beam forming in cognitive radio
TRANSCRIPT
Beamforming In Cognitive Radio
By: Betty Nagy
Supervised by: Prof.Dr. Salwa El Ramly
Dr. Maha Mohammed
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Introduction Beamforming Beamforming in CR Introduced Models Future Work
Agenda
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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