Efficient Control Signaling for Resource Allocation Control Signaling for Resource Allocation Gwanmo Ku May 21, 2014 Ph.D. Thesis Defense Adaptive Signal Processing and Information

Adaptive Signal Processing and Information Theory Group

Efficient Control Signaling

for Resource Allocation

Gwanmo Ku

May 21, 2014

Ph.D. Thesis Defense

Adaptive Signal Processing and Information Theory Group 2

Overview

Control (Collaboration) Info.

System Performance

(Spectral Efficiency)

for Data

Information Theory Bound

Practical Source Coding

LTE Control Signaling

Independent CEO

Rate Region

Calculation

Independent CEO with

Resource Allocation

1

2

3

4


Overview


System Performance


for Data



LTE Control Signaling*

Independent CEO

Rate Region

Calculation


Resource Allocation

* G. Ku, J.M. Walsh, “Resource Allocation and Link Adaptation in LTE and LTE Advanced : A Tutorial”, IEEE Communications Surveys and Tutorial


Units : Resource Allocation & Scheduling 1/26

Resource Grid


Downlink Control Region by PCFICH 1/26

Control Region : PDCCH Region


Contents of Downlink Control Information 1/26

Downlink Control Information in PDCCH


2/26

Resource Allocation


2/26

Reference : 3GPP Technical Specification TS 36.213

MCS Index and CQI


2/26


CQI Reporting Modes


Control Channels 21% 32% 11% Reference Signals 2/26


Control Signaling Overhead


Overview


System Performance


for Data




Independent CEO

Rate Region

Calculation


Resource Allocation


Overview


System Performance


for Data




Independent CEO

Rate Region

Calculation**


Resource Allocation

**G. Ku, J. Ren, J.M. Walsh, “Computing the Rate Distortion Region for the CEO Problem with Independent Sources”,

IEEE Transactions on Signal Processing


System Diagram & Rate Region Expression 1/26

Independent CEO Model

(𝓡,𝐷)

∀𝑚 ∈ 𝓜 𝑅𝑚 ≥ 𝐼(𝑋𝑚; 𝑈𝑚)𝑈𝑚 ↔ 𝑋𝑚 ↔ 𝑿𝓜\𝑚, 𝑼𝓜\𝑚, 𝑇

𝑇 ↔ 𝑼𝓜 ↔ 𝑇,𝑿𝓜

𝔼 𝑑(𝑇, 𝑇 ) ≤ 𝐷


Calculating Rate Region 1/26

Rate Region Calculation

(𝓡, 𝐷)

∀𝑚 ∈ 𝓜 𝑅𝑚 ≥ 𝐼(𝑋𝑚; 𝑈𝑚)𝑈𝑚 ↔ 𝑋𝑚 ↔ 𝑿𝓜\𝑚, 𝑼𝓜\𝑚, 𝑇

𝑇 ↔ 𝑼𝓜 ↔ 𝑇,𝑿𝓜

𝔼 𝑑(𝑇, 𝑇 ) ≤ 𝐷

Algorithm

Fixed

𝑝𝑋𝑚(𝑥𝑚),𝑑


Calculating Rate Region 1/26

Flowchart

Grid of 𝝀 and 𝜇

min 𝜆𝑖(𝑘)

𝐼 𝑋𝑖; 𝑈𝑖

𝑖∈𝓜

+ 𝜇(𝑘)𝔼 𝑑(𝑇, 𝑇 )

Polyhedral Rep. conversion

𝑟 , 𝑑 |𝐇𝑟 + ℎ𝑑 ≥ 𝟎

(𝑟𝑖(𝑘)

, 𝑑(𝑘)) Redundancy Removal

different

slope


Calculating Rate Region

where

1/26

Standard BA Relaxation

𝓛𝝀𝜇 𝑸,𝒒, Λ = 𝜆𝑖𝑖∈𝓜

𝑝𝑋𝑖𝑥𝑖 𝑄𝑖 𝑢𝑖 𝑥𝑖 log

𝑄𝑖(𝑢𝑖|𝑥𝑖)

