同济大学：《传播信道特征估计和建模》课程教学资源（教案讲义）Chapter 04 Geometry based stochastic channel modeling.pdf_大学文库

4 Geometry based stochastic channel modeling Among various modeling approaches introduced in Chapter 4, this chapter concentrates on the introduction of geometry-based stochastic modeling approach. Geometry-based stochastic modeling approach is one of the most important and popular modeling approach due to its flexibility. This means that the geometry-based stochastic modeling approach can be either very simple and thus be useful for theoretical investigation of channels, or relatively complicated and be used for reproducing real channels. No matter what the aim of geometry-based stochastic modeling approach is, i.e., either simply theoretical investigation of channels or complete reproduction of real channels, this approach deals with scatterers and thus can grab the essential of channels. Chapter 5 will introduce the geometrybased stochastic modeling approach in more detail and present how this modeling approach is used to model and study real channels. 4.1 General modeling procedure (5.1) As mentioned in Chapter 4, geometry-based stochastic modeling approach belongs to the so-called scattering modeling approach that also includes geometry-based deterministic modeling approach. Compared with geometry-based deterministic modeling approach that needs detailed description of real communication environment, geometry-based stochastic modeling approach is more simple and general and thus has been widely used. The general modeling procedure of geometry-based stochastic modeling approach is summarized as shown in FIGURE 5.1. From FIGURE 5.1, it is clear that the modeling procedure of geometry-based stochastic modeling approach consists of the following steps. 1) Basic setting of communication environment: this includes the position and/or moving direction and velocity of the Tx/Rx, as well as the classification of effective scatterers, e.g., moving scatterers and static scatterers. 2) Scatterers placement: place scatterers in the predefined scattering region based on the PDF of scatterers. As mentioned in Chapter 4, according to the shape of scattering region being regular shape (e.g., one/two-ring, ellipse, etc.) or irregular shape (randomly), we have regular-shape geometry-based stochastic modeling approach or irregular-shape geometry-based stochastic modeling approach, respectively. 3) Parameterization: in this step, there are two manners to parameterize scatterers. The first manner considers the finite number of scatterers and assigns fading properties to each scatterer based on measurement data. The second manner assumes the infinite number of scatterers and thus the channel characteristics can be determined only by the PDF of scatterers without the assignment of fading properties to each scatterer. In this case, the obtained channel model cannot be implemented into practice and is referred to as the reference model, which is useful for the theoretical analysis of channel characteristics. 4) Addition of all scatterers’ contributions: sum at the received side of all these scatterers’ contributions to obtain the channel impulse response. Note that since the reference model has infinite number of scatterers, corresponding simulation model, which has finite number of scatterers and thus is realizable in practice, should be obtained first in this step. This is a Book Title Name of the Author/Editor c XXXX John Wiley & Sons, Ltd

Geometry based stochastic channel modeling 81 4.2 Regular-shaped geometry-based stochastic model (5.2) As mentioned in Chapter 4, a channel model obtained via geometry-based stochastic modeling approach is named as a GBSM. As introduced in Chapter 5.1, a GBSM is derived from a predefined stochastic distribution of effective scatterers by applying the fundamental laws of wave propagation. Such models can be easily adapted to different scenarios by changing the shape of the scattering region and/or the PDF of the location of the scatterers. From Chapter 5.1, we know that GBSMs can be further classified as regular-shaped GBSMs (RS-GBSMs) and irregular-shaped GBSMs (ISGBSMs) depending on whether effective scatterers are placed on regular shapes (e.g., one/two-ring, ellipse, etc.) or irregular shapes (randomly). In Chapter 5.2, the RS-GBSM will be introduced in more detail. In general, RS-GBSMs are used for the theoretical analysis of channel statistics and theoretical design and comparison of communication systems. Therefore, to preserve the mathematical tractability, RS-GBSMs assume all effective scatterers are located on a regular shape. In the following, we will first introduce a very famous RS-GBSM for conventional cellular systems and then introduce RS-GBSMs for V2V communication systems. 