cloud processing for 5g systems v6simeone/cloud processing for 5g systems v6.pdf · cloud...
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Cloud Processing for 5G Systems
O. SimeoneNew Jersey Institute of Technology (NJIT)
Joint work with S.-H. Park1, O. Sahin2, S. Shamai3, J. Kang4 and J. Kang4
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Cloud Processing for 5G Systems
[Barbarossa et al ‘14]
• What will 5G be? Highly integrative with a flexible and intelligent core network [Andrews et al ‘14]
• Enabling technologies: mmwave, massive MIMO, extreme densification, cloud processing, software defined networking,…
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Cloud Processing for 5G Systems
Cloud Radio Access Network (C-RAN): Baseband processing offloading from the base stations to the cloud
Interference management (CoMP), simplified base station deployment
Cloud Mobile Computing: Code offloading from mobile users to the cloud
Increase in battery lifetime, enabling computation-heavy mobile applications (e.g., video processing, object recognition, gaming, …)
• Examples:
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Cloud Processing for 5G Systems
Cloud Radio Access Network (C-RAN): Baseband processing offloading from the base stations to the cloud
Interference management (CoMP), simplified base station deployment
Cloud Mobile Computing: Code offloading from mobile users to the cloud
Increase in battery lifetime, enabling computation-heavy mobile applications (e.g., video processing, object recognition, gaming, …)
• Examples:
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 6
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Cloud Radio Access Networks
• Heterogeneous dense network• Macro, femto, pico-BSs, relays• C-RAN: Baseband processing
takes place in the “cloud”
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Cloud Radio Access Networks
• Base stations act as radio units (RUs), or remote radio heads (RRHs): up/down-converters withno need for codebook information
• Fronthaul links carry complex (IQ) baseband signals
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Advantages:• Low-cost “green” BSs (RUs)• Dense deployment with enhanced indoor coverage• Flexible radio and computing resource allocation• Effective interference mitigation via joint baseband processing (e.g., eICIC and CoMP in LTE-A)
Key challenge: Effective transfer of the IQ signals on the fronthaul links
Cloud Radio Access Networks
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Cloud Radio Access Networks
The distribution of backhaul connections for macro BSs (green: fiber, orange: copper, blue: air) [Segel and Weldon].
• Fronthaul/backhaul links
• Mmwave backhauling for 5G systems [Ghosh ‘13]• Convergence of wireless access and backhaul [Dahlman et al
14]• Copper (LAN cable) for indoor coverage [Lu et al ‘14]
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Cloud Radio Access Networks• CPRI standard based on ADC/DAC
… Rate higher than supported by standard optical fiber channels (10GE)… 11
[IDT, Inc]
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Scope of the talk• How to design C-RANs? An information-theoretic view• Implications on system design• Topics:
o Advanced fronthaul compression inspired by network information theory
o Structured coding (compute-and-forward)o Joint design of fronthaul and wireless communication o Optimal functional split RU-CU: channel estimation, precoding o Single-hop vs. multi-hop fronthaul network
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 13
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System Model
MS
MS 1
RU1
RU
RU
MN
i
BN
,1Bn antennas
,B in antennas
, BB Nn antennas
iH
1H
BNH
CU
1C
iC
BNC
x
1y
iy
BNy
,1Mn antennas
, MM Nn antennas
Single-cluster single-hop fronthaul topology14
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• Point-to-point fronthaul compression:– Algorithms [Segel and Weldon] [Samardzija et al ‘12] [Nieman
and Evans ’13]– Testbed results [Irmer et al ’11] [Vosoughi et al ‘12]
Point-to-Point Fronthaul Compression
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RU 1
Decompressor
Decoder
RU NR
ul1y
ul2y
ulRNy
Fronthaul
RNC
1C ul1y
ul2y
ulˆRNy
Control Unit
