New Deterministic and Stochastic Simulation Models for Nonisotropic

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WIRELESS COMMUNICATIONS AND MOBILE COMPUTING Wirel. Commun. Mob. Comput. 2011; 11:829–842 Published online 30 October 2009 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.864

SPECIAL ISSUE PAPER New deterministic and stochastic simulation models for non-isotropic scattering mobile-to-mobile Rayleigh fading channels† Xiang Cheng1∗, Cheng-Xiang Wang1, David I. Laurenson2, Sana Salous3 and Athanasios V. Vasilakos4

1 Joint Research Institute for Signal and Image Processing, School of Engineering & Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, U.K. 2 Joint Research Institute for Signal and Image Processing, Institute for Digital Communications, University of Edinburgh, Edinburgh, EH9 3JL, U.K. 3 Center for Communication Systems, School of Engineering, University of Durham, Durham, DH1 3LE, U.K. 4 Department of Computer and Telecommunications Engineering, University of Western Macedonia, GR 50100 Kozani, Greece

ABSTRACT

For the practical simulation and performance evaluation of mobile-to-mobile (M2M) communication systems, it is desirable to develop accurate M2M channel simulation models for more realistic scenarios of non-isotropic scattering. In this paper, by using a ‘double-ring’ concept to describe M2M non-isotropic scattering environments, we propose new deterministic and stochastic sum-of-sinusoids (SoS) based simulation models. The proposed simulation models extensively consider the distributions of the angle of arrival (AoA) and the angle of departure (AoD), and thus provide a good approximation to the desired statistical properties of the reference model. Copyright © 2009 John Wiley & Sons, Ltd.

KEYWORDS mobile-to-mobile communications; sum-of-sinusoids channel simulator; Rayleigh fading; non-isotropic scattering

*Correspondence Xiang Cheng, Joint Research Institute for Signal and Image Processing, School of Engineering & Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, U.K. E-mail: [email protected]

1. INTRODUCTION Besides the modeling of a M2M channel and the investigation of its statistical properties, the development In recent years, mobile-to-mobile (M2M) communica- of accurate M2M channel simulation models also plays a tions have received increasing attention due to some new major role in the practical simulation and performance eval- applications, such as wireless mobile ad hoc networks uation of M2M systems. However, in the literature, most [1], relay-based cellular networks [2], and dedicated short channel simulation models for wireless communications range communications for intelligent transportation sys- were developed for conventional fixed-to-mobile (F2M) tems (IEEE 802.11p) [3]. Such M2M systems consider that cellular radio systems [11--17].As mentioned in Reference both the transmitter (Tx) and receiver (Rx) are in motion [18], simulation models for a F2M channel cannot be and are equipped with low elevation antennas. To success- readily used to simulate a M2M channel due to the dif- fully analyze and design such M2M systems, it is necessary ferences of their statistical properties. Wang and Cox [19] to have proper mathematical reference models for the were the first to propose a simulation model for isotropic underlying propagation channels. Many M2M mathemati- scattering M2M Rayleigh fading channels by using the cal reference models have been proposed for both isotropic line spectrum filtering method. Due to the application of scattering environments, e.g., the models in References [4] line spectrum filtering, the model has high complexity and [5], and more realistic environments of non-isotropic and severe performance deficiencies as pointed out in scattering, e.g., the models in References [6--10]. Reference [18]. Therefore, the sum-of-sinusoids (SoS)

† This paper was presented in part at VehiCom’09, co-located with IWCMC’09, Leipzig, Germany, 21–24 June 2009.

Copyright © 2009 John Wiley & Sons, Ltd. 829 New deterministic and stochastic simulation models X. Cheng et al. method was used in References [18] and [20] to develop The paper is structured as follows. Section 2 gives a better isotropic scattering M2M Rayleigh fading simulation brief description of the reference model for non-isotropic models. Generally speaking, the SoS method allows us to scattering M2M Rayleigh fading channels. In Section approximate the underlying random fading processes by 3, we propose two new SoS based simulation models the superposition of a finite number of properly weighted (deterministic and stochastic models). The performance harmonic functions. An SoS based simulation model can be evaluation of our models is presented in Section 4. Finally, either deterministic or stochastic in terms of the underlying conclusions are drawn in Section 5. parameters (gains, frequencies, and phases) [16]. For a deterministic model, all the parameters are fixed for all simulation trials. In contrast, a stochastic model has at 2. REFERENCE MODEL least one parameter (gains and/or frequencies) as a random variable which varies for each simulation trial. Therefore, Using Akki and Haber’s mathematical model [4] and the relevant statistical properties of a stochastic model considering the directions of movement of the Tx and vary for each simulation trial but converge to the desired Rx, we can express the complex fading envelope of ones when averaged over a sufficient number of trials. In our reference model, under a narrowband non-isotropic Reference [18], the authors used the ‘double-ring’ concept scattering M2M Rayleigh fading assumption, as to derive two SoS based simulation models (deterministic and stochastic models) for isotropic scattering M2M 1 h(t) = hi(t) + jhq(t) = lim √ channels. The stochastic model in Reference [18] was N→∞ N further improved in Reference [20] by choosing orthogonal N functions for in-phase and quadrature components of the jψ j πf t φn −γ + πf t φn −γ e n e [2 Tmax cos( T T ) 2 Rmax cos( R R)] complex fading envelope. More recently, in Reference n= [21] the Rayleigh M2M stochastic simulation model in 1 Reference [18] was extended to include a line-of-sight (1) component, i.e., for Ricean fading channels. However, it is worth noting that all the aforementioned simulation models where hi(t) and hq(t) are in-phase and quadrature compo- limit their applications to isotropic scattering environments. nents√ of the complex fading envelope h(t), respectively, The simulation models for M2M Rayleigh fading channels j = −1, N is the number of harmonic function represent- f f under a more realistic scenario of non-isotropic scattering ing propagation paths (effective scatterers), Tmax and Rmax are scarce in the current literature. are the maximum Doppler frequency due to the motion To the best of the authors’ knowledge, only one of the Tx and Rx, respectively. The Tx and Rx move in stochastic SoS based simulation model [22] has been directions determined by the angles of motion γT and γR, proposed for the simulation of non-isotropic scattering respectively. The random AoA and AoD of the nth path are n n M2M Rayleigh fading channels. However, this model only denoted by φR and φT , respectively, and ψn is the random considered the symmetrical property of the distributions phase uniformly distributed on [−π, π). It is assumed that n n of the angle of arrival (AoA) and angle of departure φR, φT , and ψn are mutually independent random variables. (AoD) and was designed based on the acceptance rejection Since the number N of effective scatterers in the algorithm (ARA). This leads to the ARA model having reference model h(t) tends to infinity, the discrete expres- (n) (n) a notable difficulty in reproducing the desired statistical sions of the AoA φR and AoD φT can be replaced properties of the reference model and a comparatively by the continuous expressions φR and φT , respectively. high computational complexity. Furthermore, it is worth Note that since h(t) describes a non-isotropic scattering noting that accurate deterministic simulation models for M2M Rayleigh fading channel, the AoA φR and AoD φT non-isotropic scattering M2M Rayleigh fading channels exhibit non-uniform distributions. In the literature, many are not available in the current literature. different non-uniform distributions have been proposed to To fill the above gap, in this paper, based on the ‘double- characterize the AoA φR and AoD φR, such as Gaussian, ring’ concept in Reference [18], we first propose a new wrapped Gaussian, and cardioid PDFs [23]. In this paper, M2M deterministic SoS based simulation model. By allow- the von Mises PDF [24] is used, which can approximate ing at least one parameter (frequencies and/or gains) to be all the aforementioned PDFs and match well the measured a random variable, our deterministic model can be further data in References [7] and [24]. The von Mises PDF is modified to be a stochastic model. It is worth noting that defined as f (φ) exp[k cos(φ − µ)]/[2πI0(k)], where the proposed simulation models incorporate the probability φ ∈ [−π, π), I0(·) is the zeroth-order modified Bessel density functions (PDFs) of the AoA and AoD, and thus can function of the first kind, µ ∈ [−π, π) accounts for the approximate the desired statistical properties of the refer- mean value of the angle φ, and k (k ≥ 0) is a real-valued ence model for any non-isotropic scattering M2M Rayleigh parameter that controls the angle spread of the angle φ.For fading channel. Moreover, compared to the ARA stochastic k = 0 (isotropic scattering), the von Mises PDF reduces model in Reference [22], our stochastic model presents bet- to the uniform distribution, while for k>0 (non-isotropic ter approximation to the desired properties of the reference scattering), the von Mises PDF approximates different model with an even smaller number of harmonic functions. distributions based on the values of k [24]. Applying

