This paper introduces TIME: Trajectory-Informed Movement Emulation, a novel approach to arm gesture recognition in indoor environments using the fusion of mmWave radar and optical tracking systems (Qualisys). TIME leverages a trajectory-driven channel model to construct realistic micro-Doppler signatures of arm movements. We capture and process detailed full-body motion data with a specific focus on arm segments like the hand, forearm, and upper arm. This targeted data allows us to emulate the micro-Doppler shifts that naturally occur with arm motions. These shifts help to characterize the distinctive patterns of natural arm movements. By reducing the need for extensive real-world measurement campaigns, this framework offers a time-efficient alternative to traditional data collection. Results demonstrate that the TIME framework effectively replicates patterns observed in actual mmWave radar data, showcasing its potential to advancing gesture recognition systems and human-computer interaction applications powered by artificial intelligence (AI).

In this research, we introduce a novel trajectory-driven channel model for non-stationary indoor millimeter wave (mmWave) communication environments. The model incorporates optimized time-variant (TV) path gains, particularly focusing on scenarios with multiple moving point scatterers. Determining optimal TV path gain values for each moving point scatterer requires estimating the respective radar cross-sections (RCSs). To address this challenge, we formulate an optimization problem based on the $L_{p}$-norm, utilizing the TV mean Doppler shift as a key parameter. We then estimate RCSs by fitting the TV mean Doppler shift of the channel model as closely as possible to that computed from real radar measurements. The efficacy of this approach is validated through experiments in a controlled laboratory setting using a 24 GHz radar kit. Two distinct experiments with right arm movements are examined, allowing us to estimate the RCSs of various arm segments; hand, upper arm, forearm, and shoulder. Our numerical results demonstrate the accuracy and effectiveness of the proposed methodology in emulating real radio channel conditions.

The rapid advancement of millimeter-wave (mm Wave) radio-frequency (RF) sensor technology has unlocked new possibilities for tracking human activities indoors. This requires a comprehensive understanding of indoor signal propagation in the presence of moving objects and/or persons. In this context, we present a trajectory-driven non-stationary indoor channel model focusing on backscattering analysis. Expressions for the time-variant (TV) channel transfer function (CTF), the micro-Doppler signatures, and the mean Doppler shift are presented. We perform two distinct experiments in a laboratory environment to extract and analyze the micro-Doppler signatures of a moving person (walking) considering solely the backscattered (double-bounced) signal components. In addition, we also use inertial measurement unit (IMU) sensors integrated in a smartsuit to track the TV trajectories of different human body parts, such as head, chest, and hips. The collected data undergoes rigorous processing to ensure precision and reliability. A good agreement is found between the micro-Doppler signatures computed from the measured RF data and those obtained with the trajectory-driven channel model. The findings also demonstrate the relevance and validity of considering backscattering components to extract the micro-Doppler signature patterns resulting from human motion in a complex indoor environment. This paper offers a comprehensive exploration of the methodology, results, and potential applications, ultimately contributing to the realization of smarter, more efficient, and citizen-centric smart environments.

Modern human activity recognition (HAR) systems are designed using large amounts of experimental data. So far, real-data-driven or experimental-based HAR systems using Wi-Fi or radar systems have shown considerable results. However, the acquisition of large, clean, and labeled training datasets remains a crucial impediment to the progress of experimental-based HAR systems. Therefore, in this paper, a paradigm shift from the experimental to a fully simulation-based design of HAR systems is proposed in the context of radar sensing. An end-to-end simulation framework is proposed as a proof-of-concept that can simulate realistic millimeter-wave radar signatures for synthesized human motion. We designed a human motion synthesis tool that emulates different types of human activities and generates the spatial trajectories accordingly. These trajectories are processed by a geometric model with respect to user-defined antenna configurations. Considering the long-and short-time stationarity of wireless channels, we synthesize the raw in-phase and quadrature data and process the data to simulate the radar signatures for emulated human activities. Finally, a simulated and a real HAR dataset were used to train and test a simulation-based HAR system, respectively, which gave an average (maximum) classification accuracy of 94% (98.4%). The main advantage of the proposed simulation framework is that the training effort for radar-based classifiers, e.g., gesture recognition systems, can be minimized drastically.

In indoor environments, backscattering components play a key role in radio-frequency (RF) sensing, especially with the blockage of line-of-sight components by the furniture. Thus, it is paramount to investigate the Doppler characteristics of backscattering millimeter wave (mmWave) channels in the presence of moving objects. In this regard, this paper presents a trajectory-driven non-stationary channel model for a mmWave single-input single-output communication system. This backscattering channel model takes into account the impact of a single moving object on the indoor radio wave propagation phenomena. First, the expression of the complex channel gain is presented. Then, the time-variant (TV) micro-Doppler signatures of the moving object are studied. The validity of the proposed channel model is confirmed by real-world measured RF data, which were collected in a laboratory room using a software defined radar system operating at 24 GHz. For fair comparison, we consider as a moving object a swinging pendulum for which the exact TV trajectory is known. In addition, inertial measurement unit sensors are attached to the pendulum to track its TV trajectory. A good agreement can be seen between the Doppler characteristics of the backscattering channel model and those computed from the measured RF data. This demonstrates that backscattering components can be employed to accurately extract the micro-Doppler signatures of a moving object in indoor spaces. The exhibited results can serve as a basis for the development of future robust backscattering-based RF sensing.

In this paper, we analyze the symbol error probability (SEP) performance of M-ary differential phase shift keying (M-DPSK) modulation schemes over frequency-flat fast-varying Hoyt multipath fading channels. Assuming general non-isotropic scattering conditions, we first derive a finite-range integral expression for the probability density function (PDF) of the phase difference between two non-isotropic Hoyt vectors perturbed by additive white Gaussian noise (AWGN). Based upon the theory of M-DPSK modulation and the obtained PDF formula, the SEP of M-DPSK and its corresponding asymptotic behavior in non-isotropic fast-Hoyt fading channels are derived. Specifically, a double semi-finite range integral expression for the corresponding SEP is investigated. A closed-form expression for the SEP and bit error probability (BEP) of M-DPSK and DPSK, respectively, over non-isotropic frequency-flat fast-Rayleigh fading channels is also deduced. Moreover, the obtained SEP and BEP expressions are fully validated by reducing them to already known results corresponding to the special cases like isotropic Hoyt and isotropic Rayleigh fading channels. By considering a mobile-to-mobile (M2M) non-isotropic Hoyt scattering model, we finally validate the obtained expressions for the PDF and SEP by means of computer simulations.

