feedback in a small outdoor cell. In IEE 6th International Conference - - PDF document

Nix, AR., Webb, MW., Hunukumbure, RMM., & Beach, MA. (2005). Evaluation of the capacity of multiple-access MIMO schemes with feedback in a small outdoor cell. In IEE 6th International Conference

• n 3G and Beyond (pp. 19 - 23). Institution of Engineering and

Technology (IET). https://doi.org/10.1049/cp:20050186

Peer reviewed version Link to published version (if available): 10.1049/cp:20050186 Link to publication record in Explore Bristol Research PDF-document

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University of Bristol University of Bristol Centre for Communications Research Centre for Communications Research

Matthew Webb, Matthew Webb, Mythri Mythri Hunukumbure Hunukumbure, Mark Beach, Andrew Nix , Mark Beach, Andrew Nix

IEE Conference on 3G and Beyond IEE Conference on 3G and Beyond

London, 7 London, 7th

th November 2005

November 2005

EVALUATION OF THE CAPACITY OF MULTIPLE-ACCESS MIMO SCHEMES WITH FEEDBACK IN A SMALL OUTDOOR CELL

Introduction Introduction

• Use measured data from a highly-scattering environment to

explore effect of waterfilling and 2 other transmit beamforming algorithms (e.g. by feedback of weights from BS)

• Generalized waterfilling (Nash equilibrium)
• Zero-forcing at TX
• Successive zero-forcing at TX
• Examine how the algorithms could be used to provide

differential QoS

Measurement setup Measurement setup

• 4 TX antennas
• Two dual polarized 65º

BW UMTS panel antennas

• 20λ separation
• Atop 30m-high building
• verlooking city centre
• 8 RX antennas
• UCA,8 monopoles
• λ/2 radial spacing
• 24 positions, each 20.7s
• 2x512 snapshots
• 128 frequencies in

20MHz centred on 1.92GHz

1 11 10 9 17 16 15 14 13 12 20 19 18 24 23 22 21 3 4 5 6 7 8 2

Tx

Algorithms Algorithms – – Nash equilibrium Nash equilibrium

• Waterfilling – Nash Equilibrium – non-cooperative game
• Waterfill pre-whitened channel
• R is different from each user’s perspective
• One user waterfills their channel – affects all others
• So next user waterfills current channel etc…
• Each user tends not to deviate from this profile since it

would ultimately reduce their own capacity

• Requires knowledge of the current covariance for each

user – either locally or centrally H R

2 / 1 −

Algorithms Algorithms – – Diagonalization Diagonalization

• AP has nT antennas, jth receiver has nRj antennas
• jth receiver weights with Rj, BS uses Tj to communicate with it

∑

≠

+ + =

j i j i i j j j j j j j

w s T H R s T H R y

† †

• Block diagonalization chooses Tj to satisfy
• and Rj to maximize end-to-end channel gain

[ ] [

]

L j j j L j j

Λ T T T H R L L L

1 1 1 2 1 † + −

=

• Successive-diagonalization chooses Tj to satisfy
• Uses identity for Rj, so is non-iterative – but order matters

[ ] [

]

X X

j j L j j

L L L Λ T T T H R

1 1 2 1 † −

=

‘ ‘Transposing’ the algorithms Transposing’ the algorithms

• Instead of having one, large BS communicating with several,

smaller users, we will reverse the situation:

• Construct a ‘virtual’ BS by aggregating the users
• Actual BS appears as multiple users, separated by the

different channels from the users

• Calculate weights the same way, but transpose everything
• User j TX’s with Rj

* and is RX’d by filtering with Tj T

• i.e.
• Limits on number of antennas and independent streams:

( )

∗

=

j T j T j T j j j

R H T T H R†

∑

=

≥

L j j R

N n

1

and

j T

N n

j ≥

Assumptions etc. Assumptions etc.