the von Mises PDF to the AoA φR and AoD φT ,we To model non-isotropic scattering environments, the obtain f (φR) exp[kR cos(φR − µR)]/[2πI0(kR)] and effective scatterers are assumed to be non-uniformly f (φT ) exp[kT cos(φT − µT )]/[2πI0(kT )], respectively. distributed. The Tx and Rx move with speeds υT and υR The autocorrelation function (ACF) of the reference in directions determined by the angles of motion γT and model h(t) can be expressed as [10] γR, respectively. Based on the ‘double-ring’ model, we can then design a new deterministic simulation model ∗ ρhh(τ) = E h (t) h (t − τ) as 1 1/2 = I A2 + B2 0 T T h˜ (t) = h˜ i (t) + jh˜ q (t) (4) I0(kT )I0(kR) 1/2 2 2 Ni,Mi × I0 AR + BR (2) ˜ 1 hi (t) = √ cos ψ˜ nimi NiMi with ni,mi=1 + πf t φ˜ mi − γ 2 Tmax cos( T T ) AT = kT µT + j πτfT γT cos( ) 2 max cos( ) (3a) ni + 2πf R t cos(φ˜ R − γR) (5) B = k µ + j πτf γ max T T sin( T ) 2 Tmax sin( T ) (3b) A = k µ + j πτf γ Nq,Mq R R cos( R) 2 Rmax cos( R) (3c) 1 h˜ q (t) = sin ψ˜ nqmq BR = kR sin(µR) + j2πτfR sin(γR) (3d) NqMq max nq,mq=1 m ∗ + πf t φ˜ q − γ where τ is the time separation, (·) denotes the complex 2 Tmax cos( T T ) conjugate operation, and E[·] is the statistical expectation nq + 2πf R t cos(φ˜ R − γR) (6) operator. max

where h˜ i(t) and h˜ q(t) are in-phase and quadrature compo- 3. NEW SIMULATION MODELS nents of the complex fading envelope h˜(t), respectively, Ni/q is the number of effective scatterers located on the ring In this section, based on the reference model introduced in around the Rx, Mi/q is the number of effective scatterers ni/q Section 2, we propose the corresponding deterministic and located on the ring around the Tx, the AoA φ˜ R and the mi/q stochastic SoS based simulation models. AoD φ˜ T are discrete realizations of the random variables ˜ φR and φT , respectively, the phases ψni/qmi/q are the single outcomes of the random phases ψn in Equation (1). It 3.1. New deterministic simulation model ni/q mi/q ˜ is assumed that φ˜ R , φ˜ T , and ψni/qmi/q are mutually (ni/q) (mi/q) independent. Note that the AoA φ˜ and the AoD φ˜ Before proposing a new deterministic simulation model, R T remain constant for different simulation trials due to the which needs only one simulation trial to obtain the desired deterministic nature of the proposed simulation model. statistical properties, we would like to first introduce It is worth stressing that the single summation in the the ‘double-ring’ concept [18] to model non-isotropic reference model (1) is replaced by a double summation due scattering M2M scenarios. In such a case, the ‘double-ring’ to the double reflection incorporated by the ‘double-ring’ model defines two rings of effective scatterers, one around model. However, the channel essentially remains the same the Tx and the other around the Rx, as shown in Figure 1. for the following two reasons: (1) the assumption of the independence between the AoA and AoD is used in both the reference model (1) and the deterministic simulation model (4); and (2) for both the reference model (1) and the deterministic simulation model (4), each path will be subject to a υ T υ different Doppler shift due to the motion of both the Tx and R γ T Rx. From the above proposed deterministic simulation T R γ X X R model, it is obvious that the key issue in designing a M2M deterministic simulation model is to find the sets {φ˜ ni/q }Ni/q {φ˜ mi/q }Mi/q of AoAs R ni/q=1 and AoDs T mi/q=1 that make the simulation model reproduce the desired statistical properties of the reference model as faithfully as possible with reasonable complexity, i.e., with a finite number of Ni/q and Mi/q. Under the condition of non-isotropic Figure 1. Mobile-to-mobile scattering environment. scattering environments, the PDFs of the AoA φR and AoD

