6 Deterministic channel parameter estimation inthishaprer we inroduce theoand reiques foretmhanelpreters rom mesuem (.thecap-fmethd()d the MUSIC Schmidt (c the maximum likelihood estimation method is elaborated we introduce the EM and the SAGE is described.In Section6.5,some new techniques relying on the Bayesian estimation methods are introduced.In section subspace-bas ebased techniquesare desribed which are applicable for tracking the variation of channels with relatively ow complexity. 6.1 Spectral-based method either maximiznor minimin the spectral height over the parameter(s),it is possible to obtain certain estimates o cteristi of the componentsin the propagation ett (1948).the Ca beamformer Capon (199),and the MUSIC Schmidt (16),as well as numerous variants of these method ic methods and the n-Tukey In the sequel,we briefly introduce these techniques,and illustrate the results when they are applied to processing the measurement data collected in real environment. 6.1.1 Beamforming method 了p In order tounderstand what is the refinements of the Bartlett beamformer,it is necessary to know the periodogram d new the the equation l=它 (6.1) thathas very regular formulation,which does not include the intrinsic system responses for thethsample. O础y6 Deterministic channel parameter estimation In this chapter, we introduce the algorithms and techniques used for estimating channel parameters from measurement data. In Section 6.1, we introduce the spectral-based method, such as the Bartlett beamforming method Bartlett (1948), the Capon-beamforming method Capon (1969), and the MUSIC algorithm Schmidt (1986). In Section 6.2, the maximum likelihood estimation method is elaborated. In Section 6.3, we introduce the EM and the SAGE algorithm used for channel parameter estimation. In Section 6.4, the Richter’s Maximum likelihood estimation method is described. In Section 6.5, some new techniques relying on the Bayesian estimation methods are introduced. In Section 6.6, typical subspace-based method is elaborated. In Section 6.7, the Kalman filtering algorithms are described which are used to track the variation of the parameters of the channels. Finally, in Section 6.8, the modified particle filtering based techniques are described, which are applicable for tracking the variation of channels with relatively low complexity. 6.1 Spectral-based method The methods belonging to the category of spectral-based method have a common feature that a smooth spectrum with respect to a specific parameter, such as delay, direction of arrival, etc., is computed based on the observations. By either maximizing or minimizing the spectral height over the parameter(s), it is possible to obtain certain estimates of the parameters that represent the characteristics of the components in the propagation channel. The spectral-based method includes the periodogram, correlogram, Bartlett beamformer Bartlett (1948), the Capon beamformer Capon (1969), and the MUSIC Schmidt (1986), as well as numerous variants of these methods. Generally speaking, the spectral-based methods can be grouped into two classes, i.e. the nonparametric methods and the parametric methods. Typical nonparametric methods are the periodogram, correlogram, the Blackman-Tukey method, and the refined Blackman-Tukey method based on windows, and other refined periodogram methods, such as the Bartlett method, the Welch method, Daniell method, etc. To be added some new methods. Include some new citations after 2005 for examples. In the sequel, we briefly introduce these techniques, and illustrate the results when they are applied to processing the measurement data collected in real environment. 6.1.1 Beamforming method The reason that we focus on the refined periodogram method is that for channel parameter estimation, we cope with the samples collected not only in time, in frequency, but also in space. Sometimes, we also need to consider polarization domains. In order to understand what is the refinements of the Bartlett beamformer, it is necessary to know the periodogram and correlogram spectral estimators first. The periodogram power spectral estimation method can be represented by the computations in the following equation: pˆp(ω) = 1 N     X N n=1 y(n)e −jωn     2 , (6.1) where y(n) is the received signal observation for the nth sampling instance in time or location in space, e −jωn represents the system response at the nth sample when the signal component has the frequency of ω. Its obvious that e −jωn has very regular formulation, which does not include the intrinsic system responses for the nth sample. This is a Book Title Name of the Author/Editor c XXXX John Wiley & Sons, Ltd