multi-user gain maximum eigenmode beamforming, and idma · 1 multi-user gain maximum eigenmode...

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Multi-User Gain Maximum Eigenmode Beamforming,

and IDMA

Peng Wang and Li PingCity University of Hong Kong

2

Contents

IntroductionMulti-user gain (MUG)Maximum eigenmode beamforming (MEB)MEB performance analysisSIMO, MEB and optimal MIMO Implementation of MEB using IDMAConclusions

3

For detail see

Peng Wang and Li Ping, “On multi-user gain in MIMO systems with rate constraints,” IEEE GlobeCom, Washington, DC, USA, Nov. 26-30, 2007.

4

Contents


5

A 8×8 MIMO System

Great performance, but do we want to buy such a bulky handset?

Also, performance may be seriously affected by imperfect feedback and correlation among antennas.

6

Advantage of MIMO

R (bits/symbol)

MSP

(dB

)

4 4×

1 4×

0 1 2 3 4 5 6 7 8

-5

0

5

10

15

20

25

Rate

AveragePower

4 ×4

1×4

7

Can we do better?

8R (bits/symbol)

MSP

(dB

)

0 1 2 3 4 5 6 7 8

-5

0

5

10

15

20

25

Rate

AveragePower

1×4 single user 4 ×4 single user

4 ×4 multi-user

Multi-user MIMO

9

The Problems with Multi-user MIMOOptimized multi-user MIMO are very complicated, involving

- decoding order optimization,- correlation matrix optimization,- singular value decomposition (SVD),- eigenmode water filling.

10

The Focus of This Talk

- What are the advantages of multi-user MIMO? - Are there simple approaches to multi-user MIMO?

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Contents

IntroductionMulti-user gain (MUG)Maximum eigenmode beamforming (MEB)SIMO, MEB and MIMO Implementation of MEB using IDMAConclusions

12

Multi User Gain

We know that power saving can be achieved by multi-user concurrent transmission. But how much is the multi-user gain (without scheduling)?

MUG

13Rate

AveragePower

1×4 single user

Multi-user Gain for SIMO

1 ×4 multi-user

14Rate

AveragePower

4 ×4 single user

4 ×4 multi-user

Multi-user Gain for MIMO

15R (bits/symbol)

MSP

(dB

)

0 1 2 3 4 5 6 7 8

-5

0

5

10

15

20

25

Rate

AveragePower

1×4 single user 4 ×4 single user

4 ×4 multi-user

Multi-user Gain

1 ×4 multi-user

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(1) There is subtle difference between multi-user gain and multi-user diversity gain (used by David Tse).

- The former is for up-link multi-user concurrent transmission. - The latter is for down-link opportunistic transmission.

(2) For the down-link, multi-user detection is more difficult. Thus single-user opportunistic transmission becomes attractive.

(3) For the up-link, multi-user detection is relatively easier.(4) Quasi-static fading model.(5) No scheduling is assumed. (Fixed rates.)

Notes

17

What is the reason of multi-user gain?

For detail, seePeng Wang, Jun Xiao, and Li Ping, "Comparison of orthogonal and non-orthogonal approaches to future wireless cellular systems," IEEE Vehicular Technology Magazine, vol. 1, no. 3, pp. 4-11, Sept. 2006.

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Stripping Decoding

Decode x’’ by treating x’ as noise

Decoding x’

)'

''1(log2/ 2 qNqR+

+=

)'1(log2/ 2 NqR +=

t

arrival power q’’

arrival power q’t

Assume that q’’ > q’.

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Power Matching Strategy

channel gain g1user-2 signal


arrival power q2

arrival power q1

The question is to assign (q’, q ‘’) to (q1, q2). If we do it randomly, the resultant sum-power is the same as TDMA.

However, we can do better.

q’’t tq’>

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Power Matching Strategy



arrival power q2

arrival power q1

(1) Assign q2=q’’ and q1=q’. Thensum transmitted power = q’’ /g2 + q’ /g1

(2) Assign q2=q’ and q1=q’’. Thensum transmitted power = q’’ /g1 + q’ /g2

Assume q’’ > q’ . Which method leads to smaller transmitted power?

q’’t tq’>

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Multi User Gain in SISO ChannelsTransmitted power can be minimized by matching smaller receiving power with smaller channel gain.

This principle can be generalized to any number of users.

This is the reason of multi-user gain in multi-user SISO fadingchannels.

There is no such gain in AWGN (or when g1=g2).



arrival power q2

arrival power q1

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Multi-User Gain in MIMO ChannelsIn a MIMO channel, there is one more reason for multi-user gain. A MIMO system provides more dimensions for signaling. This is explained in the following example.

If there is one user, we need more antennas to achieve these degrees of freedoms.

However, if there are multiple users, we can achieve these degrees of freedoms more easily by allowing con-current transmission.

Three receiver antennas can provide a maximum three degrees of freedom. We need the help of the transmitters to achieve this degree of freedom. (We may view each degree of freedom as an eigenvector.)