φ {φ˜ ni/q }Ni/q become T should be used to design the sets of AoAs R ni/q=1 mi/q Mi/q and AoDs {φ˜ T }m = that guarantee the uniqueness of the n − / i/q 1 n −1 1 4 (n) φ˜ R = FR (8a) sine and cosine functions related to the AoA φR and AoD N (n) φT in the reference model (1). This means that the design m − / of the sets of AoAs and AoDs for the reference model h(t) m −1 1 4 φ˜ T = FT (8b) in Equation (1) should meet the following two conditions: M n ni/q i/q (1) cos(φ˜ R − γR) = cos(φ˜ R − γR), ni/q = ni/q; and (2) m Note that the value of 1/4 used in Equations (8a) and mi/q i/q cos(φ˜ T − γT ) = cos(φ˜ T − γT ), mi/q = mi/q. (8b) guarantees that the designed sets of AoAs and Considering the non-isotropic scattering M2M environ- AoDs can meet the aforementioned two conditions n (n) m m ments, we now design the sets of AoAs and AoDs of our (φ˜ R =−φ˜ R + 2γR, n = n and φ˜ T =−φ˜ T + 2γT , deterministic simulation model. Via extensive investigation m = m) for Case I. The proof of the above statement is of the PDFs of the AoA φR and AoD φT , we find that unlike omitted here since one can easily prove it by following the isotropic scattering M2M environments [18], it is difficult procedure provided in Reference [25]. The performance of to obtain sets of AoAs and AoDs that meet the two condi- this design will be validated in Section 4. tions for any non-isotropic scattering M2M environments. Under the condition of Case II, the cross-correlation Therefore, we divide the non-isotropic scattering M2M between the in-phase component hi(t) and quadrature environment into the following three categories in terms of component hq(t) of the complex fading envelope h(t) the mean AoA µR and mean AoD µT (i.e., the PDFs of the in Equation (1) is equal to zero. Therefore, by setting AoA and AoD), and the angles of motion γR and γT and Ni = Nq and Mi = Mq in this case, we can directly use the then design the sets of AoAs and AoDs separately for these expression of our simulation model itself to guarantee the three cases: (1) Case I: the main transmitted and received aforementioned cross-correlation is equal to zero rather powers come from the same direction as or opposite than through the design of the AoAs and AoDs. This makes direction to the movements of the Tx and Rx, respectively, for a more efficient use of the number of harmonic func- ◦ i.e., |µT − γT |=|µR − γR|=0 or π; (2) Case II: the tions and thus results in better performance of the model. main transmitted and received powers come from the Following the similar parameter computation method directions that are perpendicular to those of the move- of Case I, we design the AoA and AoD of our model ments of the Tx and Rx, respectively, i.e., |µT − γT |= as ◦ |µR − γR|=90 ; and (3) Case III: different from Cases I n n − / n and II. i/q −1 i/q 1 2 i/q φ˜ R = FR , φ˜ R ∈ [−π, π) For Case I, the in-phase component hi(t) and quadrature Ni/q component hq(t) of the reference model h(t) in Equation ni/q = 1, 2,...,Ni/q (9a) (1) are correlated. Therefore, to meet this correlation, we set Ni = Nq = N and Mi = Mq = M and thus the AoA n m i/q i/q n m mi/q − mi/q − 1/2 mi/q φ˜ R and AoD φ˜ T can be replaced by the φ˜ and φ˜ , φ˜ = F 1 , φ˜ ∈ −π, π R T T T M T [ ) respectively. Inspired by the modified method of equal area i/q

(MMEA) proposed in Reference [25] for non-isotropic scat- mi/q = 1, 2,...,Mi/q (9b) tering F2M channels, we design the AoA and AOD of our model as Note that the value of 1/2 is applied in Equations (9a) and (9b) instead of the value of 1/4 in Equations (8a) and φ˜ n R (8b). The reason is that unlike Case I, for Case II it is n − 1/4 n n n = f (φ˜ R)dφ˜ R, φ˜ R ∈ [−π, π) difficult to design sets of AoAs and AoDs that meet the N φ˜ n−1 R two conditions. Although it is difficult to find one value n = 1, 2,...,N (7a) that can guarantee the designed sets of AoAs and AoDs have the best approximation to the two conditions. Based φ˜ m m − / T on simulations and motivated by the modified method of 1 4 = f φ˜ m dφ˜ m, φ˜ m ∈ −π, π ( T ) T T [ ) exact Doppler spread (MEDS) in Equations (37) and (38) M φ˜ m−1 T in Reference [18] for the simulation of isotropic scattering m = 1, 2,...,M (7b) M2M channels, we found that with the value of 1/2, the proposed simulation model presents better performance than the one with other values, e.g., 1/4. The performance φ˜ 0 =−π φ˜ 0 =−π f φ˜ n f φ˜ m where R and T , ( R) and ( T ) denote of this design will be validated in Section 4. φ˜ n φ˜ m the PDFs of the AoA R and the AoD T , respectively. The For Case III, since the in-phase and quadrature com- cumulative distribution functions (CDFs) of the AoA φ˜ R x n ponents of the reference model h(t) in Equation (1) are φ˜ F x = f φ˜ n dφ˜ and the AoD T are defined as R( ) −∞ ( R) R and N = N = N x m correlated (similarly to Case I) we set i q and F x = f φ˜ m dφ˜ ni/q T ( ) −∞ ( T ) T , respectively. If the inverse func- Mi = Mq = M as well and thus the AoA φ˜ R and AoD m −1 −1 i/q n m tions FR (·)ofFR(·) and FT (·)ofFT (·) exist, (7a) and (7b) φ˜ T can be replaced by the φ˜ R and φ˜ T , respectively.

Following the similar parameter computation method of and frequencies to be random variables. Unlike the deter- Case I, we design the AoA and AoD of our model as ministic model, the properties of the stochastic model vary for each simulation trial, but will converge to the desired n − 1/2 ones when averaged over a sufﬁcient number of simula- φ˜ n = F −1 , φ˜ n ∈ −π, π R R N R [ ) tion trials. A hat is used to distinguish this model from the deterministic one, thus n = 1, 2,...,N (10a)

hˆ (t) = hˆ i (t) + jhˆ q (t) (14) m − m − 1/2 m φ˜ = F 1 , φ˜ ∈ −π, π N ,M T T M T [ ) i i ˆ 1 hi (t) = √ cos ψˆ nimi NiMi m = 1, 2,...,M (10b) ni,mi=1

mi + 2πf T t cos(φˆ − γT ) Note that the value of 1/2 is used in Equations (10a) and max T + πf t φˆ ni − γ (10b) due to the same reason as Case II. 2 Rmax cos( R R) (15) The correlation properties of the proposed deterministic Nq,Mq simulation model must be analyzed by using time average 1 rather than statistical average. The time-average ACF of the hˆ q (t) = sin ψˆ nqmq NqMq proposed simulation model h˜(t) is deﬁned as nq,mq=1

mq ∗ + πf t φˆ − γ ρ τ = h˜ t h˜ t − τ 2 Tmax cos( T T ) ˜ h˜h˜ ( ) ( ) ( ) (11) + πf t φˆ nq − γ 2 Rmax cos( R R) (16) where · denotes the time average operator. Substituting Equation (4) into Equation (11), we have where hˆ i(t) and hˆ q(t) are in-phase and quadrature compo- ni/q nents of complex fading envelope hˆ(t), respectively, φˆ R ρ τ = ρ τ − jρ τ mi/q ˜ h˜h˜ ( ) 2˜ h˜ih˜i ( ) 2 ˜ h˜ih˜q ( ) (12) and φˆ T denote the AoA and AoD of our stochastic simula- ˆ tion model, respectively, and the phases ψni/qmi/q are random where variables uniformly distributed on the interval [−π, π). ni/q mi/q ˆ Parameters φˆ R , φˆ T , and ψni/qmi/q are independent of each Ni,Mi 1 m n ρ τ = πf τ φ˜ i − γ + πf τ φ˜ i − γ ˜ h˜ih˜i ( ) cos 2 Tmax cos( T T ) 2 Rmax cos( R R) (13a) 2NiMi ni,mi=1   N,M  1 m − sin 2πf T τ cos(φ˜ − γT ) ,Ni = Nq = N and Mi = Mq  2NM max T n,m=1 ρ˜ h˜ h˜ (τ) = (13b) i q  + πf τ φ˜ n − γ = M Case  2 Rmax cos( R R) ( I and III)  0,Ni = Nq and Mi = Mq (Case II)