Decompressor
Decompressor
Point-to-Point Fronthaul Compression
Compressor
RU 2
Fronthaul
2CCompressor
FronthaulCompressor
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Point-to-Point Fronthaul Compression
uly000
001
010
100
……
101 uly
17
• Ex.: Scalar quantizer
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niy
ˆ niy
110010011
Point-to-Point Fronthaul Compression
18
• Ex.: Vector quantizer
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• Information-theoretic analysis (rate-distortion theory)– Compression at RU described by a test channeli ˆ( | )i ip y y
ˆ( | )i ip y yiy ˆ iy
iy ˆ iy
Quantizationnoise
Point-to-Point Fronthaul Compression
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- The test channel determines the shape of the quantization regions
- Fronthaul rate = ˆ( ; )i i iI Cy y
ˆ( | )i ip y y
niy
ˆ niy
110010011
Point-to-Point Fronthaul Compression
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- MSE bound closely approximated by sufficiently large vector quantizers [Gray and Neuhoff ‘98] or scalar quantizers with entropy encoding [Ziv ‘85]
- Gaussian noise model asymptotically correct with dithered lattice quantizers such as TCQ, o at high resolution [Zamir and Feder‘96]
-Graphical codes [Nagpal et al 09]
niy
ˆ niy
110010011
Point-to-Point Fronthaul Compression
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 22
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Decoder
ul(1)y
ul(2)y
ul( )RNy
ul(1)ˆ y
ul(2)ˆ y
ul( )ˆ
RNy
Control Unit
Decompressor
WZDecompressor
WZDecompressor
Distributed Fronthaul Compression
RU 1
RU NR
Fronthaul
RNC
1CCompressor
RU 2
Fronthaul
2CWZ
Compressor
Fronthaul
WZCompressor
[Sanderovich et al ’09] [del Coso and Simoens ’09] [Zhou and Yu ’11]
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Point-to-Point Fronthaul Compression
uly000
001
010
100
……
101 uly
24
• Ex.: Scalar quantizer
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Distributed Fronthaul Compression
uly
uly
000
001
010
100
101
……
25
• Ex.: Scalar WZ compression
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10010
10010
10010
10010
10010
10010
10010
ˆ niy
niy
Distributed Fronthaul Compression
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• Ex.: Vector WZ compression
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10010
10010
10010
10010
10010
10010
10010
- Fronthaul rate =
ˆ niy
niy
ˆ ˆ( ; | )i i S iI Cy y y
Distributed Fronthaul Compression
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• Information-theoretic analysis (rate-distortion theory):
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• Practical implementations:o Quantization code that can be partitioned into cosets that are good
channel codes: trellis codes [Pradhan and Ramchandran ’03], polar codes [Korada and Urbanke '10], compound LDGM-LDPC code [Martinian and Wainwright '06]
o Separate quantization and channel coding: scalar quantization and vector binning [Liu et al '06], scalar quantization and turbo codes [Aaron et al ‘02]
Distributed Fronthaul Compression
QuantizernX Binning M
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Distributed Fronthaul Compression
• Max-Rate compression problem at BS
– is the set of BSs previously selected by BS ordering
ˆ( | )ˆ ˆmaximize ( ; | )
ˆ ˆs.t. ( ; | )i i
ip
i i i
I
I Cy y
x y y
y y y
S
S
S
ˆ( | )i ip y yiyˆ iy
BS i
cloud
yS
i
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• Proposition [del Coso and Simoens ’09]. The optimal test channel for (P1) is Gaussian, i.e.,
– Linear transformation given as
ˆ( | )i ip y y
ˆ i i i i y A y q with ~ ( , ).iq 0 ICN
,
†ˆ| 1diag , ,
i B in y y U US
1 11 ,1ll
,
1/2 †1diag , ,
B ii n A U
where
iA
Distributed Fronthaul Compression
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• Block diagram of Max-Rate compression
†Uiy
1y
,B iny
1
,B in
,1iq
,, B ii nq
,1ˆiy
,,ˆB ii ny
ySuncorrelated
conditioned on
ConditionalKLT
1† †ˆ|
x y x x x t xH H H H
S SS S S S
Distributed Fronthaul Compression
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• Simulation setting:– Three-cell heterogeneous network– One MBS, HBSs and MSs per cell
• MBS located at the cell center• HBSs and MSs are uniformly distributed within the cells to
which they belong.
