Coordinated Beamforming Strategies in TDD Mode

IMANET+ Technical Seminar, Aug 30th 2013

Petri Komulainen

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•  Petri Komulainen, “Coordinated Multi-Antenna Techniques for Cellular Networks – Pilot Signaling and Decentralized Optimization in TDD Mode,” doctoral thesis, 2013.

•  Petri Komulainen, Antti Tölli, and Markku Juntti, “Effective CSI Signaling and Decentralized Beam Coordination in TDD Multi-Cell MIMO Systems,” IEEE Transactions on Signal Processing, May 2013.

•  Petri Komulainen, Antti Tölli, and Markku Juntti, “Low Overhead Effective CSI Signaling for Beam Coordination in TDD Multi-Cell MIMO Systems,” IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Sydney, Australia, September 2012.

•  Petri Komulainen, Antti Tölli, and Markku Juntti, “Decentralized beam coordination via sum rate maximization in TDD multi-cell MIMO systems,” IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Toronto, Canada, September 2011.

Our publications

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Content

•  Assumptions & scope •  Weighted sum rate (WSR) maximization •  Pilot signaling concepts •  Decentralized strategies •  Extensions

•  Reducing complexity •  Reducing pilot overhead •  CSIT uncertainty

•  Summary

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System assumptions

•  MIMO interfering broadcast channel (IBC) •  Downlink •  Multi-antenna base stations (BS) and user terminals (UT) •  Mutually interfering adjacent cells •  Static BS association for UTs

•  Linear TX-RX processing •  TDD mode

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•  Beam coordination –  Scheduling (user and beam selection) –  TX – RX design –  Weighted sum rate maximization

•  Effective CSI acquisition –  Pilot signaling –  Backhaul signaling

•  Support for independent user scheduling by BSs

Scope

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System model

TX beamformers data

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channel

•  Received signal of terminal k of cell b

inter-cell interference

WSR max via WSMSE min

•  WSR maximization is equivalent to minimizing

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MSE-weight matrix

•  Variables: Bb , Ab,k and Wb,k for all b,k •  Not jointly convex •  Convex (separately) in variables Bb , Ab,k and Wb,k

RX

MSE-matrix:

Alternating optimization with cell-specific loops

•  Monotonic convergence to a local optimum guaranteed •  From overloaded initialization to beam selection (scheduling)

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Cell-specific optimization loop

Cell-specific cost function (cell b)

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effect from other cells effect to other cells

own WSR cost (MIMO broadcast channel problem)

Information needed from other cells

•  Inter-cell-interference-plus-noise covariance in RX

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•  Weighted effective channels in TX

Cell-specific optimization at BS

•  Optimize all own (cell-specific) variables •  Assume other cells fixed •  For different cells cost functions are not separable •  Monotonic convergence of network-wide

problem lost if done in parallel, but on the average adaptation becomes faster

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•  Traditionally: Antenna-specific pilot (training) signals –  Spatial pilot precoder is an

identity matrix

•  Orthogonal pilot resources needed

•  In single-cell case, one sounding round suffices for convergence –  Centralized solution by BS

Pilot signaling: Channel sounding (CS)

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•  Method for CSI acquisition in TDD mode –  Assume channel reciprocity

Whitening and channel sounding (CS)

•  Whitening matrix

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•  Uplink sounding response i.e. observed channel

•  Interference covariance signaled implicitly via CS •  CS signals may be observed by all BSs

sounding precoder

Signal processing decomposition with CS

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optimized by BS

observed by BS determined by UT

Hb,k

Ab,kHb,k Qb,kBb,k

TX precoder Channel

Ab,k

Whitening Final RX

Receiver

Sounded channel

•  BB beams obtained by turning receive filters into UL precoders

•  Effective channel: concatenation of channel and receiver

•  To neighboring cell indicates signal space that is busy

•  Effective channel may have lower rank than channel itself

Pilot signaling: Busy bursts (BB)

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•  Method for effective CSI acquisition in TDD mode –  Assume channel reciprocity

Proposed decentralized strategies

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•  Strategy B –  Optimization one cell at a time –  Separate CS and BB signaling –  Monotonic convergence

•  Strategy C –  Cells optimizing in parallel –  CS and low-rate backhaul –  No monotonic convergence –  Faster diagonal matrix

provided by BS i

weighted effective channel

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Strategy C

Phase 1: Uplink sounding

Phase 2: Data TX and backhaul

Optimize TX beamformers

Numerical results: 2-cell setup

•  Two 4-antenna BSs, five 2-antenna UTs per BS •  Cell separation defined as a1/a2

•  Uncorrelated Rayleigh (quasistatic) fading

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Numerical results: convergence

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•  Convergence w.r.t. over-the-air signaling rounds (frames)

•  Parallel processing is fastest on the average 2 4 6 8 10 12 14 16 18 20

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Frame

Sum

rate

per

BS

[bits

/Hz/

s]

M = 4, N = 2, K = 5, SNR = 25dB, cell sep. = 0dB

Network-wide TX-RXOne cell at a timeCells in parallelNon-cooperative

Numerical results: SNR

•  Performance after convergence

•  Almost linear sum rate growth

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5 10 15 20 25 305

10

15

20

SNR [dB]

