This study investigates the application potential of the SAGE (space-alternating generalized expectation-maximization) algorithm to jointly estimate the relative delay, incidence azimuth, Doppler frequency, and complex amplitude of impinging waves in mobile radio environments The performance, ie, high-resolution ability, accuracy, and convergence rate of the scheme, is assessed in synthetic and real macro- and pico-cellular channels The results indicate that the scheme overcomes the resolution limitation inherent to classical techniques like the Fourier or beam-forming methods In particular, it is shown that waves which exhibit an arbitrarily small difference in azimuth can be easily separated as long as their delays or Doppler frequencies differ by a fraction of the intrinsic resolution of the measurement equipment Two waves are claimed to be separated when the mean-squared estimation errors (MSEEs) of the estimates of their parameters are close to the corresponding Cramer-Rao lower bounds (CRLBs) derived in a scenario where only a single wave is impinging The adverb easily means that the MSEEs rapidly approach the CLRBs, ie, within less than 20 iteration cycles Convergence of the log-likelihood sequence is achieved after approximately ten iteration cycles when the scheme is applied in real channels In this use, the estimated dominant waves can be related to a scatterer/reflector in the propagation environment The investigations demonstrate that the SAGE algorithm is a powerful high-resolution tool that can be successfully applied for parameter extraction from extensive channel measurement data, especially for the purpose of channel modeling

Channel parameter estimation in mobile radio environments using the SAGE algorithm

This paper presents an overview of ultrawideband (UWB) propagation channels. It first demonstrates how the frequency selectivity of propagation processes causes fundamental differences between UWB channels and "conventional" (narrowband) channels. The concept of pathloss has to be modified, and the well-known WSSUS model is not applicable anymore. The paper also describes deterministic and stochastic models for UWB channels, identifies the key parameters for the description of delay dispersion, attenuation, and directional characterization, and surveys the typical parameter values that have been measured. Measurement techniques and methods for extracting model parameters are also different in UWB channels; for example, the concepts of narrowband channel parameter estimation (e.g., maximum-likelihood estimation) have to be modified. Finally, channel models also have an important impact on the performance evaluation of various UWB systems.

Ultrawideband propagation channels-theory, measurement, and modeling

A simple statistical model of azimuthal and temporal dispersion in mobile radio channels is proposed. The model includes the probability density function (PDF) of the delay and azimuth of the impinging waves as well as their expected power conditioned on the delay and azimuth. The statistical properties are extracted from macrocellular measurements conducted in a variety of urban environments. It is found that in typical urban environments the power azimuth spectrum (PAS) is accurately described by a Laplacian function, while a Gaussian PDF matches the azimuth PDF. Moreover, the power delay spectrum (PDS) and the delay PDF are accurately modeled by an exponential decaying function. In bad urban environments, channel dispersion is better characterized by a multicluster model, where the PAS and PDS are modeled as a sum of Laplacian functions and exponential decaying functions, respectively.

http://www2.elo.utfsm.cl/~ipd465/Papers%20y%20apuntes%20varios/A%20Stochastic%20Model,%20Ped%20Mog%20Fleury.pdf

A stochastic model of the temporal and azimuthal dispersion seen at the base station in outdoor propagation environments

We introduce the concept of the double-directional mobile radio channel. It is called this because it includes angular information at both link ends, e.g., at the base station and at the mobile station. We show that this angular information can be obtained with synchronized antenna arrays at both link ends. In wideband high-resolution measurements, we use a switched linear array at the receiver and a virtual-cross array at the transmitter. We evaluate the raw measurement data with a technique that alternately used estimation and beamforming, and that relied on ESPRIT (estimation of signal parameters via rotational invariance techniques) to obtain superresolution in both angular domains and in the delay domain. In sample microcellular scenarios (open and closed courtyard, line-of-sight and obstructed line-of-sight), up to 50 individual propagation paths are determined. The major multipath components are matched precisely to the physical environment by geometrical considerations. Up to three reflection/scattering points per propagation path are identified and localized, lending insight into the multipath spreading properties in a microcell. The extracted multipath parameters allow unambiguous scatterer identification and channel characterization, independently of a specific antenna, its configuration (single/array), and its pattern. The measurement results demonstrate a considerable amount of power being carried via multiply reflected components, thus suggesting revisiting the popular single-bounce propagation models. It turns out that the wideband double-directional evaluation is a most complete method for separating multipath components. Due to its excellent spatial resolution, the double-directional concept provides accurate estimates of the channel's multipath-richness, which is the important parameter for the capacity of multiple-input multiple-output (MIMO) channels.

The double-directional radio channel

This paper presents a 3-D statistical channel impulse response (IR) model for urban line of sight (LOS) and non-LOS channels developed from 28- and 73-GHz ultrawideband propagation measurements in New York City, useful in the design of 5G wireless systems that will operate in both the ultra-high frequency/microwave and millimeter-wave (mmWave) spectrum to increase channel capacities. A 3GPP-like stochastic IR channel model is developed from measured power delay profiles, angle of departure, and angle of arrival power spectra. The extracted statistics are used to implement a channel model and simulator capable of generating 3-D mmWave temporal and spatial channel parameters for arbitrary mmWave carrier frequency, signal bandwidth, and antenna beamwidth. The model presented here faithfully reproduces realistic IRs of measured urban channels, supporting air interface design of mmWave transceivers, filters, and multi-element antenna arrays.

3-D Millimeter-Wave Statistical Channel Model for 5G Wireless System Design

In the last few years, issues concerning the spatial resolution of the received electromagnetic field have attracted a lot of attention in mobile communications. A new method for the high resolution of the electromagnetic field with respect to both the incidence direction and delay is presented. The underlying discrete propagation model relies on the assumption that a finite known number of transverse electromagnetic plane waves characterized by their complex amplitude, propagation delay, and azimuthal incidence direction are impinging in a neighborhood of the receiver position. A space-alternating generalized expectation-maximization (SAGE) algorithm is proposed to replace the high-dimensional optimization procedure necessary to compute the joint maximum-likelihood estimate of the waves parameters by several separate maximization processes which can be performed sequentially. The resolution and the mean convergence rate of the scheme are evaluated by means of Monte-Carlo simulations considering discrete synthetic propagation environments. Finally, the applicability of the SAGE algorithm to real propagation environments is demonstrated.

M. Tschudin

Papers

Channel parameter estimation in mobile radio environments using the SAGE algorithm

Wideband angle of arrival estimation using the SAGE algorithm