Deterministic radio propagation modeling and ray tracing 1) Introduction to deterministic propagation modelling 2) Geometrical Theory of Propagation I-The ray concept-Reflection and transmission 3) Geometrical Theory of Propagation II-Diffraction,multipath 4) Ray Tracing I 5) Ray Tracing II-Diffuse scattering modelling 6) Deterministic channel modelling I 7) Deterministic channel modelling II-Examples 8) Project -discussion
Deterministic radio propagation modeling and ray tracing 1) Introduction to deterministic propagation modelling 2) Geometrical Theory of Propagation I - The ray concept – Reflection and transmission 3) Geometrical Theory of Propagation II - Diffraction, multipath 4) Ray Tracing I 5) Ray Tracing II – Diffuse scattering modelling 6) Deterministic channel modelling I 7) Deterministic channel modelling II – Examples 8) Project - discussion
Envelope correlations (1/5) It is useful to define transfer function's envelope-correlations.Considering the module of the generic transfer function M(z)I in a e-kind domain z,the domain span△z and the average valueM,over△z we have:: "z-wise"correlation (envelope correlation) w(e-MlM(e+o-l] R(8)=4 R(0)=1,-1<R(⊙)s1 Jw(a-l了t {R(}=0 Especially frequency and space correlations are useful.The last one is fundamental for diversity techniques and MIMO
Envelope correlations (1/5) It is useful to define transfer function’s envelope-correlations. Considering the module of the generic transfer function |M(z)| in a e-kind domain z, the domain span Δz and the average value over Δz we have: “z-wise” correlation (envelope correlation) R z (δ ) = M (z) − M Δz ⎡ ⎣ ⎤ ⎦ M (z +δ ) − M Δz ⎡ ⎣ ⎤ ⎦ dz Δz ∫ M (z) − M Δz ⎡ ⎣ ⎤ ⎦ 2 dz Δz ∫ ; R z (0) = 1, −1< R z (δ ) ≤1 z M Δ Especially frequency and space correlations are useful. The last one is fundamental for diversity techniques and MIMO. lim δ→∞ R z { (δ )} = 0
Envelope correlations (2/5) Ex:frequency correlation Ja(r八-w]LHU+w-a风] R(w) JU-了 Space correlation (along the x direction) H(-l]He+-L] R(0=4 a(-l了
Envelope correlations (2/5) Space correlation (along the x direction) R x (l) = H (x) − H Δx ⎡ ⎣ ⎤ ⎦ H (x + l) − H Δx ⎡ ⎣ ⎤ ⎦ dx Δx ∫ H (x) − H Δx ⎡ ⎣ ⎤ ⎦ 2 dx Δx ∫ Ex: frequency correlation Rf (w) = H ( f ) − H Δf ⎡ ⎣ ⎤ ⎦ H ( f + w) − H Δf ⎡ ⎣ ⎤ ⎦ df Δf ∫ H ( f ) − H Δf ⎡ ⎣ ⎤ ⎦ 2 df Δf ∫
Envelope correlations (3/5) Ex.space correlation in a Rayleigh environment,i.e.with uniform 2D power- azimuth distribution with p)=1/2 is: 0元 R.(1)=J. 0.8 computation measurement -··Rayleigh(theoretic) 0.6 With Jo the zero-order Bessel's 0.4 function of the first kind.This means that the signal received from two Rx's 0.2 A2 apart is nearly uncorrelated (see figure),and this can be useful to decrease fast fading effects -0.2 0 0.5 11.5 22.5 33.5 Normalized distance d
Envelope correlations (3/5) Ex. space correlation in a Rayleigh environment, i.e. with uniform 2D powerazimuth distribution with pϕ(ϕ)=1/2π is: R x (l) = J 0 2πl λ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ With J0 the zero-order Bessel’ s function of the first kind. This means that the signal received from two Rx’s λ/2 apart is nearly uncorrelated (see figure), and this can be useful to decrease fast fading effects l/λ J0
Envelope correlations (4/5) Frequency correlation and time correlation allow a rigorous definition of coherence bandwidth and coherence time. Given a reference,residual frequency correlation "a",then coherence bandwidth is: B=币with R,(o)≤for w≥项 Similarly,given a reference,residual time correlation "a",then coherence time IS To=7 with R,()同sa fort≥i Coherence distance L.can also be defined in the following way: L9=I with R,(0)≤a forx≥l
Envelope correlations (4/5) Frequency correlation and time correlation allow a rigorous definition of coherence bandwidth and coherence time. Given a reference, residual frequency correlation “ a ”, then coherence bandwidth is: BC (a) = w with Rf (w) ≤ a for w ≥ w Similarly, given a reference, residual time correlation “ a ”, then coherence time is : TC (a) = t with R t(t ) ≤ a for t ≥ t Coherence distance Lc can also be defined in the following way: LC (a) = l with R x (l) ≤ a for x ≥ l
Envelope correlations (5/5) The higher the coherence distance Le the lower the angle spread All considered we have: B DS