In Appendix A, we give a brief outline of the derivations of other. Note that unlike the AoA and AoD in a determin- φˆ ni/q φˆ mi/q Equations (13a) and (13b). From Equation (13b), and based istic simulation model, the AoA R and AoD T are on the corresponding derivation in Appendix A, it is clear random variables and thus vary for different simulation tri- that by setting Ni = Nq and Mi = Mq, the cross-correlation als. The fundamental issue for the design of the sets of {φˆ ni/q }Ni/q {φˆ mi/q }Mi/q between the in-phase component h˜ i(t) and quadrature com- AoAs R ni/q=1 and AoDs T mi/q=1 is how to incor- ponent h˜ q(t) of the proposed simulation model h˜(t) is equal porate a random term into the AoA and AoD. In this paper, to zero no matter how the sets of AoAs and AoDs are to deal with this fundamental issue, we apply the method designed. When N (Ni) and M (Mi) tend to infinity, it is proposed in Reference [12] for the simulation of isotropic straightforward that the time-average ACF in Equation (12) scattering F2M channels. Based on the comparative anal- matches the ensemble average ACF in Equation (2). This ysis in Reference [26], we can conclude that the smaller ni/q allows us to conclude that for {N(Ni),M(Mi)}→∞, our (but sufficient) range on which the AoA φˆ R and AoD mi/q simulation model can represent the correlation properties φˆ T are designed, the better performance the stochastic of the reference model. model that will be obtained. Based on the extensive investigation of the PDFs of the AoA φR and AoD φT ,wefind that unlike isotropic scattering M2M environments [18], the 3.2. New stochastic simulation model appropriate range on which the AoA and AoD are designed varies for different non-isotropic scattering M2M environ- Our deterministic model can be further modified to a ments. Therefore, similarly to our deterministic model, we stochastic simulation model by allowing both the phases design the sets of AoAs and AoDs of our stochastic model

Case m m − / + θ m separately for the following three cases: (1) I: the main i/q −1 i/q 1 2 T i/q φˆ T = FT , φˆ T ∈ [−π, π) transmitted and received powers come from the same direc- Mi/q tion as the movements of the Tx and Rx that is along x axis, ◦ m = , ,...,M i.e., µT = γT = µR = γR = 0 or π; (2) Case II: the main i/q 1 2 i/q (18b) transmitted and received powers come from the directions For Case III, due to the same reason as Case Iwehave that are perpendicular to those of the movements of the Tx n ◦ N = N = N M = M = M φˆ i/q and Rx, respectively, i.e., |µT − γT |=|µR − γR|=90 ; i q and i q and thus the AoA R mi/q n m and (3) Case III: different from Cases I and II. and AoD φˆ T can be replaced by the φˆ R and φˆ T , respec- For Case I, due to the same reason as the design of our tively. In this case, analogous to Case II, we know that the −π π deterministic model for Case IwehaveNi = Nq = N and full range (i.e., from to ) is necessary for the design ni/q mi/q Mi = Mq = M and thus the AoA φˆ R and AoD φˆ T can of the AoA and AoD. Therefore, the AoA and AoD can be n m be replaced by the φˆ R and φˆ T , respectively. In this case, we designed as found that the PDFs of the AoA and AoD are symmetric with respect to the origin. Therefore, the appropriate ranges n − 1/2 + θR φˆ n = F −1 , φˆ n ∈ [−π, π) for the design of both AoA and AoD are from 0 to π because R R N R the rest of the range is redundant (i.e., the range [−π, 0) n = 1, 2,...,N (19a) provides us with the same infomation as [0,π)). Inspired by the method in Reference [12] for isotropic scattering m − 1/2 + θT φˆ m = F −1 , φˆ m ∈ −π, π F2M channels, we design the AoA and AoD of our model T T M T [ ) as m = 1, 2,...,M (19b) n − 1/2 + θR φˆ n = F −1 , φˆ n ∈ [0,π) R R N R Unlike our deterministic simulation model, the time ACF of our stochastic simulation model should be computed n = 1, 2,...,N (17a) ∗ according to ρˆ hˆhˆ (τ) = E[hˆ(t)hˆ (t − τ)]. It can be shown that our stochastic model exhibits correlation properties of m − 1/2 + θT φˆ m = F −1 , φˆ m ∈ ,π the reference model irrespective of the values of Ni/q and T T M T [0 ) Mi/q, i.e., for any Ni/q and Mi/q. Appendix B outlines the ρ τ hˆ t m = 1, 2,...,M (17b) derivation of the ACF ˆ hˆhˆ ( ) for the model ( ). It is worth noting that the proposed stochastic model shows better performance and has lower complexity than where θR and θT are random variables uniformly distributed on the interval [−1/2, 1/2) and are independent to each the ARA model [22]. Since in Reference [22] the authors other. It is worth stressing that the interval [−1/2, 1/2) and did not give the detailed explanation on how to generate the the constant value of 1/2 are chosen to guarantee that the AoAs and AoDs for their model by using the ARA, it is design of the AoA and AoD is based on the desired range impossible to reproduce this model. Therefore, to validate (here is [0,π)). This indicates that any interval and the the above statement, in Figure 2 we compare the ACF of corresponding constant value can be chosen only if they the real part of the ARA model obtained from Figure 5 in can fulﬁll the aforementioned guarantee (e.g., the interval Reference [22] with the one of our model. For a fair com- is [0, 1) and constant value is 1). Note that the introduction parison, the same parameters as those used in Figure 5 in n of the random terms θR and θT in the AoA φˆ R and AoD m φˆ 1 T , respectively, leads to the AoA and AoD being random Reference model The proposed stochastic model variables and thus varying for different simulation trials. ARA stochastic model ni/q mi/q 0.8 φ˜ R and AoD φ˜ T of our deterministic simulation model, which are constant for different simulation trials. 0.6

For Case II, analogous to our deterministic model, we 0.4 impose Ni = Nq and Mi = Mq in our stochastic model to guarantee the cross-correlation between the in-phase 0.2 hˆ t hˆ t component i( ) and quadrature component q( ) of the pro- 0 posed stochastic model hˆ(t) for one simulation trial is equal to zero. In this case, since the PDFs of the AoA and AoD are Autocorrelation, real part −0.2 asymmetric with respect to the origin, the full range (i.e., −0.4 from −π to π) is needed for the design of the AoA and AoD. Therefore, we can express the AoA and AoD as −0.6