– Single-antenna MSs, i.e.,
• Schemes:– Max-Rate, (direct/indirect) MMSE, DF– With side information and no side information
/ 3 1BN
, 1M in
MN
Example
32
[Park et al ’13]
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9, 9, 0.5B MN N 10 bps/HzC
Example
33
[Park et al ’13]
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,9, 9, 8B M B iN N n 15 bps/HzC tx 5 dBP
Example
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[Park et al ’13]
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• CSI requirements of max-rate compression
†Uiy
1y
,B iny
1
,B in
,1iq
,, B ii nq
,1ˆiy
,,ˆB ii ny
ySuncorrelated
conditioned on
ConditionalKLT
1† †ˆ|
x y x x x t xH H H H
S SS S S S
Distributed Fronthaul Compression
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[Park et al ’13]
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BSiy
i
Original Max-Rate maximization
Robust Max-Rate maximization [Park et al ’13]
Backhaul iCˆ iy
Cloud
yS
ˆ iy
ˆ|x yS
BSiy
i Backhaul iCˆ iy
Cloudˆ iy
ˆ ˆ| |ˆ ( ) x y x yS S
yS
Distributed Fronthaul Compression
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• Imperfect covariance feedback, i.e., .• Additive model
with uncertainty set , i.e., where
ˆ ˆ ˆ| | | x y x y x yS S S
U
ˆ ˆ| | x y x yS S
ˆ ˆmin | LB max | UB( ) , ( ) x y x y
S S
ˆ| x ySU
†ˆ ˆ| |i i x y x yH HS S
Distributed Fronthaul Compression
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• Max-min robust formulation
ˆ|ˆ( | )
ˆ ˆmax | UB min | LB
ˆ ˆmaximize min ( ; | )
ˆ ˆ s.t. ( ; | ) ,
and .
nMi iip
i i i
I
I C
x yy y
x y x y
x y y
y y y
S
S S
SH
S
( 2)P
Distributed Fronthaul Compression
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• Theorem [Park et al ’13].A local optimum for problem (P2) is given as
ˆ i i i i y A y q with ~ ( , ).iq 0 ICN
,
†ˆ| 1
ˆ diag , ,i B in y y U US
,1, , : solution to the following mixed integer problemB in
,
1/2†
1diag , ,B ii n A U
where,
† †
1 1B in
UU U U I
,
1 ,
,
LB, , , 1
,
UB1
max log(1 ( )) log(1 )
s.t. 0 1,( ), 1, , ,
log(1 ( )) .
B i
nB i
B i
n
l l ll
l l B i
n
l l il
l n
C
Pwhere ( ) is a discrete set dependent on .l P
Distributed Fronthaul Compression
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• Block diagram:
†Uiy
1y
,B iny
1
,B in
,1iq
,, B ii nq
,1ˆiy
,,ˆB ii ny
ConditionalKLT
ˆ|x yS
Solution of optimization problem
Distributed Fronthaul Compression
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• Simulation setting:– Single-cell heterogeneous network– One MBS and HBSs
• MBS located at the cell center• HBSs and MSs uniformly distributed within whole cell
– Single-antenna MSs, i.e.,
• Schemes:– Max-Rate, NSI– Max-Rate, imperfect SI– Max-Rate, imperfect SI, robust– Max-Rate perfect SI
1BN
, 1M in
Example
41
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,4, 8, 2B M B iN N n 0.5 tx 10 dBP
Example
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• In each macro-cell, pico-BSs and MSs are uniformly distributed.
Simulation Set-upN K
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• Frequency reuse pattern with reuse factor for 1-cell cluster [Wang and Yeh ’11]
1/ 3F
Simulation Set-up
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Simulation Set-upParameters Assumptions
System bandwidth 10 MHz
Path-loss (macro-BS - MS)
Path-loss (pico-BS - MS)
Antenna pattern for sectorized macro-BS antennas
Lognormal shadowing (macro-BS - MS) 10 dB standard deviation
Lognormal shadowing (pico-BS - MS) 6 dB standard deviation
Antenna gain after cable loss (macro-BS) 15 dBi
Antenna gain after cable loss (pico-BS, MS) 0 dBi
Noise figure 5 dB (macro-BS), 6 dB (pico-BS), 9 dB (MS)
Transmit power 46 dBm (macro-BS), 24 dBm (pico-BS), 23 dBm (MS)
Small-scale fading model Rayleigh-fading
Synchronization Perfect synchronization
Inter-site distance (site: macro-BS) 750 m
Frequency reuse factor F=1/3
Number of antennas Single antenna at each macro/pico-BS and MS
Channel state information (CSI) Full CSI at control units about BSs in the cluster
10PL(dB) 128.1 37.6log ( in km)R R
10PL(dB) 38 30log ( in m)R R 2
3dB
3dB
( ) min[12( / ) , ]( 65 , 20 dB)
m
m
A AA
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• LTE rate model [3GPP-TR-136942]
Simulation Set-up
min
attenuate min max
max max
0, if( ) ( ), if
, if
k
k k k k
k
R SR
12 max max attenuate
attenuate
max
min
: SINR at MS ; ( ) log (1 ); ( / );: attenuation factor representing implementation losses;: Maximum and minimum throughput of the codeset, bps/Hz;: Minimum SINR of the codeset.
