utilizing channel information at the cdma...

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Utilizing channel information at the CDMA transmitter

Balaji Raghothaman,

Nokia Research Center,

Irving, TX.

[email protected]


Outline

Introduction

Channel knowledge: Why?

Channel information: How?

Reciprocal beamforming

Feedback methods

Adaptive methods

Standards Proposals


Nokia Research Center, Dallas

Video/Image Radio Comm. Mobile Networks

GSM/EDGE CDMA Air Interface Prototyping

Systems Physical Layer Standardization

WLAN


Introduction

• Capacity of cellular systems can be increased by employing multiple antennas, either at the receiver or the transmitter or both.

• Multiple antennas can be placed in order to provide either diversity or directivity or both.

• Larger antenna spacing -> independent channels -> diversity.

• Smaller antenna spacing -> correlated channels -> directivity.

MobileBase Station


Introduction (2)

• Space-time code designs like the Alamouti scheme provide diversity gains by making it possible to achieve separable diversity paths from the composite signal at the receiver antenna.

• The availability of channel information makes it possible to increase these gains so that they are comparable to receiver diversity gains.

• The addition of antenna gain to the diversity gain makes this possible.

• Some of the ways in which channel information can be used are:• Power control• Link adaptation• Scheduling• Antenna switching• Beamforming / weighted diversity • MIMO transmission


Beamforming

Diversity Multiplexing

CSI

Multiantenna transmission

Throughput

SINR

Fading protection


Using Channel State Information

Data Stream 1

Data Stream 2

Data Stream K

P1

P2

PK

w1

w2

wK

Channel State Information for all users

Packet Sizeadaptation

Poweradaptation

Weightadaptation


• Alamouti Scheme:

• Weighted diversity transmission:

Channel Information: Why ?

[ ] 11 2

2

wy h h x

wγ

= +

( )2

2 22 21 2

1 22 21 2

h h Es EsSNR h hNo Noh h

+ ≤ = + +

*1 2

*1 2

12

e o e e

o oe o

r h x W h x Wr h x W h x W

γγ

+ = +

− 2 2

1 2 .2

h h EsSNRNo

+≤


Joint beamforming and power allocation

• Naguib et.al. showed the capacity gains due to the usage of multiple antennas for beamforming on the downlink.

• The problem of estimating the beamforming weights at the base station can be cast as an optimization problem which maximizes the SINR at the mobile in question.

• Beamforming can be combined with power control as a joint optimization problem over all mobiles and base-stations in a network vicinity. (Farrokhi et.al.)

2

,

,

min , subject to

H Si i ii i

i I Sb b ib b i

b

i i i ii

P GP G N

P γ

Γ =+

Γ ≥

∑

∑P A

w ww w

w%

%

% %

%


Channel Information: How?

• Reciprocity

• Feedback

Uplink Receiver

Mobile

ReciprocityTransformation

DownlinkTransmitter

Uplink ReceiverMobile

Receiver

DownlinkTransmitter

EstimateFeedback

MobileTransmitter


Reciprocity• Reciprocity applicable only to duplex systems.• In Time Division Duplex systems (TDD), the channel is assumed to be

identical in both directions. Hence transformation is not needed –except for a possible temporal interpolation.

• In Frequency Division Duplex systems (FDD), the channel on the uplink is different from the downlink channel due to the difference in carrier frequency.

• Instantaneous channel cannot be tracked using reciprocity in FDD.• However there is a relation between the average channel covariance of

the uplink and the downlink.

Uplink slot:Measurechannel

Downlink slot:Use channelinformation

Uplink slot:Measurechannel

Downlink slot:Use channelinformation

Reciprocity in TDD systems


Spatial Channel Model

• The multipath channel is modeled as having angles of arrival and angular spread associated with them.

• The correlation between antenna elements is given by:

BSBldg.

MS

Bldg.

θ

∆

( ) ( ) ( )01

( ) 2 2 2 cos sinckk

kc c

D Dr D J j J k kπ π θ πλ λ

∞

=

= + ∆

∑


0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

2 Delta = 0 deg. 2 Delta = 3 deg. 2 Delta = 5 deg. 2 Delta = 10 deg. 2 Delta = 30 deg. 2 Delta = 60 deg.

Spatial Correlation


Reciprocity in FDD

• First approach is to estimate θ and ∆ for each path on the uplink, and then use it to estimate the downlink channel covariance matrix.• ∆ is extremely difficult to estimate.

(Olivier Besson and Petre Stoica, 2000)• Errors in estimation of θ and ∆ lead to significant degradation.

• Second approach is to find a transformation that directly maps the uplink channel covariance matrix to the downlink equivalent.

• Two methods to estimate this transformation will be discussed:1. Fourier series expansion.2. Discrete Fourier Transform interpolation.