In this paper, we propose a trajectory-driven three-dimensional (3D) non-stationary channel model for millimeter wave (mm-Wave) single-input single-output (SISO) systems. The proposed channel model is designed to model and simulate the micro-Doppler characteristics of human walking activities in indoor environments. We present an expression of the time-variant (TV) channel transfer function (CTF), where its temporal variation is determined by the trajectories of moving human body segments. As moving human body segments, we study the influence of the head, chest, and hips. We investigate the TV Doppler characteristics of the proposed channel caused by the motion of the person. To do so, we focus on the TV spectrogram and the TV mean Doppler shift. To confirm the validity of the proposed channel model, we conducted a measurement campaign for human walking activities by using the Ancortek 2400T2R4 software defined radar kit operating at 24 GHz. The TV trajectories of human body segments are collected during the experiment by using the Rokoko smartsuit. The results for the micro-Doppler signature obtained from the measurements are compared with those of the trajectory-driven channel model. The findings show a good match between the proposed channel model and the real-world measurements.

This paper deals with the estimation of the time-variant (TV) radial distance of a moving person in an indoor environment. The TV radial distance is obtained from the amplitude of the demodulated TV radar response. For simplicity, the body of a person is modelled by a single point scatterer. We start by determining the TV path delay caused by the motion of the person. Then, the TV radial distance is deduced from the estimated TV path delay. To confirm the validity of the estimation method, we conduct real-world measurements. In this regard, two experiments are carried out for which the radio-frequency (RF) data is collected using the Ancortek SDR-KIT 2400T2R4 radar system operating at 24GHz. In the first experiment, we consider a swinging pendulum acting as a single moving point scatterer. We compare the estimated TV radial distance of the pendulum with the corresponding theoretical expression that provides the ground truth information. For this experiment, the good match between the measured and analytical results demonstrates the proof of concept. In the second experiment, we consider a walking person acting as a single moving for which we can accurately compute the total travelled distance. The findings confirm the validity of the estimation method.

This paper demonstrates the time-variant (TV) Doppler power characteristics of human activities using measured channel state information (CSI). We model the measured CSI as a complex channel transfer function corresponding to a 3D non-stationary multipath fading channel consisting of a fixed transmitter, a fixed receiver, fixed scatterers representing fixed objects, and a cluster of moving scatterers representing a moving person performing some human activities. We demonstrate the relationship between the TV Doppler frequency caused by each moving scatterer and the rate of change of its corresponding TV propagation delay. Furthermore, we express the TV mean Doppler shift in terms of the path gains of the fixed scatterers, the TV path gains, and the TV Doppler frequencies of the moving scatterers. To provide an insight into the TV Doppler power characteristics of the measured calibrated CSI, we employ the spectrogram from which we derive the TV mean Doppler shift. Finally, we present the spectrograms and the TV mean Doppler shifts of the measured calibrated CSI for different human activities. The results show the possibility of designing human activity recognition systems using commercial Wi-Fi devices by employing deep learning or machine learning algorithms.

In this paper, we develop a simulation model for the ego-noise of unmanned aerial vehicles (UAVs). The ego-noise is composed of spike noise and background noise. The spike noise is modelled by a finite sum of sinusoids, while the background noise is modelled by a coloured Gaussian stationary process. The main property of our model is that it only depends on physical characteristics of the UAV and it does not need real-time audio inputs to be developed. This model is very useful for training novel noise cancelling algorithms and for evaluating their performance. To validate the proposed model, we compare the statistical properties of the ego-noise simulated using our model with actual ego-noise measurements.

A robust and unobtrusive human activity recognition system is essential to a multitude of applications, such as health care, active assisted living, robotics, sports, and tele-immersion. Existing well-performing activity recognition methods are either vision- or wearable sensor-based. However, they are not fully passive. In this paper, we develop WiHAR-an unobtrusive Wi-Fi-based activity recognition system. WiHAR uses the Wi-Fi network interface card to capture the channel state information (CSI) data. These CSI data are effectively processed, and then amplitude and phase information is used to obtain the spectrogram. In the subsequent step, the time-variant mean Doppler shift (MDS) caused by the human body movements in the radio signals before their arrival at the receiver is estimated. The MDS is used to extract time and frequency domain features that are needed to train the supervised learning algorithms (i.e., decision tree, linear discriminant analysis, and support vector machines (SVM)) to assess the performance of the WiHAR. Our results show that WiHAR combined with SVM achieves 96.2% recognition accuracy on the data set consisting of 9 participants where each participant performed four activities including: walking, falling, picking up an object from the ground, and sitting on a chair.

This paper proposes a three-dimensional (3D) non- stationary fixed-to-fixed indoor channel simulator model for human activity recognition. The channel model enables the formulation of temporal variations of the received signal caused by a moving human. The moving human is modelled by a cluster of synchronized moving scatterers. Each of the moving scatterers in a cluster is described by a 3D deterministic trajectory model representing the motion of specific body parts of a person, such as wrists, ankles, head, and waist. We derive the time-variant (TV) Doppler frequencies caused by the motion of each moving scatterer by using the TV angles of motion, angles of arrival, angles of departure. Moreover, we derive the complex channel gain of the received signal. Furthermore, we analyze the TV Doppler power spectral density of the complex channel gain by using the concept of the spectrogram and present its expression in approximated form. Also, we derive the TV mean Doppler shift and TV Doppler spread from the approximated spectrogram. The accuracy of the results is validated by simulations. The channel simulator is beneficial for the development of activity recognition systems with non-wearable devices as the demand for such systems has increased recently.

This paper presents a new accurate iterative procedure to estimate the time-variant (TV) velocity, i.e., TV speed, TV vertical angle-of- motion (VAOM), and TV horizontal angle-of-motion (HAOM), of multiple moving objects/persons in three-dimensional (3D) non-stationary indoor propagation environments. The indoor space is assumed to be equipped with a distributed 3×3 multiple-input multiple-output (MIMO) system. The proposed procedure focuses on estimating the TV speed, TV VAOM, and TV HAOM by matching the spectrogram of the complex channel gain of a non- stationary indoor channel model to the spectrogram obtained from received radio frequency (RF) signals. Together with the velocity parameters, this method estimates all channel parameters, such as path gains, phases, etc. Numerical examples are presented to validate the proposed estimation algorithm by comparing the estimated parameters of interest with their corresponding exact quantities.

This paper deals with the localization of passive stationary objects from the received radio- frequency (RF) signals in 3-dimensional (3D) indoor environments. Each object located in the 3D indoor environment is modelled by a single point scatterer. The propagation space is equipped with a multiple-input multiple-output (MIMO) wireless communication system. The employed channel model is flexible and allows to have a line-of-sight (LOS) component as well as single- and double- bounce scattering components. Here, we present a new accurate iterative estimation technique for computing the optimal coordinates as well as the number of the main stationary objects (scatterers) in indoor areas. The proposed approach aims at matching the frequency correlation function (FCF) of the transfer function (TF) of the received RF signals to the FCF of the channel model. This iterative procedure is based on numerical optimization techniques to estimate the number and coordinates of the scatterers and the channel parameters by minimizing the Euclidean norm of the fitting error. Numerical results are presented to confirm the accuracy of the proposed estimation procedure by comparing the estimated positions as well as the resulting FCF with the corresponding exact quantities, known from generated RF signals.

