A SAGE Algorithm for Estimation of the Direction Power Spectrum of Individual Path Components

Abstract

Abstract-In this contribution, the Fisher-Bingham-5 (FB5) probability density function (pdf) is used to model the shape of the direction power spectral density function (psdf) of individual path components in the radio channel. The FB5 distribution is selected because, among all direction distributions, it maximizes the entropy under the constraints that the first and second distribution moments are specified. A SAGE (Space-Alternating Generalized Expectation-maximization) algorithm is derived based on this model for estimation of the parameters characterizing the direction psdf of each path component in a multi-path scenario. The performance of the SAGE algorithm is evaluated using measurement data. Preliminary results show that the estimated direction psdfs of individual path components exhibit different ovalnesses and tilt angles. These density functions are noticeably more concentrated than the corresponding footprints in the Bartlett spectrum.

Modeling and estimation of the direction-delay power spectrum of the propagation channel

“…In this subsection, we use the Maximum Entropy (ME) rationale proposed in [10], [11] to derive a pdf for modeling the component DoA-delay psd f d (Ω, τ). We make the assumption that each component psd has its fixed center of gravity and spreads in DoA and in delay.…”

“…whereΩ represents the mean direction with azimuthφ and elevationθ, i.e.Ω = e(φ,θ),τ denotes the mean delay, (11) are all free parameters. We now determine these parameters under the assumption that the conditional pdfs of (11) with respect to delay and direction coincide with the Gaussian pdf and the FB 5 pdf respectively.…”

“…An illustrative description of the meanings of γ 1 , γ 2 and γ 3 can be found in [15]. Under the assumption that the pdf f ME (Ω, τ) in (11) has the conditional direction pdf (13) pdf (12), the sought pdf (11) is calculated to be…”

“…In order to obtain accurate estimates of the dispersion parameters, a rationale relying on the maximum-entropy (ME) principle [9] is proposed in [10], [11], [12] for the selection/derivation of the pdfs characterizing component psds. This rationale utilizes the assumptions that each component psd has fixed center of gravity and spreads, and moreover, no information is available for any other properties, such as the exact shape and number of local maxima, of the component psd.…”

“…The estimates of the dispersion parameters obtained by modeling the component psd with this entropy-maximizing pdf provide the "safest" results in the sense that, they are more accurate than the estimates computed using a pdf subject to any constraint that is invalid in real situations. Based on this rationale, a bivariate von-Mises-Fisher pdf and a Fisher-Bingham-5 (FB 5 ) pdf are derived for 978-1-4244-1688-2/08/$25.00 c 2008 IEEE modeling the component psd in AoA and AoD [10] and in elevation and azimuth [11], [12] respectively. Experimental investigations using measurement data demonstrate that these characterizations are applicable in real environments.…”