176 Statistical channel parameter estimation of arrival.Retaining the terminology introduced in Asztely and Ottersten(1998);Bengtsson and Ottersten (2000) irection andhe ersion is characterized by a nominal azimuth(NA)and an azimuth spread (AS)Bengts son and Otterster anahi 1.(2001);Trump and Ottersten (1996 iapplicability with arbitrary transmit and receive arrays,e.g.arbitrary array configuration,non-isotropic element esponses. ii)low computational complexity. irobust performance against calibration errors in the measured array response,and The situation considered in Item iv)is referred to as the incoherent distributed (ID)case in Shahbaz panahi et al The cohe t distribute (CD)case where th m of the com In the sequel we briefly review the NA and As estimators available in open literature,and comment on their entional high resolution channel nara neter estimation Bresler (196):Fleury et a(19):Roy and ():md():) re derived bas 9).As a result.the contribution of each specular scatterer to the received signal is nodeled as a (s ela)plane stima significant Bengtsson and Volcker (2001) 家ro加6Mo心} d on a distribution mo erizing the shape of the Zthmopaoweenm (7);Zoubr et a (2007).The uniform distribution Besson and Stoica();Meng et al.():Sieskul( 2006) 二posG回200)nP2o0:eo2w0ee it high computational com ion requires to olve at least one a.2 6);Qiang an shun (200 ng176 Statistical channel parameter estimation from the Rx. In both cases, the received signal contributed by each of these scatterers or clusters of local scatterers can be conceived as the sum of contributions originating from multiple sub-paths with slightly different directions of arrival. Retaining the terminology introduced in Asztély and Ottersten (1998); Bengtsson and Ottersten (2000); Fleury (2000) we refer to such scatterers or clusters of local scatterers as slightly distributed scatterers (SDSs). A quantitative definition of a SDS matching the theoretical framework and purpose of this paper is provided. Notice that this definition differs from the one given in these references. Direction dispersion in the channel induced by an SDS can be characterized by means of the nominal direction and the spread of the direction power spectrum of the signal contributed by this SDS Fleury (2000). For simplicity, we consider horizontal-only propagation in this contribution. In this case, dispersion is characterized by a nominal azimuth (NA) and an azimuth spread (AS) Bengtsson and Ottersten (2000); Shahbazpanahi et al. (2001); Trump and Ottersten (1996). By abuse of terminology, we refer to the azimuth power spectrum, NA and AS as the azimuth power spectrum, the NA and the AS of the SDS. In this contribution, we are interested in the design and performance investigation of NA and AS estimators for channel sounding. Practical limitations and constraints in the sounding equipment, such as non-isotropic antenna arrays, limited processing time, calibration errors, etc., put the following stringent constraints on these estimators: i) applicability with arbitrary transmit and receive arrays, e.g. arbitrary array configuration, non-isotropic element responses, ii) low computational complexity, iii) robust performance against calibration errors in the measured array response, and iv) applicability in the case where the components in the channel response contributed by an SDS are incoherent (i.e. totally uncorrelated). The situation considered in Item iv) is referred to as the incoherent distributed (ID) case in Shahbazpanahi et al. (2001). The coherent distributed (CD) case where the samples of the component contributed by an SDS are coherent (i.e. fully correlated) is not considered in this contribution. In the sequel, we briefly review the NA and AS estimators available in open literature, and comment on their applicability in the sought application scenario, i.e. MIMO channel sounding. We will see that most hitherto published estimators do not fulfill all the above four constraints and therefore cannot be used in this scenario. Conventional high-resolution channel parameter estimation algorithms Bresler (1986); Fleury et al. (1999); Roy and Kailath (1989); Schmidt (1986); Viberg (1991) are derived based on the specular-scatterer (SS) model, which assumes that the propagation environment consists of point scatterers located in the far field of the Tx and Rx arrays Lee et al. (1997). As a result, the contribution of each specular scatterer to the received signal is modeled as a (specular) plane wave. These algorithms are not suitable for the estimation of the NAs and the ASs of SDSs, due to two reasons. First, they do not provide with an estimate of the AS. Secondly, the probability of occurrence of large estimation errors is significant Bengtsson and Völcker (2001). In recent years, various model-based methods have been proposed for the estimation of the NA and the AS of SDSs. These estimators can be categorized into two groups: the estimators based on a distribution model and the estimators based on a linear approximation model. The estimators based on a distribution model rely on a probability distribution characterizing the shape of the azimuth power spectrum of individual SDSs Besson and Stoica (1999); Han et al. (2006); Meng et al. (1996); Qiang and Zhishun (2007); Ribeiro et al. (2004); Trump and Ottersten (1996); Valaee et al. (1995); Wang and Zoubir (2007); Zoubir et al. (2007). The uniform distribution Besson and Stoica (1999); Meng et al. (1996); Sieskul (2006); Valaee et al. (1995); Zoubir et al. (2007), the (truncated) Gaussian distribution Besson and Stoica (1999); Meng et al. (1996); Qiang and Zhishun (2007); Sieskul (2006); Trump and Ottersten (1996); Wang and Zoubir (2007), the Laplacian distribution Sieskul (2006) and the von-Mises distribution Fleury (2000); Ribeiro et al. (2004) have been proposed for horizontal-only propagation. These estimators are not appropriate for applications in channel sounding due to two reasons. First, no prior information of the shape of the azimuth power spectrum of the SDS is available. Second, these algorithms exhibit high computational complexity. Their computation requires to solve at least a one￾dimensional optimization problem for a certain objective function: the objective function is usually expressed in form of an integral that needs to be calculated numerically when the antenna array response is non-isotropic. Some recently proposed algorithms within this category achieve low computational complexity by exploiting the specific structure or applying a series expansion of the sample covariance matrix Han et al. (2006); Qiang and Zhishun (2007); Wang and Zoubir (2007); Zoubir et al. (2007). However these properties of the sample covariance matrix do not hold when the array is nonlinear and the array elements are non-isotropic. Thus, these estimators are not suitable for the scenarios of interest