Modern societies are facing an ageing problem which comes with increased cost of healthcare. A major share of this ever-increasing cost is due to fall related injuries, which urges the development of fall detection systems. In this context, this paper paves the way for building of a radio-frequency-based fall detection system. This paper presents an activity simulator that generates the complex channel gain of indoor channels in the presence of one person performing three different activities, namely, slow fall, fast fall, and walking. We built a machine learning framework for activity recognition based on the complex channel gain. We assess the recognition accuracy of three different classification algorithms: decision tree, artificial neural network (ANN), and cubic support vector machine (SVM). Our analysis reveals that the decision tree, ANN, and cubic SVM achieve an overall recognition accuracy of 73%, 84.1%, and 92.6%, respectively.

The efficient control of mobile network-enabled unmanned aerial vehicles (UAVs) is targeted in this paper. In particular, a downlink scenario is considered, in which control messages are sent to UAVs via cellular base stations (BSs). Unlike terrestrial user equipment (UEs), UAVs perceive a large number of BSs, which can lead to increased interference causing poor or even unacceptable throughput. This paper proposes a framework for efficient control of UAVs. First, a communication model is introduced for flying UAVs taking into account interference, path loss and fast fading. The characteristics of UAVs make such model different compared to traditional ones. Thereafter, in order to ensure the efficient control, a solution is proposed for reducing interference. This is achieved by efficiently assigning sub-carriers to the UAVs in a way to reduce interference. A maximum independent set formulation is proposed along with an algorithm for optimal sub-carrier allocation. The obtained results demonstrate the efficiency of the proposed solution in terms of enhancing the link quality of UAVs.

This paper presents a new iterative estimation method to localize a single moving object or person in non-stationary 3-dimensional (3D) indoor environments from received radiofrequency (RF) signals. The moving object/person is modelled by a moving single point scatterer. The indoor space is equipped with a multiple-input multiple-output (MIMO) communication system. This work starts by introducing a new geometrical channel model which considers the effects of the line-of-sight (LOS) component, the fixed objects located in a room, and the moving object (point scatterer). Then, we present an iterative estimation technique for computing the time-variant (TV) coordinates of the moving scatterer. The proposed approach determines the optimal TV coordinates of the moving scatterer by matching the TV transfer function (TVTF) of the received RF signals to the TVTF of the non-stationary channel model. The proposed procedure relies on numerical optimization techniques to estimate the TV position of the moving scatterer by minimizing the Euclidean norm of the fitting error. A comparison of the estimated TV position of the moving scatterer with the corresponding exact quantities, known from generated RF signals, confirms the validity of the proposed approach.

A robust fall detection system is essential to support the independent living of elderlies. In this context, we develop a machine learning framework for fall detection and daily living activity recognition. Using acceleration data from public databases, we test the performance of two algorithms to classify seven different activities including falls and activities of daily living. We extract new features from the acceleration signal and demonstrate their effect on improving the accuracy and the precision of the classifier. Our analysis reveals that the quadratic support vector machine classifier achieves an overall accuracy of 93.2% and outperforms the artificial neural network algorithm.

This paper concerns the Doppler power spectrum of three-dimensional non-stationary indoor fixed-to- fixed channels with moving people. In this paper, we model each moving person as a moving scatterer with time-variant (TV) speed, TV vertical angles of motion, and TV horizontal angles of motion of the moving scatterers. Furthermore, we derive the TV angular parameters of each moving scatterer such as the elevation angle of departure, the azimuth angle of departure, the elevation angle of arrival, and the azimuth angle of arrival. In addition, the TV unit vectors of the departure of the transmitted wave planes and unit vectors of the arrival of the received wave planes are derived. Furthermore, to present the Doppler power spectrum characteristics of such channels, we provide the closed-form solution of the spectrogram of the complex channel gain. The correctness of the analysis is approved by simulations. The contribution of this paper is an initiative for the development of device-free indoor activity monitoring and fall detection systems.

This paper presents a non-wide-sense stationary uncorrelated scattering (non-WSSUS) model which takes accurately into account that the Doppler frequencies and propagation delays vary with time if the mobile station (MS) moves. Another feature of the proposed channel model is that the MS can change its velocity along the route. The result is that the Doppler spread and the delay spread deviate from their initial values with increasing time. This effect motivates the definition of quasi-stationary intervals. The lengths of these intervals will be analysed in terms of the velocity parameters. Our analysis shows that real- world channels can be quasi-stationary but not wide-sense stationary (WSS), neither in the time domain nor in the frequency domain. This implies that the generally accepted WSS and WSSUS assumptions are not fulfilled in practice, even not if the travelling distance is short.

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 non-stationary channel model that is important for the development of such systems. A 3-D 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 modeled by a process capturing the time-variant Doppler effect caused by the home occupant. The time-frequency behavior 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.

This paper focuses on the modeling, simulation, and experimental verification of wideband single‐input single‐output (SISO) mobile fading channels for indoor propagation environments. The indoor reference channel model is derived from a geometrical rectangle scattering model, which consists of an infinite number of scatterers. It is assumed that the scatterers are exponentially distributed over the two‐dimensional (2D) horizontal plane of a rectangular room. Analytical expressions are derived for the probability density function (PDF) of the angle of arrival (AOA), the PDF of the propagation path length, the power delay profile (PDP), and the frequency correlation function (FCF). An efficient sum‐of‐cisoids (SOC) channel simulator is derived from the nonrealizable reference model by employing the SOC principle. It is shown that the SOC channel simulator approximates closely the reference model with respect to the FCF. The SOC channel simulator enables the performance evaluation of wideband indoor wireless communication systems with reduced realization expenditure. Moreover, the rationality and usefulness of the derived indoor channel model is confirmed by various measurements at 2.4, 5, and 60 GHz.

In mobile radio channel modelling, it is generally assumed that the angles of arrival (AOAs) are independent of time. This assumption does not in general agree with real‐world channels in which the AOAs vary with the position of a moving receiver. In this paper, we first present a mathematical model for the time‐variant AOAs. This model serves as the basis for the development of two nonstationary multipath fading channels models for vehicle‐to‐infrastructure communications. The statistical properties of both channel models are analysed with emphasis on the time‐dependent autocorrelation function (ACF), time‐dependent mean Doppler shift, time‐dependent Doppler spread, and the Wigner‐Ville spectrum. It is shown that these characteristic quantities are greatly influenced by time‐variant AOAs. The presented analytical framework provides a new view on the channel characteristics that goes well beyond ultra‐short observation intervals over which the channel can be considered as wide‐sense stationary.

