Generic channel models 53 We can also express s()as (3.27 where smm(：化0)兰.pa.:exp(j2rvut)cn(L2t)U(tT)c1p(L1） 3.28) an expression similar to(7)in Fleury et al (2002). 3.4 Dispersive-path model 3.4.1 Motivation for proposing dispersive-path model along uncorrelated paths.The parameters of thes paths have differences larger than the intrinsicr tion.the obiective function which is maximized in the maximization p is derived based on a single wave signal m SAGE is not capable to separate them.Thus the mism n the non-correlated single-wave model and the h pathsisassumed to be s such as the first order el in Tan et al.(2003)and a d mode 100 nd oue 613nd Bengtsso fitting tec signal model is implemented in the SAGE agorithm.But the detail scheme of the extendedSAtandits performance was not covered by the article 3.4.2 Original model of slightly distributed sources C Le sn(8)=】 3.29 ath and The complex weight e. phase.O coul e thawhere constant in a stationary time-invariant environment. dassume tha the onary tim nvanant e ronment are independent random variables uniformlyGeneric channel models 53 We can also express s(t; θℓ) as s(t; θℓ) = X 2 p2=1 X 2 p1=1 sp2,p1 (t; θℓ), (3.27) where sp2,p1 (t; θℓ) .= αℓ,p2,p1 exp(j2πνℓt)c T 2,p2 (Ω2,ℓ)U(t; τℓ)c1,p1 (Ω1,ℓ), (3.28) an expression similar to (7) in Fleury et al. (2002). 3.4 Dispersive-path model 3.4.1 Motivation for proposing dispersive-path model In the current SAGE algorithm, the received signal is assumed to be the superposition of multiple waves propagating along uncorrelated paths. The parameters of these paths have differences larger than the intrinsic resolutions of the measurement equipment, therefore they can be well separated by the SAGE algorithm. In another word, these paths are supposed to be uncorrelated. Based on this assumption, the objective function which is maximized in the maximization step is derived based on a single wave signal model. However in real situation, the propagation paths could be correlated, for instance, the multi-ray scenario introduced in the above topic is one scenario where the multiple paths are sufficiently close that the single-wave model based SAGE is not capable to separate them. Thus the mismatch between the non-correlated single-wave model and the reality of correlation results at the poor performance of the SAGE algorithm. The solution proposed in the former topic is specified for the multi-ray scenario, where the number of correlated paths is assumed to be small. When the number is large, which corresponds to the diffuse scattering scenario, the computational complexity becomes prohibitive for practical implementation. It is therefore necessary to find an appropriate solution for this special case. Diffuse scattering cluster estimation, which is also called slightly spatially distributed source estimation, has received attention recently. Different approaches have been published in recent publications, which can be generally categorized into two classes: 1), finding approximate models for the slightly distributed sources, such as the first order Taylor expansion approximation model in Tan et al. (2003) and a two-ray model proposed by Bengtsson and Ottersten (2000); 2) finding high-resolution estimators for estimating the slightly distributed sources, such as DSPE Valaee et al. (1995), DISPARE Meng et al. (1996) and Trump and Ottersten (1996), and spread root-MUSIC, ESPRIT, MODE Bengtsson and Ottersten (2000). These high-resolution estimators are derived more or less by employing subspace fitting techniques or covariance matrix fitting techniques. Extending the SAGE algorithm for estimating diffuse scattering cluster has been briefly mentioned in an electronic letter Tan et al. (2003). In this paper, an approximation signal model is implemented in the SAGE algorithm. But the detail scheme of the extended SAGE algorithm and its performance was not covered by the article. 3.4.2 Original model of slightly distributed sources The contribution of multiple slightly distributed sources to the received signal at the output of the mth Rx antenna array can be modelled as sm(θ) = X C c=1 X Lc ℓ=1 γc,ℓ · cm(θc,ℓ), (3.29) where C is the number of clusters, Lc is the number of multipaths in cth cluster, m is the data index in the frequency and spatial domain, θ is a parameter vector containing all the unknown parameters in the model, γc,ℓ is the path weight of the ℓth path in cth cluster, cm(θc,ℓ) denotes the response which has the expression as cm(θc,ℓ) .= e −j2π(m−1)(∆s/λ) sin(θc,ℓ) . Here ∆s is the array element spacing, θc,ℓ is the direction-of-arrival (DoA) of the ℓth path in cth cluster, λ is the carrier wavelength. The complex weight γc,ℓ = αc,ℓe jψc,ℓ , where αc,ℓ represents a real-valued amplitude, and ψc,ℓ denotes the initial phase. One could assume that the initial phase is fixed as a constant in a stationary time-invariant environment, then sm(θ) is a deterministic signal. However in some applications, it is difficult to ensure the same initial phase in all snapshots. Thus, it is reasonable to assume that the initial phases are independent random variables uniformly distributed on [−π, π]. Correspondingly γc,ℓ are random variables as well