optimal relay selection and beamforming in mimo cognitive multi-relay networks
TRANSCRIPT
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamformingin MIMO Cognitive Multi-Relay Networks
Reference: Li, Quanzhong, et al. "Optimal relay selection and beamforming in MIMO cognitivemulti-relay networks." Communications Letters, IEEE 17.6 (2013): 1188-1191.
Mohamed Seif1
1Wireless Intelligent Networks Center (WINC), Nile University, Egypt
May 20, 2015
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 1
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Outline
1 Problem Statement
2 System Model
3 Signal Model
4 Optimal Relay Selection and Beamforming
5 Simulation Results
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 2
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Problem Statement
For a MIMO cognitive multi-relay network, this workproposes an optimal relay selection and beamformingscheme subject to transmit power constraints at the relaysand the interference power constraints at the primaryusers.
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 3
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
System Model
Pair of a SU are transmitting in thepresence of 2 PUs, each equippedwith one antenna
K cognitive relays, each relay isequipped with N antennas
No direct link between the SU nodes
Intference from the PUs is neglected
TX RX
UE UE
Primary User Network
K
Secondary User Network
1
Desired Link Interference Link
Figure: CRN model
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 4
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
System Model
TDD mode is considered for thesystem
During the first time slot, the SU-TXtransmits signals to the relays
At the second time slot, the k th
selected relay, multiplies thereceived signal by a linearbeamforming matrix and forwards itthe SU-RX
TX RX
UE UE
Primary User Network
K
Secondary User Network
1
Desired Link Interference Link
Figure: CRN model
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 5
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Signal Model
The received signal at the SU-RX isexpressed as:
y = h†2k Fk(h1k x + nr) + z
where,
E[∣x ∣2] = Psnr ∼ CN(0, σ2
r I)z ∼ CN(0, σ2
d )
Fk ∈ CN×N
h1k ∈ CN×1
h2k ∈ C1×N
TX RX
UE UE
Primary User Network
K
Secondary User Network
1
Desired Link Interference Link
Figure: CRN model
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 6
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Signal Model
The SNR at the SU-RX is expressedas:
SNR =Ps ∣h†
2k Fh1k ∣2
σ2r ∥h
†2k F∥+σ2
d
TX RX
UE UE
Primary User Network
K
Secondary User Network
1
Desired Link Interference Link
Figure: CRN model
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 7
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Signal Model
The transmit power of the SU-TXsatisfies that:Ps ∣g1m∣
2≤ Im, m ∈ {1,2}
then,
Ps = min(Ps,minm
Im∣g1m ∣
2 )
where,g1m ∈ C1×1
TX RX
UE UE
Primary User Network
K
Secondary User Network
1
Desired Link Interference Link
Figure: CRN model
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 8
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Signal Model
The transmit power of the k th relayis:PRk = Ps ∥Fh1k∥
2+ σ2
r ∥F∥2
and satisfies that,
Ps ∣g†2mFh1k ∣
2+ σ2
r ∥g†2m∥
2≤ Im,
m ∈ {1,2}where,
g2m ∈ CN×1
TX RX
UE UE
Primary User Network
K
Secondary User Network
1
Desired Link Interference Link
Figure: CRN model
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 9
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
The optimization problem of relay selection and beamformingfor a MIMO congnitive multi-relay network is formulated as:
Problem Formulation
arg maxk
maxF
12 log2(1 +
Ps ∣h†2k Fh1k ∣
2
σ2r ∥h
†2k F∥
2+σ2
d
)
s.t. Ps ∥Fh1k∥2+ σ2
r ∥F∥2≤ PR
Ps ∣g†2mFh1k ∣
2+ σ2
r ∥g†2mF∥
2≤ Im
k ∈ {1,2, . . . ,K}, m ∈ {1,2, . . . ,M}
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 10
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
The optimization problem of relay selection and beamformingfor a MIMO congnitive multi-relay network is formulated as:
Problem Formulation
arg maxk
maxF
12 log2(1 +
Ps ∣h†2k Fh1k ∣
2
σ2r ∥h
†2k F∥
2+σ2
d
)
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶PrecoderDesign
s.t. Ps ∥Fh1k∥2+ σ2
r ∥F∥2≤ PR
Ps ∣g†2mFh1k ∣
2+ σ2
r ∥g†2mF∥
2≤ Im
k ∈ {1,2, . . . ,K}, m ∈ {1,2, . . . ,M}
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 11
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
The optimization problem of relay selection and beamformingfor a MIMO congnitive multi-relay network is formulated as:
Problem Formulation
arg maxk
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶RelaySelection
maxF
12 log2(1 +
Ps ∣h†2k Fh1k ∣
2
σ2r ∥h
†2k F∥
2+σ2
d
)
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶PrecoderDesign
s.t. Ps ∥Fh1k∥2+ σ2
r ∥F∥2≤ PR
Ps ∣g†2mFh1k ∣
2+ σ2
r ∥g†2mF∥
2≤ Im
k ∈ {1,2, . . . ,K}, m ∈ {1,2, . . . ,M}
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 12
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
Beamforming Optimization Problem
P1: maxf
f †(Pshh†
)ff †(σ2
r H2H†2)f+σ
2d
s.t. f †(PsH1H†1 + σ
2r I)f ≤ PR
f †(PsG1mG†1m + σ
2r G2mG†
2m)f ≤ Imm ∈ {1,2, . . . ,M}
where,f=vec(F )
h = h∗1k ⊗ h1k
H1 = h∗1k ⊗ I, H2 = I ⊗ h2k
G1m = h∗1k ⊗ g2m , G2m = I ⊗ g2m
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 13
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
Beamforming Optimization Problem
P1: maxf
f †(Pshh†
)ff †(σ2
r H2H†2)f+σ
2d
s.t. f †(PsH1H†1 + σ
2r I)f ≤ PR
f †(PsG1mG†1m + σ
2r G2mG†
2m)f ≤ Imm ∈ {1,2, . . . ,M}Difficult to Solve!
