Modelling Process

In this sub-section, we introduce WINNER channel coefficient generation procedure, depicted in Figure 2.3. The following subsection is according to Figure 2.3 modeling process, generate those WINNER channel matrix parameters in (2.8) .

General parameters:

• Step 1: Set the environment, network layout and antenna array parameters

– Choose one of the scenarios (A1, A2, B1, ....).

– Give number of BS and MS.

– Give locations of BS and MS, or equally distances of each BS and MS and relative directions ϕ_LOS and φ_LOS of each BS and MS.

– Give BS and MS antenna field patterns Frx and Ftx, and array geometries.

– Give BS and MS array orientations with respect to north (reference) direction.

Table 2.5: Line-of-Sight Probabilities [5]

Scenario LOS probability as a function of distance d [m] Note

A1 P_LOS = 1, d ≤ 2.5

P_LOS = 1− 0.9(1 − (1.24 − 0.61 log d)³)^1/3, d > 2.5 B1 P_LOS = min(18/d, 1)· (1 − exp(−d/36)) + exp(−d/36)

B3 P_LOS = 1, d≤ 10 For big factory halls,

P_LOS = 2, d≤ 10 airport and train stations

C1 P_LOS = exp(−₂₀₀^d )

C2 P_LOS = min(18/d, 1)· (1 − exp(−d/63)) + exp(−d/63)

D1 P_LOS = exp(−₁₀₀₀^d )

– Give speed and direction of motion of MS.

– Give system center frequency.

Large scale parameters:

• Step 2: Assign the propagation condition (LOS/NLOS) according to the probability described in Table 2.5.

• Step 3: Calculate the path loss with formulas of Table 2.12 for each BS-MS link to be modelled.

• Step 4: Generate the correlated large scale parameters.

Small scale parameters:

• Step 5: Generate the delays τ.

Delays are drawn randomly from the delay distribution defined in Table 2.6. With

exponential delay distribution calculate

τ_n^′ =−γτστln(Xn). (2.9)

where γ_τ is the delay distribution proportionality factor, σ_τ is delay spread, X_n ∼ U ni(0, 1) and cluster index n = 1, ..., N . Normalize the delays by subtracting with minimum delays and sort the normalized delays to descending order as

τ_n= sort(τ_n^′ − min(τ_n^′))). (2.10) In LOS condition, the scaling factor of delays is required to compensate the effect of LOS peak addition to the delay spread. The scaling factor is determined as

D = 0.7705− 0.0433K + 0.0002K²+ 0.000017K³, (2.11) where K (in dB) is the Ricean K-factor defined Table 2.6. So the scaled delays are

τ_n^LOS = τ_n/D. (2.12)

They are not to be used in cluster power generation.

• Step 6: Generate the cluster powers P .

The cluster powers are calculated dependent on type of delay distribution defined in Table 2.6. If delay is exponential distribution, then the cluster powers are determined by

P_n^′ = exp(−τn

γ_τ − 1 γτστ

) (2.13)

and with uniform delay distribution they are determined by P_n^′ = exp(−τn

γ_τ − 1 γτστ

)· 10^−Zn10 (2.14)

where Zn ∈ (0, ζ) is the per cluster shadowing term in dB. In order to normalize the power, divide the power to sum of power of all cluster

P_n= P_n^′

∑N

n=1P_n^′. (2.15)

Each ray power within a cluster as P_n/M , where M is the number of rays per cluster.