In this paper, we analyze the performance of Alamouti-coded orthogonal frequency division multiplexing (OFDM) systems over time-varying underwater acoustic (UWA) channels. A realistic UWA channel model has been considered, which can be correlated in either time or space or simultaneously in both domains. An exact analytical expression for the bit error probability (BEP) is necessary to analyze accurately the performance of Alamouti-coded OFDM systems over the spatio-temporally correlated UWA channel model. Hence, by using this UWA channel model, an expression has been derived for the BEP of Alamouti-coded OFDM systems assuming that the receiver knows perfectly the channel state information. The BEPs of two special cases are also studied, where the UWA channel is only correlated in either time or space. The performance of the Alamouti-coded OFDM system over UWA channels has been assessed for different maximum Doppler frequencies and antenna spacings. All theoretical results are validated by system simulations.

When modelling mobile radio channels with moving scatterers, it is generally assumed that the angles of departure (AODs), angles of arrival (AOAs), and the speed of the scatterers are time-invariant. However, this assumption is violated as the AODs and AOAs vary with the positions of the moving scatterers. Also, the speed of the moving scatterers might vary with time due to acceleration/deceleration. In this paper, we model the time-variant Doppler frequencies by taking into account the time-variant AODs, AOAs, and the variations of the speed of the moving scatterers. Furthermore, the complex channel gain of non-stationary single-input-single-output (SISO) fixed-to-fixed (F2F) indoor channels with moving and fixed scatterers is presented. The spectrogram of the complex channel gain using a Gaussian window is provided. The correctness of the analytical solutions is confirmed by simulations. The contribution of this paper paves the way towards the development of a passive in-home activity tracking system.

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.

The level-crossing rate (LCR) and average duration of fades (ADF) are important statistical quantities describing the fading behaviour of mobile radio channels. To date, these quantities have only been analysed under the assumption that the mobile radio channel is wide-sense stationary, which is generally not the case in practice. In this paper, we propose a concept for the analysis of the LCR and ADF of non-stationary channels. Rice's standard formula for the derivation of the LCR of wide-sense stationary processes is extended to a more general formula enabling the computation of the instantaneous LCR of non-stationary processes. The application of the new concept results in closed-form expressions for the instantaneous LCR and ADF of non-stationary multipath flat fading channels. The contribution of this paper is of central importance for the statistical characterization of non-stationary mobile radio channels.

In mobile radio channel modelling, it is generally assumed that the angles of arrival (AOAs) are independent of time. This assumption does in general not agree with real-world channels in which the AOAs vary with the position of a moving receiver. In this paper, we first present a mathematical model for the time-variant AOAs. This model serves as the basis for the development of two non-stationary multipath fading channels models. The statistical properties of both channel models are analysed with emphasis on the time-dependent autocorrelation function (ACF), time-dependent mean Doppler shift, time-dependent Doppler spread, and the Wigner-Ville spectrum. It is shown that these characteristic quantities are greatly influenced by time-variant AOAs. The presented analytical framework provides a new view on the channel characteristics that goes well beyond ultra-short observation intervals over which the channel can be considered as wide-sense stationary.

This paper is concerned with the enhancement of the resolution of the spectrogram of non-stationary mobile radio channels using massive multiple-input multiple-output (MIMO) techniques. By starting from a new generic geometrical model for a non-stationary MIMO channel, we derive the complex MIMO channel gains under the assumption that the mobile station (MS) moves with time-variant speed. Closed-form solutions are derived for the spectrogram of the complex MIMO channel gains by using a Gaussian window. It is shown that the window spread can be optimized subject to the MS's speed change. Furthermore, it is shown that the spectrogram can be split into an auto-term and a cross-term. The auto-term contains the useful time-variant spectral information, while the cross-term can be identified as a sum of spectral interference components, which restrict considerably the time-frequency resolution of the spectrogram. Moreover, it is shown that the effect of the cross-term can be drastically reduced by using massive MIMO techniques. The proposed method is not only important for estimating timevariant Doppler power spectra with high resolution, but it also pioneers the development of new passive acceleration/deceleration estimation methods and the development of new non-wearable fall detection systems.

This paper aims to characterize the effects that the velocity variations of the mobile stations (MSs) produce on the correlation properties of non-stationary time-frequency (TF) dispersive mobile- to-mobile (M2M) fading channels. Toward that end, we propose a novel geometrical model for non-wide-sense stationary uncorrelated scattering (non-WSSUS) M2M channels that incorporates such variations following a plane wave propagation approach. Capitalizing on the mathematical simplicity of this approach, we derive a general expression for the four-dimensional (4D) TF correlation function (TFCF) of the proposed channel model. From this expression, we analyze the influence of the MSs' acceleration#x002F;deceleration on the channel's correlation properties. Some simulation examples illustrating our findings are presented for the particular case of the geometrical one-ring scattering model. The proposed channel model can be used as a reference to study the performance of emerging vehicular communication systems in safety-threatening scenarios, such as when a MS is forced to break suddenly.

This paper is concerned with the consistency of non-stationary multipath fading channels. We introduce conditions under which a channel model is consistent w.r.t. the average Doppler shift and the Doppler spread. The conditions are applied to two classes of non-stationary channel models. The first class, which is termed Class A, is characterized by channel models based on an integral relationship between the path phases and the associated time-variant Doppler frequencies. The second class of models, called the Class B models, emerges from standard sum-of-cisoids (SOC) models by replacing the time-independent Doppler frequencies by time-dependent Doppler frequencies. It is shown that the Class A models fulfil the consistency conditions, while the Class B models are inconsistent. The majority of existing non- stationary channel models with time-dependent Doppler frequencies fall in the Class B category, meaning that these models suffer from a lack of physical soundness. The importance of the paper comes from the fact that it provides guidelines for the design of consistent and physically reasonable non-stationary channel models.

In mobile-to-mobile (M2M) communication systems, both the transmitter and the receiver are moving with a certain velocity, which is usually assumed to be constant over time. However, in realistic propagation scenarios, the velocity of the mobile stations (MSs) is subject to changes resulting in a non-stationary fading process. In this paper, we develop a non-stationary narrow-band M2M multipath fading channel model, where the transmitter and the receiver experience changes in their velocities and trajectories. For this model, we derive expressions for the local autocorrelation function (ACF), the Wigner-Ville spectrum, the local average Doppler shift, and the local Doppler spread under isotropic scattering conditions. In addition, we investigate the correlation properties of the proposed model assuming non-isotropic scattering around the MSs. By relaxing the standard assumption of constant velocities of the MSs, this paper shows that the local ACF and the Wigner-Ville spectrum differ completely from known expressions derived for wide-sense stationary M2M channel models. Furthermore, it is shown that our model provides consistent results with respect to the Doppler spread. The proposed channel model is useful for the performance analysis of M2M communication systems under non-stationary conditions caused by velocity variations of the MSs.

