Performance Analysis of MIMO-OSTBC based Selective DF Cooperative Wireless System with Node Mobility and Channel Estimation Errors

Transcription

1 System Model Performance Analysis of MIMO-OSTBC based Selective DF Cooperative Wireless System with Node Mobility and Channel Estimation Errors Multimedia Wireless Networks (MWN) Group, Indian Institute of Technology, Kanpur March 6, 2016

2 Overview System Model 1 System Model 2 3 4

3 System Model I System Model 1 Figure: MIMO-OSTBC based selective DF cooperative system. 1 N. Varshney, A. Krishna, and A. K. Jagannatham, Selective DF protocol for MIMO STBC based single/multiple relay cooperative communication: End-to-end performance and optimal power allocation, IEEE Transactions on Communications, vol. 63, no. 7, pp , 2015.

4 System Model II System Model The received codeword matrices Y SD (k) C Nd T,Y SR (k) C N T at the destination and relay respectively are given as, where Y SD (k) = Y SR (k) = P0 H SD (k)x(k)+w SD (k), (1) P0 X(k) denotes the transmitted codeword, R c denotes the rate of the OSTBC, P 0 is the transmit power at the source, H SR (k)x(k)+w SR (k), (2) Entries of matrices W SD (k) C N d T and W SR (k) C N T are symmetric complex Gaussian with variance η 0.

5 System Model III System Model The received codeword matrix Y RD (k) C Nd T at the destination, in the second phase, is given as, P1 Y RD (k) = H RD (k)x(k)+w RD (k). (3) where P 1 is the transmit power at the relay, Entries of matrix W RD (k) C N d T is symmetric complex Gaussian with variance η 0 /2 per dimension.

6 System Model IV System Model Each of the links are time-selective in nature and can be modeled using first order Autoregressive (AR) process 2 as, H i (k) =ρ i H i (k 1)+ 1 ρ 2 i E i(k), (4) where i {SD,SR,RD}, The quantities ρ SD,ρ SR and ρ RD, are the correlation parameters for the SD, SR and RD links, The matrices E SD,E SR and E RD are the time-varying components of the SD, SR and RD links whose entries can be modeled as zero mean circularly symmetric complex Gaussian with variances σ 2 e SD,σ 2 e SR and σ 2 e RD respectively. 2 H. S. Wang and P.-C. Chang, On verifying the first-order Markovian assumption for a Rayleigh fading channel model, IEEE Transactions on Vehicular Technology, vol. 45, no. 2, pp , 1996.

7 System Model V System Model Similar to the works 3,4, assume imperfect channel knowledge Ĥ SR (1)=H SR (1)+H ǫ,sr (1), ĤSD(1)=H SD (1)+H ǫ,sd (1) and Ĥ RD (1)=H RD (1)+H ǫ,rd (1), estimated only in the beginning of each frame. The entries of the error matrices H ǫ,sr (1),H ǫsd,(1) and H ǫ,rd (1) are circularly symmetric complex Gaussian with zero mean and variances σ 2 ǫ SR,σ 2 ǫ SD and σ 2 ǫ RD respectively. 3 Y. Khattabi and M. Matalgah, Performance analysis of multiple-relay AF cooperative systems over Rayleigh time-selective fading channels with imperfect channel estimation, IEEE Transactions on Vehicular Technology, vol. 65, no. 1, pp , , Capacity Analysis for MIMO Beamforming Based Cooperative Systems over Time-Selective Links with Full SNR/One-Bit feedback based Path Selection and Imperfect CSI, Accepted in 2016 IEEE Wireless Communications and Networking Conference (WCNC), 3-6 April 2016.

8 System Model VI System Model Using AR model, one can obtain the expression for H SD (k) as, H SD (k) =ρ k 1 SD H k 1 SD(1)+ 1 ρ 2 SD ρ k i 1 SD E SD (i), =ρ k 1 SD + k 1 ĤSD(1) ρ k 1 1 ρ 2 SD i=1 i=1 SD H ǫ,sd(1) ρ k i 1 SD E SD (i). (5)

9 System Model VII System Model Substituting now the above expression for H SD (k) in (1), the received codeword matrix Y SD (k) can be expressed as, Y SD (k) = P0 ρ k 1 SD ĤSD(1)X(k) W I SD (k) +W M SD (k)+w SD(k), (6) wherew ISD (k) = P 0 ρ k 1 SD H ǫ,sd(1)x(k) denotes the noise component arising due to imperfect channel estimates WSD M (k) = P0(1 ρ 2 SD ) k 1 i=1 ρk i 1 SD E SD (i)x(k) denotes the noise component arising due to node mobility.