𝑞𝑖(𝑢𝑖)(𝑥𝑖,𝑢𝑖)

+𝜇 𝑑 𝑡, 𝑡 𝑝𝑇|𝑿 𝑡 𝒙 Λ 𝑡 𝒖 𝑄𝑖 𝑢𝑖 𝑥𝑖𝑖∈𝓜𝑢,𝑥,𝑡,𝑡

𝑸 ≐ 𝑄𝑖 𝑢𝑖 𝑥𝑖) | 𝑢𝑖 ∈ 𝓤𝑖 , 𝑥𝑖 ∈ 𝓧𝑖 , 𝑖 ∈ 𝓜

𝒒 ≐ 𝑞𝑖(𝑢𝑖) | 𝑢𝑖 ∈ 𝓤𝑖 , 𝑖 ∈ 𝓜

Λ ≐ Λ(𝑡 |𝑢)|𝑡 ∈ 𝓣 , 𝒖 ∈ 𝓤𝑖 ×⋯×𝓤𝑀


1/26

Flowchart of Calculating Rate Region


1/26

Flowchart

𝑄𝑖(𝑙,𝑘𝑖+1) 𝑢𝑖|𝑥𝑖 =

𝑞𝑖(𝑙,𝑘𝑖) 𝑢𝑖 2

−𝜇𝜆𝑖𝑑𝑖(𝑙,𝑖)

(𝑥𝑖,𝑢𝑖)

𝑞𝑖(𝑙,𝑘𝑖)(𝑢𝑖

′)𝑢𝑖′2−𝜇𝜆𝑖𝑑𝑖(𝑙,𝑖)

(𝑥𝑖,𝑢𝑖′)

𝑞𝑖(𝑙,𝑘𝑖) 𝑢𝑖 = 𝑝𝑋𝑖

𝑥𝑖 𝑄𝑖(𝑙,𝑘𝑖)(𝑢𝑖|𝑥𝑖)

𝑥𝑖

𝑑𝑖(𝑙,𝑖)

𝑥𝑖 , 𝑢𝑖 = 𝑑 𝑡, 𝑡 𝑝𝑇,𝑿 𝑡, 𝒙 Λ(𝑙,𝑖) 𝑡 𝑢

𝑡,𝑡 ,𝒙\𝑖,𝒖\𝑖

𝑄𝑗(𝑙,∗)

(𝑢𝑗|𝑥𝑗)

𝑗<𝑖

𝑄𝑗′(𝑙−1,∗)

(𝑢𝑗′|𝑥𝑗′)

𝑗′≥𝑖


1/26

Flowchart

Λ(𝑙′,𝑖′) 𝑡 𝒖 = 𝛼(𝑙′,𝑖 )′ (𝒖) 𝑡 ∈ argmin

𝑡 ∈𝓣 𝐽 𝑙,𝑖 (𝑡 , 𝑢)

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

Λ 𝑙′,𝑖′ (𝑡 |𝒖)

𝑡

= 1

𝐽 𝑙,𝑖 (𝑡 , 𝑢)

= 𝑑 𝑡, 𝑡 𝑝𝑇,𝑿 𝑡, 𝒙 𝑄𝑗(𝑙,∗)

(𝑢𝑗|𝑥𝑗)

𝑗≤𝑖

𝑄𝑗′(𝑙−1,∗)

(𝑢𝑗′|𝑥𝑗′)

𝑗′>𝑖𝑡,𝑡 ,𝒙\𝑚,𝒖\𝑚


Convex & Non-Convex 1/26

Convergence

Global minimum Local minimum

Global minimum


𝓛𝝀𝜇 𝑸, 𝒒, Λ is a convex function of 𝑸, 𝒒, Λ

⇒ Ind. CEO BA will converge to a global minimum.

