Wireless body area networks (BANs) are the latest generation of personal area networks (PANs) and describe radio networks of sensors, and/or actuators, placed in, on, around and some-times near the human body. BANs are motivated by the health-care application domain where reliable, long-term, operation is paramount. Hence understanding, and modeling, the body-area radio propagation channel is vital. In this chapter we describe channel models for wireless body area networks, in terms of operating scenarios—including on the human body, off the body, in the body, and body-to-body (or interfering); carrier frequencies from hundreds of MHz to several GHz; and bandwidth of operation, including narrowband and ultra-wideband. We describe particular challenges for accurate channel modeling such as the absence of wide-sense-stationarity in typical on-body narrowband BANs. We describe results following from a large amount of empirical data, and demonstrate that the BAN channel is dominated by shadowing with slowly-changing dynamics. Finally two particularly challenging scenarios for BAN operation are described: sleep-monitoring and also where there is a large number of co-located BANs.

Channel Modeling for Wireless Body Area Networks

This work is to popularize the method of computing the distribution of the excursion times for a Gaussian process that involves extended and multivariate Rice's formula. The approach was used in numerical implementations of the high-dimensional integration routine and in earlier work it was shown that the computations are more effective and thus more precise than those based on Rice expansions. 
The joint distribution of excursion times is related to the distribution of the number of level crossings, a problem that can be attacked via the Rice series expansion, based on the moments of the number of crossings. Another point of attack is the "Independent Interval Approximation" intensively studied for the persistence of physical systems. It treats the lengths of successive crossing intervals as statistically independent. A renewal type argument leads to an expression that provides the approximate interval distribution via its Laplace transform. 
However, independence is not valid in typical situations. Even if it leads to acceptable results for the persistency exponent, rigorous assessment of the approximation error is not available. Moreover, we show that the IIA approach cannot deliver properly defined probability distributions and thus the method is limited to persistence studies. 
This paper presents an alternative approach that is both more general, more accurate, and relatively unknown. It is based on exact expressions for the probability density for one and for two successive excursion lengths. The numerical routine RIND computes the densities using recent advances in scientific computing and is easily accessible via a simple Matlab interface. The result solves the problem of two-step excursion dependence for a general stationary differentiable Gaussian process. The work offers also some analytical results that explain the effectiveness of the implemented method.

Effective computations of joint excursion times for stationary Gaussian processes

We adopt an innovative approach, previously applied to first order statistics of body area networks (BANs), across multiple links and multiple subjects, to important second-order statistics of radio propagation for BANs. Here it is demonstrated that for statistics of fade durations, level crossing intervals and non-fade durations, where direct characterizations are made of these statistics, an absolute measure allows us to compare across a spectrum of possible second-order characterizations; ranging from single-parameter for an entire ensemble, through to per-activity, per-subject and per-link based parameterized models. The deficiency of specifying one value (or a few mean values) for either level-crossing rate, average fade duration, or average nonfade duration, with respect to either a median or mean channel gain, is demonstrated with respect to a very large “open-access” dataset, and particularly 150 hours of “everyday” on-body link data within that dataset. It is also demonstrated that a 2-parameter lognormal fit, to agglomerate empirical second-order data, is generally simple, accurate and sufficient to characterize fade durations, non-fade durations, and level-crossing intervals.

The body area network channel model: A new look at second-order statistics

The first passage time probability density function of a random process is experimentally studied for a Gaussian random process having seventh order Butterworth type power spectral density.

Some experimental results on first passage time problem for gaussian process

The authors deal with the level-crossing intervals of a stationary random process. Probability densities of the level-crossing intervals, and correlation coefficients between successive level-crossing intervals of a process consisting of a sine wave plus Gaussian random noise are experimentally investigated by digital simulation. The Gaussian random noise is selected to be of 7-th order Butterworth power spectrum density. The obtained probability densities appear with a number of isolated peaks much larger than the number observed on the corresponding probability densities of the Gaussian noise alone. When the sine wave frequency is greater than or approximately equal to half of the cutoff frequency of the noise spectrum, experimental data suggest that each isolated peak has a Gaussian-like density. The assumption of 'quasi-independence' is not valid for the level-crossing intervals of the existing process. >

T. Mimaki

Papers

A study on the multi-peak properties of the level-crossing intervals of a random process