Statistical Properties of a Parametric Channel Model for Multiple - PowerPoint PPT Presentation

Statistical Properties of a Parametric Channel Model for Multiple Antenna ANU Systems S. Durrani ∗ , M. E. Bialkowski † and S. Latif ∗ ∗ Department of Engineering, The Australian National University, Canberra, Australia. Email: salman.durrani@anu.edu.au † School of ITEE, � The University of Queensland, Brisbane, Australia. � � IEEE PIMRC Sep. 2007 � �

Outline ⊲ Introduction ANU ⋄ MIMO Channel Models 2 ⋄ Motivation ⊲ Reference Channel Model ⋄ Statistical Properties ⊲ Parametric Channel Model ⊲ Results � ⋄ Temporal and Spatial Properties � � ⊲ Conclusions � �

Introduction ⊲ MIMO Channel Models can be classified as follows: † ANU 3 1 1 2 2 MIMO CHANNEL Transmitter Receiver ... ... n m N T TX N R RX � antennas antennas � � † P. Almers et. al., “Survey of Channel and Radio Propagation Models for Wireless MIMO � Systems,” EURASIP Journal on Wireless Communications and Networking , 2007. �

Introduction ⊲ MIMO Channel Models can be classified as follows: † ANU 3 1 1 MIMO CHANNEL MODELS ANALYTICAL 2 2 PHYSICAL Transmitter Receiver ... ... n m N T TX N R RX � antennas antennas � � † P. Almers et. al., “Survey of Channel and Radio Propagation Models for Wireless MIMO � Systems,” EURASIP Journal on Wireless Communications and Networking , 2007. �

Introduction ⊲ MIMO Channel Models can be classified as follows: † ANU 3 1 1 MIMO CHANNEL MODELS ANALYTICAL 2 2 PHYSICAL Transmitter Receiver ... ... DETERMINISTIC GEOMETRY-BASED n m PARAMETRIC N T TX N R RX � antennas antennas � � † P. Almers et. al., “Survey of Channel and Radio Propagation Models for Wireless MIMO � Systems,” EURASIP Journal on Wireless Communications and Networking , 2007. �

Parametric Channel Model ⊲ Parametric channel models use important physical parameters ANU such as phases, delays, doppler frequency, angle of departure (AOD), angle of arrival (AOA) and angle spread to provide a description of 4 the MIMO channel. Each path consists of (unresolvable) S subpaths that all have the same delay, but different angles of arrival and departures distributed around the mean angles. How many subpaths are sufficient to accurately capture the statis- � tical properties of the MIMO wireless channel? � � � �

Parametric Channel Model ⊲ Parametric channel models use important physical parameters ANU such as phases, delays, doppler frequency, angle of departure (AOD), angle of arrival (AOA) and angle spread to provide a description of 4 the MIMO channel. ⊲ Each path consists of (unresolvable) S subpaths that all have the same delay, but different angles of arrival and departures distributed around the mean angles. How many subpaths are sufficient to accurately capture the statis- � tical properties of the MIMO wireless channel? � � � �

Parametric Channel Model ⊲ Parametric channel models use important physical parameters ANU such as phases, delays, doppler frequency, angle of departure (AOD), angle of arrival (AOA) and angle spread to provide a description of 4 the MIMO channel. ⊲ Each path consists of (unresolvable) S subpaths that all have the same delay, but different angles of arrival and departures distributed around the mean angles. ⊲ How many subpaths are sufficient to accurately capture the statis- � tical properties of the MIMO wireless channel? � � � �

Wireless Propagation Environment ⊲ We consider a MIMO system in an urban macro-cell environ- ANU ment . 5 � � � � �

Reference Channel Model ⊲ The channel impulse response between MS antenna m and BS ANU antenna n for user k ’s path l can be written as 6 h m,n k,l ( t ) = ( h I ) m,n k,l ( t ) + j ( h Q ) m,n k,l ( t ) For isotropic scattering, the temporal correlation properties are summarized below: R h I h I ( τ ) = E [ h I ( t ) h I ( t + τ )] = J 0 (2 πf D τ ) R h Q h Q ( τ ) = E [ h Q ( t ) h Q ( t + τ )] = J 0 (2 πf D τ ) R h I h Q ( τ ) = E [ h I ( t ) h Q ( t + τ )] = 0 R hh ( τ ) = E [ h ( t ) h ∗ ( t + τ )] = J 0 (2 πf D τ ) � R | h | 2 | h | 2 ( τ ) = 4 + 4 J 2 0 (2 πf D τ ) � � � �

Reference Channel Model ⊲ The channel impulse response between MS antenna m and BS ANU antenna n for user k ’s path l can be written as 6 h m,n k,l ( t ) = ( h I ) m,n k,l ( t ) + j ( h Q ) m,n k,l ( t ) ⊲ For isotropic scattering, the temporal correlation properties are summarized below: R h I h I ( τ ) = E [ h I ( t ) h I ( t + τ )] = J 0 (2 πf D τ ) R h Q h Q ( τ ) = E [ h Q ( t ) h Q ( t + τ )] = J 0 (2 πf D τ ) R h I h Q ( τ ) = E [ h I ( t ) h Q ( t + τ )] = 0 R hh ( τ ) = E [ h ( t ) h ∗ ( t + τ )] = J 0 (2 πf D τ ) � R | h | 2 | h | 2 ( τ ) = 4 + 4 J 2 0 (2 πf D τ ) � � � �

Reference Channel Model ⊲ The Level Crossing rate is defined as the rate at which the fading ANU envelope crosses a specified threshold in the positive slope √ 7 2 πf D ρe − ρ 2 L | h | = ⊲ The Average Fade Duration is the average duration of time that the fading envelope remains below a specified e ρ 2 − 1 √ T | h | = ρ 2 πf D � � � � �

Reference Channel Model ⊲ We assume that the angular distribution of the subpaths at the MS ANU can be modelled by a Uniform PDF over [ − π, π ] . 8 Measurements have shown that the angular distribution of the sub- paths at the BS can be modelled by a Gaussian PDF . For urban macro-cellular environment, median angular spread: 5 ◦ − 20 ◦ . � � � � �

Reference Channel Model ⊲ We assume that the angular distribution of the subpaths at the MS ANU can be modelled by a Uniform PDF over [ − π, π ] . 8 ⊲ Measurements have shown that the angular distribution of the sub- paths at the BS can be modelled by a Gaussian PDF . † For urban macro-cellular environment, median angular spread: 5 ◦ − 20 ◦ . � � † K. I. Pedersen et. al., ”A stochastic model of the temporal and azimuth dispersion seen � at the base station in outdoor propagation environments,” IEEE Trans. VT , vol. 49, no. 2, � pp. 437-447, Mar. 2000. �

Reference Channel Model ⊲ We assume that the angular distribution of the subpaths at the MS ANU can be modelled by a Uniform PDF over [ − π, π ] . 8 ⊲ Measurements have shown that the angular distribution of the sub- paths at the BS can be modelled by a Gaussian PDF . † ⋄ For urban macro-cellular environment, median angular spread: 5 ◦ − 20 ◦ . � � † K. I. Pedersen et. al., ”A stochastic model of the temporal and azimuth dispersion seen � at the base station in outdoor propagation environments,” IEEE Trans. VT , vol. 49, no. 2, � pp. 437-447, Mar. 2000. �

Reference Channel Model ⊲ The spatial envelope correlation coefficient ρ s , between the ANU p th and q th antenna elements for a ULA, is given by ρ s ( p, q ) = | R s ( p, q ) | 2 = |ℜ{ R s ( p, q ) } + j ℑ{ R s ( p, q ) }| 2 9 ⊲ Spatial Correlation at BS � π + j 2 vσ 2 ∞ � �� J 2 v ( z pq ) cos(2 vθ AOD ) e ( − 2 v 2 σ 2 � AOD ) ℜ AOD ℜ{ R s ( p, q ) } = J 0 ( z pq ) + 2 C g erf √ 2 σ AOD v =1 � − (2 v +1)2 σ 2 � � π + j (2 v + 1) σ 2 ∞ � �� AOD � 2 AOD √ ℑ{ R s ( p, q ) } = 2 C g J 2 v +1 ( z pq ) sin[(2 v + 1) θ AOD ] e ℜ erf 2 σ AOD v =0 ⊲ Spatial Correlation at MS ∞ � ℜ{ R s ( p, q ) } = J 0 ( z pq ) + 2 J 2 v ( z pq ) cos(2 vθ AOA )sinc(2 v ∆) � v =1 � ∞ � ℑ{ R s ( p, q ) } = 2 J 2 v +1 ( z pq ) sin[(2 v + 1) θ AOA ]sinc[(2 v + 1)∆] � v =0 � �

Parametric Channel Model ⊲ The channel impulse response can be written as ANU � S � Ω k,l h ( m,n ) exp[ j ( φ ( s ) k,l + 2 πf D t cos θ ( s ) � ( t )= k,l,AOA )] k,l S 10 s =1 × exp[ − jκd M ( m − 1) sin θ ( s ) k,l,AOA ] � × exp[ − jκd B ( n − 1) sin θ ( s ) k,l,AOD ] δ ( t − τ k,l ) Spatial Parameters Temporal Parameters N = No. of antennas; K = users; d = inter-element distance; L = multipaths; κ = 2 π/λ ; S = sub-paths/path; θ ( s ) k,l,AOD = θ k,AOD + ϑ ( s ) Ω k,l = mean path power; � k,l,AOD θ ( s ) k,l,AOA = θ k,AOA + ϑ ( s ) τ k,l = propagation delay; � k,l,AOA φ ( s ) k,l = random phase; θ k,AOA = Mean Angle of Arrival; � f D = Doppler frequency; θ k,AOD = Mean Angle of Departure; � �

Parametric Channel Model ⊲ The channel impulse response can be written as ANU � S � Ω k,l h ( m,n ) exp[ j ( φ ( s ) k,l + 2 πf D t cos θ ( s ) � ( t )= k,l,AOA )] k,l S 10 s =1 × exp[ − jκd M ( m − 1) sin θ ( s ) k,l,AOA ] � × exp[ − jκd B ( n − 1) sin θ ( s ) k,l,AOD ] δ ( t − τ k,l ) Spatial Parameters Temporal Parameters N = No. of antennas; K = users; d = inter-element distance; L = multipaths; κ = 2 π/λ ; S = sub-paths/path; θ ( s ) k,l,AOD = θ k,AOD + ϑ ( s ) Ω k,l = mean path power; � k,l,AOD θ ( s ) k,l,AOA = θ k,AOA + ϑ ( s ) τ k,l = propagation delay; � k,l,AOA φ ( s ) k,l = random phase; θ k,AOA = Mean Angle of Arrival; � f D = Doppler frequency; θ k,AOD = Mean Angle of Departure; � �