• Normalize channels so each user is RX’d at a specified SNR
• Will use same positions for interferers throughout
• ‘Wanted’ user at position no. 24
• Interferers at positions 5, 6, 7, 8 and 9 (i.e. 2-6 users)
• 4TX and 4RX antennas (except where noted)
• Quasi-static channel at each frequency snapshot
• Measure 10% outage capacity

Nash equilibrium I Nash equilibrium I

5 10 15 20 6 8 10 12 14 16 18 20 22 24 26 SNR (dB) 10% Outage TOTAL Capacity (bps/Hz) All users 4x4, all equal SNR - TOTAL capacity 2 users 3 users 4 users

• 2-user system makes best use of higher SNR
• 4-user system yields higher capacity than 3-user system

Nash equilibrium II Nash equilibrium II

• Prefer to operate with a ‘few’ interferers if we must have >1
• With 2 users, can waterfill away from all interference by using only

2 streams each

• Abrupt change from 2 streams/user with 3 users to 1 stream/user

with 4 users – again allows waterfilling away from interference

2 3 4 5 6 10 12 14 16 18 20 22 24 26 28 Number of Users 10% Outage TOTAL Capacity (bps/Hz) TOTAL system capacity. 4-RX throughout. 5 Tx 4 TX 3 TX 2 TX 1 TX 2 3 4 5 6 1 2 3 4 0.2 0.4 0.6 0.8 1 Nash equilibrium, all users 4x4, SNR=20dB per user Streams Users

Diagonalization schemes Diagonalization schemes – – comparison comparison

5 10 15 20 5 10 15 20 25 30 35 SNR (dB) 10% Outage TOTAL capacity (bps/Hz) All users 4x4, TOTAL capacity 2 users (2,2): BD 3 users (1,1,1): BD 3 users (1,1,2): BD 4 users (1,1,1,1): BD 2 users (2,2): SD 3 users (1,1,1): SD 3 users (1,1,2): SD 4 users (1,1,1,1): SD

Nash eq. range

• Block-diagonalization up to 8.4bps/Hz better than Nash at 20dB
• Orthogonally multiplexes users – Nash equilibrium does not
• Gain over Nash small with 2 users – same stream distribution
• Successive-diagonalization much worse than either
• Due to residual interference without any attempt to remove it
• Better with fewer users at high SNR – less residual interference

Block diagonalization Block diagonalization – – stream allocation stream allocation

1 2 3 4 16 18 20 22 24 26 28 30 32 TX Antennas 10% Outage TOTAL capacity (bps/Hz) All 4 stream allocations. 4 RX antennas. TOTAL capacity. 1,1,1,1 2,1,1 2,2 3,1

• Distributing same number of streams among more users can give

substantial improvements in total capacity

• Waterfilling is able to choose best substreams across whole

system rather than just one user – hence (1,1,1,1) is best

• Results in proportionally lower per-user capacity
• Allows for diff-QoS if user is prepared to pay for lower overall rate

Successive Successive-

• diagonalization

diagonalization -

• ordering
• rdering
• 2-stream user’s capacity varies dramatically depending on ordering
• Cannot find 2 good subchannels when avoiding two 1-stream users
• 1-stream users have useful capacities only when others are orthogonal
• Not shown, but (2,1,1) better than (1,1,2) by only 2.8bps/Hz
• Masks much wider per-user variations despite same stream nos.

5 10 15 20 2 4 6 8 10 12 14 SNR (dB) 10% INDIV. USER outage capacity (bps/Hz) (1,1,2 or 2,1,1) INDIV. USER capacity. All users 4x4 1,1,2 First (1 stream) 1,1,2 Second (1 stream) 1,1,2 Third (2 streams) 2,1,1 First (2 streams) 2,1,1 Second (1 stream) 2,1,1 Third (1 streams) 1,2,1 First (1 stream) 1,2,1 Second (2 streams) 1,2,1 Third (1 stream)

2 s 2 s tream eam us us er er

Conclusions Conclusions

• If seeking maximum system capacity use
• Block-diagonalization with most users, fewest streams/user
• Both Nash and block-diag. are much better than successive
• Nash equilibrium capacity can rise with more users, up to a point
• Distribution of available substreams among users is important
• Exploit multi-user diversity to max. block-diag capacity
• Ordering very important in successive diagonalization
• Diagonalizations could offer differential QoS
• (Does not apply to Nash equilibrium – approx. equal per-user)
• Nash and block-diag are iterative, but successive-diag is not
• Nash equilibrium converges faster and more reliably
• Successive-diag could be useful in rapidly changing channels

Acknowledgements Acknowledgements