4.2.1 RS-GBSM for conventional cellular communication systems (5.2.1) A one-ring narrowband MIMO F2M RS-GBSM is very famous channel model for conventional cellular macrocell scenarios and was first proposed in Chen et al. (2000) and further developed in Abdi et al. (2002a). The one-ring model has been widely used for narrowband MIMO F2M channels under the condition of the scenario as presented in FIGURE 5.2 (i.e., macro-cell scenario) due to its close agreement with the measured data Abdi et al. (2002b) and mathematical tractability. Let us consider a one-ring narrowband MIMO RS-GBSM shown in FIGURE 5.3, where the effective scatterers are located on a ring surrounding the MS with radius R. Here the effective scatterers, which is the terminology first proposed in Lee’s model Liberti and Rappaport (1999), are used to represent the effect of many scatterers with similar spatial location. The BS and MS have MT and MR omni-directional antenna elements in the horizontal plane, respectively. Without loss of generality, we consider uniform linear antenna arrays with MT = MR = 2 (a 2 × 2 MIMO channel). The antenna element spacing at the BS and MS are designated by δT and δR, respectively. It is usually assumed that the radius R is much smaller than D, denoting the distance between the BS and MS. Furthermore, it is assumed that both R and D are much larger than the antenna element spacing δT and δR, i.e., D≫R≫max {δT , δR}. The multi-element antenna tilt angles are denoted by βT and βR. The MS moves with a speed in the direction determined by the angle of motion γ. The angle spread seen at the BS is denoted by Θ, which is related to R and D by Θ ≈ arctan (R/D) ≈ R/D. Based on knowledge introduced in Chapter 3, the MIMO fading channel can be described by a matrix H (t) = [hoq (t)]MR×MT of size MR × MT . Without a LoS component, the sub-channel complex fading envelope between the oth (o = 1, ..., MT ) BS and the qth (q = 1, ..., MR) MS at the carrier frequency fc can be expressed as hoq (t)= lim N→∞ 1 √ N X N n=1 exp j ψn−2πfcτoq,n + 2πfDt cos φ R n − γ (4.1) with τoq,n=(εon+εnq)/c, where τoq,n is the travel time of the wave through the link To − Sn − Rq scattered by the nth scatterer Sn and c is the speed of light. The AoA of the wave travelling from the nth scatterer towards the MS is denoted by φ R n , while εon and εnq can be expressed as the function of φ R n as εon ≈ξn−δT [cos(βT )+Θ sin(βT ) sin(φ R n )]/2 (4.2a) εno≈R−δR cos(φ R n−βR)/2 (4.2b) where ξn≈D + R cos(φ R n ). The phases ψn are independent and identically distributed (i.i.d.) random variables with uniform distributions over [0, 2π), fD is the maximum Doppler frequency, and N is the number of independent effective scatterers Sn around the MS. Since we assume that the number of effective scatterers in one effective cluster in this reference model tends to infinite (as shown in (9.33)), the discrete AoA φ R n can be replaced by the continuous expressions φ R. In the literature, many different scatterer distributions have been proposed to characterise the AoA φ R, such as the uniform Salz and Winters (1994), Gaussian F. Adachi and Parsons (n.d.), wrapped Gaussian Schumacher et al. (2002), and cardioid PDFs Byers and Takawira (2004). In this chapter, the von Mises PDF Abdi et al. (2002b) is used, which can approximate all the above mentioned PDFs. The von Mises PDF is defined as f (φ) ∆=exp [k cos (φ−µ)] /2πI0 (k) (4.3)

Geometry based stochastic channel modeling 83 Rq n X S To Toc Rqc on H nq H n [ D R T In R In J E R E T G T G R 4 Figure 4.3 Geometrical configuration of a narrowband one-ring channel model with local scatters around the mobile user. where φ ∈ [−π, π), I0 (·) is the zeroth-order modified Bessel function of the first kind, µ ∈ [−π, π) accounts for the mean value of the angle φ, and k (k ≥ 0) is a real-valued parameter that controls the angle spread of the angle φ. For k=0 (isotropic scattering), the von Mises PDF reduces to the uniform distribution, while for k>0 (non-isotropic scattering), the von Mises PDF approximates different distributions based on the values of k Abdi et al. (2002a). The above described one-ring model is a narrowband MIMO F2M cellular channel model. To reach the high demand for high-speed communications, wideband MIMO cellular systems have been suggested in many communication standards, leading to the increasing requirement for wideband MIMO F2M channel models. However, the one-ring model that assumes effective scatterers located on a one-ring is overly simplistic and thus unrealistic for modeling wideband channels Latinovic et al. (2003). How to properly extend the narrowband one-ring model to wideband applications is still an open problem. In Chapter 10, we will address this open problem and give one possible solution. 