mimo multiuser schemes for downlink transmissions: theoretic bounds and practical techniques...

MIMO MULTIUSER schemes for downlink transmissions: theoretic bounds and practical techniques

Federico Boccardi (joint work with Howard Huang)

Bell Laboratories

Paris, 29/3/2007

2 All Rights Reserved © Alcatel-Lucent 2006

Outline

- An introduction to SDMA techniques.

- The capacity region of the MIMO-BC and the optimal DPC scheme.

- Suboptimal schemes, the single receive antenna case.

- Extension to multiple receive antennas.

- Imperfect channel state information at the transmitter side.


Focus of the presentation

Downlink of a narrowband packet data system

Why downlink? Uplink of a cellular network can be handled using multiantenna multiuser detection techniques.

Why narrowband only? Most principles can be extended to multiband (OFDM) systems.

Why packet data? Next-generation systems will be predominately packet (not circuit) data.

Transmitter

processing

User K data stream

User 1 data stream

User 1

User K

Base station Terminals


SINGLE USER vs MULTIUSER MIMO

Time-duplexed

transmit

diversity

Transmission

technique

Time-duplexed

spatial

multiplexingHigher

peak rate

Primary benefit

SDMA:

Sectorization or

Precoding

Higher

system

throughput

Improved

link

performance


SDMA options

Sectorization

Use physical reflectors behind each

antenna.

Performance limited by intersector

interference.

Precoding

The signal is

weighted/perturbed/successive

encoded at the transmit side.

Linear precoders (beamformers)

create beams that focus energy for

each user by weighting the phase

and amplitude of the antennas.

Performance limited by interbeam

interference.

Beam 1

Beam 2

1u

2u User 2

User 1

1u

2u User 2

User 1


System model

A narrowband MIMO downlink with M antennas at the transmitter and K

receivers with N antennas each can be modelled as MIMO Gaussian broadcast

channel.

The received signal for the kth user is given by

Under a sum-power constraint (SPC) the transmit signal is subject to the

following constraint

Under a per-antenna-power constraint (PAPC) the transmit signal is subject to

the following constraint

)1,0(~, CNhmkkkk nxHy

MmPxE mm ,,1,]|[| 2

PtrE H )]([ xx


Dirty paper coding (DPC) [C83] is a known-interference cancellation technique for reducing interference in the scalar BC.

Using coherent channel knowledge ( hk ,k = 1,…,K), users are sequentially encoded; for

example, user 1 is encoded first, then user 2, up to user K. A given user experiences interference only from users encoded after it.

DPC can be extended to the MIMO BC by incorporating beamforming.

The MIMO BC capacity region is equivalent to the MIMO dirty paper coding (DPC) region [WSS06].

Under perfect channel state information at both transmitter and receiver side, TDMA is suboptimal.

The capacity of the MIMO-GBC and the Dirty Paper Coding (DPC) region


Suboptimal linear and non-linear precoding schemes

Linear precoding

General expression:

where S is the subset of users for a given channel realization.

Non linear precoding

- Vector Precoding (VP): A data-dependent perturbation vector is used after the linear

precoding stage

- Tomlinson-Harashima and QR decomposition: Part of the interference is eliminated

by using a QR decomposition of the channel; the other part is eliminate by using the

Tomlinson-Harashima precoder for each subchannel. For the k-th streams:

||)(,)( SMCSS GuGx

))(( λuG

x

S

2]['

||)')((||minarg||

λuGλλ

SSjΖ

2]['

||'||minarg,

kkkjΖ

kkkk sdusdux


Linear precoding

Sectorization via fixed beamforming

Fixed beams + correlated antennas.

Create virtual sectors using fixed beams.

Turn on all beams simultaneously for increased throughput.

Turn on beams individually for increased range and coverage. [SH04]

User dependent beamforming

User-specific beams + uncorrelated antennas.

Transmitter uses CSI to form simultaneous beams to multiple users. Beams are designed so that, under ideal CSI knowledge, users receive no

interbeam interference.

Can be shown to achieve optimum asymptotic capacity scaling. [YG06]


ZF linear precoding with user selection

For a fixed subset of users the general ZF with per-antenna power constraint problem can be formulated as

This is a convex constrained optimization problem and in general can be solved by using an interior point method. For the particular case of sum-power constraint the optimum power allocation is given by the so-called waterfilling power allocation.

