Modelling and Analysis of Non-Stationary Mobile Fading Channels Using Brownian Random Trajectory Models

Doktorgradsavhandling i informasjons- og kommunikasjonsteknologi, Universitetet i Agder, Grimstad, 2014The demanding mobility features of communication technologies call for the need to advance channel models (among other needs), in which non-stationary aspects of the channel are carefully taken into consideration. Owing to the mathematical complexity imposed by mobility features of the mobile station (MS), the number of non-stationary channel models proposed in the literature is very limited. The absence of a robust trajectory model for capturing the mobility features of the MS also adds to the depth of this gap. Not only statistically non-stationary channels, but also physically non-stationary channels, such as vehicle-to-vehicle channels in the presence of moving scatterers, have been rarely investigated. In the literature, there exist two fundamental channel modelling approaches, namely deterministic and stochastic approaches. Deterministic approaches, such as measurement-based channel modelling, are known to be accurate, but site-specific and economically expensive. The stochastic approaches, such as geometry-based channel modelling, are known to be economically inexpensive, computationally fair, but not as accurate as the deterministic approach. Among these approaches, the geometry-based stochastic approach is the best to capture the non-stationary aspects of the channel. In this dissertation, we employ the geometry-based stochastic approach for the development of three types of channel models, namely stationary, physically nonstationary, and statistically non-stationary channel models. We geometrically track the plane waves emitted from the transmitter over the local scatterers up to the receiver, which is assumed to be in motion. Under the assumptions that the scatterers are fixed and the observation time is short enough, we develop the stationary channel models. In this regard, we propose a unified disk scattering model (UDSM), which unifies several well-established geometry-based channel models into one robust channel model. We show that the UDSM is highly flexible and outperforms several other geometric models in the sense of matching empirical data. In addition, we provide a new approach to develop stationary channel models based on delay-angle joint distribution functions. Under the assumption that the scatterers are in motion and the observation time is again short enough, we develop a physically non-stationary channel model. In this connection, we model vehicle-to-vehicle (V2V) channels in the presence of moving scatterers. Proper distributions for explaining the speed of relatively fast and relatively slow moving scatterers are provided. The statistical properties of the proposed channel model are also derived and validated by measured channels. It is shown that relatively fast moving scatterers have a major impact on both V2V and fixed-to-fixed (F2F) communication links, as they are significant sources of the Doppler spread. However, relatively slow moving scatterers can be neglected in V2V channels, but not in F2F channels. Under the assumption that the scatterers are fixed and the observation time is not necessarily short anymore, we develop the statistically non-stationary channel models. To this aim, we first introduce a new approach for generating fully spatial random trajectories, which are supposed to capture the mobility features of the MS. By means of this approach, we develop a highly flexible trajectory model based on the primitives of Brownian fields (BFs). We show that the flexibility of the proposed trajectory is threefold: 1) its numerous configurations; 2) its smoothness control mechanism; and 3) its adaptivity to different speed scenarios. The statistical properties of the trajectory model are also derived and validated by data collected from empirical studies. We then introduce a new approach to develop stochastic non-stationary channel models, the randomness of which originates from a random trajectory of the MS, rather than from the scattering area. Based on the new approach, we develop and analyze a non-stationary channel model using the aforementioned Brownian random trajectory model. We show that the channel models developed by this approach are very robust with respect to the number of scatterers, such that highly reported statistical properties can be obtained even if the propagation area is sparsely seeded with scatterers. We also show that the proposed non-stationary channel model superimposes large-scale fading and small-scale fading. Moreover, we show that the proposed model captures the path loss effect. More traditionally, we develop and analyze two non-stationary channel models, the randomness of which originates from the position of scatterers, but not from the trajectory of the MS. Nevertheless, the travelling path of the MS is still determined by a sample function of a Brownian random trajectory. It is shown that the proposed channel models result in a twisted version of the Jakes power spectral density (PSD) that varies in time. Accordingly, it is demonstrated that non-stationarity in time is not in line with the common isotropic propagation assumption on the channel

A Novel Non-Stationary Channel Model Utilizing Brownian Random Paths

This paper proposes a non-stationary channel model in which real-time dynamics of the mobile station (MS) are taken into account. We utilize Brownian motion (BM) processes to model targeted and non-targeted dynamics of the MS. The proposed trajectory model consists of both drift and random components to capture both targeted and non-targeted motions of the MS. The Brownian trajectory model is then employed to provide a non-stationary channel model, in which the scattering effects of the propagation area are modelled by a non-centred one-ring geometric scattering model. The starting point of the motion is a fixed point in the propagation environment, whereas its terminating point is a random point along a predetermined drift. The drift component can be controlled by a so-called drift parameter. Tracking the MS on the proposed Brownian path allows us to derive the local angles-of-arrival (AOAs) and local angles-of-motion (AOMs), which are expressed by stochastic processes rather than random variables. We compute the first-order densities of the AOA and AOM processes in closed form. The local power spectral density (PSD) of the Doppler frequencies and the autocorrelation function (ACF) of the complex channel gain are also provided. Given a walking speed scenario, the analytical results are demonstrated and explained in depth. It turns out that the proposed Brownian path model results in a non-stationary non-isotropic channel model. The proposed geometry-based channel model is very useful for the performance analysis of mobile communication systems under non-stationary conditions