This paper proposes a new geometry-based channel model for shallow-water ocean environments, in which the ocean bottom can slope gently down/up. The need for developing such an underwater acoustic (UWA) channel model is driven by the fact that the standard assumption of a flat ocean bottom does not hold in many realistic scenarios. Starting from a geometrical model, we develop a stochastic channel model for wideband single-input single-output vehicle-to-vehicle UWA channels using the ray theory assuming smooth ocean surface and bottom. We investigate the effect of the ocean-bottom slope angle on the distribution of the channel envelope, instantaneous channel capacity, temporal autocorrelation function, frequency correlation function, Doppler power spectral density, and the power delay profile. Theoretical and simulation results show that even a relatively small slope angle influences considerably the statistical properties of UWA channels. The validation of the proposed UWA channel model has been performed by fitting its main characteristic quantities (average delay, delay spread, and coherence bandwidth) to measurement data. In comparison with the conventional UWA channel model, which has been developed on the assumption of a flat ocean bottom, it is shown that the proposed UWA channel model enables the modeling of measured channels with higher precision.

This paper concerns the time-frequency analysis of stationary and non-stationary multipath flat fading channels. For the modelling of stationary multipath fading channels, we use a sum-of-cisoids (SOCi) process, while the non-stationary channel is modelled by a sum-of-chirps (SOCh) process that captures the time-variant Doppler effect caused by speed variations of the mobile station. For the time-frequency analysis, we apply the concept of the Wigner distribution. Closed-form solutions are provided for the Wigner distribution of SOCi and SOCh processes. It is shown that the obtained Wigner distributions can be expressed by the sum of an auto-term representing the true Doppler power spectral density (PSD) and an interfering cross-term that does physically not exist. A simple method is proposed to eliminate the interfering cross-term. The proposed method allows tracing the instantaneous Doppler frequencies of multipath fading channels in non-stationary propagation environments, which is an important topic in mobile radio channel modelling.

When modelling, analysing, and simulating mobile radio channels, it is generally assumed that the speed of the mobile station (MS) is constant. In practice, however, the mobile speed varies with time. Mobile speed variations result in nonwide- sense stationary multipath fading channels, which can be modelled by a sum-of-chirps (SOCh) processes. In this paper, we analyse the local Doppler power spectral density (PSD) of SOCh processes by using the concept of the spectrogram. The spectrogram provides an estimate of the local Doppler PSD and gives insight into how the Doppler PSD changes over time if the MS increases or decreases its speed. A closed-form solution is presented for the spectrogram of SOCh processes, which includes the spectrogram of sum-of-cisoids (SOCi) processes as a special case if the MS moves with constant speed. The results of this paper contribute to the modelling, analysis, and simulation of non-stationary mobile radio channels and provide the basis for the performance analysis of mobile communication systems under non- stationary conditions caused by mobile speed variations.

In the first part of our paper, we have proposed a highly flexible trajectory model based on the primitives of Brownian fields (BFs). In this second part, we study the statistical properties of that trajectory model in depth. These properties include the autocorrelation function (ACF), mean, and the variance of the path along each axis. We also derive the distribution of the angle-of-motion (AOM) process, the incremental traveling length process, and the overall traveling length. It is shown that the path process is in general non-stationary. We show that the AOM and the incremental traveling length processes can be modeled by the phase and the envelope of a complex Gaussian process with nonidentical means and variances of the quadrature components. In accordance with empirical studies, we prove that the AOM process does not follow the uniform distribution. As special cases, we show that the incremental traveling length process follows the Rice and Nakagami-q distributions, whereas the overall traveling path can be modeled by a random variable following either the Gaussian or the lognormal distribution. The flexibility of the results is demonstrated and discussed extensively. It is shown that the results are in line with those of real-world user tracings. The results can be used in many areas of wireless communications.

This paper deals mainly with the study of the asymptotic probability density functions (PDFs) of the outage durations of the instantaneous capacity of orthogonal space-time block code (OSTBC) multiple-input multiple-output (MIMO) systems over Rayleigh channels. Drawing upon known statistical properties for the asymptotic behavior of chi-squared processes at low levels, we provide approximate solutions for the PDF, the cumulative distribution function (CDF), and the kth-order moments of the outage intervals of the underlying capacity processes. Then, as an application of the derived PDF, the performance assessment of capacity simulators is reported. Following this, we introduce the newly defined average-to-trough capacity ratio (ATCR) metric, and investigate its PDF and CDF. The validity of the derived results is confirmed by specializing them to already known ones, although they have been obtained by using a rather different approach. The accuracy and applicability of the asymptotic analysis to practical values of capacity thresholds have been examined by means of computer simulations. The theoretical results presented contribute to the statistical characterization of outage events, the study of which has mainly been limited to the analysis of the probability, the occurrence rate, and the average duration of outages.

In this paper, the outage statistics are studied for non-isotropic Beckmann fading channel model. Non-isotropic scattering generally results in an asymmetrical Doppler power spectral density (PSD). In this context, an expression for the outage probability (OP) (or equivalently the cumulative distribution function (CDF)) of the fading envelope is first derived. Then, the probability density function (PDF) of the rate of change of the fading envelope is investigated. Thereafter, an expression for the average rate of outages (ARO) (or equivalently the level-crossing rate (LCR)) is provided. Finally, by making use of the analytical results of the ARO and OP, an expression for the average duration of outages (ADO) (or equivalently the average duration of fades (ADF)) is attained. The obtained results, which are given in the form of finite-range integrals that can efficiently be computed numerically, are verified to include a variety of already known expressions for models that are special cases of the Beckmann model. Numerical and simulation results are provided to verify the validity of the derivations and to analyze the effect of the fading parameters on the obtained metrics.

In this paper, we present a geometrical scattering model for a typical class of industrial indoor environments. The proposed industrial reference model takes into account scattering components arising from metallic structures and the surrounding walls of the investigated environment. Starting from the geometrical scattering model, we derive the analytical expressions of the probability density function (PDF) of the angle of arrival (AoA), PDF of the time of arrival (ToA), and the autocorrelation function (ACF) in the frequency domain. The obtained results reveal a large difference between industrial channels and other home and office environments. The theoretical results of the reference model are validated by simulation results of a channel simulator designed by employing the sum-of-cisoids (SOC) principle. The proposed channel model is useful for the design and performance evaluation of wireless communication systems operating in industrial environments.

The Doppler effect is caused by the relative movement between the transmitter (Tx) and the receiver (Rx) and/or the surface motion (waves) in underwater acoustic (UWA) communication systems. The inter-channel interference (ICI) caused by the Doppler effect degrades the performance of orthogonal frequency-division multiplexing (OFDM) systems over UWA channels. This paper is devoted to the ICI plus noise analysis of UWA-OFDM systems over a geometry-based channel model for shallow UWA channels. We carry out the exact calculation of the ICI power, ambient noise power, and required transmit power, as well as their effects on the performance of UWA-OFDM systems. The signal-to-interference ratio (SIR) and the signal-to-interference-plus-noise ratio (SINR) performance are analyzed for different relative speeds of the Tx and Rx, signal bandwidths, and carrier frequencies. The results show that the SIR not only depends on the maximum Doppler frequency but also on the signal bandwidth and the transmit power. The ICI power increases if the maximum Doppler frequency or the transmit power increases. If the bandwidth increases, the ICI power decreases, whereas the ambient noise power increases. Based on the simulation results, the system parameters can be optimized for the design of UWA-OFDM systems.