−0.8 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 n n − / + θ n i/q −1 i/q 1 2 R i/q Time delay, τ φˆ R = FR , φˆ R ∈ [0,π) Ni/q Figure 2. Comparison between the proposed stochastic model ni/q = 1, 2,...,Ni/q (18a) and the ARA stochastic model proposed in Reference [22].

x 10−3 (a) 6 Case I 4 Case II Case III 2

Squared error 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Normalized time delay, τ×f T max

(b) 0.03 Case I 0.02 Case III

0.01

Squared error 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Normalized time delay, τ×f T max x 10−3 (c) 4 Case I Case III 2

Squared error 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Normalized time delay, τ×f T max

Figure 3. Squared error in the CF of the proposed deterministic simulation model with kT = kR = 1 for different non-isotropic scattering ◦ ◦ ◦ ◦ ◦ M2M Rayleigh fading channels: (a) T = R = 110 and T = R = 20 ; (b) T = R = T = R = 0 ; (c) T = 30 , R = 160 , T = ◦ ◦ 10 , and R = 20 .

f = f = N = M = N = M = Reference [22] are used, namely Tmax 100 Hz, Rmax for Cases I, III and i i 10, q q 11 for Case 50 Hz, µT = π/4, µR =−π/4, kT = kR = 3, γT = γR = II of the stochastic model, and the normalized sampling ◦ N = f T = . T 0 , and the number of simulation trials stat 10. Note that period Tmax s 0 005 ( s is the sampling period). the number of harmonic functions used in the ARA model is To validate our deterministic model, in Figure 3 we com- P = 144, while in our model is Ni = Mi = 10. From Fig- pare the difference in the ACF ρ˜ h˜h˜ (τ) from the desired ρhh(τ) 2 ure 2, it is obvious that our model outperforms the ARA using the squared error |ρ˜ h˜h˜ (τ) − ρhh(τ)| for different non- model with even smaller number of harmonic functions, isotropic M2M scenarios. Similarly, to validate our stochas- i.e., Ni × Mi = 100

(a) x 10−4 1.5 Case I 1 Case II Case III 0.5

Mean squared error 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Normalized time delay, τ×f T (b) max x 10−3 2 Case I Case III 1

Mean squared error 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Normalized time delay, τ×f T (c) max 0.02 Case I Case III 0.01

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Mean squared error Normalized time delay, τ×f T max

Figure 4. Mean squared error in the CF of the proposed stochastic simulation model with kT = kR = 5 for different non-isotropic ◦ ◦ ◦ ◦ ◦ scattering M2M Rayleigh fading channels: (a) T = R = 110 and T = R = 20 ; (b) T = R = T = R = 0 ; (c) T = 20 , R = 10 , ◦ ◦ T = 10 , and R = 20 .

hence, validates the utility of our models that include three for the stochastic model are averaged over Nstat = 10 different sets of model parameters rather than only one. simulation trials. It is obvious that the deterministic model To evaluate the performance of our simulation models, in provides a fairly good approximation to the ACF of the Figures 5–7 we give a comparison between the ACF of the reference model in a shorter normalized time-delay range, reference model and the one of our simulation models for while the stochastic model presents much better approxi- various values of kT , kR, µT , and µR. The results obtained mation even with a smaller number of harmonic functions Ni/q and Mi/q. Compared to our deterministic model, our

1 stochastic model has a higher complexity since it requires Reference model Deterministic simulation model several simulation trials to achieve the desired properties. 0.9 Stochastic simulation model Notice that the quality of the approximation between the 0.8 µ =µ =10° T R ACFs of our deterministic model and the reference model

0.7 can be improved by increasing the values of Ni/q and Mi/q, µ =µ =30° T R while the quality of the approximation between the ACF 0.6 of our stochastic model and the one of the reference model 0.5 can be improved by increasing the values of Ni/q and Mi/q, N 0.4 and/or the value of stat. More interestingly, from Figure 5,

Absolute value of the CF we observe that the increase of the values of |µT − γT | and 0.3 µ =µ =100° T R |µR − γR| decreases the difﬁculty of our simulation model µ =µ =50° 0.2 T R in approximating the correlation properties of the reference

0.1 model. Similarly, Figure 6 shows that the difﬁculty of our simulation model in approximating the correlation prop- 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 erties of the reference model increases with the increase Normalized time delay, τ×f T max of the values of kT and kR. More importantly, Figures 5–7 |µ − γ | |µ − γ | Figure 5. Comparison between the CF of the reference model show that when the values of T T and R R are small and/or the values of kT and kR are large, the proposed and the one of the proposed simulation models with kT = kR = 6 ◦ and T = R = 10 for various values of the mean AoD T and deterministic simulation model cannot even approximate mean AoA R . the correlation properties of the reference model for short

1 Reference model 0.8 k =k =4 Deterministic simulation model T R Stochastic simulation model 0.6 k =k =1 T R 0.4

0.2 Absolute value of the CF

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Normalized time delay, τ×f T max

1 Reference model k =k =20 0.8 T R Deterministic simulation model Stochastic simulation model 0.6 k =k =10 0.4 T R

0.2 Absolute value of the CF

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Normalized time delay, τ×f T max

◦ Figure 6. Comparison between the CF of the reference model and the one of the proposed simulation models with T = R = 60 ◦ and T = R = 30 for various values of kT and kR . time-delays. In the aforementioned situations, to obtain an model is more suitable than the deterministic model for such acceptable approximation between the correlation proper- a non-isotropic scattering M2M scenario where the differ- ties of our deterministic model and the ones of the reference ences between the angles of motion γT and γR, and the mean model, a large number of harmonic functions (here Ni = AoA µT and AoD µR are small (i.e., the value of |µT − γT | Mi = Nq = Mq = 60 as depicted in Figure 7) is necessary. and |µR − γR| are small) and/or the received powers are This allows us to conclude that the stochastic simulation more concentrated in one direction (i.e., the value of kT and kR are large).

1 Reference model Deterministic simulation model 0.9 Stochastic simulation model 5. CONCLUSIONS Deterministic simulation model (N =M =60) 0.8 i/q i/q

k =k =10 0.7 T R In this paper, based on the ‘double-ring’ concept and µ =µ =0° T R the comprehensive analysis of the PDFs of the AoA and 0.6 AoD, new deterministic and stochastic SoS based simu- 0.5 lation models have been proposed for non-isotropic M2M k =k =5 T R µ =µ =20° T R Rayleigh fading channels. The performance of the proposed 0.4 k =k =3 T R °

Absolute value of the CF µ =µ =40 T R simulation models has been veriﬁed in terms of the CF 0.3 through the theoretical and simulation results. Results have k =k =1 T R 0.2 µ =µ =90° shown that compared to the proposed deterministic model, T R the proposed stochastic model provides better approxima- 0.1 tion of the reference model even with a smaller number of 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 harmonic functions. Moreover, our analysis has revealed Normalized time delay, τ×f T max that the proposed stochastic model performs better than the Figure 7. Comparison between the CF of the reference model ARA stochastic model. Finally, either the proposed deterministic (lower complexity) model or stochastic (higher and the one of the proposed simulation models with T = R = ◦ 0 for various values of kT , kR , the mean AoD T , and mean AoA accuracy) model can be used for simulations of M2M R . systems.