k k S S R
R
Parameter UL DL Notes
2.0 4.4 Based on 16-QAM 3/4 (UL) & 64-QAM 4/5 (DL)
-10 dB -10 dB Based on QPSK with 1/5 (UL) & 1/8 (DL)
0.4 0.6 Representing implementation losses
maxR
[3GPP-TR-136942, Annex A]
minattenuate
where
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• Proportional fairness metric
– At each time , the rate is updated as
Simulation Set-up
sum-PF1
( )( )K
k
k k
R tR tR
: fairness constant;( ) : instantaneous rate for MS at time ;: historical data rate for MS until time 1.
k
k
R t k tR k t
where
(P1)
(1 ) ( )k k kR R R t
t kR
where [0,1]: the forgetting factor.
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• Cell-edge throughput versus average spectral efficiency– macro pico maxUplink, 1-cell cluster, 3 pico-BS, 5 MSs, ( , ) (9,3) bps/Hz, 10, 0.5, 1/ 3N K C C T F
0.85 0.9 0.95 1 1.05 1.11800
2000
2200
2400
2600
2800
3000
3200
3400
3600
spectral efficiency [bps/Hz]
5%-il
e ra
te (c
ell-e
dge
thro
ughp
ut) [
kbps
]
Point-to-point compressionMultiterminal compression
=2.0
=1.0
=0.5
=0.25
1.6x
Numerical Results
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 49
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• An achievable rate with JDD was derived in [Sanderovich et al ’09]
sum ˆ ˆmin ( ; | ) ( ; ) ,j j jj
R C I I
y y x x y
BSS N
S
Joint Decompression and Decoding
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• The problem of maximizing the sum-rate is a Difference of Convex (DC) problem [Park et al ’14].
-30 -25 -20 -15 -10 -5 07.5
8
8.5
9
9.5
inter-cell channel gain [dB]
aver
age
per-c
ell s
um-ra
te [b
it/c.
u.]
cutset upper boundJDD w/ MM algorithmSDD w/ exhaustive orderingSDD w/ greedy ordering
separate decompressionand decodinng
joint decompressionand decoding
Joint Decompression and Decoding
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 52
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Compute-and-Forward[Nazer et al ’09] [Hong and Caire ’11]
• The MSs use nested lattice codes:
[B. Nazer]
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Decoder
Control Unit
Compute-and-Forward[Nazer et al ’09] [Hong and Caire ’11]
RU 1
RU NR
ul1y
ul2y
ulRNy
Fronthaul
RNC
1CInteger Decoder
RU 2
Fronthaul
2C
Fronthaul
Integer Decoder
Integer Decoder
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• Three-cell SISO circular Wyner model
Numerical Results
CU
CCC
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Numerical Results3 bit/s/Hz and =0.4C
0 5 10 15 20 25 30
1
1.5
2
2.5
3
MS transmit power [dB]
per-c
ell s
um-ra
te [b
its/s
/Hz]
Cut-set upper bound
Point-to-point compression
Single-cell processing
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Numerical Results3 bit/s/Hz and =0.4C
0 5 10 15 20 25 30
1
1.5
2
2.5
3
MS transmit power [dB]
per-c
ell s
um-ra
te [b
its/s
/Hz]
Cut-set upper bound
Distributed compression
Point-to-point compression
Single-cell processing
Compute-and-forward
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 58
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Time-Varying Channels
• So far, static channels • With static channels, the fronthaul overhead due to CSI transfer is
negligible
MS
MS 1
RU1
RU
RU
MN
i
BN
,1Bn antennas
,B in antennas
, BB Nn antennas
iH
1H
BNH
CU
1C
iC
BNC
x
1y
iy
BNy
1y
ˆ iy
ˆBNy
,1Mn antennas
, MM Nn antennas
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Time-Varying Channels
• Time-varying ergodic channel with coherence blocks of length T channel uses [Hassibi et al ’03]
• RU-CU functional split: where to perform channel estimation?