The analysis of the Doppler power spectral density (PSD) of measured and simulated data is an important topic in the area of mobile radio channel modelling. In this paper, we estimate the Doppler PSD of multipath fading channels by using the concept of the spectrogram. The spectrogram is a spectral representation that gives insight into how the distribution of the spectral density of a signal changes over time. The multipath fading channel is modelled by a sum-of-cisoids (SOC) process. A closed-form solution is presented for the spectrogram and the corresponding time-dependent autocorrelation function (ACF). The closed-form solutions disclose several unwanted effects that come with the limited sample space. One phenomenon is that the spectrogram changes with time, even if the underlying SOC process is ergodic. Another phenomenon is that the bandwidth of the spectrogram is not limited to the physical range determined by the maximum Doppler shift. These two phenomena can lead to misinterpretations of the spectrogram. Measures are discussed to reduce these effects. The results of this paper are important for the performance assessment of channel simulators as well as for the evaluation of measurement data collected in all kinds of mobile radio channels.

In this paper, we investigate the second-order statistics of Hoyt fading channels under non isotropic scattering scenarios. Assuming an asymmetrical Doppler power spectral density (PSD), we derive, in the form of single finite-range integrals, expressions for the level-crossing rate (LCR) and average duration of fades (ADF). These new results are then applied to obtain the LCR and ADF of selection combining (SC) diversity over non-isotropic Hoyt channels. In addition to their importance for studying the system performance and characterizing the dynamic behavior of multipath fading channels, the formulas derived are general in that they can be applied to many non-isotropic scattering situations. Furthermore, they are shown to unify some existing results for Rayleigh and Hoyt channels. The validity of the analytical expressions is verified by means of computer simulations where a mobile-to-mobile (M2M) propagation scenario is considered in which the angle of departure (AOD) and angle of arrival (AOA) of multipath components are both described by the von Mises distribution.

This paper studies approximate solutions for the statistical properties of the outage intervals of the instantaneous capacity in massive multiple- input multiple- output (MIMO) sys- tems with orthogonal space-time block code (OSTBC) over Rayleigh fading channels. We take advantage from the fact that the probability density function (PDF) of the channel power gain can be approximated by a left-truncated Gaussian distribution if the number of transmit and receive antennas is large. Assuming a symmetrical Doppler power spectral density (PSD), a closed- form expression is presented for the Rice probability function of the outage durations. This function, in general, approximates the PDF of the outage intervals only over its initial part. By applying the asymptotic behavior of level crossings of Gaussian processes, an alternative expression, valid only for low capacity thresholds, is obtained, which, in turn, is applied to determine an approximate solution for the kth-order moments of the outage intervals. Also presented is the PDF of the so- called instantaneous capacity loss with respect to the average capacity. Simulation results have been shown to be in good agreement with the theoretical approximations, thereby confirming their validity. Although, the focus of the study is on massive MIMO systems, it has been observed that the approximations are accurate even for a moderate number of antennas such as the case of 4×4 MIMO-OSTBC systems.

A fundamental drawback of synthetic mobility models is that the spatial configuration of the path is determined by the temporal features of the mobile station (MS), such as its speed. This is, however, not true in reality. This first part of our paper establishes a new approach for generating fully spatial random trajectory (mobility) models to which different speed scenarios can be applied. We employ the new approach to the proposal of a highly flexible trajectory model based on the primitives (integrals) of Brownian fields (BFs). We construct a drifted partial random bridge from a given starting point to a random terminating point in the 2D plane. If the bridge is partially established, a target zone with a predefined radius and center can be reached via random paths. If the bridge is fully established, a certain destination point can be achieved by means of random bridges. For the broken bridge, completely random terminating points are obtained. The smoothness of the path can be controlled by the primitives of the employed BF. The implementation aspects of the path model in simulation environments are discussed. In wireless communications, the model can be used for tracking (estimating) the location of the MS, performance analysis of mobile ad hoc networks, and channel modeling under non-stationary conditions.

The purpose of this paper is to contribute to the performance assessment of channel capacity simulators. Here, we consider the instantaneous capacity (also referred to as the mutual information) in orthogonal space-time block code (OSTBC) transceiver systems over multiple-input multiple-output (MIMO) Rayleigh fading channels. To ensure that the level-crossing rate (LCR) of the instantaneous capacity can efficiently and accurately be simulated, we derive closed-form approximate solutions to the optimal sampling period and the required number of samples to be generated. Several numerical examples will be presented to illustrate the usefulness of our procedure. It will also be shown that the distribution of the duration of the capacity outage intervals is more sensitive to the variation of the sampling period than the LCR. The presented results are important for the confirmation by simulation of the correctness of theoretical derivations of the instantaneous channel capacity's LCR.

This paper studies the statistical properties of selective combining (SC) diversity schemes over double Nakagami-m fading channels. It is assumed that all diversity branches follow independent and identically distributed (i.i.d.) double Nakagami-m fading processes, where the serial concatenated Nakagami-m processes making up the double Nakagami-m fading branches are assumed to be independent, but not necessarily identically distributed. Starting from already known statistics on double Nakagami-m processes, analytical expressions are derived for the cumulative distribution function (CDF), probability distribution function (PDF), level- crossing rate (LCR), and average duration of fades (ADF) of SC diversity schemes. A general expression is derived for the moments of the instantaneous signal-to-noise ratio (SNR). By using the general expression, we study the mean SNR, amount of fading (AoF), and the diversity gain. The derived expressions include also the corresponding results for double Rayleigh, double one-sided Gaussian, and one-sided Gaussian×Rayleigh channels as special cases. A good agreement is observed between theory and simulation, which confirms the validity of the obtained analytical expressions.

In this paper, we present a new version of the iterative nonlinear least square approximation (INLSA) algorithm for the design of measurement-based channel simulators. The proposed method aims to match the time-variant impulse response (TVIR) of the simulation model to that of the measured channel. The propagation delays are discerned directly from the measurements, whereas the gains, the Doppler frequencies, and the phases are computed iteratively by minimizing a matching error norm. We evaluate the performance of the proposed method in terms of the approximation of the transfer function and correlation properties of the measured channel. We demonstrate how the resulting channel simulator can be deployed for a more reliable estimation of the channel statistics. The obtained results indicate that the proposed method allows a precise emulation of the measured channel impulse response. Its remarkable performance and simplicity makes the proposed method a powerful tool for designing realistic channel models.