Table2.6:ParametersforGenericModels[5] ScenariosA1A2/B4/C4B1B3C1C2D1D2a LOSNLOSNLOSLOSNLOSLOSNLOSLOSNLOSLOSNLOSLOSNLOSLOS Delayspread(DS)µ-7.42-7.60-7.39/-6.621) -7.44-7.12-7.53-7.41-7.23-7.12-7.39-6.63-7.80-7.60-7.4 log([s])σ0.270.190.36/0.321) 0.250.120.120.130.490.330.360.320.570.480.2 AoDspread(ASD)µ1.641.731.760.401.191.221.050.780.9010.930.780.960.7 log([o ])σ0.310.230.160.370.210.180.220.120.360.250.220.210.450.31 AoAspread(ASA)µ1.651.691.251.401.551.581.71.481.651.71.721.201.521.5 log([o ])σ0.260.140.420.200.200.230.10.200.300.190.140.180.270.2 sadowfading(SF)[dB]σ34734344/63) 84/63) 84/63) 84 K-factor(K)[dB]µ7N/AN/A9N/A2N/A9N/A7N/A7N/A7 σ6N/AN/A6N/A3N/A7N/A3N/A6N/A6 Cross−CorrelationASDvsDS0.7-0.10.40.50.2-0.3-0.10.20.30.40.4-0.1-0.4-0.1 ASAvsDS0.80.30.40.80.4-0.400.80.70.80.60.20.10.2 ASAvsSF-0.5-0.40.2-0.5-0.4-0.20.2-0.5-0.3-0.5-0.3-0.20.1-0.2 ASDvsSF-0.500-0.500.3-0.3-0.5-0.4-0.5-0.60.20.1-0.2 DSvsSF-0.6-0.5-0.5-0.4-0.7-0.1-0.2-0.6-0.4-0.4-0.4-0.5-0.5-0.5 ASDvsASA-0.6-0.300.40.10.30.30.10.30.30.4-0.3-0.2-0.3 ASDvsK-0.6N/AN/A-0.3N/A0.2N/A0.2N/A0.1N/A0N/A0 ASAvsK-0.6N/AN/A-0.3N/A-0.1N/A-0.2N/A-0.2N/A0.1N/A0.1 DSvsK-0.6N/AN/A-0.7N/A-0.3N/A-0.2N/A-0.4N/A0N/A0 SFvsK-0.6N/AN/A0.5N/A0.6N/A0N/A0.3N/A0N/A0 DelaydistributionExpExpExpExpUniformExpExpExpExpExpExpExpExpExp AoDandAoAdistributionWrappedGaussian Delayscaligparameterγτ32.42.23.2−1.91.62.41.52.52.33.81.73.8 XPR[dB]µ11109989684871273.8 σ441133434343848 Numberofclusters1216128161015151482011108 Numberofrayspercluster2020202020202020202020202020 ClusterASD558310565262222 ClusterASA55518225135101215333 Perclustershadowingstdζ[dB]63433333333333 Correlationdistance[m]DS7421/102) 98316404040643664 ASD6515/112) 131010.515301550253025 ASA2335/172) 12920.520301550404040 SF6414/72) 141233405045504012040 K6N/AN/A10N/A1N/A10N/A12N/A40N/A40 1)TheleftvaluecorrespondstoA2/B4microcellandtherightvaluetoC4macrocell. 2)TheleftvaluecorrespondstoA2Indoor-to-OutdoorandtherightvaluetoB4/C4Outdoor-to-Indoor. 3)LossmodelsfortheC1LOSandD1LOSscenarioscontainseparateshadowingstandarddeviations.

Table 2.7: Table of Constant C [5]

clusters 4 5 8 10 11 12 14 15 16 20

C 0.779 0.860 1.018 1.090 1.123 1.146 1.190 1.211 1.226 1.289

• Step 7: Generate the azimuth arrival angles φ and azimuth departure angles ϕ

– NLOS condition :

According to (2.16), assign the azimuth arrival angles φ by multiplying with the random variable X_n ∼ Uni{1, −1} and Yn ∼ N(0, σAOA/5) as

φn= Xnφ^′_n+ Yn+ φLOS (2.16) where φ_LOS is the LOS direction defined in Step 1, and φ^′_n is determined by

φ^′_n = 2σ_AOA√

− ln(Pn/max(P_n))

C . (2.17)

In (2.17), P_n is the cluster power determined from Step 6, the standard deviation of arrival angles (σ_AOA) is equal to σ_φ/1.4 (factor 1.4 is the ratio of Gaussian standard deviation (std) ). Constant C is a scaling factor related to total number of clusters and is given in Table 2.7 .