Reciprocity in FDD: Fourier series expansion• The channel covariance matrix can be expressed as a Fourier series:

• Only the terms ckl have to be estimated online. Least squares approaches can be used:

• Once estimated, the terms ckl can be used to arrive at the downlink channel covariance matrix.

(Fonollosa et. al, 2000)

21

,1

ˆˆ arg mink

Ll

u kl u kl L F

c−

=− +

= − ∑c R Ψ

1

( ), , ( ), ( ), ( ),1

/

/

[ ] ,

( | ) ( | )

LHs l

u d k u d k u d k kl u d kl L

Ql jlQ θuk uk ukQ

E c

θ f θ f e dθ

β α

π

π

−

=− +

−

= ≈

=

∑

∫ H

R a a Ψ

Ψ v v


Reciprocity in FDD: DFT redistribution• Applicable to uniformly spaced linear arrays.

• The up(down)link spatial signature for each angle is given by

• The DFT of the first column of the uplink R gives the frequency response, sampled at radial frequencies [0 2π/N , … , 2π(N-1)/N ].

• From uplink to downlink, the angular frequencies have shifted, hence the mapping of the DFT indices is given by

• We can shift back to equally spaced DFT by using a nearest neighbor interpolation.

• Finally IDFT gives first column of downlink channel correlation matrix.

( ) ( )2 cos ( 1) 2 cos

( )( | ) [1, ]u d u dz zj f j M f Tc c

u df e eπ θ π θ−

=v θ , . . . ,

( )

0,1, 2, , ( 1) 0,1, 2, , ( 1) ,2 2

, ( 1), , ( 1) 1 ( 1), ,1,0 , where 2 2 2

d

u

N N

fN N NN Nf

α

α α

− → − + − → − − − =

K K

K K


Reciprocity in FDD: DFT redistribution

0 20 40 60 80 100 120 140 160 1808

8.5

9

9.5

Direction of Arrival deg.

Bea

mfo

rmer

gai

nddB

IdealIgnore DeltaDFT Redistribution


Feedback Methods for Tx. Diversity : Issues

• There is very limited feedback bandwidth. Hence these methods suffer from severe quantization effects.

• They try to keep up with instantaneous channel –hence they fail in fast fading conditions.

• The delay involved in receiving feedback also causes degradation in fast fading.

• There is currently no error protection for the feedback channel (in WCDMA). Any errors due to feedback result in incorrectly weighted transmission.

• There is no simple soft handoff solution.


Effect of Feedback Delay

100

101

102

0

0.5

1

1.5

2

2.5

3

3.5

Velocity kph

−P

(τ)/

P(0

) dB

(a) Mag + Phase Fdbk

τ = 1/1500 s.τ = 2/1500 s.

100

101

102

0

0.5

1

1.5

2

2.5

3

3.5(b) Phase only Fdbk

Velocity kph

−P

(τ)/

P(0

) dB

τ = 1/1500 s.τ = 2/1500 s.


Channel prediction to combat delay• The fading channel can be modeled as an autoregressive (AR) model:

• The parameters aj can be estimated using a prediction model.

• The feedback is calculated based on the predicted channel conditions instead of the currently measured conditions.

( )1

1

1( ) ,1

( )

pj

jj

p

j pj

H za z

h t a h t jT γ

−

=

=

=−

= − +

∑

∑

+

Adaptive filterDelay-

Prediction Error

Channel Estimate


Channel Prediction (2)

Fr a m e e rr o r r a t e a t 5 0 k p h , P i l o t S N R = 1 5 d B

0.001

0.01

0.1

1

5 6 7 8 9 10 11 12Eb / N o d B

1 -a nt e nna

2-a nt . , f ul lpr e c i s ion f dbk, nopr e di c t i on

2-a nt . , qua nt .Fdbk. , nopr e di c t i on

2-a nt . , f ul lpr e c i s ion f dbk. ,wi th pr e di c t i on

2-a nt . , qua nt .Fdbk. , wi thpr e di c t i on


Combating feedback error• Incorrectly received feedback leads to erroneous weighted transmisison.

• The process of correcting feedback errors at the mobile receiver is called verification.

• Dedicated pilots are used to aid this process of verification.

• The hypothesis being tested is given as:

• We assume that the error probability associated with the feedback is known:

• The Bayesian rule gives:

• Assuming that the noise is AWGN,

( )( )

0 , , 1, , 2 ,

1 , , 1 , 1 ,

ˆ ˆ: , , ,

ˆ ˆ: , , ,

cl k l k l k l k N

el k l k l k l k N

H w

H w

θ θ θ

θ θ θ

− − −

− − −

= ℑ

= ℑ

K

K

( ) ( ), , , ,ˆ ˆ and 1l k l k c l k l k e cp p p p pθ θ θ θ= = = = = −

011 0

0 1

( )( / ) , else ( / ) ( )

p Hp z H H Hp z H p H

> ⇒

( )**, , 12

2 Re lne c cd c l k l k

e

ph h w w Hp

γσ

− > ⇒


Transmission subspace tracking

• Feedback methods discussed so far have related to some kind of instantaneous quantized feedback.

