An Iterative Optimization Strategy in Multiple Points to Multiple Points MIMO (M4)

Mobile Communication Systems

MCL

Yun-Shen Chang

2006-08-07

2

Motivation MIMO channels often suffer from the rank-

deficiency problem, eg. most outdoor channels., resulting in significant throughput degradation.

The proposed M4 system provides a solution for achieving high spectral efficiency in a less scattered wireless MIMO channel with rank deficient channel matrix.

As opposed to conventional DPC requiring large number of transmit antennas, the M4 system effectively mitigate the limitation by using receive beamformers.

3

The M4 System

BS 1

1,1H

1 1,1 1 1 y H x z

2 1,2 1 2,2 2 2 y H x H x z

1x

MS 3

BS 2

1,2H

1,3H2,3H

2,2H

3 1,3 1 2,3 2 3 y H x H x z

Dirty Paper Encoder 1

Dirty Paper Encoder 2

MS 1

MS 2

Receive Beamformer

Receive Beamformer

Receive Beamforming

1 MS 1, MS 2, MS 3

2 MS 2, MS 3

2 BS 1, BS 2

3 BS 1, BS 2

1 BS 1

4

Notations

T

R

,

: number of mobile stations

: number of base stations

: number of antennas at each BS

: number of antennas at each MS

: number of data streams sent from BS to MS

base stations having links

k m

m

M

K

n

n

U k m

,

with MS

BS

: total number of data streams sent by BS k

k m

k k mm

m

m k

U U k

5

System Model

, , ( )

, , ,, , R R, , T T, ,

1 1

,

,

Parametric channel model

: number of multipath clusters present between BS and MS

( ) : number of multipaths in the cluster

k m k mW r wk m k m k mH

k m w p w p w pw p

k m

thk m

W k m

r w w

H a a

,,

,R R, , R

: complex Gaussian random variable representing the complex fading

amplitude of the multipath

: 1 receive antenna array response vector of the multipath

k mw p

k m thw p n p

a

,R , ,

, ,T T, , T T, ,

,

'

of the cluster w.r.t. the DOA

: 1 transmit antenna array vector w.r.t. the DOD

BS sees the channel of each user ,

but is blind to

k mthw p

k m k mw p w p

k m k

k

w

n

k m

a

H

H ,

,

, '

, '

MS can see both , , but is

blind to ; '

m

k m m

k m

k k

m k

m m

H

H

6

System Model

T

,

, ,

,

,

The receive signal at MS can be expressed as

,

where ; , 1, ,

: is the transmit matrix of BS , with

: the data stream sent by BS

m

k

k

m k m k mk

uk k k m k k m

U nk k k mm

u thk m

m

T d m u U

T C C k U U

d u k

y H x z

x

intended for MS

: AWGN

m

m

z

7

Interference Suppression

,

', ''

, ,

To decode , we have to combat

1) Interference from other BSs ' , ' :

, referred to as the s.

2) Interference from the same BS , but intended for

other u

M

s

AI

ers:

uk m

m

k m kk

k m k k

d

k k k

k

T d

H x

H ', ,; , ' 1, , , 0 ,

referred to as the CCIs.

u um k k m k mm u U d

8

Interference Suppression

,

In the proposed approach:

The MAIs are suppressed at the receive side (the MSs)

by forming a set of beamformers for each receiving data stream.

The CCIs are pre-cancelk mU

,

led by the orthogonal signaling

(or dirty paper coding) at the transmit side (the BSs).

The number of data streams depends on the

significant singular values of the channel matrixk mU

, .k mH

Iterative Receive Beamformer design

(Steps 1-4)

Using THP for payload data transmission

(Step 5)

Training Stage Data Transmission Stage

9

IRBStep 1: MMSE Beamforming

, ,

, ,

2

, , ,

1,

=

~ transmit matrix of BS

; , 1, , ~ trainning sequence

MMSE Beamforming at iteration :

min

m m

m k m k m k m k k mk k

k

Tu

k k m k k m

Hu u uk m k m k m m

uk m m

n n n n n n

n k

n t n m u U

n

n E t n n n

n n

w

y H x z H T t z

T

t

w w y

w R p

,

,

,

is fedback to BS for channel reconfigulation.

uk m

uk m

n

n k w

10

IRBStep 2: Channel reconfiguration

,

, ,

, , ,

With the fedback , BS reconfigures the subchannel to MS

by combining with the channel matrix as

The subchannel bw. BS and the MS is

eq

u thk m

uk m k m

H Tu uk m k m k m

th

n k u m

n

n n

u k m

w

w H

w H h

T

, ,

uivalent to a MISO channel.