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An Example: 2×2 MAC

More concurrent transmitting user, more gain.

0 1 2 3 4 5 6 7 8

0

5

10

15

20

25

R (bits/symbol)

aggregate power (dB)

K = 1 (TDMA)

K = 2K = 4K→∞

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Delay sensitive services without scheduling.

Perfect channel state information (CSI).

Channel includes path loss, lognormal and Rayleigh fading

Assumptions

r

Rayleigh fading

Lognormal fading

Path loss

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Contents

IntroductionMulti-user gain (MUG)Maximum eigenmode beamforming (MEB)MEB performance analysisSIMO v.s. MIMOImplementation of MEB using IDMAConclusions

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The MEB Strategy

Each mobile transmits only on its maximum eigenmode.

Power allocation is applied according to the maximumeigenmode gains {gk}.

Stripping decoding is applied at the receiver. The user with the largest channel gain is decoded first.

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The Advantages of MEB

simple and nearly optimal.

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Optimal MIMO MAC and MEB

Optimal MIMO MAC

MEB

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Contents

IntroductionMulti-user gain (MUG)Maximum eigenmode beamforming (MEB)MEB performance analysisSIMO, MEB and MIMOImplementation of MEB using IDMAConclusions

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Theorem 1

When K→ ∞, the MSP for a multi-user N×M MIMO system is given by

∫∞

××

×

=0

/)(

)(22ln),( dxxfx

RRKMSP MN

MxRF

MN

MN

K: the number of users number;R: sum rate;FM×N(x) the CDF of |λmax|2; fM×N(x) the PDF of |λmax|2;

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Theorem 2

When K→ ∞, the MSP for a multi-user MEB N×M MIMO system is given by

Therefore MEB is asymptotically optimal.

∫∞

××

×

=0

/)(

)(22ln),( dxxfx

RRKMSP MN

MxRF

MN

MN

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Proof Outline

The derivation is based on upper and lower bounds.

When K→ ∞, the upper and lower bounds converge so we obtain the true MSP.

The upper bound is derived from a realizable system using maximum eigenmode beamforming (MEB).

The lower bound is derived from an idealized parallel channel.

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Upper Bound (Achievability)

KKkFRRKMSP

K

Kk MN

MKkR

MN1

)/(2)1(2ln),( 1

/)1(

⋅+

≤ ∑=

−×

−

×ε

δ

The MEB provides an upper bounds on the MIMO MSP.

where δ is an arbitrarily small constant, ε the outage probability and FN×M(⋅) the CDF of the maximum singular value.

When K→ ∞,

∫ −×

× ≤1

0 1

/

)(22ln),( dt

tFRRKMSP

MN

MRt

MN

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Proof

( )( ) ( )

( )( ) ( )

1/ /

11 / /1

2 1 1 (2 1) / 1lim

11 2 1 1 (2 1) / 1

kR K R K

k iK k R K R Ki

MSNR

MM

δ

δ

−

−→∞ −

=

− + − +=

+ − + − +∑

( )( )( )

1/ /

/ 11 /1

2 1 1 (2 1) /

2 11 1 (2 1) /

kR K R K

R K ik R K

M

MM

−

−−

=

− + −≥

−+ + −∑ i

/2 1R K= −

2 2, m ax , m ax , m ax

1 2 2, m ax , m ax , m ax1

|

1 |

Hk k k k

k k Hi i k ii

p dS N R

p d−

=

=+ ∑

| u u

| u u

2,max

1 2,max1

1k k

ki ii

p d

p d φ−

=

=+∑ k,i

( ) ( 1) /

1

1 2 ln 2 1lim lim( / )

R k MKK K

kK Kk K k K N M

Rp

KF k Kε ε

δ −

−→∞ →∞= = ×

+= ⋅∑ ∑

/1

1

2(1 ) ln 2( )

Rt M

N M

R dtF tε

δ −×

= + ⋅ ∫

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Lower Bound

∫ −×

× ≥1

0 1

/

)(22ln),( dt

tFRRKMSP

MN

MRt

MN

∑=

+=k

kkMkd

1

max nxIy

maxkd

1

K

k kk=

= +∑y H x n

Its minimum sum-power (MSP) is lower bounded by that of thefollowing idealized system:

MIMO:

Parallel Channel:

where is the maximum singular value of Hk. Each user in this channel sees M parallel sub-channels. Thus

same as the upper bound when K→ ∞

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When K→ ∞, the upper and lower bounds converge to

End of the Proof

∫∞

××

×

=0

/)(

)(22ln),( dxxfx

RRKMSP MN

MxRF

MN

MN

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Observations

MEB is asymptotically optimal when K→ ∞.

MEB is nearly optimal even for a quite small K.

MEB is insensitive to antenna correlation.

MEB is insensitive to CSI error.