An external optimization has to be used for the choice of the transmitting user subset

The optimal solution requires a brute force search over all possible sets S of users. A practical greedy algorithm can be used. [YG06, BH06]

MmPv

Skv

vSR

mk

k

k

S

kk

Skvk

,,1,|g| and

||,,1,0tosubject

)1log(max)(

|S|

1k

2mk

||

1||,...,1,

)(max

,,1SR

KS

beamforming coefficients

power allocation

scheduling coefficients


SDMA for single antenna receivers – full CSI

ZF with greedy user selection gives good performance with low complexity! [BTC06]

cmp. between linear precoders linear vs. non-linear precoders


Linear precoding with multiple receive antennas – basic idea

In single-user MIMO, the number of independent streams is optimally found by using the SVD of channel. The power is optimally allocated to the different streams by using the waterfilling scheme.

In Multiuser MIMO, the different streams can be allocated to a given user or allocated between different users. We want to design a technique that optimally allocates the streams in order to maximize the sum-rate [BH07].

A B C Etc…


Block diagonalization based algorithms

The BD algorithm [SSH04,VVH03] is a generalization of the ZF precoder for receivers with multiple antennas. A precoding matrix is used in order to block diagonalize the channel.

Some improvements are proposed in [S06,W05,P04].

The problem of block diagonalization is that the choice of the active eigenmodes belonging to different users can not be optimized.

The multiuser eigenmode transmission (MET) [BH07] technique tries to solve this problem.

-The following equivalent channel is considered

where is a submatrix of whose columns correspond to the selected

eigenmodes of user k, according to the SVD

- is |Ek| x M, where Ek is the set of selected eigenmodes.

-How do we choose the set of users and eigenmodes?

kkHkk E HWH )(

)( kHk EW kW

Hkkkk VΣWH

kH


Choosing users and eigenmodes for MET

For a given transmission interval, we need to determine the set T of users and eigenmodes to allocate so that the weigheted sum rate performance metric R(T) is maximized:

Given M transmit antennas and K users, each with N antennas (assume N<M), there are up to KN eigenmodes to choose from, but the base can only provide M. Finding the optimum set requires a brute-force search over all possible allocation of 1,2,…,M eigenmodes. The following greedy algorithm is proposed (based on [DS05]) algorithm works in a greedy manner and chooses up to M modes for transmission.

1. For a given set of eigenmodes, find the eigenmode among the unallocated ones that maximizes the metric.

2. If the metric is higher with the new eigenmode, keep it and goto step 1. Otherwise, exit.

2max ( ) max max log(1 )

0,subject to

( )

jj j j

T T vj T

j

j

R T v

v j T

F v P

Power allocation, function of MET precoding matrix and T

QoS weights.


Average sum rate performance, fixed SNR

M = 4, K = 20, N = 4

MET-SPC is within 2dB of optimum DPC

Even under the more restrictive PAPC, MET-PAPC outperforms BD-RAS-SPC andBD-GUS-PSC.


Allocation of eigenmodes for each user under MET

M = 4 or 12, K = 20, N = 4

For M = 4 and large number of users, scheduler chooses to transmit to each user on its single largest mode.

For M = 12 and large number of users, scheduler could choose to transmit on smaller modes or multiple modes for high SNR.


SDMA schemes with partial CSI

SDMA with estimated or partial CSI:

Jindal, Love, Honig, Heath, Caire, Cioffi, Goldsmith, Huang, Boccardi, Trivellato.

Random beamforming techniques:

Sharif, Hassibi, Viswanath, Tse, Laroia Papadias, Avidor.

Multiuser multiplexing with interference cancellation at the receiver:

Heath, Andrews, Airy,…

Beamforming with fixed codebook:

PU2RC: Samsung proposal for UMTS LTE, grid of beams: Alcatel, Ericsson.

Sectorization.


ZF with partial CSI

Each receiver sends to the transmitter a channel direction information (CDI) and a channel

quality information (CQI) [J06].