10 System Model VIII System Model The effective instantaneous SNR at the destination node for each symbol can be obtained using (6) as, where γ SD (k) = C SD (k) ĤSD(1) 2, (7) C SD (k) = (1+ γ SD ρ 2(k 1) SD γ SD ρ 2(k 1) SD σ 2 ǫ SD + γ SD ( 1 ρ 2(k 1) SD ) σ 2 esd ), and γ SD = P 0 η 0. The quantities σ 2 ǫ SD =N a σ 2 ǫ SD and σ 2 e SD =N a σ 2 e SD, where N a is the number of non-zero symbol transmissions per codeword instant.

11 System Model IX System Model The effective instantaneous SNRs at the relay and destination nodes corresponding to the transmission over the SR and RD links as, γ SR (k)=c SR (k) ĤSR(1) 2, and γ RD (k)=c RD (k) ĤRD(1) 2, where C SR (k) = (1+ γ SR C RD (k) = (1+ γ RD ρ 2(k 1) SR ρ 2(k 1) RD and γ SR = P 0 η 0, γ RD = P 1 η 0. γ SR ρ 2(k 1) SR σ 2 ǫ SR + γ SR γ RD ρ 2(k 1) RD σ 2 ǫ RD + γ RD ( 1 ρ 2(k 1) SR ( 1 ρ 2(k 1) RD ) σ 2 esr ), ) σ 2 erd ),

12 System Model PDF and CDF of various SNR quantities γ SD (k), γ SR (k) & γ RD (k) where f γ (x) = ΛΘ x Θ 1 Γ(Θ) e Λx }{{} Gamma Distribution, F γ (x) = γ(θ,λx), (8) Γ(Θ) 1 1 Θ = NN d,λ = C SD (k) δ sd 2 and δ sd 2 = δ2 sd +σ2 ǫ SD for SD link. 2 Θ = N 2 1, Λ = C SR (k) δ sr 2 and δ sr 2 = δsr 2 +σǫ 2 SR for SR link. 3 1 Θ = NN d,λ = C RD (k) δ rd 2 and δ rd 2 = δ2 rd +σ2 ǫ RD for RD link.

13 System Model Pair-wise Error Probability (PEP) I Theorem (Per-frame average PEP) The per-frame average PEP bound at the destination for the selective DF based MIMO-OSTBC cooperative system is given by P e 1 N b C P e (X 0 (k) X i (k)), (9) N b k=1 i=1 where P e (X 0 (k) X i (k)) = P S D (X 0 (k) X i (k)) P (k) S R ( 1 P (k) S R and P (k) S R +P S D,R D (X 0 (k) X i (k)) P S R (X 0 (k) X j (k)). X j (k) C, X j (k) X 0 (k) ),

14 System Model Pair-wise Error Probability (PEP) II P S R (X 0 (k) X j (k)) =E γsr (k) ( =G { 1 π π/ λ2 j C SR(k) δ 2 sr 4sin 2 θ ( exp λ2 j γ ) } SR(k) 4sin 2 dθ, θ ) N 2, (10) π 2 0 where the function G(ν(θ)) is defined as G(ν(θ))= 1 π Similarly, ( ) NNd P S D (X 0 (k) X i (k)) = G 1+ λ2 i C SD(k) δ 2 sd 4sin 2 θ 1 ν(θ) dθ [?]. (11)

15 System Model Pair-wise Error Probability (PEP) III P S D,R D (X 0 (k) X i (k)) { 1 π/2 = E γsd (k),γ RD (k) exp π 0 (( ) NNd ( = G 1+ λ2 i C SD(k) δ 2 sd 4sin 2 θ ( λ2 i (γ SD(k)+γ RD (k)) 4sin 2 θ 1+ λ2 i C RD(k) δ 2 rd 4sin 2 θ ) NNd ) ) } dθ,. (12)

16 Outage Probability I System Model Theorem (Per-frame average outage probability) The per-frame average outage probability P out (γ 0 ) at the destination for the selective DF based MIMO-OSTBC cooperative system is given by, P out (γ 0 ) = 1 N b N b k=1 P (k) out(γ 0 ) (13) where P (k) out(γ 0 ) =E γ { Pr(γSD (k) γ 0 )Pr(γ SR (k) γ 0 ) +Pr (γ SD (k)+γ RD (k) γ 0 )Pr(γ SR (k) > γ 0 ) }, =F γsd (k)(γ 0 )F γsr (k)(γ 0 )+F γsd (k)+γ RD (k)(γ 0 ) (1 F γsr (k)(γ 0 )), (14)

