Cloud Radio Access Downlink with Backhaul Constrained Oblivious - - PowerPoint PPT Presentation
Page 1 of 66 Cloud Radio Access Downlink with Backhaul Constrained Oblivious Processing Shlomo Shamai Department of Electrical Engineering Technion Israel Institute of Technology Joint work with S.-H. Park, O. Simeone and O. Sahin HyNeT
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Shlomo Shamai Department of Electrical Engineering Technion−Israel Institute of Technology Joint work with S.-H. Park, O. Simeone and O. Sahin
HyNeT Colloquium, University of Maryland October 2013
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– Promoted by
Huawei [Liu et al], Intel [Intel], Alcatel-Lucent [Segel-Weldon], China Mobile [China], Texas Inst. [Flanagan], Ericsson [Ericsson]
– Base stations (BSs) (e.g., macro-BS and pico-BS) operate as soft relays.
An Illustration of the downlink of cloud radio access networks
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– Low-cost deployment of BSs
– Effective interference mitigation
– But, the backhaul links have limited capacity
The distribution of backhaul connections for macro BSs (green: fiber, orange: copper, blue: air) [Segel-Weldon].
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– Notation:
Central ENC
1,
,
M
N
M M
BS
1
,1 B
n
antennas
1
x
1
C
BS
B
N
,
B
B N
n
antennas
B
N
x
B
N
C
MS
1
DEC
1
ˆ M
1
,1 M
n
antennas
1
y
MS
DEC
M
N
ˆ
M
N
M
M
N
,
M
M N
n
antennas
M
N
y
1
H
M
N
H
{ 1, , }, { 1, , }
B M
N N
B M
N N
focus
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by where
– The results of this work can be extended to more general power constraints:
2
,
i i
P i x
B
N k
,1 , 1
, , , , , , ~ ( , )
B B
k k k N H H H N k
H H H x x x z 0 I CN
k k k
M
, 1, , .
H l i
l L x Θ x
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– Each BS is connected to the central encoder via a backhaul link of capacity bits per channel use (c.u.).
– The codebooks of the MSs are not known to the BSs.
– Systems with informed BSs treated in [Ng et al][Sohn et al][Zakhour-Gesbert][Simeone et al: 12].
i
i
C
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– Received signals at different BSs are statistically correlated. – This correlation can be utilized to improve the achievable rates
[Sanderovich et al][dCoso-Simoens][Park et al:TVT][Zhou et al].
Conventional compression Distributed compression
: Side information
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– Potentially larger rates can be achieved with joint decompression and decoding (JDD) at the central unit [Sanderovich et al]. – Optimization of the Gaussian test channels with JDD [Park et al:SPL].
Joint decompression and decoding Numerical results in 3-cell uplink [Park et al:SPL]
(SDD: separate decompression and decoding)
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– Joint dirty-paper coding [Costa] for all MSs
– Followed by independent compression
1
C
1
M
Channel encoder 1 Joint Dirty-Paper Coding BS 1 Central encoder
M
N
M
Channel encoder
1
s
M
N
s
Compression ENC 1
1
x
B
N
x
B
N
C
1
x
BS
B
N
x
B
N
B
N
Compression ENC independent compression
Page 14 of 66 Quantization is performed at the central unit using the forward test channel where
2 2 2 2 2 per-cell
1 (1 ) 1 2(1 ) (1 ) log 2 P P P R ,
m m m
X X Q
System model
a modified BC with the added quantization noises.
where is the effective SNR at the MSs decreased from to
P P
2
. 1 (1 ) / (2 1) 1
C
P P P
: DPC precoding output, : quantization noise with ~ (0, / 2 ), : cell-index, thus is independent over the index .
m C m m m
X Q Q P m Q m CN
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– Downlink counterpart of the compute-and-forward (CoF) scheme proposed for the uplink in [Nazer et al].
– System model
, for all { 1, , }.
