84 Gec ·DB Effective scatterers and 3)the double.bounced r hpo (t,T)=htos (tT)+hies (tT)+hR (tT)+h (tT). (4.4) ing chant the ollo written as T，)=F{h化，}-Ts(化，f)+T(,)+TBR(，f)+TB(,f). (4.5) How all the afo study the 4.3 Irregular-shaped geometry-based stochastic model(5.3) certair e.In Karedal et al.(2009).to pr nent with the m presented in Paier et al.(2008),the impulse response is further divided into four parts:1)the LoS component,which (e.g..building and r oad sign cated on the adside);and 4)diffus compone nts from reflections of weak static the of the of the effective aterers.With the ray-racing approach,the BSM in (4.6 g=1 1
84 Geometry based stochastic channel modeling LoS SB DB Effective scatterers Figure 4.4 The geometrical description of the RS-GBSM according to the typical V2V environment in FIGURE 4.1. SB: singlebounced; DB: double-bounced. effective scatterers located on either of the two cylinders; and 3) the double-bounced rays produced from the effective scatterers located on both cylinders, as illustrated in FIGURE 5.4, and can be expressed as hpq (t, τ)=h LoS pq (t, τ) + h LoS pq (t, τ) + h SBR pq (t, τ) + h DB pq (t, τ). (4.4) As mentioned in Chapter 3, there are in total eight system functions. The choice of which system function for investigating channels is mainly based on the analysis purpose. This means the selected system function should make the following channel analysis easier. Therefore, to simply further analysis, the authors in Zajic and Stubber (2008); Zajic and Stuber (2009) use the time-variant transfer function instead of the channel impulse response. As addressed in Chapter 3, the time-variant transfer function is the Fourier transform of the channel impulse response and can be written as Tpq (t, t)=F {hpq (t, τ)} = T LoS pq (t, f) + T LoS pq (t, f) + T SBR pq (t, f) + T DB pq (t, f). (4.5) However, all the aforementioned RS-GBSMs cannot study the impact of the VTD on channel statistics and investigate per-tap channel statistics in wideband cases. Furthermore, a RS-GBSM does not have the ability to study the nonstationarity due to the static nature of the geometry in RS-GBSMs. 4.3 Irregular-shaped geometry-based stochastic model (5.3) Unlike RS-GBSMs, IS-GBSMs intend to reproduce the physical reality and thus need to modify the location and properties of the effective scatterers of RS-GBSMs. IS-GBSMs place the effective scatterers with specified properties at random locations with certain statistical distributions. The signal contributions of the effective scatterers are determined from a greatly-simplified ray-tracing method and finally the total signal is summed up to obtain the complex impulse response. In Karedal et al. (2009), to provide better agreement with the measurement results presented in Paier et al. (2008), the impulse response is further divided into four parts: 1) the LoS component, which may contain more than just the true LOS signal, e.g., ground reflections; 2) discrete components from reflections of mobile scatterers (e.g., moving cars); 3) discrete components from reflections of significant (strong) static scatterers (e.g., building and road signs located on the roadside); and 4) diffuse components from reflections of weak static scatterers located on the roadside, as depicted in FIGURE 5.5. Therefore, IS-GBSMs are actually a greatly-simplified version of GBDMs introduced in Chapter 4, while suitable for a wide variety of V2V scenarios by properly adjusting the statistical distributions of the location of the effective scatterers. With the ray-tracing approach, the IS-GBSM in Karedal et al. (2009) can easily handle the non-stationarity of V2V channels by prescribing the motion of the Tx, Rx, and mobile scatterers. Therefore, the complex channel impulse response can be expressed as Karedal et al. (2009) h (t, τ)=hLoS (t, τ) +X P p=1 hMD (t, τp) +X Q q=1 hSD (t, τq) +X R r=1 hDI (t, τr) (4.6)
Geometry based stochastic channel modeling 85 Figure 4.5 The geometrical description of the IS-GBSM according to the typical V2V environment in FIGURE 4.1 where hLs(，化r）is the LoS component,,∑1hMD(亿，n)are the discrete components stemming from reflections off mobile scatterers(MD)with Pbeing the number of mobile disc crere,∑hsp(.）are the discret 2 ).For a high V ered as we IS CRSN
Geometry based stochastic channel modeling 85 Static discrete scatterers Moving discrete scatterers Moving trucks Diffuse scatterers Figure 4.5 The geometrical description of the IS-GBSM according to the typical V2V environment in FIGURE 4.1. where hLoS (t, τ) is the LoS component, PP p=1 hMD (t, τp) are the discrete components stemming from reflections off mobile scatterers (MD) with P being the number of mobile discrete scatterers, PQ q=1 hSD (t, τq) are the discrete components stemming from reflections off static scatterers (SD) with Q being the number of mobile static scatterers, and PR r=1 hDI (t, τr) are the diffuse components (DI) with R being the number of diffuse scatterers. Note that only single-bounced rays are considered in this IS-GBSM due to the fairly low VTD of the measurements in Paier et al. (2008). For a high VTD environment, it is possible that double-bounced rays should be considered as well. It is worth noting that compared with the NGSM Sen and Matolak (2008) introduced in Chapter 4, the IS-GBSM in Karedal et al. (2009) can easily handle the drift of scatterers into different delay bins but with relatively higher complexity. Finally, the recently important V2V channel models introduced in Chapters 4 and 5 are summarized and classified into Table 4.1
86 Geometry based stochastic channel modeling Table 4.1 Important V2V channel models a saany s 二 SB+MB N/A het) wo网 stationary nono DB u时 o 2冰rm MIMO 20* SB+DB SB+DB o stationary nono SB+DB cylinder) M SB This isa tabe foomnote boun ed:DB:
86 Geometry based stochastic channel modeling Table 4.1 Important V2V channel models Channel Antenna Stationarity Impact Per-tap Scatterer region/ Scattering Applicable Model and FS of VTD CS Distribution Assumptions Scenarios Ref. Maurer et al. (2008) MIMO non- yes no 3D non-isotropic SB+MB siteGBDM wideband stationary (deterministic) specific midrule Ref. Acosta-Marum and Ingram (2007) SISO stationary no yes 2D non-isotropic N/A Micro NGSM wideband (N/A) Pico Ref. Sen and Matolak (2008) SISO non- yes yes 2D non-isotropic N/A Micro NGSM wideband stationary (N/A) Pico Ref. Akki and Haber (1986) SISO stationary no no 2D isotropic DB Macro RS-GBSM narrowband (two-ring) Ref. Patzold et al. (2008) MIMO stationary no no 2D non-isotropic DB Marco RS-GBSM narrowband (two-ring) Micro Ref. Zajic and Stubber (2008) MIMO stationary no no 2D non-isotropic SB+DB Macro RS-GBSM narrowband (two-ring) Micro Ref. Zajic and Stuber (2008) MIMO stationary no no 3D non-isotropic SB+DB Macro RS-GBSM narrowband (two-cylinder) Micro Ref. Zajic and Stubber (2008); Zajic and Stuber (2009) MIMO stationary no no 3D non-isotropic SB+DB Macro RS-GBSM wideband (two concentric- Micro cylinder) Ref. Karedal et al. (2009) MIMO non- yes no 2D non-isotropic SB Micro IS-GBSM wideband stationary (randomly) Pico This is a table footnote FS: frequency-selectivity; CS: channel statistics; SB: single-bounced; MB: multiple-bounced; DB: double-bounced; Macro: Macro-cell; Micro: Micro-cell; Pico: Pico-cell; N/A: not-applicable