60
… p d
T T T
p d p d …
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Compress-Forward-Estimate (CFE)[Hoydis et al ‘11]
H CU
C1
MS NM
...
MS 1RU 1
RU NB CNB
,1 ,1p dY Y
, , B Bp N d NY Y
ˆ ˆp dY Y
• The RUs compress both training and data fields• The CU estimates the channel and performs coherent decoding
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Estimate-Compress-Forward (ECF)
H CU
C1
MS NM
...
MS 1RU 1
RU NB CNB
[Kang et al ‘14]
• Motivated by the information-theoretic argument of separate estimation and compression [Witsenhausen ‘80]
• The RUs estimate the channel and compress both CSI and data field• The CU performs coherent decoding
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Semi-Coherent Processing[Kang et al ‘14]
• For low fronthaul capacities…• BS estimates the CSI and performs local equalization • BS compresses and forwards the equalized data signals to CU• CU jointly decodes the data signal by mismatched decoding metric
[Weingarten et al ’04]
63
H
CU
C1MS 1
RU 1
,1dX
ˆdX
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Semi-Coherent Processing[Kang et al ‘14]
H
CU
C1MS 1
RU 1
,1dX
ˆdX
is a weight factor for each coherence block
• Mismatched decoding:
• With one fronthaul bit per coherent block
weigh less blocks with poor CSI64
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Non-Coherent Capacity
H CU
C1
MS NM
...
MS 1RU 1
RU NB CNB
• Do not impose training + data structure [Marzetta and Hochwald ’99]• The RUs quantize the received signal
[Kang et al ‘14]
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66
NB=NM=2, Nt=Nr=4, C=6, T=10, K=0
Example
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67
ExampleNt = Nr = 2, P = 10dB, T = 4, and K = 0
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68
Nt = Nr = 2, P = 5dB, C=5 bits/s/Hz, T = 4, and K = 0Example
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 69
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System Model
CU1, ,
MNM M
RU1
,1Bn antennas
1x1C
RU
BN
, BB Nn antennas
BNxBNC
MS 1M1
,1Mn antennas
1y
MSˆ
MNMMN
, MM Nn antennas
MNy
1H
MNH
Single-cluster single-hop fronthaul topology70
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Point-to-Point Fronthaul Compression
1C1M Channel
encoder 1
Precoding
RU 1
Central Unit
MNM Channelencoder NM
1s
MNs
Compressor1
1x
BNxBNC
1x
RU BNx
BNBN
Compressor
[Simeone et al ’09] [Patil and Yu ’14]
71
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Point-to-Point Fronthaul Compression
2x
1x
Ex.: Scalar quantization
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2x
1x
… uncorrelated quantization noise
Point-to-Point Fronthaul Compression
73
Ex.: Scalar quantization
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 74
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Multivariate Fronthaul Compression
1C1M Channel
encoder 1
Precoding
RU 1
Central Unit
MNM Channelencoder NM
1s
MNs
1x
BNxBNC
1x
RU BNx
BN
Multivariatecompression
[Park et al ’14]
75
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• Multivariate compression produces compressed signals with correlated quantization noises: new design degree of freedom
Multivariate Fronthaul Compression
can be reduced by controlling 1,2 2,1
HΩ Ω
RU 1
RU 2
MS
1 1 1H x E As q
2 2 2H x E As q
1,1H
1,2H
1z1
11 1 12
qH
qy H As z
1,1 1,21 1
2,1 2,2
, H
Ω Ω0 H H
Ω ΩCN
CU
1C
2C
76
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Multivariate Fronthaul Compression
2x
1x
77
Ex.: Scalar quantization
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Multivariate Fronthaul Compression
2x
1x
78
Ex.: Scalar quantization
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Multivariate Compression Lemma
| , for all {1, , }i ii i
h X h X X R M
SS S
S
1, , MC C
1 1( , , , ) ( ) ( , , | )M Mp x x x p x p x x x
i.i.d.joint typicality wrt
79
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• Multivariate compression lemma– Ex.: With , , we have
while with separate compression, we have
1 1 1
2 2 2
1
1 1
2 2
2 1 2 1 21 2 1 2
| , ( 1)
| , (
;
;
; ,
2)
, | . ( 3; )
Ih h C A
h h C A
h h h C
I
I CI A
x x x
x x x
x x x x
x x
x x
x x x x xx
1 1 1
2 2 2
; , ( 1)
; . ( 2)
I C B
I C B
x x
x x
2BN
Multivariate Compression Lemma
80
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Multivariate Compression Lemma
(contrapolymatroid)81
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• Linear precoding (DPC treated in a similar way)
• Gaussian test channel:
• The compressed signal is given as
with and
Multivariate Fronthaul Compression
,, ~ ( , ),i i i i i i i x x q q 0 Ω BCN N
, x As q1 , ,
B
HH HN x x x
1 , , ~ ( , )B
HH HN 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 ΩΩ
Ω Ω Ω
82
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• Joint optimization of precoding and compression:
where
• DC problem: Local optimum via MM algorithm
, 1
,
maximize ,
s.t. , , for all ,
tr , for all .
