beam forming in cognitive radio

35
Beamforming In Cognitive Radio By: Betty Nagy Supervised by: Prof.Dr. Salwa El Ramly Dr. Maha Mohammed

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Page 1: Beam Forming in Cognitive Radio

Beamforming In Cognitive Radio

By: Betty Nagy

Supervised by: Prof.Dr. Salwa El Ramly

Dr. Maha Mohammed

Page 2: Beam Forming in Cognitive Radio

04/10/2023Beamforming in CR 2

Introduction Beamforming Beamforming in CR Introduced Models Future Work

Agenda

Page 3: Beam Forming in Cognitive Radio

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Cognitive Radio Network [1]

INTRODUCTION

Why?

1. Severe shortage of the radio spectrum.2. The already licensed spectrum is not

utilized most of the time and space.

How?

1. Spectrum Sensing :Sense the Radio Spectrum assigned to a licensed user (Primary user) looking for unoccupied regions (Spectrum holes).

2. Spectrum Adaptation :Once finding a spectrum hole the CR unlicensed user (Secondary user) adapts its Power, Frequency Band so that interference on Primary is min.

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Spectrum Interweave◦ PU & SU signals are ⊥ => (TDMA - FDMA)◦ Cognition :

spectral holes Spectrum Underlay

◦ PU & SU same spectrum ◦ Cognition :

Acceptable level of Interference of PU Channel between PU & SU

Spectrum Overlay◦ PU & SU same spectrum ◦ Cognition :

Channel between PU & SU Info about PU system and operation

INTRODUCTION : CR Behavior[2]

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Interweave

INTRODUCTION Underlay Overlay

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Introduction Beamforming Beamforming in CR Introduced Models Future Work

Agenda

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It is a Signal processing technique used antenna arrays for a directional signal transmission or reception.

How? With the aid of received data and By adjusting the weights of the beam former to maximize the beam toward the SOI (Signal of Interest) and ideally nulls toward the SNOI (Signal Not of Interest).

Beamforming[3]

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Beamforming

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Beamforming Beamforming Techniques[4]:1. Maximum SNR :

2. Maximum SINR :

3. Minimum Mean Square Error (MMSE) :

4. Linearly Constrained Minimum Variance (LCMV) :

Subject to

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Introduction Beamforming Beamforming in CR Introduced Models Future Work

Agenda

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We can’t use the conventional Beamformer WHY ?

CR Network has specific constraints Limited SU power Limited Interference on PU

Channel State Information (CSI) is unknown unlike the other systems.

Thus we had to use what is called

Robust Beamformig[5],[6]&[7]

Beamforming in CR

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Introduction Beamforming Beamforming in CR Introduced Models Future Work

Agenda

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Introduction Beamforming Beamforming in CR Introduced Models

◦Model 1 System Model Mathematical Model Solution Robustness

◦Model 2◦Model 3

Future Work

Agenda

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System Model: ◦ 1 SU Link & K PU Links◦ Each tx has N transmit antenna ◦ Each rx has M receive antenna

Model 1[5]:

PU 1

PU 2

PU k

...

SU tx

SU rx

Hs,s

Hs,1

1

2

H1,s

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Mathematical Model:◦ Objective

◦ Subject to

Model 1

022

,

2,

,NwwH ksw

wH sswSINR

rsw

tsw

Max

rstkHrs

tsHrs

max,

2

2

, ,....,1

sts

ktsskHrk

Pw

KkwHw

Note ! All signals are normalized i.e. 1

22 ks xExE

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Mathematical Model:◦ The problem is reformulated to have a quadratic

form as follows:

Where

Model 1

maxs,

P

K1,....,k 11 ..

ww

wQwwAw

ts

H

ts

ts

H

ts

ts

H

tsw

kts

Maxts

HH

ss,

1H

ss, A

skHrkrk

Hsk

kk HwwHQ ,,1 1

Q objectiveQ constraints=>QCQP!

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Solution:◦ 1quadratic term in objective => homogeneous

QCQP

◦ Homogeneous QCQP => SDP relaxation method

Model 1

Thus an optimum solution can be found

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Model 1 Robustness: assume ambiguity in CSI

◦ (Channel matrix & primary beamforming vectors)

Scenario 2 : Channel matrix (H)

Beamforming vector (wrk)

Known

Unknown

KkwHw kstskH

kr ,....,1 2

, ?

K1,....,k 1Pr k

2

,

kssk

H

krk tr wHw

W rk random variable

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Model 1 Robustness: Scenario 2:

◦ Problem:

◦ where

maxs,

P

K1,....,k 12 ..

tt

tktts

tstMax

ww

wQw

Aww

s

H

s

s

H

s

H

sw ts

skHsk

k

Nk

k HHQk

,,

11

2 1

Q objectiveQ constraints=>QCQP!

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Model 1 Robustness: assume ambiguity in CSI

◦ (Channel matrix & primary beamforming vectors)

Scenario 3 : Channel matrix (H)

Beamforming vector (wrk) Unknown

KkwHw kstskH

kr ,....,1 2

, ?

