Sparse and Low-Rank Optimization for Dense Wireless Networks Part - - PowerPoint PPT Presentation

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Sparse and Low-Rank Optimization for Dense Wireless Networks Part - - PowerPoint PPT Presentation

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Sparse and Low-Rank Optimization for Dense Wireless Networks Part I: Models Jun Zhang Yuanming Shi HKUST ShanghaiT ech University 1 GLOBECOM 2017 TUTORIAL Outline of Part I Motivations T woVignettes Structured Sparse Models

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Sparse and Low-Rank Optimization for Dense Wireless Networks Part I: Models

1 GLOBECOM 2017 TUTORIAL

Yuanming Shi

ShanghaiT ech University

Jun Zhang

HKUST

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Outline of Part I

 Motivations  T

woVignettes

Structured Sparse Models

Group Sparse Beamforming for Network Power Minimization

Sparsity Control for Massive Device Connectivity

Generalized Low-Rank Models

Low-Rank Matrix Completion for T

  • pological Interference Management

Extensions

 Future Directions

2 GLOBECOM 2017 TUTORIAL

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Motivations: Dense Wireless Networks

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Challenge: Ultra mobile broadband

 Era of mobile data deluge

4

Source: Cisco VNI Mobile, 2017

18 x

Over past 5 years

60 %

in 2016

429 M

Mobile devices added in 2016

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Cooper’s Law

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25 5 5 1600

Factor of Capacity Increase since 1950 Network densification is a dominant theme!

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Solution: cloud radio access networks

 Dense

Cloud-RAN: a cost-effective way for wireless network densification and cooperation

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Baseband Unit Pool

S uperCompute r SuperCom puter S uperComput er S uperComput er SuperCom puter

Remote Radio Head (RRH) Fronthaul Network

Cloud-RAN

4 Cs

Centralization Resource Pooling Improved Coordination

Cloud-RAN

Cost and Energy Optimization Cloud Virtualized Functions

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Dense Cloud-RAN

 Higher network capacity

 Denser deployment

 Scalable connectivity

 Flexible resource management

 Higher energy efficiency

 Low-power RRHs, flexible energy management

 Higher cost efficiency

Low-cost RRHs, efficient resource utilization

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Baseband Unit Pool

S uperCompute r S uperComput er SuperCom puter SuperCom puter SuperCom puter

RRH Fronthaul Network Cloud-RAN

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Intelligent things for smart city

 A smart city highly depends on intelligent technology: connected sensors,

intelligent devices and IoT networks become wholly integrated

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Challenge: Intelligent IoT

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Internet of Things

People to People

Mobile Internet

Tactile Internet

Fundamental shift: from content- delivery to skillset-delivery networks

  • Low Latency
  • High Computation Intensity
  • Massive Connectivity
  • …

(internet of skills)

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Grid Power Local Processing Power Supply Discharge Wireless Network

Active Servers Inactive Servers

Fog center Cloud Center User Devices Edge device

Charge

Solution: fog radio access networks

 Dense Fog-RANs: push computation and storage resources to

network edge – Overcome the long distance problem

Caching at the edge

Computing at the edge

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share computation, storage, communication resources across the whole network

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A new paradigm for wireless networking

 Goal: support ultra-low latency, reliable, Gbps communications, massive

device connectivity, massive data analytics, edge-AI…

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Difficulties

 Networking issues:

Huge network power consumption

Massive device connectivity

Severe network interference  Computing issues:

Complicated (non-convex) problem structures

Limited computational resources

12

Source: Alcatel-Lucent, 2013

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Sparse and low-rank optimization

 Successful Stories

Compressed sensing/matrix completion: Collect random measurements; reconstruct via optimization

Statistical machine learning: Random data models; fit model via

  • ptimization

 Advantages

Modeling flexibility: Low-dimensional structures in high-dimensional data

Fundamental bounds: Computational and statistical tradeoffs

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Sparse and low-rank optimization

 Emerging examples in wireless

Structured sparse models: Group sparse beamforming, user admission control, massive device connectivity…

Generalized low-rank models: T

  • pological interference management,

mobile edge caching, wireless distributed computing, index coding…  Motivations

Modeling flexibility: Structured models in dense and complex networks

Computational scalability: Convex optimization, manifold optimization…

Theoretical guarantees: Convex geometry, differential geometry…

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Vignette A: Structured Sparse Models

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Case I: Group Sparse Beamforming for Network Power Minimization Case II: Sparsity Control for Massive Device Connectivity

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Case I: Group Sparse Beamforming for Network Power Minimization

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Network power consumption

 Goal: Design green dense Cloud-RANs  Prior works: Physical-layer transmit power consumption

Wireless power control: [Chiang, et al., FT 08], [Qian, et al., TWC 09], [Sorooshyari, et al.,TON 12], …

Transmit beamforming: [Sidiropoulos and Luo, TSP 2006], [Yu and Lan, TSP 07], [Gershman, et al., SPMag 10],…  Challenge:

Network power consumption:

Radio access units, fronthaul links, etc.