MN
k kk
i Bi
Hi i i i i B
w f
g C
P i
A Ω 0
A Ω
A Ω
E AAE Ω
SS
S N
N
,
, ;
log det ( ) log det ,
, |
log det log det .
k k k
H H H Hk k k l l k
l k
ii
H H Hi 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 SS
S SS S
Multivariate Fronthaul Compression
83
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Step :
• The implementation of joint compression is complex• A successive architecture with a given permutation .
– Compression rate at step :
i
: B BN N
Step 1:
( 1)i
(1)x
(1)q
(1)x
(1) (1), (1)~ , q 0 ΩCN
compression
(1)
( )( 1)
( )
ii
i
x
uxx
( ) ( ) ( )
1,i i i
x u u
( )ˆ iq
( )ix
MMSE estimationof given( )ix ( )iu
compression
(1) (1)( ) |ˆ ~ ,i x uq 0CN
( )ˆ ix
( ) ( )ˆ ;i iI x x( 1)i i
Multivariate Fronthaul Compression
84
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• Successive estimation-compression architecture
Multivariate Fronthaul Compression
85
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• In each macro-cell, pico-BSs and MSs are uniformly distributed.
Simulation Set-upN K
86
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• Cell-edge throughput versus average spectral efficiency–
Numerical Results
macro pico maxDownlink, 1-cell cluster, 1 pico-BS, 4 MSs, ( , ) (3,1) bps/Hz, 5, 0.5, 1/ 3N K C C T F
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.250
500
1000
1500
2000
2500
3000
3500
4000
spectral efficiency [bps/Hz]
5%-il
e ra
te (c
ell-e
dge
thro
ughp
ut) [
kbps
]
Point-to-point compressionMultiterminal compression
=1.5
=0.5
=0.25
2x
87
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 88
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• Reverse compute-and-forward (RCoF) [Hong and Caire ‘12]
Compute-and-Forward
1C1M Channel
encoder 1
Integerprecoding
RU 1
Central encoder
MNM Channelencoder NM
1s
MNs
1x
BNx BNC
1x
RU BNx
BN
89
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• Three-cell SISO circular Wyner model
Numerical Results
CU
CCC
90
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0 2 4 6 8 10 12 140
1
2
3
4
5
6
C [bits/s/Hz]
per-c
ell s
um-ra
te [b
its/s
/Hz]
Cut-set upper bound
Multivariate compression
Point-to-point compression
Linear precoding
Single-cell processing
• Three-cell SISO circular Wyner model ( and )
Numerical Results20 dBP 0.5
91
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• Three-cell SISO circular Wyner model ( and )
Numerical Results20 dBP 0.5
0 2 4 6 8 10 12 140
1
2
3
4
5
6
C [bits/s/Hz]
per-c
ell s
um-ra
te [b
its/s
/Hz]
Cut-set upper bound
Multivariate compression
Point-to-point compression
DPC precoding
Linear precoding
Single-cell processing
92
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• Three-cell SISO circular Wyner model ( and )
Numerical Results20 dBP 0.5
0 2 4 6 8 10 12 140
1
2
3
4
5
6
C [bits/s/Hz]
per-c
ell s
um-ra
te [b
its/s
/Hz]
Cut-set upper bound
Multivariate compression
Point-to-point compression
DPC precoding
Compute-and-forward
Linear precoding
Single-cell processing
93
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 94
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95
• Ergodic channel with coherence blocks of length T channel uses [Hassibi et al ’03]
Time-Varying Channels
T T T
… …
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96
• RU-CU functional split: where to perform precoding?
