228 Measurement based statistical channel modeling 670 1的0 delay in samples Fig.8.4 Example of the powers of paths versus the delays of the paths.The parameters of the paths are estimated from measurement data collected in a macro suburban environment.The Tx moves at a pedestrian speed,following the first route. used to compute 8.6 whereP=denotes the total power of all the paths,is calculated as 1-p>mn (8.7刀 rewritten a MCD=0.0357.lm-l (8.8) 二然 of the Dopple (8.9) =1 Calculation shows that=-1.1591Hz,=1.9091Hz,and Ar=13.8Hz.Thus,(8.4)turns out to be MCD=0.01C·lw-w,l, (8.10) Nicolai's MCD-ba ironment.The s er-Delay domain the clusters are we aling factors multiplied withand aths. rs for the ct of the path distance MCD and MCD on the overall distance 228 Measurement based statistical channel modeling 150 155 160 165 170 175 180 185 0 0.5 1 1.5 2 2.5 3 3.5 x 10−9 delay in samples Amplitude in linear Fig. 8.4 Example of the powers of paths versus the delays of the paths. The parameters of the paths are estimated from measurement data collected in a macro suburban environment. The Tx moves at a pedestrian speed, following the first route. Fig. 8.4 depicts the power estimates of the paths versus the delays of the paths. In order to implement Nicolai’s clustering method based on the MCD, we calculate the standard deviation στ of the delays. The following equation is used to compute στ : στ = vuut 1 P X L ℓ=1 pℓ · (τℓ − τ¯) 2 (8.6) where P = PN ℓ=1 pℓ denotes the total power of all the paths, τ¯ is calculated as τ¯ = 1 P X L ℓ=1 pℓ · τℓ (8.7) For the example shown in Fig. 8.4, τ¯ is calculated to be 159.6377 delay samples, στ reads 6.4334 delay samples. In addition, ∆τmax is 30 delay samples. Thus, (8.2) can be rewritten as MCDτ,ij = 0.0357 · |τi − τj |. (8.8) It is necessary to explain what the multiplicative factor 0.0357 stands for. We now compute the maximum duration ∆νmax, the mean ν¯ and the standard deviation σν of the Doppler frequencies of the paths. Fig. 8.5 depicts the powers of the paths versus the Doppler frequencies of those paths. The following equations are used to calculate ν¯ and σν ν¯ = 1 P X L ℓ=1 pℓ · νℓ, σν = vuut 1 P X L ℓ=1 pℓ · (νℓ − ν¯) 2 (8.9) Calculation shows that ν¯ = −1.1591Hz, σν = 1.9091Hz, and ∆νmax = 13.8Hz. Thus, (8.4) turns out to be MCDν,ij = 0.01ζν · |νi − νj |, (8.10) Now we show the clustering result when the Nicolai’s clustering method based on MCD is used. The number of clusters is set to 6. The scaling factors ζτ = ζν = 5 are selected. Fig. 8.6 depicts the result obtained when applying Nicolai’s MCD-based clustering method to the estimated 500 paths in a macro suburban environment. The square marks in the plots in Fig. 8.6 indicates the centroid of the clusters. We observe from Fig. 8.6 that the overlapping of the clusters in the angular domain is significant. However, in the Doppler-Delay domain, the clusters are well separated. We have some difficulties to understand this observation. The scaling factors multiplied with |τi − τj | and |νi − νj | are much less than the scaling factor for the directions. But the above observation shows that the distance of paths in the directional domain does not change significantly for all the paths. Although the scaling factors for the delay and Doppler frequency are small, the impact of the path distance MCDτ,ij and MCDν,ij on the overall distance MCDij is more significant than the impact of MCDΩAoA,ij