4.2.2 RS-GBSM for V2V communication systems (5.2.2) Unlike the rich history of RS-GBSMs for cellular systems, the development of RS-GBSMs for V2V communication systems is still in its infancy. Akki and Haber Akki (1994); Akki and Haber (1986) were the first to propose a 2D two-ring RS-GBSM with only double-bounced rays for narrowband isotropic scattering SISO V2V Rayleigh fading channels in macro-cell scenarios. In Patzold et al. (2008), a two-ring RS-GBSM considering only double-bounce rays was presented for non-isotropic scattering MIMO V2V Rayleigh fading channels in macro-cell scenarios. In Zajic and Stubber (2008), the authors proposed a general 2D two-ring RS-GBSM with both single- and double-bounced rays for non-isotropic scattering MIMO V2V Ricean channels in both macro-cell and micro-cell scenarios. The 2D two-ring narrowband model in Zajic and Stubber (2008) was further extended to a 3D two-cylinder narrowband model in Zajic and Stuber (2008) and a 3D two-concentric-cylinder wideband model in Zajic and Stubber (2008); Zajic and Stuber (2009). Based on the real V2V environment shown in FIGURE 4.1 in Chapter 4, FIGURE 5.4 shows the geometrical description of the 3D two-concentric-cylinder wideband model that consists of LoS, single-, and double-bounced rays. In agreement with real V2V environments, the authors in Zajic and Stubber (2008); Zajic and Stuber (2009) divide the complex impulse response into three parts: 1) the LoS component; 2) the single-bounced rays generated from the

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 87 4.4 Filter simulation model (5.4) As mentioned in Chapter 5.1, by assuming the infinite number of scatterers, GBSMs can be easily obtained but cannot be implemented into practice due to the infinite complexity. In this case, these GBSMs are called as reference models. Therefore, corresponding simulation models, which have a finite complexity and thereby are realizable in practice, are necessary in the practical simulation and performance evaluation of a wireless communication system. Note that the RS-GBSMs introduced in Chapter 5.2 are actually reference models since they assume an infinite number of effective scatterers, as shown in (9.33) and (9.36), where the number of effective scatterers N tends to be infinite. As mentioned in Stüber (2001), a reference model can be used for theoretical analysis and design of a wireless communication system, and also is a starting point to design a realizable simulation model that has the reasonable complexity, i.e., finite numbers of effective scatterers. Therefore, the development of a simulation model aims to design a simulator with a reasonable complexity while representing the desired statistical properties of the reference model as faithfully as possible. Before introducing different simulation models, it is worth emphasizing that the described GBDMs and NGSMs in Chapter 4, as well as IS-GBSMs introduced in Chapter 5.3 can be categorized as the other type of simulation models since these models have finite complexity (i.e., the number of scatterers are finite as shown in (9.37)) and thus can be directly implemented in practice. In this sense, the reference model is the real measurement data. FIGURE 5.6 clearly shows the relationship between the reference model and simulation model. This book concentrates on the Type I simulation model. Therefore, for simplicity, the mention of a reference model and a simulation model refers to a theoretical/mathematical reference model and a Type I simulation model, respectively. There are several different methods for simulating fading channels. The most accepted methods are filter methods Fechtel (1993); Verdin and Tozer (1993); Wang and Cox (2002); Young and Beaulieu (1998, 2000) and SoS methods Clarke (1968); Jakes (1994); Patel et al. (2005b); Pätzold (2002); Pop and Beaulieu (2001); Wang and Zoubir (2007); xiang Wang et al. (2008); Zajic and Stuber (2006); Zheng and Xiao (2002, 2003). The filter method has been widely used and is shown in FIGURE 5.7. In this method, two uncorrelated Gaussian random processes with zero mean and Reference Model Simulation Model Real Measurement Data Type I Simulation Model Type II Simulation Model Theoretical/Mathematical Reference Model Figure 4.6 Relationship between the reference model and simulation model