17 GLOBECOM 2017 TUTORIAL Baseband Unit Pool

SuperCo mputer Super Comp uter Super Comp uter Super Comp uter Super Comp uter

RRH Fronthaul Network Cloud-RAN

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Network adaptation

 Goal: Provide

a holistic approach to minimize network power consumption (including RRHs, fronthaul links, etc.)

 Key observation: Spatial and temporal mobile data traffic variation

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Network adaptation: adaptively switch off network entities to save power

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System model

 The received signal at the k-th MU is given by

: channel propagation between MU and RRH

: transmit beamforming vector from the -th RRH to

  • th MU

Per-RRH transmit power constraint:  The signal-to-interference-plus-noise ratio (SINR) for MU

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Network power consumption

 Continuous function: Transmit power consumption

: Drain inefficiency coefficient of the radio frequency power amplifier  Combinatorial function: Relative fronthaul link power consumption

: a partition of

: relative fronthaul link power consumption, i.e., the static power saving when both the fronthaul link and the corresponding RRH are switched off

Aggregative beamformer:

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Problem formulation

 Goal: Minimize network power consumption in Cloud-RAN

Simultaneously control both the combinatorial function and the continuous function

Challenges: Non-convex, high-dimensional  Prior algorithms: heuristic or computationally expensive [Philipp, et. al,

TSP 13], [Luo, et. al, JSAC 13], [Quek, et. al,TWC 13],…

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combinatorial composite function

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Finding structured solutions

 Proposal: group sparse beamforming

Switch off the

  • th RRH

, i.e., group sparsity structure in

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Beamforming coefficients of the first RRH, forming a group

Baseband Unit Pool

SuperComputer Super Comp u ter Super Comp u ter Super Comp u ter Super Comp u ter

RRH Fronthaul Network Cloud-RAN [Ref]

  • Y. Shi, J. Zhang, and K. B. Letaief, “Group sparse beamforming for green Cloud-RAN,” IEEE

Trans. Wireless Commun., vol. 13,

  • no. 5, pp. 2809-2823, May 2014. 2014. (The 2016 Marconi Prize Paper Award)

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Group sparse beamforming algorithm

 Adaptive RRH selection: Switch off the RRHs with small coefficients in

the aggregative beamformers

 Stage I: The tightest convex positively homogeneous lower bound of the

combinatorial composite objective function (network power)

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mixed -norm induce group sparsity RRH ordering

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Group sparse beamforming algorithm

 Stage II: Find the optimal active RRHs via solving a sequence of

following feasibility detection problems (e.g., bi-section search)

 Stage III: Transmit power minimization via coordinated beamforming

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Active RRH set

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Summary of group sparse beamforming

 SINR constraints can be reformulated as second-order cone constraints

Key observation: phases of ’s do not change objective and constraints 

Group sparse beamforming via convex programming

Stage I: Group sparsity inducing via solving one convex program

Stage II: A sequence of convex feasibility problems need to be solved

Stage III: Coordinated beamforming via solving one convex program

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convex

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The power of group sparse beamforming

 Group spare beamforming for green Cloud-RAN (10 RRHs, 15 MUs)

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Conclusions:

1) Enabling flexible network adaptation; 2) Offering efficient algorithm design via convex programming 3) Empowering wide applications

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Extension: Wireless cooperative networks

 A comprehensive consideration: 1) Active BS selection; 2) Transmit

beamforming; 3) Backhaul data assignment

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Network power consumption: 1) Static power consumption at BSs 2) Transmit power consumption from BSs 3) Traffic-dependent backhaul power consumption

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Layered group sparse beamforming

 Proposal: A generalized layered group sparse beamforming (LGSBF)

modeling framework

T

  • induce the layered sparsity structure in the beamformers

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Active BS selection Backhaul data assignment

[Ref] X. Peng, Y. Shi, J. Zhang, and K. B. Letaief, “Layered group sparse beamforming for cache-enabled wireless networks,” IEEE Trans. Commun., to appear.