On the spatial configuration of scatterers for given delay-angle distributions

Published version of an article in the journal: Engineering Letters. Also available from the publisher at: http://www.engineeringletters.com/issues_v22/issue_1/EL_22_1_05.pdf. Open accessThis paper investigates the distribution of scatterers located around the mobile station (MS) for given delay-angle distributions. The delay-angle distribution function represents the joint probability density function (PDF) of the time-ofarrival (TOA) and angle-of-arrival (AOA). Given such a joint PDF, we first derive a general expression for the distribution of the scatterers in both polar and Cartesian coordinates. We then analyze an important special case in which the TOA and the AOA follow the multiple negative exponential (MNE) and the uniform distributions, respectively. The considered MNE PDF is the sum of several decaying exponential functions, which allows us to describe the TOA in a variety of propagation environments. For the delay profiles specified in COST 207, the scatterer distribution is simulated and visualized in scatter diagrams. The marginal PDF of the distance from the scatterers to the MS is also computed, illustrated, and confirmed by simulations. For the MNE TOA PDF, it is shown that the local scatterers are not symmetrically distributed around the MS even if the AOAs are uniformly distributed. In addition, the obtained scattering area is not confined by firm geometric constraints, which complies with real propagation environments. The importance of the work is to provide a novel approach to channel modelling, in which obtaining the desirable TOA (AOA) PDF is assured

The Impact of Human Walking on the Time-Frequency Distribution of In-Home Radio Channels

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A Non-Stationary Channel Model for the Development of Non-Wearable Radio Fall Detection Systems

The emerging non-wearable fall detection systems rely on processing radio waves reflected off the body of the home user who has no active interaction with the system, increasing the user privacy and acceptability. This paper proposes a nonstationary channel model that is important for the development of such systems. A three-dimensional stochastic trajectory model is designed to capture targeted mobility patterns of the home user. The model is featured with a forward fall mechanism, which is actuated at a random point along the path. A transmitter emits radio waves throughout an indoor propagation environment, while a receiver collects fingerprints of the scattering objects on the emitted waves. The corresponding radio channel is modelled by a process capturing the time-variant Doppler effect caused by the home occupant. The time-frequency behaviour of the non-stationary channel is studied by computing the Doppler power spectral density and by performing spectrogram analysis. The instantaneous mean Doppler shift and Doppler spread are derived and simulated. The model is confirmed with experimental results performed at 5.9 GHz. The results are insightful for developing reliable fall detection algorithms, while the model is useful for studying the impact of different walking/falling patterns on the overall fall detection system performance.A Non-Stationary Channel Model for the Development of Non-Wearable Radio Fall Detection SystemsacceptedVersionNivå

A Highly Flexible Trajectory Model Based on the Primitives of Brownian Fields---Part II: Analysis of the Statistical Properties

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The Effect of Music Therapy on Anxiety and Vital Signs of Patients with Acute Coronary Syndrome: A Study in the Cardiac Care Unit of Vali-Asr Hospital, Eghlid, Iran

Background: Acute coronary syndrome is an emergency situation, characterized by a sudden decrease of blood flow to the heart and chest pain during a heart attack or unstable angina. High levels of anxiety increases mortality risk up to three times. The aim of this study was to determine the effect of music therapy on anxiety level and vital signs of patients with acute coronary syndrome admitted in the coronary care unit of Vali- Asr hospital, in Eghlid city. Methods: This clinical trial was conducted on 70 acute coronary syndrome patients who were eligible for the study during 2011-2012. Anxiety level was measured by the standard Spielberger Questionnaire and vital signs of patients were recorded before and after the intervention. Data were analyzed through SPSS18 and using mean, percentage, standard deviation, independent and paired t- test. Results: Music had no effect on vital signs but significantly reduced anxiety level (P=0.049). Anxiety was significantly higher in females, but showed no significant relationship with age and education. There was no significant relationship between age, sex and education with respiratory rate, heart rate and systolic or diastolic blood pressure. Conclusions: Music as an easy and low cost intervention without any complication can be used to reduce anxiety in patients in Coronary Care Units

A Random Trajectory Approach for the Development of Nonstationary Channel Models Capturing Different Scales of Fading

This paper introduces a new approach to developing stochastic nonstationary channel models, the randomness of which originates from a random trajectory of the mobile station (MS) rather than from the scattering area. The new approach is employed by utilizing a random trajectory model based on the primitives of Brownian fields (BFs), whereas the position of scatterers can be generated from an arbitrarily 2-D distribution function. The employed trajectory model generates random paths along which the MS travels from a given starting point to a fixed predefined destination point. To capture the path loss, the gain of each multipath component is modeled by a negative power law applied to the traveling distance of the corresponding plane wave, whereas the randomness of the path traveled results in large-scale fading. It is shown that the local received power is well approximated by a Gaussian process in logarithmic scale, even for a very limited number of scatterers. It is also shown that the envelope of the complex channel gain follows closely a Suzuki process, indicating that the proposed channel model superimposes small-scale fading and large-scale fading. The local power delay profile (PDP) and the local Doppler power spectral density (PSD) of the channel model are also derived and analyzed.acceptedVersionnivå

On the spectral moments of non-WSSUS mobile-to-mobile double Rayleigh fading channels

This paper deals with the mathematical analysis of the spectral moments of non-wide-sensestationary uncorrelated-scattering (non-WSSUS) mobile-to-mobile (M2M) double-Rayleigh fading channels. The point of departure is a recently proposed geometry-based statistical model (GBSM) for M2M double-Rayleigh fading channels from which general analytical expressions are derived for the average Doppler shift, Doppler spread, average delay, and delay spread. Closed-form solutions of such expressions are presented for the particular case of the geometrical two-rings scattering model. The obtained results indicate that the average Doppler shift and Doppler spread are directly influenced by not only the carrier frequency, but also the bandwidth of the communication system. A consistency analysis is carried out to assess the physical soundness of the reference channel model. The results show that the channel model fulfills all the consistency criteria pertaining to the spectral moments. The analysis presented here can be used as a guideline for the statistical characterization of non-WSSUS time- and frequency-selective M2M fading channels.acceptedVersionnivå