B M i
N N L C C i L L
Central encoder BS 1 BS L
C C
MS 1 MS L
1
h
L
h
1
z
L
z
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– The same lattice code is used by each BS. – Each MS estimates a function by decoding on the lattice code. – Achievable rate per MS is given by
per-MS
min ,min , ,SNR
l l l
R C R
h a
L
1 1
SNR , ,SNR max log ,0 SNR
H H
R
h a a I hh a
, 1
ˆ
L k k j j j a
w w k
where
Central encoder BS 1 BS L
C C
MS 1 MS L
1
h
L
h
1
z
L
z
1 1 1 L L
w w Q w w
1
w
L
w
1 eff 1 1 1
( , , ) mod t z h a Λ
eff (
, , ) mod
L L L L
t z h a Λ
Point-to-point channels
Precoding over finite field
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– Precoding: interference mitigation – Compression: backhaul communication – Achievable rate for MS (single-user detection)
k
k k k
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– Assume Gaussian codewords where
k
k k k
k
nR k k
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– Remark: Non-linear dirty-paper coding [Costa] can be also considered.
treated as a Gaussian vector.
1 1
B B
H H N N
, 1 , , , ,
1 1 , , , 1 1 ( )
, , , , , , , ,
M M B i B i B B i B B i B i
H H H N N n n N j i n B j B l B B l l l n n n
n n n n
A A A s s s E I
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1
BS
1
1
Precoding
1
1
1
1
B
N
BS
B
N
B
N
B
N
B
N
B
N
Central encoder
B
N
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1
Precoding
B
N
Central encoder
1
1
1
1
BS 1 BS
B
N
B
N
B
N
B
N
B
N
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– Gaussian test channel [dCoso-Simoens][Simeone et al:09] – Overall, the compressed signal is given as with the compression noise where and .
,
, ~ ( , ),
i i i i i i
i x x q q 0 Ω
B
CN N
1 ,
,
B
H H H N
x x x
1 ,
, ~ ( , )
B
H H H N
q q q 0 Ω CN
1,1 1,2 1, 2,1 2,2 2, ,1 ,2 ,
,
B B B B B B
N N N N N N
Ω Ω Ω Ω Ω Ω Ω Ω Ω Ω
, H i j i j
E Ω q q
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– For a precoder and a compression correlation , we have the following modified BC. – Received signal at MS
A Ω
Central Encoder MS 1
1
y
1
H
MS NM
M
N
H
M
N
y
k k k
k
~ ( , ).
k k k H k k
z z H q 0 I H ΩH CN
where
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– Leverages correlated compression in order to better control the effect of the additive quantization noises at the MSs.
special case of multivariate compression by setting
,
H i j i j
can be reduced by controlling
1,2 2,1 H
Ω Ω
BS 1 BS 2 MS
1 1 1 H
x E As q
2 2 2 H
x E As q
1,1
H
1,2
H
1
z
1 1 1 1 1 2
q H q y H As z
1,1 1,2 1 1 2,1 2,2
,
H
Ω Ω 0 H H Ω Ω CN
Central ENC
1
C
2
C
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– Lemma 1 [ElGamal-Kim, Ch. 9] Consider an i.i.d. sequence and large enough. Then, there exist codebooks with rates , that have at least
with with respect to the given joint distribution with probability arbitrarily close to one, if the inequlities are satisfied.
n
X
| , for all {1, , }
i i i i
h X h X X R M
S S S
S
n
1,
,
M
C C
1,
,
M
R R
1 1
( , , )
n n M M
X X C C
n
X
1 1
( , , , ) ( ) ( , , | )
M M
p x x x p x p x x x
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– Lemma 2 (Lemma 1 applied to our setting) [Park et al:13] The signals obtained via (1) can be reliably transferred to the BSs on the backhaul links if the condition is satisfied for all subsets .
