On the Plane Wave Assumption in Indoor Channel Modelling

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1 On the Plane Wave Assumption in Indoor Channel Modelling Markus Landmann 1 Jun-ichi Takada 1 Ilmenau University of Technology www-emt.tu-ilmenau.de Germany Tokyo Institute of Technology Takada Laboratory Japan Phone Fax Sapporo Japan, September 5 IEICE 5

2 motivation measurement based parametric channel modelling (MBPCM reliability of parameter estimation results in Indoor environments influence of the plane wave assumption on the estimation residual and the dense multipath components (DMC Slide magnitude [db] measured channel impulse response remaining channel impulse response after substraction of the estimated pathes estimated diffuse Scattering scattering DMC normalized τ Sapporo Japan, September 5 diffuse scattering [db] α τ ( = α + -β α 1 e ( ( τ-τ n 1 log 1 α -7 τ n normalized τ ( 1 log 1 α 1 IEICE 5

3 outline Slide 3 antenna array calibration analytic array data model antenna phase centre estimation estimation results Specification of the used antenna array centre frequency 4.5 GHz bandwidth antenna arrangement 1 MHz stacked rings of 4 dual polarized patch antennas (in total 96 ports Sapporo Japan, September 5 IEICE 5

4 antenna array calibration TX (dual polarized horn antenna Calibration Setup measurement of the complete beam patterns in the range of 36 azimuth and 18 elevation of the spherical coordinate system maximum step size in both dimensions is especially defined by the aperture size of the array 6.38 m sampled D beam pattern (measured Azimuth RX (antenna array Slide 4 Elevation 18 5 gain [db] B max( B elevation [deg] azimuth [deg] Sapporo Japan, September 5 IEICE 5

5 analytic array data model Slide 5 phase term plane wave assumption b ph -j π k ( ϕ, ϑ ri /( λ k ( ϕ, ϑ, i = e spherical wave fronts b ph ( ϕ, ϑ, i = e r r -j π k r r ( ϕ, ϑ r / λ i source k r z ϑ i r r i xi = yi z i y r r i vector to the phase centre of the i-th antenna i-th antenna complex beam pattern ( ϑ,ϕ b A,i related to the phase centre ϕ i x measured complex beam pattern and its D Fourier Transform b ( ϑ, ϕ, i b A ( ϑ, ϕ, i b ( ϑ, ϕ, i ; ϑ = n ϑ ϕ = n ϕ = ph 1, D Fourier transform leads to the EADF Model g ( µ 1, µ, i = g A( µ 1, µ, i g ph ( µ 1, µ, i ; f1 = µ 1 f1, f = µ f Sapporo Japan, September 5 IEICE 5

6 antenna phase centre estimation (1D example Slide 6 determine the position r i by estimating b ph,i estimator will minimize the width of the aperture function of the beam pattern b A,i by optimizing b ph,i beam domain aperture domain g A,i (f g ph,i (f g i (f b/b max [db] b i (φ b ph,i (φ g/g max [db] b A,i (φ φ [deg] f [1/deg] Sapporo Japan, September 5 IEICE 5

7 estimation error neglecting spherical wave fronts Slide 7 single path estimation calculation of the array response for different distances (.5 m 1 m and different DoA DoA estimation using RIMAX and an antenna model for a fixed distance of 6.38 m SNR 7 db Calibration distance of the used data model.5 m 6.38 m..1 m Sapporo Japan, September 5 IEICE 5

8 estimation error neglecting spherical wave fronts Slide 8 normalized spectrum [db] azimuth spectra of the measurement and residual measurement h measurement v azimuth [deg] normalized spectrum [db] estimation residual h estimation residual v azimuth [deg] after subtraction still signal power with angular information spurious path will be estimated in case of the analysis of measurement data Sapporo Japan, September 5 IEICE 5

9 estimation error neglecting spherical wave fronts Slide 9 Single path versus multiple path estimation (case relative power [%] r =.5 m r = 6 m r = 5 m azimuth [deg] model error [db] case 1 (max No. of paths = 1 case (max No. of paths = distance [m] No. of estimated paths case in case in average up to 5 paths are estimated estimation of spurious path in real environment dependent on the distance the spurious paths are distributed in azimuth the power of the real path is reduced up to 5 % Sapporo Japan, September 5 IEICE 5

10 conclusions Slide 1 neglecting the curvature will cause insufficient estimation result in indoor environments based on this estimation results the evaluation of application specific antenna configuration is limited it may explain the high number of spurious paths in LOS cases the proposed antenna model may improve the estimation results in future implementation of the ML estimator RIMAX Sapporo Japan, September 5 IEICE 5

11 estimation error neglecting spherical wave fronts Slide 11 error of azimuth single path estimation error of elevation azimuth spectra of the measurement and residual normalized spectrum [db] normalized spectrum [db] azimuth [deg] measurement h measurement v estimation residual h estimation residual v azimuth [deg] after subtraction still signal power with angular information in case of the analysis of measurement data of a real environment additional spurious path will be estimated Sapporo Japan, September 5 IEICE 5

12 antenna phase centre estimation (1D example Slide 6 measured complex beam pattern b i ( ϕ = b ( ϕ b ( A, i ph, i ϕ weighting function w ( f = sign( f ( f π beam domain * gˆ ( ( ( (, ˆ, ˆ A, i f1 = F bi ϕ bph, i ϕ ϕm ri The estimator has to minimize the width of ˆ ϕ, rˆ i i estimated complex beam pattern ( ϕ = b ( ϕ b ( ϕ, ˆ ϕ, rˆ ˆ * b A, i i ph, i i i ( ϕ ĝ A,i f max arg min ( ˆ ( ˆ (,, ( d, = g A i f g A i f w f f ϕi ri f min aperture domain g A,i (f g ph,i (f g i (f b/b max [db] b i (φ b ph,i (φ g/g max [db] b A,i (φ φ [deg] f [1/deg] Sapporo Japan, September 5 IEICE 5

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