• Adaptive subspace tracking is a possibility, but is limited by feedback bandwidth.

• A perturbation based gradient approach was recently proposed.

• The concept originated in stochastic control theory and neural network learning.

• This class of methods works for correlated environments. It also gives good performance in uncorrelated low mobility conditions.

• The feedback bandwidth required is independent of the number of antennas.


Transmission subspace tracking (2)

• The cost function to be maximized is given by

• The gradient of the cost function is then and the adaptation is given as

• Feedback of entire gradient vector is not feasible.

• Perturbation approach: If we perturb the weight vector by a random complex vector in either direction as , and estimate the received power in each case, then,

• Now the scalar quantity c can be fed back with any precision.

ˆHk k k

k Hk k

J = w R ww w

ˆ2k k kk H

k k k

J∂= =∂

R wgw w w

1k k kµ+ = +w w g

( )e o k kβ= ± ∆w w w

[ ]ˆ ˆ

, where H H

e k e o k ok H H

e e o o

E c c∆ ∆ ∝ = −ww R w w R ww g

w w w w


Deterministic perturbation

• Consider where form an orthonormal set of M-length vectors. The perturbation vector is selected from this set.

• Using an approximation from the gradient:

• The expected value is given as:

[ ]M M Mj=Q Q Q% [ ]0 1 1, , ,M M −=Q q q qK

( )2 H Hk kc β∆ = ∆ + ∆ ∆w g w w g w

[ ] ( ) ( ) ( )( )( )

( )2

, since

HH H Hk i i k i k i i k i

i i

Hi k i

i

HM M k

Hk M M

E c j j jM M

M

M

M

β β

β

β

β

∆ = + + + =

=

= =

∑ ∑

∑

w g q q g q g q q g q

q g q

Q Q g

g Q Q I


Transmission subspace tracking (3)Base Station

∆wRandom Perturbation Vector

e k β= + ∆w w w

o k β= − ∆w w w 1−D

He e eP = w Rw

Ho o oP = w Rw

1−D

( )sgn e oP P−

Mobile Station

1 sgn( )k k e oP Pµ+ = + − ∆w w w


Transmission subspace tracking (4)

0 2 4 6 810-4

10-3

10-2

10-1

100

SNR dB

Uncoded BER

3 km/h flat fading

1 Ant.4 Ant.Q-Phase4-Ant.Adapt.

0 2 4 6 810-4

10-3

10-2

10-1

100

SNR dB

10 km/h flat fading

0 2 4 6 810-4

10-3

10-2

10-1

100

SNR dB

40 km/h flat fading


WCDMA/HSDPA

1. Mode 1: Involves phase feedback only. Feedback rate is 1500 bps.• Phase quantized to 1-bit according to set partitioning in table:

• Weight is obtained by filtering over multiple phase feedbacks.

2. Mode 2: Magnitude and phase feedback.• Two bits magnitude and three bits phase.• Successive updating using 1-bit feedback each time.

Bit Even Slot Odd Slot0 0 π/21 π -π/2

,1 1

k l k l

N Nj j

m kl l

w e eθ θ− −

= =

= ∑ ∑


Proposals for Release 6: Eigenbeamformer

• Tracks long term covariance matrix at the mobile, and estimates the eigenvectors corresponding to 2 largest eigenvalues.

• Feeds back the 2 quantized eigenvectors at rate of 1 bit per frame.

• The short term feedback consists of selecting between the 2 eigenvectors.

• Has shown good performance with correlated antennas.

Slot 1 Slot 2 Slot 15 Slot 1 Slot 2


Per Antenna Rate Control (PARC)

• 2x2 MIMO scheme.

• Takes “water filling” approach.

• Control the modulation and coding schemes, as well as packet size of data stream emanating from each antenna, using strength of channel as criteria.

• Decoder complexity and design is an issue

MobileBase Station

Packet A

Packet B


Challenges : System evaluation

0 2 4 6 8 10 12 14 16 18 200

20

40

60

80

100

120

140

160

180

Simulated Time (second)

Computer Time (second)

Simulation time with different fast fading simulation approaches

ReadFileJakesNo Fading

1.7 * t

3.8 * t

9.0 * t

System simulation : 19 cells, 57 sectors, 120 mobiles, 2Tx-1Rx antenna

(Ack: Zhouyue Pi, NRC Dallas)


Further study areas

• Packet data is moving towards shorter bursts of high density transmissions.

• In this paradigm, is most of the gain in better scheduling rather than in space-time code design or MIMO design ? ( Pramod Vishwanath, IT, 2002)

• Better (more) feedback on the reverse link leads to better downlink design -> For higher capacity on one link, we sacrifice some capacity on the other link. What is the trade-off ?

utilizing channel information at the cdma...

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