A standard assumption in mobile fading channel modelling is that the mobile station (MS) moves along a straight line with constant speed. In practice, this assumption is violated in most propagation scenarios. For the development of more realistic channel models, it is therefore important to relax this restriction by allowing the MS to change its velocity. In this paper, we study the effect of velocity changes on the statistical properties of multipath fading channels. Expressions will be derived for the local autocorrelation function (ACF), the Wigner-Ville spectrum, the average Doppler shift, and the Doppler spread. Our findings show that a variation of the speed and/or the direction of the MS results in a non-stationary channel model. The Wigner-Ville spectrum cannot be interpreted physically as a generalized Jakes (Clarke) power spectral density (PSD); although it includes the latter one for the special case that the MS moves with constant velocity.

In this paper, we study the performance of hybrid automatic repeat request (HARQ) with incremental redundancy over double Rayleigh channels, a common model for the fading amplitude of vehicle-to-vehicle communication systems. We investigate the performance of HARQ from an information theoretic perspective. Analytical expressions are derived for the e-outage capacity, the average number of transmissions, and the average transmission rate of HARQ with incremental redundancy assuming a maximum number of HARQ rounds. Moreover, we evaluate the delay experienced by Poisson arriving packets for HARQ with incremental redundancy. We provide analytical expressions for the expected waiting time, the packet's sojourn time in the queue, the average consumed power, and the energy efficiency. In our study, the communication rate per HARQ round is adjusted to the average signal-to-noise ratio (SNR) such that a target outage probability is not exceeded. This setting conforms with communication systems in which a quality of service is expected regardless of the channel conditions. Our analysis underscores the importance of HARQ in improving the spectral efficiency and reliability of communication systems. We demonstrate as well that the explored HARQ scheme achieves full diversity. Additionally, we investigate the tradeoff between energy efficiency and spectral efficiency.

In this paper, we present a wideband single-input single-output (SISO) car-to-car (C2C) channel model based on a geometrical semicircular tunnel (SCT) scattering model. Starting from the geometrical scattering model, a reference channel model is derived under the assumption of single-bounce scattering in line-of-sight (LOS) and non-LOS (NLOS) propagation environments. In the proposed channel model, it is assumed that an infinite number of scatterers are uniformly distributed on the tunnel wall. Starting from the geometrical scattering model, the time-variant transfer function (TVTF) is derived and its correlation properties are studied. Expressions are presented for the two-dimensional (2D) time-frequency correlation function (TFCF), the temporal autocorrelation function (ACF), and the frequency correlation function (FCF). Owing to the semicircular geometry, we reduced the originally threefold integrals to double integrals in computations of the correlation functions, which are easy to solve numerically. From the TVTF characterizing the reference model, an efficient sum-of-cisoids (SOC) channel simulator is derived. Numerical results show that both the temporal ACF and the FCF of the SOC channel simulator match very well with those of the reference model.

A sparse multipath channel is characterized by a small number of randomly distributed scatterers. This study proposes a methodology for the modelling of sparse multipath channels. The new methodology is then used to develop a sparse narrowband multipath channel model by applying the sum-of-cisoids (SOC) principle. The statistical properties of the presented sparse SOC multipath channel model are studied. Analytical expressions are derived for the mean value, variance, autocorrelation function (ACF) and cross-correlation function (CCF) of the complex channel gain, as well as for the probability density function (PDF) of the envelope. Our study shows that mobile radio channels behave in sparse scattering environments completely different from what is known from innumerable studies assuming rich scattering. The derived analytical expressions unfold their full significance if the number of multipath components is small and the path gains are unbalanced, which prevents invoking the central limit theorem.

This paper deals with the study of asymptotic probability density functions (PDFs) of the outage durations of the instantaneous capacity (also referred to as the mutual information) in orthogonal space-time block code (OSTBC) transceiver systems over multiple-input multiple-output (MIMO) Rayleigh fading channels. The Rayleigh fading subchannels are assumed to be frequency-nonselective and mutually uncorrelated, whereas the associated Doppler power spectral density is supposed to be symmetric about the origin. In addition, the channel state information (CSI) is considered to be available only at the receiver side. Taking these assumptions into account, and drawing upon known statistical properties for the asymptotic behavior of chi-square processes at low levels, we provide a closed-form approximate solution for the PDF of the outage intervals of the underlying capacity processes. Furthermore, an analytical expression is also provided for the kth-order moments of the outage intervals. These statistical quantities will as well be shown to be useful for studying the statistics of the capacity outage durations of single-input multiple-output (SIMO) and multiple-input single-output (MISO) systems. The validity of the obtained approximate asymptotic solutions has been confirmed by means of computer simulations.

This paper introduces a non-stationary one-ring scattering model in which the mobile station (MS) can move along a straight line from the ring's center to the border of the ring. This movement results in a time-variant angle-of-arrival (AOA), which is modeled by a stochastic process. We derive the first-order density of the AOA process in closed form. Subsequently, a closed-form expression is provided for the local power spectral density (PSD) of the channel. We also formulate the local autocorrelation function (ACF) of the complex channel gain in integral form, from which a highly accurate closed-form approximation is derived. Furthermore, the average Doppler shift and the Doppler spread of the channel are computed. The analytical results are illustrated and physically explained. It is shown that non-stationarity in time contradicts the common isotropic scattering assumption. The merit of this study is to open a new window to the performance analysis of mobile communication systems under non-stationary channel conditions.

ABSTRACT We present in this paper a generalized version of the method of equal areas (MEA) that is well suited for the design of sum‐of‐cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels characterized by any type of Doppler power spectral densities (DPSDs). Unlike the original MEA, the generalized MEA (GMEA) can be applied to the simulation of fading channels with asymmetrical DPSDs. This is an important feature because the simulation of such channels is of great interest for the laboratory analysis of mobile communication systems under non‐isotropic scattering conditions. We show that irrespective of the underlying DPSD, the GMEA results in a very good approximation to the autocorrelation function, average Doppler shift, Doppler spread, and envelope distribution of the channel. We compare the performance of the GMEA with that of the Lp‐norm method (LPNM), which is the method that has been most widely used for designing SOC simulators for fading channels with arbitrary DPSDs. The obtained results demonstrate that the performance of the GMEA measures up to that of the LPNM. In addition, the results show that the determination of the model parameters is easier and less time‐consuming when applying the GMEA. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, we derive a vehicle-to-vehicle~(V2V) channel model assuming a typical propagation scenario in which the local scatterers move with random velocities in random directions. The complex channel gain of the proposed V2V channel model is provided. Subsequently, for different scatterer velocity distributions, the corresponding autocorrelation functions~(ACFs) are derived, illustrated, and compared with the classical ACF derived under the assumption of fixed scatterers. Furthermore, under specific conditions, highly accurate approximations for the ACFs are provided in closed form. Since the proposed V2V channel model covers several communication scenarios as special cases, including fixed-to-vehicle~(F2V) and fixed-to-fixed~(F2F) scenarios in the presence of both fixed and moving scatterers, it is obvious that the presented results are important for the designers of cutting-edge vehicular communication systems.