Each receiver quantizes the “direction” of its channel vector to a unit norm vector,

selected from a quantization codebook formed by 2B unit norm column vectors

The quantization criterion is minimum chordal distance

Each user feeds back the channel quantization index to the transmitter, which requires B

bits. Moreover, each user is assumed to use an independently generated codebook.

We assume a random vector quantization (RVQ) scheme, where the 2B quantization

codewords are independently chosen from an isotropic distribution on the unit sphere.

RVQ gives a lower bound in terms of performance!


Beamforming design

The beamformer is calculated at the transmitter side by using the CDIs collected from the K users

where the channel of the selected users is given by

The power allocated to each user is the same (no waterfilling!)

The SINR at the kth receiver is given by

The SINR cannot be exactly computated neither at the TX side nor at the RX side!

A good estimation of the SINR is very important for the user selection task.


CQI feedback/SINR estimation

A first approach is to consider no quantization error (perfect cancellation of the interference

with ZF precoding) and approximate the channel with its projection along the quantized

direction

A second approach takes into account the quantization error by averaging with respect to the

statistic of the quantization codebooks (that affect the interference term)

A third approach considers a worse lower bound, but with only one CQI feedback


ZF with partial CSI – user selection schemes

Original user selection scheme [JGJ06]

ITERATE:

1) Identification of a quasi-orthogonal set of users

2) Selection of best candidate in the quasi-orthogonal set

the following lower bound for the SINR estimation is used

drawback: The parameter is difficult to optimize. If it is chosen too small, chances are that very few users are scheduled for transmission. If it is large, the transmitter may select unwanted users that cause too much interference.


ZF with partial CSI – user selection schemes

Algorithm 1: It’s a simple extension of the scheme proposed by Dimic and Sidiropoulus

for the case of perfect CSI. The users are added successively one at a time, up to a

maximum of Ntx if the estimated achievable throughput is increased. Any of previous

described CQI feedbackmethods can be used to estimate the users’ SINRs.

Algorithm 2: The drawback of Algorithm 1 is that, under imperfect CSI, it use SINR

estimates that are lower bounds of the real SINRs. The consequence of this is that it

allocates too a few users. Representing the possible sets of selected users as paths in

a tree, a modified scheme just consider more “candidates leaves”.


Simulation results – narrow band, Rayleigh i.i.d. channel

Ntx=4, K=20


Extension to multiple receive antennas (MET-MMSE)

An extension of the previous ZF with partial CSI scheme is represented by a

modified MET, where a CDI and CQI are fed back for each eigenmode.

For practical systems (ex.: 3 sectors with 4 transmit antennas each and

receivers with 2 antennas), even though multiple streams could be sent to a

single user (and these streams could be jointly detected), the dominant

eigenmode it is almost always the one scheduled for the transmission to a

given user.

This effect is even more pronounced in the case of imperfect CSI at the

transmitter side, because weaker modes would be the most affected by the

effect of the quantization error.

For this reason, for the case of partial CSI at the transmitter side, we only

consider the case of dominant eigenmode transmission [BHT 07].


MET-MMSE: brief description

Processing at the transmit side

-Send common pilots to the K users in the systems

Processing at the kth receive side

-Calculate the SVD of single user channel matrix and select the

Hermitian of the left eigenvector associated to the dominant

eigenmode as combining vector.

-Calculate and send to the transmitter CDI and the CQI.

Phase I

Phase II

Processing at the transmit side

-Use CQI and CDI to select a set of active users, and the precoding

matrix associated to this set.

-Send a dedicated pilot for each selected user, in order to estimate the

equivalent channel (channel+precoder).

Processing at the kth receive side

-MMSE detector.


MET-MMSE, simulation results

-Rayleigh fading channel model

-sum-rate vs SNR

-M=4 transmit antennas

-K=20 users

-B=10 feedback bits

-baseline: Beamforming with fixed

precoding unitary matrix

(DFT), and MMSE receiver.



-sum-rate vs number of

feedback bits


-K=20 users

-SNR = 12dB






-sum-rate vs number of users


-SNR = 12 dB





Thanks for your attention!

contacts:

Federico Boccardi

Wireless/Broadband Access Networks

Bell Labs Research

e-mail: [email protected]

Tel: +44-(0)1793-776670


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mimo multiuser schemes for downlink transmissions: theoretic bounds and practical techniques...

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