1/26

Theorem

𝔼 𝑑(𝑇, 𝑇 ) is Convex

𝓛𝝀𝜇 𝑸, 𝒒, Λ is Convex

Global Convergence


Binary Hamming, Global Convergence 1/26

Convex


Convex & Non-Convex 1/26

Convergence

Global minimum Local minimum

Global minimum


Initialization by Graph Entropy at 𝒅𝐦𝐢𝐧 1/26

Non-convex

min𝑄𝑖 ⋅ ⋅)∈Γ(𝓖𝑖)

𝐼(𝑋𝑖; 𝑈𝑖)

𝑀

𝑖=1

𝐷

𝑅𝑖

𝑖

𝑑min

𝓖𝑖 : Characteristic graph of vertices ढ𝑖

Adjacent 𝑥𝑖 and 𝑥𝑖′

∃ 𝒙\𝑖 ∈ 𝑿\𝑖 s.t. 𝑡 𝑥𝑖 , 𝒙\𝑖 ≠ 𝑡 𝑥𝑖′, 𝒙\𝑖

Γ(𝓖𝑖): Maximal independent sets of 𝓖𝑖

Convex optimization problem

* V. Doshi, D. Shah, M. Medard, and M. Effros, "Functional compression through graph coloring," IEEE

Transactions on Information Theory, vol. 56, no. 8, pp. 3901-3917, August 2010.

** V. Doshi, D. Shah, M. Medard, and S. Jaggi, “Graph coloring and conditional graph entropy," in 40th

Asilomar Conf. on Signals, Systems, and Computers, 2006, pp. 2137{2141.


Tracking Previous Initialization,

1/26

Non-convex (Continued)

𝐷

𝑅𝑖

𝑖

𝑑min

Start from Graph Entropy

Initialize BA for this point nearby

Lagrange multiplier

×

×

Initialize BA for this point nearby

Lagrange multiplier Same point


Argmax [1 2 3] & [1 2 3 4] 1/26

Non-convex Examples


Redundancy Removal Description 1/26

Calculating Convex Hulll

Grid of 𝝀 and 𝜇

min 𝜆𝑖𝐼 𝑋𝑖; 𝑈𝑖

𝑖∈𝓜

+ 𝜇𝔼 𝑑(𝑇, 𝑇 )

Polyhedral Rep. conversion

𝑟 , 𝑑 |𝐇𝑟 + ℎ𝑑 ≥ 𝟎

(𝑟 ∗, 𝑑∗) Redundancy Removal

different

slope

𝑟𝑖(𝑙) = 𝑝𝑋𝑖

𝑥𝑖 𝑄𝑖(𝑙,∗)

𝑢𝑖 𝑥𝑖 log𝑄𝑖(𝑙,∗)

(𝑢𝑖|𝑥𝑖)

𝑞𝑖(𝑙,∗)

(𝑢𝑖)(𝑥𝑖,𝑢𝑖)

𝑑(𝑙) = 𝑑 𝑡, 𝑡 𝑝𝑇|𝑿 𝑡 𝒙 Λ(𝑙,∗) 𝑡 𝒖 𝑄𝑖(𝑙,∗)

𝑢𝑖 𝑥𝑖𝑖∈𝓜𝑢,𝑥,𝑡,𝑡

𝐇 =0𝑀+1×1 𝕀𝑀+1

1𝐾×1 𝐕

𝐕 =𝑟1(1)

… 𝑟𝑀(1)

𝑑(1)

𝑟1(2)

… 𝑟𝑀(2)

𝑑(2)

… … … …


Overview


System Performance


for Data




Independent CEO

Rate Region

Calculation


Resource Allocation


Overview


System Performance


for Data




Independent CEO

Rate Region

Calculation


Resource Allocation


Performance overhead tradeoff via Rate Distortion Curve

System Performance in Spectral Efficiency

Simple Model for Physical Layer employing DL communication

Broadcast Communication

Reteless coded Communication

Adaptive Modulation and Coding (AMC) Communication

Overhead Performance Tradeoff*

UE1

(Encoder 1)

UE2

(Encoder 2)

eNB

(CEO)

Resource Allocation Function : 𝒁

Inefficiency in Resource Allocation : 𝑫

CQI 1

CQI 2

*J. Ren, G. Ku, B. D. Boyle, S. Weber, and J. M. Walsh, “Overhead Performance Tradeoffs - A Resource Allocation Perspective,“

IEEE Transactions on Information Theory, to be submitted.


