Channel Modelling for Beamforming in Cellular Systems

Transcription

1 Channel Modelling for Beamforming in Cellular Systems Salman Durrani Department of Engineering, The Australian National University, Canberra. DERF June 26

2 Outline Introduction Evolution of cellular systems Background & Motivation 2 Proposed Channel Model Parameterization Mobile Station Mobility Model Results Temporal and Spatial Properties Conclusions

3 Evolution of Cellular Systems Australia:- System Standard Launch Peak Data Rate 2G GSM kbps 3 3G WCDMA 23, kbps, 2 Mbps 3.5G HSDPA Mbps 3.75G HSDPA + MIMO 21? 45 Mbps 3.9G 3G LTE + MIMO 215? 1 Mbps 4G OFDM + MIMO 22? 1 Mbps, 1 Gbps

4 Beamforming Typically λ/2 spaced antenna elements are used (at 2 GHz frequency, 8 element uniform linear array antenna.5 m). 4 Interferer s signal attenuated Desired user s signal enhanced Base Station Smart Antenna Beamforming can improve the performance of cellular systems by mitigating Multiple Access Interference (MAI).

5 Propagation Environment Typical propagation scenario:- Dominant reflector 5 Subpaths y Mean AOA θ k x Angular dispersion of received signal at the BS, characterized by angle spread σ AOA BS antenna array Local scattering structures around the MS

6 Channel Model - Parameterization The channel impulse response can be written as Ωk,l S [ ] h k,l,n (t) = exp j(φ (s) k,l S + 2πf D t cos Ψ (s) k,l ) s=1 [ ] exp jkd(n 1) sin(θ (s) k,l ) δ(t τ k,l ) 6 S. Durrani and M. E. Bialkowski, A Parametric Channel Model for Smart Antennas Incorporating Mobile Station Mobility, Proc. IEEE 63rd Vehicular Technology Conference (VTC), Melbourne, May 7-1, 26.

7 Channel Model - Parameterization The channel impulse response can be written as Ωk,l S [ ] h k,l,n (t) = exp j(φ (s) k,l S + 2πf D t cos Ψ (s) k,l ) s=1 [ ] exp jkd(n 1) sin(θ (s) k,l ) δ(t τ k,l ) 6 Temporal Parameters K = users; L = multipaths; S = sub-paths/path; Ω k,l = mean path power; τ k,l = propagation delay; φ (s) k,l = random phase; f D = Doppler frequency; Spatial Parameters N = BS antennas; d = inter-element distance; K = 2π/λ; = Angle of Departure (AOD); θ (s) k,l = θ k (t) + ϑ (s) k,l θ k (t) = Angle of Arrival (AOA); σ AOA = angle spread; Ψ (s) k,l

8 MS Mobility Model AOA Initialisation: Desired user s AOA= 6, Interferer s AOA = uniformly distributed over the azimuth range. AOA Evolution: A drop is defined as the simulation time required by the desired user to traverse the entire azimuth range [ 6, 6 ] with mean AOA change θ =.1 per snapshot. 7 MS k MS 1 MS 2 MS K d θ k θ N BS Array Antenna

9 Simulation Assumptions Temporal Parameter Value Carrier frequency f c = 2 GHz (λ/2 = 7.5 cm) No. of paths L = 1 No. of subpaths S = 2 Doppler frequency f D = 1 Hz Spatial Parameter Value No. of BS antenna elements N = 1 8 Antenna geometry Uniform linear array Inter-element distance d = λ/2 Angle of Arrival 6 θ 6 PDF in AOD Uniform PDF in AOA Gaussian Angle spread σ AOA = 2 Mobility Parameter Value User mobility.1 per snapshot 8

10 Results - Space Time Fading Space Time Fading Profile Magnitude of Channel Response (db) Space (d/λ) Time t (ms) Doppler frequency f D = 1 Hz, angle spread σ AOA =

11 Results PDF of Channel Amplitudes 1.5 Rayleigh fading Simulated Theoretical 1 1 PDF Channel Amplitude We see that the simulation result provide a good match with theory.

12 Results Temporal Correlation Normalized Autocorrelation of R{h(t)} AutoCorrelation of R{h} Theoretical Simulated Normalised Time f D *τ Theory: R(τ) = J (2πf D τ)

13 Results Temporal Correlation Squared Envelope AutoCorrelation Normalized Autocorrelation of h(t) Normalised Time f D *τ Theory: R(τ) = J 2 (2πf D τ) Theoretical Simulated 12

14 Results Spatial Correlation Spatial Envelope Correlation ρ Spatial Correlation Coefficient ρ 12 vs. distance d/λ Mean AOA = Mean AOA = 6 σ = 5 AOA σ AOA = 1 σ = 2 AOA Spatial Envelope Correlation ρ 12 1 σ = 5 AOA σ.8 AOA = 1 σ = 2 AOA Distance (d/λ) Theory: Distance (d/λ) J. Luo, J. R. Zeidler and S. McLaughlin, Performance analysis of compact antenna arrays with MRC in correlated Nakagami fading channels, IEEE Transactions on Vehicular Technology, vol. 5, no. 1, pp , Jan. 21.

15 Results Smart Antenna Simulations Smart Antenna Simulation Using Proposed Channel Model 1 1 lines analytical model, markers simulation 14 N = 8 ULA antenna M = 64, N c = 256 (IS-95 CDMA Parameters) L = 2, 3 paths/user (uniform PDP s) K = 5, 2 users Mean BER L = 2, K = 2 L = 3, K = 2 L = 2, K = 5 L = 3, K = E b /N o (db)

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