1,
,
B
N
x x
,
, | logdet logdet
i i H H H i i i i i i i
g h h C
A Ω x x x E AA E Ω E ΩE
S S S S S S S
B
S N
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– Consider the case with two BSs.
to
– The introduction of correlation among the quantization noises for different BSs leads to additional constraints on the backhaul link capacities.
1 1 1 2 2 2 1 1 1 2 2 2 1 2 1 2 1 2 1 2
| , ( 1) | , ( ; ; ; , 2) , | . ( 3 ; ) I h h C A h h C A h h h C I I C I A x x x x x x x x x x x x x x x x x x x x
1 1 1 2 2 2
; , ( 1) ; . ( 2) I C B I C B x x x x
1,2
Ω
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where
, 1 ,
maximize , s.t. , , for all , tr , for all .
M
N k k k i B i H i i i i i B
w f g C P i
A Ω 0
A Ω A Ω E AAE Ω
S S
S N N
,
, ; logdet ( ) logdet , , | logdet logdet .
k k k H H H H k k k l l k l k i i H H H i i i i i i i
f I g h h C
A Ω s y I H AA Ω H I H A A Ω H A Ω x x x E AA E Ω E ΩE
S S S S S S S
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– We can use a Majorization Minimization (MM) algorithm
[Beck-Teboulle] to find a stationary point of the problem.
H k k k
R A A k
M
N { } ,
k k
R Ω
M
N
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where the functions are the local approximations of the functions at the point . Initialize and and set .
(1) 1
{ }
M
N k k
R
(1)
Ω 1 t
, 1 ,
maximize , s.t. , , for all , tr , for all .
M
N k k k i B i H i i i i i B
w f g C P i
A Ω 0
A Ω A Ω E AAE Ω
S S
S N N
, , ,
k
f g A Ω A Ω
S
1 t t
Update and as a solution to the following (convex) problem:
( 1) 1
{ }
M
N t k k
R
( 1) t
Ω
, , ,
k
f g A Ω A Ω
S
( ) ( ) 1
{ } ,
M
N t t k k
R Ω Converged? Yes No Stop
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Step :
compression is relatively complex.
– Compression rate at step :
( , ) A Ω
:
B B
N N Step 1:
(1)
x
(1)
q
(1)
x
(1) (1), (1)
~ ,
q 0 Ω CN
compression
(1) ( ) ( 1) ( ) i i i
x u x x
( ) ( ) ( )
1 ,
i i i
x u u
( )
ˆ
i
q
( ) i
x
MMSE estimation
( ) i
x
( ) i
u
compression
(1) (1)
( ) |
ˆ ~ ,
i
x
u
q CN
( )
ˆ
i
x
( ) ( )
ˆ ;
i i
I
x x
( 1) i i
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satisfying the constraints (2b) is a contrapolymatroid [Tse-Hanly, Def. 3.1]. Therefore, it has a corner point for each permutation of the BS indices , and each such corner point is given by the tuple with where
– Thus, we have
1
( , , )
B
N
C C
B
N
(1) ( )
( , , )
B
N
C C
( ) ( ) (1) ( ) ( 1 ) ( )
; , , , ˆ ;
i i i i i
C I I
x x x x x x
( ) ( ) (1) ( 1)
i i i
B
( ) ( ) (1) ( 1)
i i i
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2
B
N
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[Simeone et al:09], i.e.,
,
i j
B
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– Selection of the precoding matrix
– e.g., zero-forcing [RZhang], MMSE [Hong et al], sum-rate max. [Ng-Huang]
– Optimization of the compression covariance
respect to .
A Ω A
i i
P
precoded quantization noise i i i
x x q 1
i
Ω A
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Compute and
A Ω
Precoding and compression BS 1 BS NB
1
C
B
N
C
,1 ,1
ˆ
k k k
H H
M
N
, ,
ˆ
B B
k N k N k
H H
M
N
Central encoder
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– The actual CSI is modeled as where – Worst-case optimization problem
k k k
max
ˆ : the CSI known at the central encoder, : the multiplicative uncertainty with ( ) 1.
k k k k
H Δ Δ
k
H
max
: ( ) , 1 ,
maximize min , s.t. , , for all , tr , for all .
