antennas, the importance of applying the optimal receiver increases.

Pilotpower[mW]

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50 100 150 200P mW

0.005

0.010

0.050

0.100

0.500

MSE

50 100 150 200P mW

2

3

4

5

6SE

MSE And SE With Comb Pilot Pattern

#antennas=10

#antennas=100

#antennas=10

#antennas=100

#antennas=500

#antennas=500

Gain due to optimal MMSE receiver (over naïve MMSE)

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› The gain of the optimal receiver increases with increasing number of antennas. In the massive MIMO domain, this gain can be up to 8-10 dB in terms of MSE;

› The true MMSE receiver well approximates the perfect channel estimation case, independently of the number of antennas (as opposed to the naïve receiver);

› With the true MMSE, the transmit power that minimizes the MSE, does not depend on the number of receive antennas (as opposed to the naïve receiver);

›  Impact of antenna spacing and angular spread on MSE decreases with increasing number of antennas.

Take Away

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› 3GPP Technical Report: Study on Elevation Beamforming and FD-MIMO for LTE

›  See also: -  36.873 Study on 3D Channel Model for LTE -  37.105 Active Antenna System BS Radio Transmission and Reception

› Full Dimension MIMO (FD-MIMO) ›  Greater number of antenna ports ›  Efficient MU MIMO Spatial Multiplexing ›  Robustness against CSI Impairments (e.g. intercell interference)

Full Dimension in 3GPP

on minimizing the mean squared error in the presence of

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