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 on 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 University of Bristol - Explore Bristol Research General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/user-guides/explore-bristol-research/ebr-terms/

EVALUATION OF THE CAPACITY OF MULTIPLE-ACCESS MIMO SCHEMES WITH FEEDBACK IN A SMALL OUTDOOR CELL Matthew Webb, Mythri Mythri Hunukumbure Hunukumbure, Mark Beach, Andrew Nix , Mark Beach, Andrew Nix Matthew Webb, IEE Conference on 3G and Beyond IEE Conference on 3G and Beyond th November 2005 London, 7 th November 2005 London, 7 University of Bristol University of Bristol Centre for Communications Research Centre for Communications Research

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 1 antennas Tx 2 9 7 8 • 20 λ separation 10 6 24 3 • Atop 30m-high building 4 5 overlooking city centre 11 23 • 8 RX antennas 16 15 • UCA,8 monopoles 22 17 12 21 14 • λ /2 radial spacing 13 20 • 24 positions, each 20.7s 19 18 • 2x512 snapshots • 128 frequencies in 20MHz centred on 1.92GHz

Algorithms – – Nash equilibrium Nash equilibrium Algorithms • Waterfilling – Nash Equilibrium – non-cooperative game − R H 1 / 2 • 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

Algorithms – – Diagonalization Diagonalization Algorithms • AP has n T antennas, j th receiver has n Rj antennas • j th receiver weights with R j , BS uses T j to communicate with it ∑ = + + y R H T s R H T s w † † j j j j j j j i i j ≠ i j • Block diagonalization chooses T j to satisfy ] [ ] [ = R H T T T 0 0 Λ 0 0 † L L L − + j j L j j j L 1 2 1 1 1 • and R j to maximize end-to-end channel gain • Successive-diagonalization chooses T j to satisfy ] [ ] [ = R H T T T 0 0 Λ X X † L L L − j j L j j 1 2 1 1 • Uses identity for R j , so is non-iterative – but order matters

‘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 * and is RX’d by filtering with T j • User j TX’s with R j T ( ) T ∗ = T T • i . e . R † H T T H R j j j j j j • Limits on number of antennas and independent streams: L ∑ j ≥ ≥ n N n N and T j R j = j 1

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 All users 4x4, all equal SNR - TOTAL capacity 26 2 users 24 3 users 10% Outage TOTAL Capacity (bps/Hz) 4 users 22 20 18 16 14 12 10 8 6 0 5 10 15 20 SNR (dB) • 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 TOTAL system capacity. 4-RX throughout. 28 Nash equilibrium, all users 4x4, SNR=20dB per user 1 5 Tx 26 4 TX 3 TX 0.8 10% Outage TOTAL Capacity (bps/Hz) 2 TX 24 1 TX 0.6 22 0.4 20 0.2 18 16 0 6 5 14 Users 4 12 3 2 10 2 3 4 5 6 Number of Users 1 2 3 4 Streams • 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

Diagonalization schemes – – comparison comparison Diagonalization schemes All users 4x4, TOTAL capacity 35 2 users (2,2): BD 3 users (1,1,1): BD 30 3 users (1,1,2): BD 10% Outage TOTAL capacity (bps/Hz) 4 users (1,1,1,1): BD Nash 2 users (2,2): SD 25 3 users (1,1,1): SD eq. 3 users (1,1,2): SD range 20 4 users (1,1,1,1): SD 15 10 5 0 0 5 10 15 20 SNR (dB) • 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 – – stream allocation stream allocation Block diagonalization All 4 stream allocations. 4 RX antennas. TOTAL capacity. 32 1,1,1,1 2,1,1 30 2,2 10% Outage TOTAL capacity (bps/Hz) 3,1 28 26 24 22 20 18 16 1 2 3 4 TX Antennas • 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- -diagonalization diagonalization - - ordering ordering Successive (1,1,2 or 2,1,1) INDIV. USER capacity. All users 4x4 14 1,1,2 First (1 stream) 1,1,2 Second (1 stream) 10% INDIV. USER outage capacity (bps/Hz) 12 1,1,2 Third (2 streams) 2 s 2 s tream eam us us er er 2,1,1 First (2 streams) 2,1,1 Second (1 stream) 10 2,1,1 Third (1 streams) 1,2,1 First (1 stream) 8 1,2,1 Second (2 streams) 1,2,1 Third (1 stream) 6 4 2 0 0 5 10 15 20 SNR (dB) • 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.

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