ACKNOWLEDGMENTS The integral of Equation (20) is trivial as the integrand does not contain the variable of integration. Therefore, ρ τ X. Cheng, C.-X. Wang, and D. I. Laurenson acknowledge the expression of ˜ h˜ ih˜ i ( ) in Equation (13a) can be easily the support from the Scottish Funding Council for the Joint obtained from Equation (20). Research Institute in Signal and Image Processing between The derivation of the time-average cross-correlation ρ τ h˜ t the University of Edinburgh and Heriot-Watt University- function ˜ h˜ ih˜ q ( ) between the in-phase component i( ) (5) which is a part of the Edinburgh Research Partnership in and the quadrature component h˜ q(t) (6) of the proposed Engineering and Mathematics (ERPem). deterministic simulation model is outlined as follows:

T 1 ρ˜ h˜ h˜ (τ) = h˜ i (t) h˜ q (t − τ) = lim h˜ i (t) h˜ q (t − τ) dt i q T →∞ 2T −T T Ni,Mi Nq,Mq 1 1 mi = lim √ cos ψ˜ nimi + 2πf T t cos(φ˜ T − γT ) T →∞ 2T N M N M max i i q q n ,m = n ,m = −T i i 1 q q 1 + πf t φ˜ ni − γ ψ˜ + πf t − τ φ˜ mq − γ 2 Rmax cos( R R) sin nqmq 2 Tmax ( ) cos( T T ) + πf t − τ φ˜ nq − γ t 2 Rmax ( ) cos( R R) d  T  N,M  1 1 m  − lim sin 2πf T τ cos(φ˜ T − γT ) Ni = Nq = N and Mi = Mq  T →∞ 2T 2NM max n,m= = −T 1  (21)  + πf τ φ˜ n − γ t, = M Cases  2 Rmax cos( R R) d ( I and III)  0 Ni = Nq and Mi = Mq (Case II)

where at the third equality of Equation (21), setting Ni = Nq and Mi = Mq results in the integrand for Case II containing Appendix A: Derivation of Equation the variable of integration t unlike the integrand for other (13a) and (13b) cases.

In this appendix, we ﬁrst derive the time-average ACF ρ τ h˜ t ˜ h˜ ih˜ i ( ) of the in-phase component i( ) (5) of the proposed deterministic simulation model T 1 ρ˜ h˜ h˜ (τ) = h˜ i (t) h˜ i (t − τ) = lim h˜ i (t) h˜ i (t − τ) dt i i T →∞ 2T −T T Ni,Mi NiMi 1 1 m = ψ˜ + πf t φ˜ i − γ lim cos nimi 2 Tmax cos( T T ) T →∞ 2T NiMi n ,m = n ,m = −T i i 1 i i 1 m ni i + πf R t φ˜ − γR ψ˜ n m + πf T t − τ φ˜ − γT 2 max cos( R ) cos i i 2 max ( ) cos( T ) n + πf t − τ φ˜ i − γ t 2 Rmax ( ) cos( R R) d

T Ni,Mi 1 1 m n = ψ˜ + πf t φ˜ i − γ + πf t φ˜ i − γ lim cos nimi 2 Tmax cos( T T ) 2 Rmax cos( R R) T →∞ 2T NiMi n ,m = −T i i 1 × ψ˜ + πf t − τ φ˜ mi − γ + πf t − τ φ˜ ni − γ t cos nimi 2 Tmax ( ) cos( T T ) 2 Rmax ( ) cos( R R) d n = n m = m, ρ τ = (since i i and/or i i ˜ h˜ ih˜ i ( ) 0) T Ni,Mi 1 1 m n = πf τ φ˜ i − γ + πf τ φ˜ i − γ t lim cos 2 Tmax cos( T T ) 2 Rmax cos( R R) d (20) T →∞ 2T 2NiMi n ,m = −T i i 1

Appendix B: Derivation of the CF ρ τ ˆ hˆ hˆ ( )

In this appendix, we derive the CF ρˆ hˆhˆ (τ) for the stochastic simulation model in Equation (14) ∗ ρˆ hˆhˆ (τ) = E hˆ (t) hˆ (t − τ)  1 1  N,M 2 2  − m−1/2+θT − n−1/2+θR  1 j πτ fT F 1 −γT +fR F 1 −γR  e 2 max cos vM max cos uN θ θ ,  NM d T d R  n,m=  1 −1 −1  2 2   Ni = Nq = N and Mi = Mq = M (Cases I and III)   1 1  2 2  Ni,Mi  1 mi − 1/2 + θT  πτ f F −1 − γ  cos 2 Tmax cos T  2NiMi Mi  n ,m = i i 1 −1 −1 = 2 2  ni − 1/2 + θR  + f F −1 − γ θ θ  Rmax cos R d T d R  Ni   1 1  2 2  Nq,Mq  1 mq − 1/2 + θT  + πτ f F −1 − γ  cos 2 Tmax cos T  2NqMq Mq  nq,mq=1  −1 −1  2 2   nq − 1/2 + θR  + f F −1 − γ θ θ , Case  Rmax cos R d T d R ( II) Nq

 F −1 n F −1 m  N,M ( uN ) ( vM ) m n  kT cos(β −µT )+kR cos(β −µR)  NM j πτ f βm−γ +f βn −γ e T R  2 T cos( T T ) R cos( R R) m n  e max max dβ dβ  2 T R  NM 4π I0(kT )I0(kR)  n,m=1  F −1 n−1 F −1 m−1  uN vM   Ni = Nq = N and Mi = Mq = M (Cases I and III)   n m  F −1 i F −1 i  N M  N ,M i i  N M i i  i i πτ f βmi − γ + f βni − γ  cos 2 Tmax cos T T Rmax cos R R 2NiMi n ,m = = i i 1 n − m − −1 i 1 −1 i 1  F N F M  i i  n m  −1 q −1 q  F N F M  m n N ,M q q  k β i −µ +k β i −µ q q  e T cos( T T ) R cos( R R) N M  × βmi βni + q q πτ f  d T d R cos 2 Tmax  4π2I (kT )I (kR) 2NqMq  0 0 n ,m =  q q 1 nq− mq−  F −1 1 F −1 1  Nq Mq  m n  k β q −µ +k β q −µ  e T cos( T T ) R cos( R R)  mq nq mq nq  × cos β − γT + fR cos β − γR dβ dβ (Case II)  T max R 2 T R  4π I0(kT )I0(kR)