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Case II: Sparsity Control for Massive Device Connectivity

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Motivation

 Downlink transmission with massive devices: user admission control  Uplink machine-type communication (e.g., IoT devices) with sporadic

traffic: massive device connectivity

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Sporadic traffic: only a small fraction of potentially large number of devices are active

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Downlink user admission control

 Coordinated beamforming for transmission power minimization  SINR constraints can be reformulated as second-order cone constraints

Key observation: phases of ’s do not change objective and constraints

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Infeasibility

 Set of convex inequalities:  Power minimization problem is generally infeasible: large number of

users, unfavorable channel conditions, high data rate requirements,…

 Goal: Maximize the user capacity, i.e., the number of admitted users  Solution: Choose

to minimize the number of violated inequalities

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Sparse optimization for user admission control

 Average number of admitted mobile users versus target SINR

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MDR: membership deflation by convex relaxation ( ) IR2A: iterative reweighted -algorithm

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Massive device connectivity in uplink

 Cellular network with a massive number of devices

Single-cell uplink with a BS with antennas; Block-fading channel with coherence time ; T

  • tal

single-antenna devices, devices are active (sporadic traffic)  Define diagonal activity matrix

with non-zero diagonals

denotes the received signal across antennas

: channel matrix from all devices to the BS

: known transmit pilot matrix from devices

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Challenges of massive connectivity

 Sporadic traffic

User activity detection is a key requirement

Massive number of devices mean pilot sequences cannot be orthogonal

Device identification is a sparse optimization problem  Prior works on compressed sensing for massive connectivity: 1) Without

channel estimation [Zhang-Luo-Guo’13]; 2) Joint user activity detection and channel estimation [Xu-Rao-Lau’15]; 3) Approximate Message Passing (AMP) [Wei’16]

 Proposal: User activity detection and channel estimation based on the

compressed sensing techniques (without channel distribution prior)

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Group sparsity estimation

 Let

(unknown): group sparsity in rows

  • f matrix

Simultaneous user activity detection and channel estimation  Let

be a known measurement operator (pilot matrix)

 Observe  Find estimate

by solving a convex program

is mixed

  • norm to reflect group sparsity structure

 Hope:

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Sparse estimation for massive connectivity

 Normalized MSE versus pilot matrix length

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Summary: structured sparse models

 Generalized structured sparse optimization for dense networks

is the index set of non-zero coefficients of a vector

: combinatorial positive-valued set-function to control sparsity in

: continuous convex function to represent the system performance

: to model system constraints, e.g., QoS constraints

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group-structured sparsity layered group sparsity

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Vignette B: Generalized Low-Rank Models

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1 1 1 1 1

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Case I: Low-Rank Matrix Completion for T

  • pological

Interference Management Case II: Extensions to Mobile Edge Caching, Distributed Computing and Index Coding

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Case I: Topological Interference Management

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Interference channel

 Channel model:  Degrees-of-freedom: simplify the analysis; lead to physical insights

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capacity is unknown

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Interference alignment

 Assume the channel coefficients change over time:  Consider

channel uses:

 Transmitter

sends information symbols across channel uses

 The -th interference term

lives in the range space of matrix

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represents the precoding matrix

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Interference alignment

 Interference alignment condition: find precoding matrices and

decoding matrices such that

 Each user can send

symbols: interference free across channel uses

 Intuition: The interference has aligned onto

a dimensional subspace at each receiver.

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Interference alignment

 Everyone gets half the cake [Cadambe-Jafar’08]:

Diagonal are time-varying and generic, , is almost surely asymptotically achievable  Remarks:

Require very long block lengths

Require the channels to vary generically over time

Require full knowledge of the channel coefficients of every link in the network, at each transmitter and for all times!

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Can we exploit the interference alignment principle in practical systems?

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Practical interference management

 Goal: Exploit the IA principle under realistic assumptions on CSIT  Prior works: Abundant CSIT

relaxed CSIT

Perfect CSIT [Cadambe and Jafar,TIT 08]

Delayed CSIT [Maddah-Ali andTse,TIT 12]

Alternating CSIT [Tandon, et al., TIT 13], partial and imperfect CSIT [Shi, et al.,TSP 14],…  Curses: CSIT is rarely abundant (due to training & feedback overhead)

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No CSIT Perfect CSIT CSIT Prior works Applicable? Start here?

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T

  • pological interference alignment

 Blessings: partial connectivity in dense wireless networks  Approach: topological interference management (TIM) [Jafar,TIT 14]

Maximize the achievable DoF: only based on the network topology information (no CSIT)

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path-loss shadowing

transmitter receiver transmitter receiver

Degrees of Freedom?

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Index coding approach

 Theorem [Jafar, TIT 14]: under linear (vector space) solutions, TIM

problem and index coding problem are equivalent

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transformation

TIM problem

complements

Bottleneck: the only finite-capacity link

Antidotes

Index coding problem

Only a few index coding problems have been solved! wireless wired

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Low-rank matrix completion approach

 Goal: Deliver one data stream per user over

time slots

Transmitter transmits , receiver receives

Receiver decodes symbol by projecting

  • nto the space

 T

  • pological interference alignment condition

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: network connectivity pattern

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Generalized low-rank model

 Generalized low-rank optimization with network side information

: precoding vectors and decoding vectors

equals the inverse of achievable degrees-of-freedom (DoF)

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topological interference alignment condition

side information

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Nuclear norm fails

 Convex relaxation fails: always returns the identity matrix!