K1,....,k 1Pr k

2

,

kssk

H

krk tr wHw

Unknown

W rk Hk random variable

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Model 1 Robustness: Scenario 3:

◦ Problem:

◦ where

maxs,

P

K1,....,k 13 ..

tsHts

tsHts

tsHtsts

ww

wk

wts

wwMax

QA

2 constraints => 1A simple solution !

IQkk

k3

)1

log(

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System Model: ◦ 1 SU Link & K PU Links◦ Each tx has N transmit antenna ◦ Each rx has 1 receive antenna

Model 2[6]:

PU 1

PU 2

PU k

...

SU tx

SU rx

Hs,s

Hs,1

1

2

H1,s

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Mathematical Model:◦ Objective

Power at the receiver !

◦ Subject to

Model 2

2

, tsHssreceiverw wHPowerMax

ts

...K 1,2,...k 2

, ktsHsk wH

max,

2

sts Pw

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Mathematical Model:◦ The problem is reformulated to have a convex

form as follows:

Model 2

linear objectiveQ constraints=>SOCP!

tsHssw wHMax

ts ,

Subject to:...K 1,2,...k

2

, ktsHsk wH

max,

2

sts Pw

0Im , tsHss wH

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Model 2 Robustness: assume ambiguity in CSI

◦ (Secondary & Primary Channel matrices have uncertainties)

Scenario : Channel matrices (Hs,s) , (Hk,s)

Mathematical Model:

Imperfect

Uncertain ∆’s are random variables

Objective :s.t.

)|(|Prob 2, tsHssw wHMax

ts

...K 1,2,...k )||Prob( k2

, tsHsk wH

max,

2

sts Pw

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Solution:◦ Probabilistic Objective and Constraint =>

Marcum’s function

◦ Marcum’s function is solved(by getting its inverse) => SOCP

Model 2

Thus an optimum solution can be found

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System Model: ◦ L SU Links & K PU Links◦ Each tx has N transmit antenna ◦ Each rx has 1 receive antenna

Model 3[7]:

PU 1

PU 2

PU k

...

SU 1 tx

SU 1 rx

Hs1,s1

Hs1,p1

1

2

Hp1,s1

SU L rx

HsL,s1 …

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Mathematical Model:◦ Objective

◦ Subject to

Model 3

KkwRwL

iLitkLkL

H

it ,....,1 1

2

,

LlNwRw

wRwSINR lL

lii

itllH

it

ltllH

lt

,....,1

01

,

,

Channel covariance matrix

L

itsiw wMin

ts1

2

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Model 3 Robustness: assume ambiguity in CSI

◦ (Secondary & Primary Channel covariance matrices have uncertainties)

Scenario : ◦ Channel matrices (Rl,s) , (Hk,s)

Mathematical Model:

Imperfect

Uncertain ∆’s are random variables

LlNwRw

wwSINR lL

lii

illHi

kHl

,.....,1 )ˆ(

)R̂(

01

k,

lll,

KkwRwL

ilikLkLkL

Hi ,....,1 )ˆ(

1

2

,

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Solution:◦ Find the Dual Problem of our Model

◦ The Dual is of linear objective & convex constraints except one non-convex constraint.

◦ Thus solved by SDP relaxation method.

Model 3

Thus an optimum solution can be found

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Introduction Beamforming Beamforming in CR Introduced Models Future Work

Agenda

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Build the introduced Models on Matlab. Verify the optimum solution of each model. Study different innovations that could be

done:◦ Investigate new cost functions and constraints and

optimization algorithms.◦ Fitting a new system model on the introduced

optimization techniques.◦ Study different degrees of knowledge of the CSI on

the rest of the mathematical models.◦ Add the effect of mobility, dynamic channel

adaptation. Build the new system and study its

advantages and disadvantages.

Future Work

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Thank You

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[1](2008) Cognitive Radio Project website. [Online]. Available:http://kom.aau.dk/project/cognitive/cognitive_radio_project.htm

[2]Alexander M. Wyglinski, Maziar Nekovee, Y. Thomas Hou, Cognitive Radio Communications and Networks, Elsevier Inc., 2010.

[3](2011) The Wikipedia website. [Online]. Available: http://en.wikipedia.org/wiki

[4]Constantine A. Balanis and Panayiotis I.Ioannides, Introduction to Smart Antennas, 1st ed., Morgan & Claypool, 2007.

[5]Ying Jun (Angela) Zhang, Member, IEEE and Anthony Man-Cho So, “Optimal Spectrum Sharing in MIMO Cognitive Radio Networks via Semidefinite Programming,” IEEE Journal On Selected Areas In Communications, Vol. 29, No. 2, February 2011.

References

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[6]Gan Zheng, Shaodan Ma, Kai-Kit Wong, and Tung-Sang Ng, “Robust Beamforming in Cognitive Radio”, Wireless Communications, IEEE Transactions,vol.9, issue:2, p. 570-576, February 2010.

[7]Imran Wajid,Marius Pesavento, Yonina C. Eldar and Alex Gershman, “Robust downlink beamforming for cognitive radio networks”, IEEE Globecom 2010 proceedings.

References