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Stochastic differential equations (SDEs) are used to model ultrawideband (UWB) indoor wireless channels. We show that the impulse responses for time-varying indoor wireless channels can be approximated in a mean-square sense as close as desired by impulse responses that can be realized by SDEs. The state variables represent the inphase and quadrature components of the UWB channel. The expected maximization and extended Kalman filter are employed to recursively identify and estimate the channel parameters and states, respectively, from online received signal strength measured data. Both resolvable and nonresolvable multipath received signals are considered and represented as small-scaled Nakagami fading. The proposed models together with the estimation algorithm are tested using UWB indoor measurement data demonstrating the method’s viability and the results are presented.

Ultrawideband (UWB) communication systems have recently attracted significant interest from both the research community and industry since the Federal Communications Commission (FCC) allowed limited unlicensed operation of UWB devices in the USA [

The ultimate performance limits of a communication system are determined by the channel it operates in [

A necessary and sufficient condition for representing any time-varying (TV) impulse response (IR) in stochastic state-space form is that it is factorizable into the product of two separate functions of time and space [

Recently, there have been several papers on the application of SDEs to modeling propagation phenomena in radar scattering and wireless communications. SDEs have been successfully used to analyze

The paper is organized as follows. In Section

The general TV impulse response (in complex baseband) of an indoor wireless fading channel is typically represented by Saleh-Valenzuela (SV) model given as [

For narrowband systems, complex Gaussian fading is conventionally used to describe the small-scale fading. More precisely, the equivalent complex baseband representation consists of Rayleigh-distributed amplitude and uniformly distributed phase. This can be related theoretically to the fact that a large number of multipath components fall into each resolvable delay bin, so that the central limit theorem is valid [

In UWB systems, the central limit theorem is not valid, and a number of alternative amplitude distributions have been proposed in the literature. The most common empirically determined amplitude distribution in many UWB environments is Nakagami distribution, which is observed in [

Now, we want to represent the TV IR in (

The impulse response

It is readily seen from the expression of the IR

In general, the IR

The IR

The space

The optimal approximation of

The corresponding SDE is then given by [

In narrowband systems, the equivalent indoor complex baseband representation consists of Rayleigh-distributed amplitude and uniformly distributed phase [

In UWB systems, as mentioned earlier, the most common amplitude distribution of the received signal is Nakagami distribution [

Since multiple orthogonal independent Rayleigh-distributed random variables can generate Nakagami distribution, the stochastic UWB indoor state-space channel model can be represented by

It can be noticed in (

A simple Gaussian pulse with clean pulse shape and narrow pulse width is chosen as UWB source signal. The experimental setup is similar to the one in [

Transmitted signal of a 300-picosecond Gaussian pulse shape.

The transmitter is located next to a metal wall. The receiving antenna is placed 10 cm away from the transmitter and then moved along the same direction away from the transmitter for 20 cm, 50 cm, 1 m, and 2 m. This scenario is demonstrated in Figure

The indoor environment considered in our experiment.

The measured UWB received signal.

Histogram of measurement data for the dominant paths within the three clusters that are best fit to Nakagami distributions.

Measured and estimated received signals using the EM algorithm combined with the EKF for the 1st, 2nd, and 3rd clusters.

Notice that the EM algorithm estimates

This paper describes a general scheme for extracting mathematical UWB indoor channel models from noisy received signal measurements. The UWB channel models are represented in stochastic state-space form, in which its system output produces Nakagami-distributed received signal strength and it is shown to approximate the general TV IR of the channel as close as desired. Experimental results indicate that the measured data can be regenerated with high accuracy.

This paper has been authored by employees of UT-Battelle, LLC, under Contract no. DE-AC05-00OR22725 with the US Department of Energy. Also, this work was supported in part by NSF Grant no. CMMI-1334094.