Modeling Mutual Coupling and OFDM System with Computational Electromagnetics

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1 Modeling Mutual Coupling and OFDM System with Computational Electromagnetics Nicholas J. Kirsch Drexel University Wireless Systems Laboratory Telecommunication Seminar October 15, 004

2 Introduction MIMO Communications Mutual Coupling and Local Scattering MIMO-OFDM Mobile Ad-hoc Networking Conclusions

3 MIMO Communications Multiple transmitting antennas to multiple receiving antennas

4 Modeling MIMO Channels Effects of scatterers in the near field Incorporate effects of OFDM Extend simulations to experimental test bed

5 Mutual Coupling and Local Scattering Motivation Determine the degree of importance of including mutual coupling (MC) Accurately model vehicular mobile ad hoc networks (MANETs) which include local scattering (LS) Hybrid Computational Electromagnetic Simulation Near field Method of Moments (NEC, FEKO) Far field Ray tracing (FASANT)

6 Inclusion of mutual coupling and local scattering Run simulation with isotropic radiation patterns to determine the electric fields and geometric solutions for multipath rays : E θ (θ) and E φ (φ)

7 Inclusion cont d

8 Inclusion cont d Create antenna e-field weight signal components with appropriate radiation pattern value (which includes MC and LS) Sum L the appropriate multipath E z rays for every pairwise combination of transmit and receive antennas to create the channel matrix H

9 Inclusion cont d ( n, m) weight ( n, m) weight ( ) ( θ ) E ( θ ) R ( θ ) E = T θ m θ n ( ) ( ϕ) E ( ϕ) R ( ϕ) E = T ϕ m ϕ n L 1 h = n, m E l= 0 ( n, m) z, l H=, [ h ] n m N M

10 Method of Analysis Spatial Multiplexing (SM) Capacity - to evaluate spectral efficiency due to multipath richness (without path loss) Beamforming (BF) Capacity used to compare the effectiveness of antennas in vehicular MANET SM and BF capacities are used to evaluate which signaling technique is best in a MANET C B ρhh ( H) = log + I N Mα( H) + ρλ ( ) = max H log 1 α( H) α 1 ( H ) = F M H H ( H)

11 Angular spread Angular Spread used to understand the multipath richness Λ = 1 F 1 F 0 F k = π 0 p jkθ ( θ ) e d θ

12 Simulations Inclusion of MC at both ends of the link 4 x 4 MIMO System, ULA Performance analysis of a vehicular MANET 4x4 MIMO, antennas arranged on each side of vehicle

13 Radiation patterns.4 GHz dipole antenna in a λ/ ULA.4 GHz patch antenna on the front of a bumper of a vehicle Radiation patterns due to near field effects are shown

14 Results: Inclusion of MC at both ends of the link Inclusion of MC at both ends of the link results in greater capacity in both the LOS and NLOS cases. Case Philadelphia - LOS Philadelphia - NLOS Angle Spread

15 Results: Performance evaluation of a vehicular MANET Due to the array geometry, some transmitting antennas may not communicate with certain receiving antennas even in a multipath rich environment A rank deficient channel will have lower spatial multiplexing capacity, but higher beamforming capacity

16 MIMO-OFDM Current research on MIMO-OFDM based on statistical channel models Statistical channel model: either insufficiently wideband or not suited for the physical environment of interest Ray-tracing simulation: site-specific information

17 Electromagnetic Ray Tracing Computational electromagneticbased simulation technique; ERT is computationally complex and demanding; ERT has been applied to narrowband system so far.

18 Channel Response Extrapolation Assumptions Subcarrier frequencies are not so far apart that the geometric ray solutions remain the same across all subcarriers The number and type of multipath signal components remain the same from one subcarrier to another

19 Channel Response Extrapolation FASANT computes the electric field of each ray The response E z,n at carrier f n can be computed by extrapolation where m m f c d j z d jk z m z e E e E E π, = = f c d j m z f c d j z n z e E e E E n = = π π,, f n f m f =

20 SISO Channel Model Time-varying channel For a finite bandwidth receiver, some of the rays cannot be distinguished in time. Group them to be a cluster The time-clustered channel is = = 1 0 ) (, ) ( ), ( ) ( N i i t f j i m z i d e E t τ τ δ τ α π = = p l i i m z l t E t 1 ) (, ) ( ) ( β = = 1 0 ) ( ) ( ), ( L l l l t t τ τ δ β τ α

21 MIMO Channel Model and Capacity Input Output relation Frequency response of wideband channel matrix at kth subcarrier If CSI is not available at the transmitter If CSI is known at the transmitter: use water-filling to maximize mutual information. = = 1 0 ) ( ) ( L l l l n n x H y = = 1 0 / / ) ( L l N lk j l N k j e e π π H H ( ) ( ) = = + = = 1 0 / / 1 0 det log 1 1 N k N k j H N k j n t Mr N k k e e NM P N I N I π π σ H H I

22 Simulated Capacity in Ad Hoc network 0m 50m Street Street Center frequency =.4GHz Number of carriers = 64 Channel spacing = 31.5KHz 50m 0m

23 Simulated Capacity Capacity vs Subcarrier(Node 7 to Node 3) Equal power SNR=15dB Equal power SNR=0dB 1D Waterfilling SNR=15dB 1D Waterfilling SNR=0dB Capacity vs Subcarrier(Node 9 to Node ) Equal power SNR=15dB Equal power SNR=0dB 1D Waterfilling SNR=15dB 1D Waterfilling SNR=0dB Capacity(bit/sec/Hz) Capacity (bit/sec/hz) Subcarrier Subcarrier Capacities fluctuate at different subcarriers

24 EigenvaluesvsSubcarriers 4 Dominant eigenvalues vs Subcarrier(Node 9 to Node ) 3.5 Dominant eigenvalue vs Subcarrier(Node 7 to Node 3) Eigenvalue # Eigenvalue # Subcarrier Subcarrier Eigenvalue # Eigenvalue # Subcarrier Subcarrier The larger the eigenvalue an eigenmode has, the more power flows to that mode Frequency diversity achieved

25 Mobile Ad hoc Network Ad-hoc network MIMO Communications Software Defined Radio Modular Networking Layer Wide bandwidth (10MHz Baseband)

26 Node infrastructure overview

27 Summary Demonstrated importance of including MC and LS for design of ad hoc network nodes making use of antenna arrays Developed simulation methodology for including these practical electromagnetic effects

28 Summary cont d Fast way to generate channel responses in OFDM system with CEM. This technique is used for simulating MIMO- OFDM Ad Hoc network, which shows both spatial and frequency diversity are achieved. Combine ray tracing channel model with correlation (stochastic) channel model to provide site-specific information as well as numerous channel realizations Semi-stochastic spatialtemporal channel model.

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