4 Geometry based stochastic channel modeling Among various modelingroheod Chapterhihpertheo important and popular modeling approach due to its This m eans that the eome -based stochastic approach is,i.e..either simply theoretical investigation of channels or complete reproduction of real channels,this a present how ing approach is used【o 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 stochastis modeng is more simple and general and thus has been widely used.The general modeling of the followin steps. eling approach consists 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 n Chaptera or rresular-shape gcometry-based stochastic modeling approach,respectively ndhi邮s step the finite number of scatt sthe infinite num 一mp nened mo mn5流 er of scatterers d thus the channel characteristics can b de【ermin 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 first in this step. ,倍
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
80 Geometry based stochastic channel modeling e.Basie setting of communication environmen Step 2.Scatters placement Regular shaper scattering Iregular shaper scattering region(one/two-ring. region(randomly） ellipse.etc.) step3.Parameterization Finite number of scatters Infinite number of scatter Measurement-based Reference model model Finite number of scatters Simulation mode Channel Impulse Response(CIR) Figure 4.1 A general modeling procedure of geometry-based stochastic modeling approach
80 Geometry based stochastic channel modeling Step 1. Basic setting of communication environment Step 2. Scatters placement Regular shaper scattering region (one/two-ring, ellipse, etc.) Step 3. Parameterization Finite number of scatters Infinite number of scatters Measurement-based model Reference model Step 4. Addition of all scatters' contributions Simulation model Channel Impulse Response (CIR) Finite number of scatters Irregular shaper scattering region (randomly) Figure 4.1 A general modeling procedure of geometry-based stochastic modeling approach
Geometry based stochastic channel modeling 81 4.2 Regular-shaped geometry-based stochastic model(5.2) oach is named as a wthat GBSMs can be further Ms (RGBSMs)andreu-haped Med orh eoretical of hamnelch comparison of systems.T theonwewtduvry famouM 4.2.1 RS-GBSM for conventional cellular communication systems(5.2.1) Ae-ring narowband MIMO F2M RS-GBSM is very famous channel model forcoventional a macroce wband MIMO F2M chan of the The one-ring mathematical tractability.Let us consider a one-ring narro .3,where th the temino is much sma er than denoting the distance BS and max).The multi-element antenna tilt angles are denoted byr and .The MS moves with a speed in motion y.The angle spread seen at the BS is denoted by e,which is related -.不∑e即5-2m+2(-7川} (4.1) denoted bywhileandexpreedthectin of con~En-6r[cos(Br)+sin(Br)sin()1/2 (4.2a) EnoR-6Rcos(R-BR)/2 (4.2b) n7meaa ributed (i.id.)random variables with scatterers S around the M e)e odel tends to he p eee on Mise etud,which mate f()exp[cos(-p)]/2Io(k) (4.3)
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)
82 Geometry based stochastic channel modeling Local scatterers Figure 4.2 A typical F2M cellular propagation environment for macro-cell scenarios
82 Geometry based stochastic channel modeling BS MS Local scatterers Figure 4.2 A typical F2M cellular propagation environment for macro-cell scenarios
Geometry based stochastic channel modeling 83 Figure 4.3 Geometrical rion of a narrowband one-ring channel model with local scatters around the mobile user. that controls the a ngle spread of the angle tropic model that assumes effective scatterers located on a one-ring is overly simplistic and thus unrealistic for modelin 4.2.2 RS-GBSM for V2V communication systems(5.2.2) wortgRs-GBsMwithomydoubletbonoedaonarotandotoptcCaeringsS0V2yRalehading nels MIMO V2V Rayl cha ing only double )the posed a genera .and double-bounced rays and Stuber(2008)and a 3D two-concentric-cylinder wideband model in Zajic and Stubber(2008);Zajic and Stuber real .in( e FIGURE 5.4 ent with real V2V environments,the authors oS component;2)the single-bou rays generated from the
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