where,f=vec(F )
h = h∗1k ⊗ h1k
H1 = h∗1k ⊗ I, H2 = I ⊗ h2k
G1m = h∗1k ⊗ g2m , G2m = I ⊗ g2m
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 14
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
Beamforming Optimization Problem
P2: maxW≽0
tr(A1W)tr(A2W)+σ2
d
s.t. tr(A3W ) ≤ PRtr(BmW ) ≤ Im
m ∈ {1,2, . . . ,M}
where,A1 = Pshh†
A2 = σ2r G2mG†
2m
A3 = PsH1H†1 + σ
2r I
W = ff †
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 15
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
Beamforming Optimization Problem
P2: maxW≽0
tr(A1W)tr(A2W)+σ2
d
s.t. tr(A3W ) ≤ PRtr(BmW ) ≤ Im
m ∈ {1,2, . . . ,M}
rank (W )=1, then rank of W has been relaxed
where,A1 = Pshh†
A2 = σ2r G2mG†
2m
A3 = PsH1H†1 + σ
2r I
W = ff †
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 16
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
Beamforming Optimization Problem
P2: maxW≽0
tr(A1W)tr(A2W)+σ2
d
s.t. tr(A3W ) ≤ PRtr(BmW ) ≤ Im
m ∈ {1,2, . . . ,M}rank (W )=1, then rank of W has been relaxed
where,A1 = Pshh†
A2 = σ2r G2mG†
2m
A3 = PsH1H†1 + σ
2r I
W = ff †
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 16
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
Beamforming Optimization Problem(Charnes-Cooper transformation)
P3: maxS≽0,ν≥0
tr(A1S)
s.t. tr(A1S) + σ2dν = 1
tr(A3S) ≤ νPRtr(BmS) ≤ νIm, m ∈ {1,2, . . . ,M}
where,W =
Sν
tr(A2W) + σ2d =
1ν
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 17
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
Beamforming Optimization Problem
P4: maxW≽0
tr(A3W )
s.t. tr(A1W)tr(A2W)+σ2
d≥ γ −∆γ
tr(BmW ) ≤ Im, m ∈ {1,2, . . . ,M}
where,γ = max
S≽0,ν≥0tr(A1S) (P3)
0 ≤∆γ < γ
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 18
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
Beamforming Optimization Problem
Solution of P4 is tight to P2 by (1 − ∆γγ ) (Proof Hint)
Solution of P4 has rank one (Proof Later ,)
then,f =√λiUiU
†i , λi ≠ 0
where, Ui ⇐ W = U∆U†
Relay Selection
arg maxk
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶RelaySelection
maxF
12 log2(1 +
Ps ∣h†2k Fh1k ∣
2
σ2r ∥h
†2k F∥
2+σ2
d
)
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 19
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Optimal Relay Selection and Beamforming
Beamforming Optimization Problem
Solution of P4 is tight to P2 by (1 − ∆γγ ) (Proof Hint)
Solution of P4 has rank one (Proof Later ,)
then,f =√λiUiU
†i , λi ≠ 0
where, Ui ⇐ W = U∆U†
Relay Selection
arg maxk
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶RelaySelection
maxF
12 log2(1 +
Ps ∣h†2k Fh1k ∣
2
σ2r ∥h
†2k F∥
2+σ2
d
)
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 19
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Simulation Setup
Symbol Description RealizationM Number of PUs 2K Number of relays ∼
N Number of antennas per relay ∼
PR Transmitted power at the relay ∼
σ2r Noise power at the relay per anetenna Normalized
P Number of iterations 50σ2
d Noise power at SU-RX Normalized
Table: Parameters of Simulation
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 20
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Simulation Results
0 5 10 15 200.5
1
1.5
2
2.5
3
PR
(dB)
Rav
e(bps
/Hz)
ORSB, N=3, K=3
Figure: Average capacity versus the maximum allowable transmitpower of the relay
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 21
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Simulation Results
0 5 10 15 200.5
1
1.5
2
2.5
3
PR
(dB)
Rav
e(bps
/Hz)
ORSB, N=3, K=3ORSB, N=3, K=2ORSB, N=3, K=1
k=1,2,3
Figure: Effect of number of relays
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 22
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Simulation Results
0 5 10 15 200.5
1
1.5
2
2.5
3
PR
(dB)
Rav
e(bps
/Hz)
ORSB, N=4, K=3ORSB, N=5, K=3ORSB, N=6, K=3ORSB, N=3, K=3ORSB, N=2, k=3
N=2,3,4,5,6
Figure: Effect of number of antennas
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 23
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Simulation Results
0 5 10 15 200.5
1
1.5
2
2.5
3
PR
(dB)
Rav
e(bps
/Hz)
ORSB, N=3, K=3, I1=I2=20dBORSB, N=3, K=3, I1=I2=10dBORSB, N=3, K=3, I1=I2=5dBORSB, N=3, K=3, I1=I2=0dB
I=0,5,10,20 (dB)
Figure: Effect of Interference Thresholds
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 24
Problem Statement System Model Signal Model Optimal Relay Selection and Beamforming Simulation Results
Thank You!
Mohamed Seif Nile University
Optimal Relay Selection and Beamforming in MIMO Cognitive Multi-Relay Networks 25