Fact:  Proposal: Solve the nonconvex problems directly with rank adaptivity

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Riemannian manifold

  • ptimization problem

manifold constraint

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Numerical results

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1 1 1 1 1 1 .1 9.5 6.8 1 64 .1 1

  • 1
  • .1
  • 1

1 .1

  • .1

.1 1

Recover all the optimal DoF results for the special TIM problems in [Jafar ’14] Provide numerical insights (optimal/lower- bound) for the general TIM problems

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Phase transitions for topological IA

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The heat map indicates the empirical probability of success (blue=0%; yellow=100%)

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Extension to cache networks

 Cache

gains: load balancing, interference cancellation/alignment, cooperative transmission, …

 Placement phase: populate caches (prefetching)  Delivery phase: reveal request, deliver content

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wired cache network wireless cache network

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Caching at receivers

 Cached receivers: topological interference alignment

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Side information: 1) Cached files 2) Network topology

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When index coding meets low-rank matrices

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Index Coding

[Birk, Kol, INFOCOM’98] [Maddah-Ali & Niesen ’13] [Jafar ’14] [Rouayheb et al. ’10, ’15] Li-Maddah-Ali-Avestimehr’14

Caching Network Coding Interference Alignment Distributed Computing

Low-rank model offers a new way to investigate these problems!

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Summary: generalized low-rank models

 Generalized low-rank optimization for dense edge networks

encodes network side information, e.g., cached files, network topology, computed intermediate values for data shuffling

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Concluding remarks

 Structured sparse models

Group sparse optimization offers a principled way for network adaptation, e.g., to minimize network power consumption

Sparsity control and estimation is powerful to support massive device connectivity  Future directions:

More application scenarios: IoTs,V2X …

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Concluding remarks

 Generalized low-rank models

Low-rank matrix completion provides a systematic approach to investigate the topological interference alignment problem

Low-rank model is powerful for performance optimization in mobile edge caching and distributed computing systems  Future directions:

More applications: blind deconvolution for IoT, big data analytics (e.g., ranking)

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T

  • learn more...

Web: http://shiyuanming.github.io/sparserank.html

Papers:

  • Y. Shi, J. Zhang, and K. B. Letaief, “Group sparse beamforming for green Cloud-RAN,”

IEEE Trans. Wireless Commun., vol. 13, no. 5, pp. 2809-2823, May 2014. (The 2016 Marconi Prize Paper Award)

  • Y. Shi, J. Zhang, B. O’Donoghue, and K. B. Letaief, “Large-scale convex optimization for

dense wireless cooperative networks,” IEEE Trans. Signal Process., vol. 63, no. 18, pp. 4729-4743, Sept. 2015. t. 2015. (The 2016 IEEE Signal Processing Society Young Author Best Paper Award)

  • Y. Shi, J. Zhang, K. B. Letaief, B. Bai and W. Chen,“Large-scale convex optimization for

ultra-dense Cloud-RAN,” IEEEWireless Commun. Mag., pp. 84-91, Jun. 2015.

  • Y. Shi, J. Zhang, W. Chen, and K. B. Letaief, “Generalized sparse and low-rank optimization

for ultra-dense networks,” IEEE Commun. Mag., to appear.

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T

  • learn more...

  • Y. Shi, J. Zhang, and K. B. Letaief, “Optimal stochastic coordinated beamforming for wireless

cooperative networks with CSI uncertainty,” IEEE Trans. Signal Process., vol. 63,, no. 4, pp. 960-973,

  • Feb. 2015.

  • Y. Shi, J. Zhang, and K. B. Letaief, “Robust group sparse beamforming for multicast green Cloud-

RAN with imperfect CSI,” IEEETrans. Signal Process., vol. 63, no. 17, pp. 4647-4659, Sept. 2015.

  • Y. Shi, J. Cheng, J. Zhang, B. Bai, W. Chen and K. B. Letaief, “Smoothed -minimization for green

Cloud-RAN with user admission control,” IEEE J. Select.Areas Commun., vol. 34, no. 4,Apr. 2016.

  • Y. Shi, J. Zhang, and K. B. Letaief, “Low-rank matrix completion for topological interference

management by Riemannian pursuit,” IEEETrans.Wireless Commun., vol. 15, no. 7, Jul. 2016.

  • Y. Shi, B. Mishra, and W. Chen, “T
  • pological interference management with user admission control

via Riemannian optimization,” IEEETrans.Wireless Commun., to appear.

  • X. Peng, Y. Shi, J. Zhang, and K. B. Letaief, “Layered group sparse beamforming for cache-enabled

wireless networks,” IEEETrans. Commun., to appear.

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