Finally add the offset angles αm from Table 2.8 to cluster angles

φ_n,m = φ_n+ C_AOAα_m (2.18)

where C_AOA is the cluster-wise rms azimuth spread of arrival angles in Table 2.6.

– LOS condition:

In the LOS case, the azimuth arrival equation is changed

φ_n = (X_nφ^′_n+ Y_n)− (Xnφ^′₁ + Y₁− φLOS). (2.19)

And the constant C is substituted by C^LOS, which is determined by C^LOS = C · (1.1035 − 0.028K − 0.002K² + 0.0001K³), where K (in dB) is the Ricean K-factor defined in Table 2.6. Then the following procedure is same as NLOS.

Table 2.8: Ray Offset Angles Within A Cluster, Given for 1^o rms Angle Spread [5]

Ray number m Basis vector of offset angles α_m

1,2 ±0.0447

For departure angles φ_n the procedure is analogous.

• Step 7b: If the elevation angles are supported:

Generate elevation arrival angles ψ and elevation departure angles γ. Draw elevation angles with the same procedure as azimuth angles on Step 7. Azimuth rms angle spread values and cluster-wise azimuth spread values are replaced by corresponding elevation parameters from Table 2.11.

• Step 8: Random coupling of rays within clusters.

Couple randomly the departure ray angles ϕ_n,m to the arrival ray angles φ_n,m within a cluster n, or within a sub-cluster in the case of two strongest clusters (see Step 11 and Table 2.9 ). If the elevation angles are supported they are coupled with the same procedure.

• Step 9: Generate the cross polarization power ratios (XP R) κ for each ray m of each cluster n. XP R is log-Normal distributed. Draw XP R values as

κ_m,n = 10^X/10 (2.20)

where ray index (m = 1, .., M ), X ∼ N(σ, µ) is Gaussian distributed with σ and µ from Table 2.6 for XPR.

Coefficient generation:

• Step 10: Draw the random initial phase {Φ^vvn,m, Φ^vh_n,m, Φ^hv_n,m, Φ^hh_n,m} for each ray m of each cluster n. Distribution for the initial phases is U ni(−π, π). In the LOS case draw also random initial phases {Φ^vvLOS, Φ^hh_LOS} for both VV and HH polarizations.

• Step 11: Generate the channel coefficients for each cluster n

– NLOS case:

∗ For the N − 2 weakest clusters:

The channel coefficients are given by H_u,s,n(t) = √

where F_rx,u,V and F_rx,u,H are the antenna element u filed patterns for vertical and horizontal polarizations respectively, d_s and d_u are uniform distances m (in meters) between transmitter and receiver element respectively, and λ₀ is the wave length on carrier frequency. If polarization is not considered, 2× 2 polarization matrix can be replaced by scalar exp(jΦ_n,m) and only vertically polarized field patterns applied.

· B5 scenarios - Fixed feeder link model:

The Doppler frequency component νn,m is tabulated for the first ray of each cluster. For the other rays ν_n,m = 0.

· Other scenarios:

The Doppler frequency is calculated from

νm,n = ∥v∥ cos(φn,m− θv)

λ₀ . (2.22)

∗ For the 2 strongest clusters:

The clusters ray are spread in delay to three sub-clusters (per cluster), with

Table 2.9: Sub-cluster Information for Intra Cluster Delay Spread Clusters.

Sub-cluster mapping to rays power delay

offset

1 1,2,3,4,5,6,7,8,19,20 10/20 0 ns

2 9,10,11,12,17,18 6/20 5 ns

3 13,14,15,16 4/30 10 ns

fixed delay offset 0, 5, 10ns (see Table 2.9). Delays of sub-cluster are

τn,1 = τn+ 0ns, τn,2= τn+ 5ns, τn,3 = τn+ 10ns. (2.23)

– LOS case: Adding single line of sight ray and scaling down the other channel coefficient generated by (2.21). The channel coefficients are given by

H_u,s,n(t) =

where H_u,s,n(t)^′ is the NLOS channel coefficient from the above step, δ(·) is the Dirac’s delta function, and K_R is the Ricean K-factor defined in Table 2.6 con-verted to linear scale.