• Instantaneous CSI: Design different precoders for each coherence period
• Stochastic CSI: o CU only knows the spatial correlation (e.g., [Adhikari et al ‘14])
o Design a single precoder across all coherence periods
Time-Varying Channels
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97
Compress-After-Precoding
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98
Compress-Before-Precoding[Park et al ‘13] [Kang et al ‘14] [Patil and Wu ‘14]
• Clustering: Send each user’s message to a subset of RUs• Precoding performed at the RUs
Precodingdesign
CSIMUX
...
CU
MUX
Q
Q
...
De-MUX
De-MUX
Q-1Pre-
coding
Pre-coding
RU1
RUNR
data streams
Cluster-ing
Fronthaul
Fronthaul
Channelcoding
Q-1
Channelcoding
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99
Compress-Before-Precoding[Park et al ‘13] [Kang et al ‘14] [Patil and Wu ‘14]
• Perfect CSI: Precoding overhead gets amortized over T• Stochastic CSI: Since the precoding matrix is the same across all the
coherence periods, negligible overhead
Precodingdesign
CSIMUX
...
CU
MUX
Q
Q
...
De-MUX
De-MUX
Q-1Pre-
coding
Pre-coding
RU1
RUNR
data streams
Cluster-ing
Fronthaul
Fronthaul
Channelcoding
Q-1
Channelcoding
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100
Example
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101
ExampleNR = 4, Nt,i = 2, Nr,j = 1, P = 10 dB, C=4 bits/s/Hz, T = 10
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102
ExampleNR = NM = 4, Nt,i = 2, Nr,j = 1, P = 20 dB, C= 2 bits/s/Hz,
instantaneous CSI
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103
ExampleNR = NM = 4, Nt,i = 2, P = 10 dB, C= 3 bits/s/Hz, T=10
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 104
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Inter-Cluster Multivariate Compression Design
[Park et al ‘14]
CU 1
1,1C
CU 2
RU(1,1)
RU(1,2)1,2C
2,1C RU(2,1)
RU(2,2)2,2C
MS(1,1)
MS(1,2)
MS(2,1)
MS(2,2)
1,1 1,2,M M
2,1 2,2,M M
Inter-cluster interference
1,1M
1,2M
2,1M
2,2M
105
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Inter-Cluster Multivariate Compression Design
106
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 107
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Multi-Hop Fronthaul Topology [Park et al ‘14]
108
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• Multiplex-and-Forward (MF)• Decompress-Process-and-Recompress (DPR): In-network
processing• Optimization of the uplink sum-rate
Multi-Hop Fronthaul Topology
109
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• [Ni et al ’13] Simulation-based study of in-network processing on the LLRs
• [Goela and Gastpar ’12] Optimal linear in-network processing strategies in a multihop network for estimation
• [Avestimehr et al ‘08] Deterministic and Gaussian relay networks• [Cuff et al ‘09] Cascade source coding
Related Works
110
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MS 1
MS K
x
RU 1
RU 3
RU 5
RU 7
RU 4
RU 2
CU
RU 6
1y
2y
3y
4y
5y 6y
7y
i i i y H x z
1,2C
1,3C 2,8C
3,8C
4,3C4,8C
6,8C5,6C
5,7C7,8C
MS: mobile stationRU: radio unit
Uplinkchannels
System Model
Capacitated directed acyclic graph (DAG)111
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RU i
?1
| ( ) |
i
iiI
i
e
i
e
yu
r
u
1
| ( ) |
i
iiO
e
e
u
u
RU Operation
• Multiplex-and-Forward (MF)• Decompress-Process-and-Recompress (DPR): In-network
processing
112
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Compressioniy ˆ iy
RU i
MU
X / DEM
UX
( )I i ( )O i
From RUs inprevious layers
To RUs and CUin next layers
Multiplex-and-Forward
113
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Multiplex-and-Forward
~ ( , ).i iq 0 ΩCNˆ ,i i i y y q• Gaussian test channel
Compressioniy ˆ iy
114
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• Define as the capacity used to convey the signal compressed at node on edge for act ,e i E M
0ief
iv e
act,ie e
if C e
M
E
Multiplex-and-Forward
Edge capacity constraint
Flow conservation at each RU
115
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• Sum-rate maximization:
• Difference-of-convex (DC) problem: Majorization Minimization (MM) approach to find a locally optimal solution.