Private messages

• Wish to select modulation and coding rate to match the channel capacity

→ Want to know a UE attaining maximum CQI

→ Want to know the maximum CQI

AMC Communication

UE1

(Encoder 1)

UE2

(Encoder 2)

eNB

(CEO) Private Message 1

Private Message 2

𝒁?

𝒁 = ( 𝐦𝐚𝐱 𝑿𝟏, … , 𝑿𝑵 , 𝐚𝐫𝐠𝐦𝐚𝐱 𝑿𝟏, … , 𝑿𝑵 )


AMC 𝑍 = (max 𝑋1, 𝑋2 , argmax 𝑋1, 𝑋2 )

• Estimation at Basestation

1/26

Max & Argmax for AMC

𝑑 (𝑍, 𝑖), (𝑍 , 𝑖 ) = 𝑍 − 𝑍 𝑍 ≤ 𝑋𝑖

𝑍 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒


1/26

Simulation : Max & Argmax


Private messages

• Employs a near-perfect rateless code (Ex. HARQ)

→ Need to know a scheduled UE attaining the maximum CQI

Rateless Coded Communication

UE1

(Encoder 1)

UE N

(Encoder N)

eNB

(CEO) Private Message N

Private Message N

𝒁 = 𝐚𝐫𝐠𝐦𝐚𝐱(𝑿𝟏, … , 𝑿𝑵)

𝒁?


Rateless Communication 𝑍 = argmax(𝑋1, 𝑋2)

• Estimation at Basestation

1/26

Argmax

𝑑 𝑍, 𝑍 = 𝑋𝑍 − 𝑋𝑍


1/26

Simulation : Argmax


Common message

• For each UE to successfully decode on each channel

→ Need to know the lowest CQI level between UEs

→ Want to know the maximum negative CQI

Broadcast Communication

UE1

(Encoder 1)

UE N

(Encoder N)

eNB

(CEO)

A Common Message 𝒁?

𝒁 = 𝐦𝐚𝐱(𝑿𝟏, … , 𝑿𝑵)


𝑍 = max(𝑋1, 𝑋2)

• Estimation at eNB

1/26

Max Function for Broadcast

𝑑 𝑍, 𝑍 = 𝑍 − 𝑍 𝑍 ≤ 𝑍𝑍 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒


1/26

Simulation : Max


1/26

Simulation : Overall


Overview


System Performance


for Data




Independent CEO

Rate Region

Calculation


Resource Allocation


Overview


System Performance


for Data




Independent CEO

Rate Region

Calculation


Resource Allocation


Flowchart 1/26

Quantizer

Find Bayes detector for fixed thresholds

argmin𝑡

𝔼 𝑑 𝑇, 𝑡 |𝑋1 ∈ 𝐈1,𝑘1 , … , 𝑋𝑀 ∈ 𝐈1,𝑘𝑀

Average distortion of Bayes detector

in terms of thresholds

min𝔼 𝑑(𝑇, 𝑇 )

Minimize distortion w.r.t. thresholds

min𝔼 𝑑(𝑇, 𝑇 )


1/26

Max & Argmax Quantizer


1/26

Max & Argmax Quantizer

Converging

𝑲 → ∞


1/26

Argmax Quantizer


1/26

Argmax Quantizer

Converging

𝑲 → ∞


1/26

Max Quantizer


1/26

Max Quantizer

Converging

𝑲 → ∞


Summary


System Performance


for Data




Independent CEO

Rate Region

Calculation


Resource Allocation


Thank you

2/26

Documents

Efficient Control Signaling for Resource Allocation Control Signaling for Resource Allocation Gwanmo Ku May 21, 2014 Ph.D. Thesis Defense Adaptive Signal Processing and Information