Utilizing channel information at the CDMA...
Transcript of Utilizing channel information at the CDMA...
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Utilizing channel information at the CDMA transmitter
Balaji Raghothaman,
Nokia Research Center,
Irving, TX.
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Outline
Introduction
Channel knowledge: Why?
Channel information: How?
Reciprocal beamforming
Feedback methods
Adaptive methods
Standards Proposals
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Nokia Research Center, Dallas
Video/Image Radio Comm. Mobile Networks
GSM/EDGE CDMA Air Interface Prototyping
Systems Physical Layer Standardization
WLAN
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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
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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
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Beamforming
Diversity Multiplexing
CSI
Multiantenna transmission
Throughput
SINR
Fading protection
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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
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• 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
+≤
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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%
%
% %
%
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Channel Information: How?
• Reciprocity
• Feedback
Uplink Receiver
Mobile
ReciprocityTransformation
DownlinkTransmitter
Uplink ReceiverMobile
Receiver
DownlinkTransmitter
EstimateFeedback
MobileTransmitter
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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
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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
∞
=
= + ∆
∑
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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
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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.
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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
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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
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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
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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.
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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.
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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
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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
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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
− > ⇒
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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.
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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
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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
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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
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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
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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− −
= =
= ∑ ∑
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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
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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
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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)
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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 ?