Sum

rate

per

BS

[bits

/Hz/

s]

M = 4, N = 2, K = 5, cell sep. = 0dB

Network-wide TX-RXOne cell at a timeCells in parallelAntenna-pwr constraintsNon-cooperative

Complexity reduction concept: Stream-specific RX processing

•  RX beams of a UT are treated separately •  For sounding, UT just normalizes its receiver vectors •  BS treats each sounding beam response as the

channel of a single-antenna UT

•  Savings at UT •  Decomposition of interference covariance avoided •  Rotation of the CS matrix not needed (SVD avoided)

•  Savings at BS •  Receiver matrices become stream-specific scalar

variables

•  Even single-cell case: Multiple CS rounds needed

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Pilot overhead reduction concept : Rank-1 sounding

•  Single pilot beam per UT (determined by UT) •  Consequence: max one DL data beam per UT •  Assumption: UT knows DL channel

•  Common pilot present •  To initialize sounding before transmission begins

•  BSs observe just effective vector channels •  True number of UT antennas hidden from the

network

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Numerical results: Convergence

•  Two 2-antenna UTs per cell

•  Decoupling RXs is suboptimal

•  Rank-1 sounding (C1a) is suboptimal, if cannot use all degrees of freedom

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2 4 6 8 10 12 14 16 18 2011

12

13

14

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Frame

Avg

. sum

rate

per

cel

l [bi

ts/H

z/s]

M = 4, N = 3, K = 2, SNR = 20dB, cell sep. = 3dB

Strategy AStrategy CStrategy C1aStrategy C - decoupled RXs

CSIT uncertainty

•  Possible channel uncertainty sources •  Limited sounding power •  Estimation noise and interference •  Duplexing or feedback delay •  Calibration mismatch

•  Modification of the optimization problem •  Centralized design only addressed so far

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CSIT uncertainty

•  Channel uncertainty model

•  Signal propagating via unknown part of the channel constitutes additional interference

•  Estimate and error uncorrelated

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Channel Known part of the channel (MMSE

estimate)

Unknown part of the channel

(estimation error)

CSIT uncertainty: Effect on signal covariance in RX

•  Additional signal covariance in UT (b,k) caused by BS i

•  Affects precoder and receiver optimization steps •  Merely a diagonal loading

•  Alternating optimization still applicable

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Numerical results: CSIT uncertainty level

•  Sum rate vs. relative sounding energy

•  Taking uncertainty into account pays off

•  CSI accuracy critical

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-5 0 5 10 15 20 256

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ΔS [dB]

Sum

rate

per

BS

[bits

/Hz/

s]

M = 4, N = 2, K = 4, cell sep. = 12dB, SNR = 15dB

CB: Orig. alg.CB: Noisy alg.

inf

Numerical results: SNR

•  When CSIT accuracy grows with SNR, sum rate scales almost linearly with SNR

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5 10 15 20 25 302

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SNR [dB]

Sum

rate

per

BS

[bits

/Hz/

s]

M = 4, N = 2, K = 4, cell sep. = 3dB

CB: ΔS=0dBCB: ΔS=6dBCB: ΔS=∞

Numerical results: Number of UTs

•  When sounding power shared between UTs => adding UTs reduces CSI accuracy

•  Orthogonal access (OA): separate resources for the cells (doubled SNR, hallved bandwidth)

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1 2 3 4 5 6 7 8 9 106

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Number of users per cell (K)

Sum

rate

per

BS

[bits

/Hz/

s]

M = 4, N = 2, cell sep. = 3dB, SNR = 15dB

CB: ΔS=6dBCB: ΔS=∞

OA: ΔS=6dBOA: ΔS=∞

•  Decentralized strategies for WSR maximization –  Spatial scheduling implicitly carried out –  BS-specific decision making

•  Effective CSI signaling concepts for TDD mode –  Over-the-air pilot signaling –  Scalar weighting information exchange via backhaul

•  Extensions –  Concept for reducing UT signal processing complexity –  Concept for reducing pilot overhead –  CSIT uncertainty addressed

Summary

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MIMO-BC (broadcast channel) •  Søren Skovgaard Christensen, Rajiv Agarwal, Elisabeth de Carvalho, and John M. Cioffi,

”Weighted Sum-Rate Maximization using Weighted MMSE for MIMO-BC Beamforming Design,” IEEE Trans. Wireless Commun., Dec 2008.

MIMO-IFC (interference channel) •  David A. Schmidt, Changxin Shi, Randall A. Berry, Michael L. Honig, and Wolfgang

Utschick, ”Minimum Mean Squared Error Interference Alignment,” Asilomar 2009. •  Francesco Negro, Shakti Prasad Shenoy, Irfan Ghauri, Dirk T.M. Slock, “Weighted sum

rate maximization in the MIMO interference channel,” PIMRC 2010.

MIMO-IBC (interfering broadcast channel) •  Qingjiang Shi, Meisam Razaviyayn, Zhi-Quan Luo, and Chen He, ”An Iteratively Weighted

MMSE Approach to Distributed Sum-Utility Maximization for a MIMO Interfering Broadcast Channel,” IEEE Trans. Signal Processing, September 2011.

References for WSR via WSMSE

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