• Step 11b: If non-ULA arrays: Generate the channel coefficients for each cluster n For arbitrary array configurations on horizontal plane, see Figure 2.4. The distance d_u is replaced by

d^′_u,n,m =

√x²_u + y²_ucos(arccos(y_u/x_u)− φn,m)

sin φ_n,m (2.25)

where (x_u, y_u) are co-ordinates of uth element A_u and A₀ is reference element.

Figure 2.4: Modified distance of antenna element u with non-ULA array. [5]

• Step 11c: If the elevation is considered The channel coefficient matrix equation will be written as

r_s is location vector of Tx array element s, Φ_n,m is departure angle unit vector of ray n,m and x_s,y_sand z_sare component of r_sto x,y and z-axis respectively. ϕ_n,m is ray n,m arrival azimuth angle and γn,m is ray n,m arrival elevation angle. ru· Ψn,m is a scalar product of Rx antenna element u and arrival angle n,m. The Doppler component will also be written as

υ_n,m = v· Ψn,m

λ₀ = ∥v∥ cos θvcos γn, m cos ϕn, m +∥v∥ sin θvcos γn, m sin ϕn, m

λ₀ .

(2.28)

• Step 12: Apply the path loss and shadowing for the channel coefficients.

Table 2.10: Far Scatterer Radii and Attenuations for B2 and C3 [5]

Scenario FS_minFS_max FS_loss B2 150m 500m 4dB/us C3 300m 1500m 2dB/us

Generation of bad urban channels (B2, C3):

The procedures of bad urban channel realization as modified B1 and C2 NLOS as follows:

• Step 1: Drop five far scatterers within a hexagonal cell, within radius [F Smin, F Smax].

For each mobile user determine the closest two far scatters, which are then used for calculating far scatterer cluster parameters. For F Smin and F Smax values see Table 2.10.

• Step 2: For C3 create 20 delays as described for C2 model in section 4.3.2, Step 5. For the shortest 18 delays create a typical urban C2 channel profile (powers and angles) as in section 4.3.2. Similarly, create 16 delays for B1 NLOS, and for the shortest 14 delays create a typical B1 NLOS channel profile as in section 4.3.2. The last two delays in B2 and C3 are assigned for far scatterer clusters.

• Step 3: Create typical urban channel powers P for FS clusters substituting equation of section 4.3.2, Step 6 with P_n^′ = 10^−Zn10 , where Z_n ∼ N(0, ξ) is the per cluster shadowing term in dB.

• Step 4: Next create excess delays due to far scatterer clusters as

τ_excess = d_{BS→F S→MS}− dLOS

c . (2.29)

Attenuate F S clusters as F Sloss, given in Table 2.10.

• Step 5: Select directions of departure and arrival for each F S cluster according to far scatterer locations, i.e., corresponding to a single reflection from far scatterer. It is

Table 2.11: Elevation-Related Parameters for Generic Models [5].

Scenarios A1 A2/B4/C4

LOS NLOS NLOS

Elevation AOD µ 0.88 1.06 0.88

spread(ESD) σ 0.31 0.21 0.34

Elevation AoA µ 0.94 1.10 1.01

spread(ESA) σ 0.26 0.17 0.43

ESD vs DS 0.5 -0.6 N/A

Cross- ESA vs DS 0.7 -0.1 0.2

Correlations ESA vs SF -0.1 0.3 0.2

ESD vs SF -0.4 0.1 N/A

ESD vs ESA 0.4 0.5 N/A

Elevation AoD and AoA distrbution Gaussian

Cluster ESD 3 3 3

Cluster ESA 3 3 3

worth noticing that depending on the location of the mobile user within the cell the FS clusters may appear also at shorter delays than the maximum C2 or B1 NLOS cluster. In such cases the far scatterers do not necessarily result to increased angular or delay dispersion. Also the actual channel statistics of the bad urban users depend somewhat on the cell size.

在文檔中 寬頻無線通道模型及模擬之研究 (頁 27-37)