Envelope correlations (5/5) The higher the coherence distance Lc the lower the angle spread. All considered we have: B c 0.1 1 DS L c 0.1 ≈ λ 4 1 σ Ω
Multidimensional parameters and MIMO (1/2) For optimum antenna/space diversity performance the received signal at the different antennas should be incorrelated,i.e.the signal envelope should have fast changes with space (along s). Therefore the power-angle profile should be very spread-there must be a large angle spread. To achieve good spatial multiplexing there must be a large number of strong paths well spaced(independent)in the angle domain in order for the MIMO matrix to have high rank-there must be a large angle spread. In other words there must be a high multipath richness Also absolute-time and Doppler domains(not considered here)are very important for space-time coding,i.e.transmit diversity and other MIMO coding techniques
Multidimensional parameters and MIMO (1/2) For optimum antenna/space diversity performance the received signal at the different antennas should be incorrelated, i.e. the signal envelope should have fast changes with space (along s). Therefore the power-angle profile should be very spread → there must be a large angle spread. To achieve good spatial multiplexing there must be a large number of strong paths well spaced (independent) in the angle domain in order for the MIMO matrix to have high rank → there must be a large angle spread. In other words there must be a high multipath richness Also absolute-time and Doppler domains (not considered here) are very important for space-time coding, i.e. transmit diversity and other MIMO coding techniques
Multidimensional parameters and MIMO (2/2) Angle spread and delay spread are two possibile measures of multipath richness. SNR remains however the most important parameter for the performance pf small-size MIMO schemes(i.e.2x2 or 4x4 etc) Recent studies have shown that for unnormalized channel,the channel capacity usually rises when moving from NLOS into LOS since the loss in multipath richness is more than compensated for by an increase in SNR. Dual-polarized MIMO schemes are very attractive as a doubling in the MIMO order is achieved with a less-than-proportional increase in the antenna size. In Dual polarized MIMO schemes the XPD(Cross-Polarization Discrimination) is very important.If the XPD is high (low correlation btw polarization states) then multiplexing is possible,otherwise polarization diversity is preferable
Multidimensional parameters and MIMO (2/2) Angle spread and delay spread are two possibile measures of multipath richness. SNR remains however the most important parameter for the performance pf small-size MIMO schemes (i.e. 2x2 or 4x4 etc) Recent studies have shown that for unnormalized channel, the channel capacity usually rises when moving from NLOS into LOS since the loss in multipath richness is more than compensated for by an increase in SNR. Dual-polarized MIMO schemes are very attractive as a doubling in the MIMO order is achieved with a less-than-proportional increase in the antenna size. In Dual polarized MIMO schemes the XPD (Cross-Polarization Discrimination) is very important. If the XPD is high (low correlation btw polarization states) then multiplexing is possible, otherwise polarization diversity is preferable
Multidimensional measurementsl*(1/2) Transmitter Receiver *]V-M.Kolmonen.J.Kivinen.L.Vuokko.P.Vainikainen."5.3 GHz MIMO radio channel sounder."IEEE Trans. Instrum.Meas.Vol.55.No.4.pp.1263-1269.Aug 2006
Multidimensional measurements[*] (1/2) Transmitters Receiver [*] V.-M. Kolmonen, J. Kivinen, L. Vuokko, P. Vainikainen, ”5.3 GHz MIMO radio channel sounder,” IEEE Trans. Instrum. Meas., Vol. 55, No. 4, pp. 1263-1269, Aug. 2006
Multidimensional measurements(2/2) Ex:power-angle 20° 30° profile at the Rx Street #2 Street 1 Dominant path structure P1,t,6,X,V1 Power profiles, etc
Multidimensional measurements (2/2) Impulse responses for each couple of antenna elements H(t) = h11 (t) . . h1M (t) . . . . . . . . hN1 (t) . . hNM (t) ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ Superresolution algorithm Es: SAGE RiMAX etc. Dominant path structure ρi ,ti ,θi , χi , ψi Power profiles, etc. Ex: power-angle profile at the Rx