 π π   1 j πτ f β −γ +f β −γ  e 2 [ Tmax cos( T T ) Rmax cos( R R)]  π2I k I k  2 0( T ) 0( R)  0 0  m n  kT cos(β −µT )+kR cos(β −µR)  × e T R dβT dβR, (Case I)  π π   1 cos 2πτ fT cos (βT − γT ) + fR cos (βR − γR) 2 max max = 4π I0(kT )I0(kR)  −π −π   × ekT cos(βT −µT )+kR cos(βR−µR) β β , Case  d T d R ( II)  π π   1 j πτ f β −γ +f β −γ  e 2 [ Tmax cos( T T ) Rmax cos( R R)]  π2I k I k  4 0( T ) 0( R)  −π −π  m n kT cos(β −µT )+kR cos(β −µR) × e T R dβT dβR (Case III) (22) where at the second equality of Equation (22), the integration variables θT and θR were replaced by mi/q k β −µ m m − / +θ M e T cos( T T ) m i/q −1 i/q 1 2 T i/q i/q 7. Zajic´ AG, Stuber¨ GL, Pratt TG, Nguyen S. Wideband βT = F ( ), dθT = dβT , Mi/q 2πI0(kT ) ni/q MIMO mobile-to-mobile channels: geometry-based sta- k β −µ n n − / +θ N e R cos( R R) i/q −1 i/q 1 2 R i/q tistical modeling with experimental verification. IEEE βR = F ( ), dθR = Ni/q 2πI0(kR) m n kT cos(β −µT ) Transactions on Vehicular Technology 2009; 58(2): 517– i/q m −1 m−1/2+θT Me T dβ , β = F ( ), dθT = R T M 2πI (kT ) 634. 0 n kR cos(β −µR) m n −1 n−1/2+θR Ne R β β = F θR = 8. Sen I, Matolak DW. Vehicle-vehicle channel models for d T , R ( N ), and d 2πI (kR) n 0 dβR. The tow single definite integrals in the last the 5-GHz band. IEEE Transactions on Intelligent Trans- equality of (22) can be solved by using the equality portation Systems 2008; 9(2): 235–245. π √ ea sin c+b cos c c = πI a2 + b2 −π d 2 0( ) [27]. After some 9. Cheng X, Wang C-X, Laurenson DI, Vasilakos AV. Sec- ρ τ manipulation, the closed-form expression of the CF ˆ hˆhˆ ( ) ond order statistics of non-isotropic mobile-to-mobile ρ τ can be obtained and is the same as hh( ) in Equation (2). Ricean fading channels. Proceedings of IEEE ICC’09, Dresden, Germany, June 2009. 10. Cheng X, Wang C-X, Laurenson DI, Salous S, Vasilakos REFERENCES AV. An adaptive geometry-based stochastic model for 1. Kojima F, Harada H, Fujise M. Inter-vehicle communi- non-isotropic MIMO mobile-to-mobile channels. IEEE cation network with an autonomous relay access scheme. Transactions on Wireless Communications 2009; 8(9): Transactions on Communications 2001; E83-B(3): 566– 4824–4835. 575. 11. Jakes WC (ed.). Microwave Mobile Communications. 2. Pabst R, Walke BH, Schultz DC, et al. Relay-based IEEE Press: New Jersey, 1994. deployment concepts for wireless and mobile broadband 12. Zheng YR, Xiao CS. Improved models for the genera- radio. IEEE Communications Magazine 2004; 42(9): 80– tion of multiple uncorrelated Rayleigh fading waveforms. 89. IEEE Communication Letter 2002; 6(6): 256– 3. IEEE P802.11p/D2.01. Standard for wireless local area 258. networks providing wireless communications while in 13. Youssef N, Wang C-X, Patzold¨ M. A study on the second vehicular environment. Technical Report, March 2007. order statistics of Nakagami-Hoyt mobile fading chan- 4. Akki AS, Haber F. A statistical model for mobile-to- nels. IEEE Transactions on Vehicular Technology 2005; mobile land communication channel. IEEE Transactions 54(4): 1259–1265. on Vehicular Technology 1986; 35(1): 2–10. 14. Wang C-X. Patzold¨ M, Yuan D. Accurate and effi- 5. Akki AS. Statistical properties of mobile-to-mobile land cient simulation of multiple uncorrelated Rayleigh fading communication channels. IEEE Transactions on Vehicu- waveforms. IEEE Transactions on Wireless Communica- lar Technology 1994; 43(4): 826–831. tions 2007; 6(3): 833–839. 6. Zajic´ AG, Stuber¨ GL. Space-time correlated mobile- 15. Wang C-X, Patzold¨ M, Yao Q. Stochastic modelling to-mobile channels: modelling and simulation. IEEE and simulation of frequency correlated wideband fading Transactions on VehicularTechnology 2008; 57(2): 715– channels. IEEE Transactions on Vehicular Technology 726. 2007; 56(3): 1050–1063.