The downlink channels observed by BS :

1 , , 1, ,k

Tuk k m k k m

U n

k

n n m u U

H h

11

IRBStep 3: Transmit side ZF

†

T

†

1 1

training signal sent by BS during the ( 1) iteration

Now we have MISO channels between

BS and MS , assume

updated transmit matrix

=

1 1

k

k

k k

th

k k k

k

n n

k n

t

U

k m n U

n n

HT

x H t

t

,

, , 1, ,

,

:

a 1 vector with representing the training symbol

for the subchannel from BS to MS

k k m

uk m m u U

k

th

uk mU

u k m

t

12

IRB Step 4: End of training stage

k

, , ,

At the receiver side, each MS redesign the MMSE beamformers

according to the receive signal in the ( 1) iteration.

The procedure repeats until

1 1

: vector no

th

u u uk m k m k m

m

n

J n n n

w w

T

,

, , , , ,

rm; : prescribed threshold value

Let denotes the final value of the receive beamformer weight vectors and

, , 1, , with =

represent the f

k

uk m

Tuk k m k k m

U n

T Hu uk m k m k mm u U

w

H h h w H

,

inalized reconfigured channel matrices.

The algorithm enters the second stage for finer transmit signaling design where

is used to carry out the THP at BS while is used at MS as a key

kuk mk m

H

w to open

the subchannel assigned by BS .

thu k

13

Step 5: Data transmission The Tomlinson Harashima Precoder (THP) is used for

payload data transmission to prevent the BSs.

from the transmit power penity.

At each MS , the outputs of the beamformers

developed km

,

, , 1, ,1

, ,

for receiveing signals from BS can be stacked into a column vector as :

where is the output of the corresponding beamformer.

QR decomp

k k mk

uk k m k k km u U

U

Hu uk m k m m

k

y

y

y H x z

w y

,

osition of

, (*)

unitary matrix with

( , ) ; 0, if lower trianguk k

k

k k k

H

k k i jU Ur i j r i j

H

H R Q

QQ I

R

lar matrix

The signal transmitted through BS is modulated by

, (**)

wh

Hk k k

k

x Q s

,1 ,ere is the 1 vector produced by the THP at BS .T

k k k n ks s U k s

} k k k k y R s z

14

THP

The THP adopts the modulo function to keep the amplitude

of the transmit singnal within a specific range so as to prevent

the transmit amplifier from saturation.

modulo operation

2 y

f y y

1 1

2,1 2,12 2 1 2 1 2

2,2 2,2

1 1, ,

1 1, ,

;

denotes the floor operation

Let

2

i ii l i l

i i l i l il li i i i

r rs f d s d s I i

y I

s d

r rs f d s d s I

r r

r r

, ,n

15

Decoding

,

, ,

, , ,

At the receiver, assume that is the element of

,:

( , ) ( , )

,: : the row of

The data symbol can be decoded by

ˆ

u thk m k

uk m k k k l

k k l k l k k l

thk k

k

y l

y l z

r l l d I r l l z

l l

d

y

R s

R R

,, , with the assumption that

( , )

( , ) is known at the receiver.

uk m

lk

k

ydec f

r l l

r l l

16

Example:

, ,

R T

( ), , ,

, , R R, , T T, ,1 1

,

,

,R , ,

2, 2, 4,

Multipaths:

2, , 1, 2

( ) 10, , , 1, 2

: Gaussian r.v. with randomly selected mean and

angular spre

k m k mW r wk m k m k mH

k m w p w p w pw p

k m

k m

k mw p

M K n n

W k m

r w k m w

H a a

,R , ,

,T, ,

,R , ,

,,

ad 30 as its variance.

: Gaussian r.v. with randomly selected mean and

angular spread 3 as its variance.

: Complex Gaussian with normalized 0 power.

k mw p

k mw p

k mw p

k mw p dB

17

BS 2BS 1 MS 2

11,2

21,2

andn

n

w

w

2,2

The largest two Eigen

vectors of as the

tranmit vector signals

H

2 2, 2,

†2 2

1 ;

1 1

Hum mn n

n n

H w H

T H

1,

1

1,

,

1, ,

um

m

n

m

u U

w

No

Yes

Data Transmission

,2 1 , 1,2

Converged ?

ukJ n k

1,2

The largest two Eigen

vectors of as the

tranmit vector signals

H

12,2

22,2

and n

n

w

w

2,

2

2,

,

1, ,

um

m

n

m

u U

w

18

Singular values

1,1 11.6819 7. 0.9257 0.9854 0044H

1,2 14.4537 11. 0.1823 0.9991 0069H

2,1 9.4850 7.0309 0.1896 0.0399H

2,2 14.4233 8. 0.1521 0.1805 0011H

BS 1

MS 2

BS 2

1,1H

1,2H

2,1H

2,2H

MS 1

, 2, , 1,2k mU k m

19

20

vs.

BS 1

MS 2

BS 2

1,1H

2,2H

MS 1

Alamouti or

VBLAST

BS 1

MS 2

BS 2

1,1H

1,2H

2,1H

2,2H

MS 1

21

22

Potential research directions Convergence analysis of IRB Iteratively updating from Non-orthogonal signaling with individual

SINR constraints

, 1uk m n w ,

uk m nw