M k k k k
N k k k i B i H i i i i i B
w f g C P i
Δ Δ A Ω 0
A Ω A Ω E AAE Ω
NM
S S
S N N
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– Lemma. The problem (3) is equivalent to the original weighted sum-rate maximization problem with for , i.e., where
k
M
N
ˆ (1 )
k k k
H H
, 1 ,
maximize , s.t. , , for all , tr , for all .
M
N k k k i B i H i i i i i B
w f g C P i
A Ω 0
A Ω A Ω E AAE Ω
S S
S N N
2 2
ˆ ˆ , logdet (1 ) ( ) ˆ ˆ logdet (1 ) .
H H k k k k H H k k l l k l k
f
A Ω I H AA Ω H I H A A Ω H
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– Consider MISO case such that . – The actual channel is modeled as where
H k k
M
k H k k k k k
h e e C e C
k
h ˆ
k k k
h h e
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– The “dual” problem of power minimization under SINR constraints for all MSs, i.e., where
, { } , 1 1 \{ }
minimize tr s.t. , 1 for all with 1 and , , , for all .
B M k k
N N H i i k i i i i k H k k k k H H k j k k k j k H k k k k i B i
k g C
R Ω 0
E R E Ω h R h h R h h Ωh e e C e A Ω
NM M
N M S S
N S N
, .
H k k k
k R A A
M
N
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– Lemma. Constraint (4b) holds if and only if there exist constants such that the condition is satisfied for all where we have defined pf: Follows by applying the S-procedure [Boyd-Vandenberghe, Appendix B-2].
ˆ ˆ ˆ ˆ 1
k k k k k H H k k k k k k
Ξ Ξ h C h Ξ h Ξ h { }
k k
M
N
k
M
N
\{ }
, for .
k k k j k j k
k
Ξ R R Ω
M
M N
N
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– The channel coefficients given by – Compare the following schemes
– Structured codes, but sensitive to the channel coefficients.
– Multivariate compression – Independent quantization (this case corresponds to the compressed DPC in [Simeone et al:09])
– Multivariate compression – Independent quantization (this case corresponds to quantized network MIMO in [Zakhour-Gesbert, Sec. IV-A])
1 1 1 2 2 2 3 3 3
1 1 1 y g g x z y g g x z y g g x z
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– Per-cell sum-rate versus when and .
20 dB P
2 4 6 8 10 12 14 1 2 3 4 5 6 C [bit/c.u.] per-cell sum-rate [bit/c.u.] RCoF DPC precoding Linear precoding RCoF multivariate compression independent compression
advantageous for both linear and DPC precoding.
effective approach in the regime of moderate backhaul , although multivariate compression allows to compensate for most of the rate loss of standard DPC precoding in the low- backhaul regime.
integer approximation penalty when the backhaul capacity is large enough.
C
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– There are three BSs and three MSs, i.e., . – Each BS uses two antennas while each MS uses a single antenna. – The elements of between MS and BS are i.i.d. with .
– In the separate design,
scheme in [Ng-Huang].
– Under the power constraint for each BS with selected so that the compression problem be feasible.
, k i
H
| |
(0, )
i k
CN
P
3
B
N N
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– Sum-rate versus for the separate design of linear precoding and compression with and
5 dB P 0 dB
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7 8 9 10
average sum-rate [bit/c.u.] multivariate compression independent compression C=2 bit/c.u. C=4 bit/c.u. C=6 bit/c.u.
sum-rate.
value, the problem of optimizing the correlation given the precoder is more likely to be infeasible.
backhaul capacity, since a larger backhaul capacity allows for a smaller power of the quantization noises.