16. Wang C-X, YuanD, Chen HH, Xu W. An improved deter- AUTHORS’ BIOGRAPHIES ministic SoS channel simulator for efficient simulation of multiple uncorrelated Rayleigh fading channels. IEEE Xiang Cheng (S’05) received B.Sc. Transactions on Wireless Communications 2008; 7(9): and M.Eng. degrees in communication and information systems from 3307–3311. Shandong University, China, in 2003 17. Pätzold M, Wang C-X, Hogstad BO. Two new sum-of- and 2006, respectively. Since Octo- sinusoids-based methods for the efficient generation of ber 2006, he has been a Ph.D. student multiple uncorrelated Rayleigh fading channels, IEEE at Heriot-Watt University, Edinburgh, Transactions on Wireless Communications 2009; 8(6): U.K. 3122–3131. His current research interests include 18. Patel CS, Stuber¨ GL, Pratt TG. Simulation of mobile propagation channel modeling, Rayleigh-faded mobile-to-mobile communication chan- and simulation, multiple antenna technologies, mobile-to- nels. Transactions on Communications 2005; 53(11): mobile communications, and cooperative communications. 1876–1884. He has published approximately 30 research papers in ref- 19. Wang R, Cox D. Channel modeling for ad hoc mobile ereed journals and conference proceedings. Mr Cheng was awarded the Postgraduate Research Prize wireless networks. Proceedings of IEEE VTC’02-Spring, from Heriot-Watt University in 2007 and 2008, respectively, Birmingham, USA, May 2002; pp. 21–25. for academic excellence and outstanding performance. He 20. Zajic´ AG, Stuber¨ GL. A new simulation model for served as a TPC member for IEEE HPCC2008 and IEEE mobile-to-mobile Rayleigh fading channels. Proceedings CMC2009. IEEE WCNC’06, Las Vegas, USA, April 2006; pp. 1266– 1270. Cheng-Xiang Wang (S’01-M’05- 21. Wang LC, Liu WC, YH Cheng. Statistical analysis SM’08) received the B.Sc. and of a mobile-to-mobile Rician fading channel model. M.Eng. degrees in communication and IEEE Transactions on VehicularTechnology 2009; 58(1): information systems from Shandong 32–38. University, China, in 1997 and 2000, 22. Zheng YR. A non-isotropic model for mobile-to-mobile respectively, and Ph.D. degree in wire- fading channel simulations. Proceedings IEEE MCC’06, less communications from Aalborg Washington, USA, October 2006; pp. 1–6. University, Denmark, in 2004. 23. Cheng X, Wang C-X, Laurenson DI. A generic space- Dr Wang has been a lecturer at time-frequency correlation model and its corresponding Heriot-Watt University, Edinburgh, U.K. since 2005. He simulation model for MIMO wireless channels. Proceed- is also an honorary fellow of the University of Edinburgh, U.K., a guest researcher of Xidian University, China, and ings of EuCAP’07, Edinburgh, UK, November 2007; an adjunct professor of Guilin University of Electronic pp. 1–6. Technology, China. He was a research fellow at the Uni- 24. Abdi A, Barger JA, Kaveh M. A parametric model for versity of Agder, Grimstad, Norway, from 2001–2005, a the distribution of the angle of arrival and the asso- visiting researcher at Siemens AG-Mobile Phones, Munich, ciated correlation function and power spectrum at the Germany, in 2004, and a research assistant at Techni- mobile station. IEEE Transactions on Vehicular Technol- cal University of Hamburg-Harburg, Hamburg, Germany, ogy 2002 51(3): 425–434. from 2000–2001. His current research interests include 25. Gutierrez´ CA, Patzold¨ M. Sum-of-sinusoid-based simu- wireless channel modeling and simulation, error models, lation of flat fading wireless propagation channels under cognitive radio networks, vehicular communication net- non-isotropic scattering conditions. Proceedings of IEEE works, green radio communications, cooperative (relay) GLOBECOM’07, Washington, D.C., USA, November communications, cross-layer design of wireless networks, MIMO, OFDM, UWB, and 4G wireless communications 2007; pp. 3842–3846. and beyond. He has published one book chapter and over 26. Patel CS, Stuber¨ GL, Pratt TG. Comparative analy- 120 papers in refereed journals and conference proceedings. sis of statistical models for the simulation of Rayleigh Dr Wang serves as an Editor for four international faded cellular channels. Transactions on Communica- journals: IEEE Transactions on Wireless Communications, tions 2005; 53(6): 1017–1026. Wireless Communications and Mobile Computing Journal 27. Gradshteyn IS, Ryzhik IM. Table of Integrals, Series, and (John Wiley & Sons), Security and Communication Net- Products (5th edn), Jeffrey A (ed.). Academic: San Diego, works Journal (John Wiley & Sons), and Journal of Com- CA, 1994. puter Systems, Networks, and Communications (Hindawi).

He is the leading Guest Editor for IEEE Journal on Selected Athanasios V. Vasilakos (M’89) is Areas in Communications, Special Issue on Vehicular Com- currently Professor at the Dept. of munications and Networks. He served or is serving as a TPC Computer and Telecommunications member, TPC Chair, and General Chair for more than 40 Engineering, University of Western international conferences. Dr Wang is listed in ‘Dictionary Macedonia, Greece, and Visiting Pro- of International Biography 2008 and 2009’, ‘Who’s Who in fessor at the Graduate Programme of the World 2008 and 2009’, ‘Great Minds of the 21st Century the Department of Electrical and Com- 2009’, and ‘2009 Man of the Year’. He is a Senior Member puter Engineering, National Technical of the IEEE, a member of the IET, and a Fellow of the HEA. University of Athens (NTUA). He is coauthor (with W. Pedrycz) of the books Computa- tional Intelligence in Telecommunications Networks (CRC David I. Laurenson (M’90) is cur- press, USA, 2001), Ambient Intelligence, Wireless Net- rently a Senior Lecturer at The working, Ubiquitous Computing (Artech House, USA, University of Edinburgh, Scotland. His 2006), coauthor (with M. Parashar, S. Karnouskos, W. interests lie in mobile communications: Pedrycz) Autonomic Communications (Springer, to appear at the link layer this includes mea- ), Arts and Technologies (MIT Press, to appear), coau- surements, analysis and modeling of thor (with Yan Zhang, Thrasyvoulos Spyropoulos) Delay channels, whilst at the network layer Tolerant Networking (CRC press, to appear), coauthor this includes provision of mobility (with M. Anastasopoulos) Game Theory in Commu- management and Quality of Service nication Systems (IGI Inc, USA, to appear). He has support. His research extends to practical implementa- published more than 200 articles in top international tion of wireless networks to other research fields, such as journals (i.e IEEE/ACM Transactions on Networking, prediction of fire spread using wireless sensor networks IEEE Transactions on Information Theory, IEEE JSAC, (http://www.firegrid.org), to deployment of communication IEEE Transactions on Wireless Communications, IEEE networks for distributed control of power distribution net- Transactions on Neural Networks, IEEE Transactions on works. He is an associate editor for Hindawi journals, and Systems, Man, and Cybernetics, IEEE T-ITB, IEEE T- acts as a TPC member for international communications CIAIG, etc.) and conferences. He is the Editor-in-chief conferences. He is a member of the IEEE and the IET. of the Inderscience Publishers journals: International Journal of Adaptive and Autonomous Communications Sana Salous (M’95) received B.E.E. Systems (IJAACS, http://www.inderscience.com/ijaacs), degree from the American Univer- International Journal of Arts and Technology (IJART, sity of Beirut, Beirut, Lebanon, in http://www.inderscience.com/ijart). He was or is at the 1978 and M.Sc. and Ph.D. degrees editorial board of more than 20 international journals from the University of Birmingham, including: IEEE Communications Magazine (1999–2002 Birmingham, U.K., in 1979 and 1984, and 2008-), IEEE Transactions on Systems, Man and respectively. She was an Assistant Pro- Cybernetics (TSMC, Part B, 2007-), IEEE Transactions fessor with Yarmouk University, Irbid, on Wireless Communications(invited), IEEE Transactions Jordan, until 1988 and a Research on Information Theory in Biomedicine (TITB, 2009-) etc. Associate with the University of Liverpool, Liverpool, U.K., He chairs several conferences, e.g., ACM IWCMC’09, until 1989, at which point, she took up a lecturer post with ICST/ACM Autonomics 2009. He is a chairman of the the Department of Electronic and Electrical Engineering, Telecommunications Task Force of the Intelligent Sys- University of Manchester Institute of Science and Technol- tems Applications Technical Committee (ISATC) of the ogy (UMIST), Manchester, U.K. In 2003 she took up the IEEE Computational Intelligence Society (CIS). Senior Chair in Communications Engineering with the School of Deputy Secretary-General and fellow member of ISIBM Engineering, Durham University, Durham, U.K, where she www.isibm.org (International Society of Intelligent Bio- is currently the Director of the Centre for Communications logical Medicine (ISIBM)). He is member of the IEEE and Systems. ACM.