,act
{ } ,{ 0}
( 1)
maximize log det log det
log det log det ,
s.t.
i iie e i
i
I
f
ii i e
e M
f i
xΩ 0
y
HΣ H I Ω I Ω
Ω Σ Ω
M
E M
M
Multiplex-and-Forward
act,ie e
if C e
M
E
116
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( )O i
Compression
( )Ie e i
u
iy
i
Compression
Decom
pression
LinearProcessing
( )I i
RU
From RUs inprevious layers
To RUs and CUin next layers
Decompress-Process-and-Recompress
( )Oe e iu
ir
117
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• Process and decompress:
with
,e e i e u L r q
Decompress-Process-and-Recompress
~ ( , )e eq 0 ΩCN
• Characterization of the relation between input and output vector [Goela and Gastpar ’12]
118
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• Sum-rate maximization
act
,
{ , }
act
rxact
log detmaximize
log det
s.t. log det log det , tail(e), ,
, , .
e e e
i
i e iee R i l l
H H H H
H H
He e e e e
d dd n ee e
C i e
e
x
L Ω 0
r
T HΣ H T TT TΩT
TT TΩT
Ω L Σ L Ω
L L
E
E
E
Decompress-Process-and-Recompress
119
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• Lemma. We can set for without loss of optimality.
• The optimization over is a DC problem: MM algorithm
e L I
act{ }e eΩ E
acteE
Decompress-Process-and-Recompress
120
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RU1
RUN
1y NyRUN+1
RU2N
1Ny 2Ny
RU2N+1
RU2N+2
RU2N+32 1Ny 2 2Ny 2 3Ny
CU
1,2 1NC
1,2 2NC
,2 1N NC ,2 2N NC 1,2 2N NC 2 ,2 2N NC
2 ,2 3N NC
1,2 3N NC
2 1,2 4N NC
2 2,2 4N NC
2 3,2 4N NC
1 {1, ,2 }N V
2 {2 1, ,2 3}N N V
3 {2 4}N V
Layer 1
Layer 2
Layer 32 3M N
• Each MS and RU have a single antenna• All RUs have the same average SNR• Rayleigh fading channels
Numerical Results
121
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K=4, SNR = 20 dB
Numerical Results
2 4 6 8 10 12 14 16 18 20 222.5
3
3.5
4
4.5
5
5.5
6
6.5
7
Number N of RUs in layer 1
Aver
age
sum
-rate
[bits
/s/H
z]DPRMF
=4 bits/s/Hz
=3 bits/s/Hz
=2 bits/s/Hz
eC
eC
eC
122
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K=5, N=2, SNR = 0 dB
0 5 10 15 200
2
4
6
8
10
12
14
16
18
Fronthaul capacity of each edge [bps/Hz]
Aver
age
sum
-rate
[bps
/Hz]
cutset boundDPRMF
Numerical Results
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Overviewo Introduction and Motivationo Uplink with Single-Hop Fronthaul Topology
– Point-to-Point Fronthaul Compression– Distributed Fronthaul Compression– Joint Decompression and Decoding– Compute-and-Forward– Time-Varying Channels
o Downlink with Single-Hop Fronthaul Topology – Point-to-Point Fronthaul Compression– Multivariate Fronthaul Compression– Compute-and-Forward– Time-Varying Channels– Inter-Cluster Multivariate Fronthaul Compression
o Uplink with Multi-Hop Fronthaul Topologyo Conclusions 124
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Conclusionso Information-theoretic view on C-RAN
o Novel approaches inspired by theory: distributed/multivariate fronthaul compression, compute-and-forward, joint decompression and decoding, estimate-compress-forward, semi-coherent processing, in-network processing,…
o Implementation: linear codes, scalar quantization, successive estimation and compression,…
o Performance of conventional techniques can be drastically improved by strategies inspired by information theory
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