Ω A
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– Sum-rate versus for linear precoding with and
P 2 C 0 dB
5 10 15 20 25 30 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 transmit power P [dB] average sum-rate [bit/c.u.] cutset bound multivariate compression independent compression joint design separate design
more pronounced when each BS uses a larger power.
more efficient compression strategies are called for.
partly compensating for the suboptimality
multivariate compression approaches the cutset bound as the transmit power increases.
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– Sum-rate versus for the joint design with and
P 2 C 0 dB
5 10 15 20 25 30 3.5 4 4.5 5 5.5 6 transmit power P [dB] average sum-rate [bit/c.u.] cutset bound multivariate compression independent compression DPC precoding linear precoding
backhaul links.
with perfect backhaul links where there exists constant sum-rate gap between DPC and linear precoding at high SNR (see, e.g., [Lee-Jindal]).
the compression strategy rather than precoding method when the backhaul capacity is limited at high SNR.
P
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– Sum-rate versus for linear precoding with and
C
5 dB P
0 dB
2 4 6 8 10 12 2 4 6 8 10 12 C [bit/c.u.] average sum-rate [bit/c.u.] cutset bound multivariate compression independent compression joint design separate design
capacity, the benefits of multivariate compression or joint design of precoding and compression become negligible.
becomes limited by the sum-capacity achievable when the BSs are able to fully cooperate with each other.
compression outperforms the joint design with independent quantization for backhaul capacities larger than 5 bit/c.u.
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– Sum-rate versus the inter-cell channel gain for linear precoding with and
2 C
5 dB P
3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 inter-cell channel gain [dB] average sum-rate [bit/c.u.] multivariate compression independent compression sum-of-backhaul-capacities joint design separate design
approaches the system consisting of parallel single-cell networks as the inter-cell channel gain decreases.
is not significant for small values of , since introducing correlation of the quantization noises across BSs is helpful only when each MS suffers from a superposition of quantization noises emitted from multiple BSs.
B
N
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strategies for the donwlink of cloud radio access networks.
– The BSs are connected to the central encoder via finite-capacity backhaul links.
– In order to control the effect of the additive quantization noises at the MSs.
and backhaul constraints was formulated.
– An iterative MM algorithm was proposed that achieves a stationary point.
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multivariate compression.
– based on successive per-BS estimation-compression steps.
– The proposed approach based on multivariate compression and on joint precoding and compression strategy outperforms the conventional approaches based on independent compression and separate design of precoding and compression strategies.
and when the limitation imposed by the finite-capacity backhaul link is significant.
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– Impact of CSI quality
– Broadcast approach [Shamai-Steiner][Verdu-Shamai]
fading states among the MSs.
– Combination of structured codes [Nazer et al][Hong-Caire], partial decoding
[Sanderovich et al][dCoso-Ibars] and multivariate processing [Park et al:13].
– Multi-hop backhaul links
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The talk considers the downlink of cloud radio access networks, in which a central encoder is
connected to multiple multi-antenna base stations (BSs) via finite-capacity backhaul links. The processing is done at the central encoder, while the distributed BSs employ only oblivious (robust)
different BSs are compressed independently, or alternatively the recently introduced structured coding ideas (Reverse Compute-and-Forward) are employed. We propose to leverage joint compression, also referred to as multivariate compression, of the signals of different BSs in order to better control the effect of the additive quantization noises at the mobile stations. We address the maximization of a weighted sumrate. For joint compression this is associated with the optimization
and backhaul capacity constraints. An iterative algorithm is described that achieves a stationary point of the problem, and a practically appealing architecture is proposed based on successive steps
the channel state information and overviewing some aspects for future research.
Cloud Radio Access Downlink with Backhaul Constrained Oblivious Processing
Joint work with S.-H. Park, O. Simeone (NJIT), and O. Sahin (InterDigital)