For detail, seeLi Ping and Peng Wang, "Multi-user gain and maximum eigenmodebeamforming for MIMO systems with rate constraints," IEEE Inform. Theory Workshop (ITW), Bergen, Norway, July 1-6, 2007.

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Optimal MIMO MAC and MEB

Optimal MIMO MAC

MEB

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MEB Is Nearly Optimal

AveragePower

rate (bits/channel use)

2×2 MIMO MAC

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Summary

MIMO asymptotic MSP

The degrees of freedom is increased by M times.Why M? Effectively, we have a KN× M system. The limiting factor is M.What is the impact of N? FN×M(⋅)

∫∞

××

×

=0

/)(

)(22ln),( dxxfx

RRKMSP MN

MxRF

MN

MN

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Delay sensitive services without scheduling.

Perfect channel state information (CSI).

Channel includes path loss, lognormal and Rayleigh fading

Conditions

r

Rayleigh fading

Lognormal fading

Path loss

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Contents


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Comparison of Different Gains

R (bits/symbol)

MSP

(dB

)

4 4×

2 4×

1 4×

1 4×

4 4×2 4×

1K =

K =∞

0 1 2 3 4 5 6 7 8

-5

0

5

10

15

20

25

multi-user SIMO

multi-user MEB

single-user SIMO

BFgain

multi-user gain

K=16 multi-user MIMO

optimization gain

single-user MIMO

MIMO gain

single-userSIMO

Single-userMIMO

multi-userSIMO

Multi-userMEB

multi-userMIMO

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Some details …

For detail, seePeng Wang and Li Ping, “On multi-user gain in MIMO systems with rate constraints,” IEEE GlobeCom, Washington, DC, USA, Nov. 26-30, 2007.

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(1) Single-User SIMOThis is used as the reference.

single-userSIMO

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(2) Single-User MIMOSVD is sensitive to channel information error (water-filling).

Bulky .

Closely located antennas may be rank-deficient. This is a serious problem for a handset unit.

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(3) Multi-User SIMOSIMO MAC is a special case of MIMO MAC.

SIMO MAC can also achieve good MUG.

SIMO MAC requires only one antenna per handset.

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(4) Multi-User MEBEasy to design (no water filling).

Robust against imperfect CSI

Near optimal performance with multi-user detection.

But, multiple transmit antennas.

Rank deficiency is not a problem.

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(5) Multi-User MIMOVery sensitive to channel information error.

Bulky .

Very complicated to optimize.

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Comparison of Different Gains

R (bits/symbol)

MSP

(dB

)

4 4×

2 4×

1 4×

1 4×

4 4×2 4×

1K =

K =∞

0 1 2 3 4 5 6 7 8

-5

0

5

10

15

20

25

multi-user SIMO

multi-user MEB

single-user SIMO

BFgain

multi-user gain

K=16 multi-user MIMO

optimization gain

single-user MIMO

MIMO gain

single-userSIMO

Single-userMIMO

multi-userSIMO

Multi-userMEB

multi-userMIMO

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Types of Gains in Multi-User MIMO

- MIMO gain achievable by single-user MIMO

- Multi-user gain achievable by multi-user SIMO

- Beamforming gain achievable by multi-user MEB

- Optimization gain achievable by multi-user MIMO

single-userSIMO

Single-userMIMO

multi-userSIMO

Multi-userMEB

multi-userMIMO

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Optimization Gain

Optimization involvesdecoding order optimization,correlation matrix optimization,singular value decomposition (SVD),eigenmode water filling.

Therefore to achieve optimization gain is a very complicated task.

As we can see, the difference between MEB and optimal MIMO Is marginal. Thus optimization gain is not significant.

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Contents

IntroductionMulti-user gain (MUG)Maximum eigenmode beamforming (MEB)MEB performance analysisSIMO v.s. MIMOMulti-user gain (MUG)Implementation of MEB using IDMAConclusions

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MEB-Based IDMA

1p

Kp

1c 1x

KπKc Kx

1π

1π

Kπ

Kπ

1π

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Performance of MEB-Based IDMA

R = 4 bits/symbol

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Based on the MAC-BC duality principle (Yu, Cioffi, Vishwanath, Jindal, Goldsmith), the conclusions in this talk can be also applied to BC channels. For simplicity, we will concentrate on MIMO MAC below.

MIMO Broadcasting and Duality

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Contents

IntroductionMulti-user gain (MUG)Maximum eigenmode beamforming (MEB)MEB performance analysisSIMO v.s. MIMOImplementation of MEB using IDMAConclusions

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Conclusions

Optimal MIMO systems are bulky and sensitive. They are also complicated to design and to decode.

Multi-user SIMO can achieve very impressive gain.

If multiple antennas are affordable, MEB is a low-cost, almost optimal strategy.

IDMA provides an efficient framework to realize MUG.

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Thank You !

multi-user gain maximum eigenmode beamforming, and idma · 1 multi-user gain maximum eigenmode...

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