17 Outage Probability II System Model CDF F γsd (k)+γ RD (k)(γ 0 ) is given by F γsd (k)+γ RD (k)(γ 0 ) 1 = Γ(2NN d )(C SD (k) δ sd 2 )NN d (CRD (k) δ rd 2 )NN d ( K NN (n) d n=0 2NN (n) d n!(c RD(k) δ rd )2NNd+n C RD (k) δ rd 2 C SD (k) δ sd 2 ( γ γ 0 2NN d +n, C RD (k) δ rd 2 ) 2NNd +n where N 0 d = 1,N(n) d = N d (N d +1) (N d +n 1). ) n, (15)

18 System Model Optimal Power Allocation I The convex optimization problem for optimal source-relay power allocation can be formulated as, ( ) N {C 2 +NN d ( ) NNd ( ) } NNd 1 +C 2 1P0 1P0 1P1 min P 0,P 1 where C 1 = s.t. P 0 +P 1 = P. (γ 0 η 0 ) N2 +NN d N 2!(NN d )!(δ 2 sr) N2 (δ 2 sd )NN d and C 2 = (γ 0 η 0 ) 2NN d (2NN d )!(δ 2 sd )NN d(δ 2 rd )NN d.,

19 System Model Optimal Power Allocation II Theorem (Optimal Power Allocation) One non-negative zero of the polynomial equation below ζ(n,n d )(P P 0 ) NN d+1 P N P N2 0 (P P 0 ) = 0, (16) determines the optimal power factor P0 at the source and hence, the optimal power factor P1 at the relay is P 1 = P P 0 for a given total cooperative power budget P. where ζ(n,n d ) = 2(2N 2 )!(δ 2 rd )N2 (N 2!) 2 (δ 2 sr) N2 for N d = N, (N 2 +NN d )(2NN d )!(δrd 2 )NN d(γ 0 η 0 ) N2 NN d for N > N N 2!(NN d )!NN d (δsr 2 d, )N2 (N 2 +NN d )(2NN d )!(δrd 2 )NN d for N < N N 2!(NN d )!NN d (δsr) 2 N2 (γ 0 η 0 ) NN d N2 d.

20 System Model Simulation Result I: PEP Performance Per Frame Average PEP PEP (Analytical) PEP (Simulated) Asymptotic Floor (Analytical) All nodes are mobile with speed 58 mph All nodes are mobile with speed 32 mph All nodes are static with imperfect CSI SNR(dB) All nodes are static with perfect CSI Figure: Per-block average PEP, asymptotic floor, simulated PEP for a Alamouti-coded selective DF-MIMO cooperative communication with N=N d =2,N b =20, channel gains δsd 2 =δ2 sr =δ2 rd =1 and error variances σe 2 = 0.1, σǫ 2 = 0.01.

21 System Model Simulation Result II: PEP Performance 10 0 Per Frame Average PEP PEP (Analytical) PEP (Simulated) Either source or destination is mobile, i.e., ρ rd =1,ρ sd =ρ sr = or ρ sr =1,ρ sd =ρ rd = All nodes are static, i.e., ρ sd =ρ sr =ρ sr = SNR(dB) Only relay is mobile, i.e., ρ sd =1,ρ sr =ρ sr = Figure: Per-block average PEP, asymptotic floor, simulated PEP for a Alamouti-coded selective DF-MIMO cooperative communication with N=N d =2,N b =20, channel gains δsd 2 =δ2 sr =δ2 rd =1 and error variances σe 2 = 0.01, σǫ 2 = 0.

22 System Model Simulation Result III: Outage Performance Per Frame Avg.Outage Probability (a) 10 6 Analytical, (P /P) 0 Equal Simulated, (P /P) Equal R =1/2, (δ =0.5,δsd=0.3,δrd=0.3) c sr 10 7 Simulated, (P 0 /P) Optimal Asymptotic Floor Simulated, Fixed DF [1] SNR(dB) R =1, (δ =0.5,δsd=0.5,δrd=0.5) c sr R c =1, (δ =1,δsd=0.5,δrd sr =0.5) R =1/2, (δ =0.3,δsd=0.3,δrd=0.3) c sr Figure: Simulated outage performance with equal power i.e., P0 and optimal power allocation. P =P1 P =1 2

23 System Model Simulation Result IV: Outage Performance 10 0 Per Frame Avg.Outage Probability Mobile S only, (P 0 /P) Equal Mobile S only, (P 0 /P) Optimal Mobile R or D only, (P 0 /P) Optimal Asymptotic Floor R =1, (δ =0.5,δsd=0.5,δrd=0.5) c sr R =1, (δ =1,δsd=0.5,δrd=0.5) c sr R =1/2, (δ =0.3,δsd=0.3,δrd=0.5) c sr SNR(dB) Figure: Simulated outage performance with equal power i.e., P0 and optimal power allocation. P =P1 P =1 2

24 System Model Thank You