For time-invariant frequency-selective channels, the transfer function is a superposition of waves having different propagation delays and path gains. In order to estimate the frequency correlation function (FCF) of such channels, the frequency averaging technique can be utilized. The obtained FCF can be expressed as a sum of auto-terms (ATs) and cross-terms (CTs). The ATs are caused by the autocorrelation of individual path components. The CTs are due to the cross-correlation of different path components. These CTs have no physical meaning and leads to an estimation error. We propose a new estimation method aiming to improve the estimation accuracy of the FCF of a band-limited transfer function. The basic idea behind the proposed method is to introduce a kernel function aiming to reduce the CT effect, while preserving the ATs. In this way, we can improve the estimation of the FCF. The performance of the proposed method and the frequency averaging technique is analyzed using a synthetically generated transfer function. We show that the proposed method is more accurate than the frequency averaging technique. The accurate estimation of the FCF is crucial for the system design. In fact, we can determine the coherence bandwidth from the FCF. The exact knowledge of the coherence bandwidth is beneficial in both the design as well as optimization of frequency interleaving and pilot arrangement schemes.

In this paper, we study the performance of hybrid automatic repeat request (HARQ) with code combining (CC) over double Rayleigh channels. This channel can be utilized to model the fading envelope of vehicle-to-vehicle (V2V) channels. We derive analytical solutions for the characteristic quantities of double Rayleigh channels, such as the outage probability, the ergodic capacity, and the bit error probability (BEP). Moreover, we study the performance of HARQ with CC. Our analysis focuses on information theoretic aspects of HARQ with CC. closed-form analytical approximations are derived for the ε-outage capacity, the average number of transmissions, and the average transmission rate of HARQ with CC assuming a maximum number of rounds M for the HARQ protocol. In our study, the communication rate per HARQ round is adjusted to the average signal-to-noise ratio (SNR) such that a target outage probability ε is not exceeded. This setting is conform with modern communication systems, in which a quality of service should be ensured independently of the channel conditions. We demonstrate that HARQ with CC allows to communicate at a rate close to the ergodic capacity, especially at low and medium SNR. This rate is achieved in absence of channel state information (CSI) at the transmitter. This feature makes HARQ very attractive for V2V communications. In fact, in V2V channels, the coherence time is too short to allow for feedback of the instantaneous channel conditions from the receiver to the transmitter.

In this paper, we study the performance of hybrid automatic repeat request (HARQ) with incremental redundancy (IR) over double Rayleigh channels. Such channels can be used to model the fading amplitude for vehicle-to-vehicle (V2V) communications. We study the performance of HARQ from an information theoretic perspective. Analytical expressions are derived for the e-outage capacity, the average number of trans missions, and the average transmission rate for HARQ with IR, assuming a maximum number of rounds for the HARQ protocol. In our study, the communication rate per HARQ round is adjusted to the average signal-to-noise ratio (SNR) such that a target outage probability is not exceeded. This setting conforms with communication systems in which a quality of service is expected regardless of the channel conditions. It is well known that the ergodic capacity is achievable only if the power is adapted to the channel conditions, which requires channel state information (CSI) at the transmitter. We demonstrate that HARQ allows to communicate at a rate close to the ergodic capacity even in absence of CSI at the transmitter. Our analysis underscores the importance of HARQ in improving the spectral efficiency and reliability of communication systems.

In this paper, we derive a non-stationary multiple-input multiple-output (MIMO) vehicle-to-vehicle (V2V) channel model from the geometrical street model. Single-bounce scattering is assumed for both fixed and moving scatterers. The high mobility of the transmitter, the receiver, and the surrounding vehicles results in time-variant angles-of-departure (AODs) and angles-of-arrival (AOAs). This fact makes the model non-stationary. Starting from the geometrical model, an analytical expression is derived for the channel gain taking into account the impact of fixed and moving scatterers. The statistical properties of the proposed channel model are studied. Analytical solutions are provided for the generalized local autocorrelation function (ACF), the generalized local power spectral density (PSD), and the local space cross-correlation function (CCF). Moreover, we illustrate the cumulative distribution function (CDF) of the stationarity interval. The proposed channel model is useful for the design and analysis of future MIMO V2V communication systems operating in non-stationary propagation conditions.

Time averaging is a well-known technique for evaluating the temporal autocorrelation function (ACF) from a sample function of a stochastic process. For stochastic processes that can be modelled as a sum of plane waves, it is shown that the ACF obtained by time averaging can be expressed as a sum of auto-terms (ATs) and cross-terms (CTs). The ATs result from the autocorrelation of the individual plane waves, while the CTs are due to the cross-correlation between different plane wave components. The CTs cause an estimation error of the ACF. This estimation error increases as the observation time decreases. For the practically important case that the observation time interval is limited, we propose a new improved method for estimating the time ACF of a sum of plane waves. The main idea behind the proposed method is to introduce a kernel function aiming to reduce the CT effect, while preserving the ATs. In this way, we can improve the estimation of the ACF. We show that the proposed method outperforms the standard time averaging technique. The performance of both methods is evaluated using a synthetic channel model consisting of a sum of complex plane waves.

This article deals with the statistical analysis of equal gain combining (EGC) over mobile-to-mobile (M2M) fading channels in a dual-hop amplify-and-forward relay network. Here, we analyze narrowband M2M fading channels under nonline-of-sight (NLOS) propagation conditions. It is assumed that there exist K diversity branches between the source mobile station and the destination mobile station via K mobile relays. The received signal envelope at the output of the equal gain (EG) combiner is thus modeled as a sum of K double Rayleigh processes. It has been shown that the evaluation of the probability density function (PDF) of this sum process using the characteristic function (CF) is rather intractable. However, the target PDF can efficiently be approximated by the gamma distribution. Exploiting the properties of the gamma distribution, the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the sum process are also approximated. The approximation of the mentioned sum process by a gamma distributed process makes it possible to provide simple and closed-form analytical expressions for the aforementioned statistical quantities. The validity of the obtained analytical expressions is confirmed by simulations. The presented results can easily be utilized in the performance analysis of EGC over relay-based M2M fading channels.

In this article, the performance of M-ary phase shift keying (PSK) modulation schemes over mobile-to-mobile (M2M) fading channels with equal gain combining (EGC) in cooperative networks is analyzed. Narrowband M2M fading channels under line-of-sight (LOS) propagation conditions are modeled as double Rice processes. A dual-hop amplify-and-forward relay network, where LOS components can exist in the transmission links between the source mobile station and the destination mobile station via K mobile relays, is studied. Here, the average bit error probability (BEP) is utilized to evaluate the performance of Mary PSK modulation schemes. A simple analytical approximation for the average BEP of M-ary PSK modulations over relay-based M2M fading channels with EGC is derived. The accuracy of the approximation is assessed by simulations. The presented results show that in a dual-hop relay system with EGC, the presence of LOS components in the relay links improves the systems' performance. In addition, a significant enhancement in the diversity gain can be achieved as the number of diversity branches K increases.

This paper deals with the design and simulation of narrowband indoor propagation channels under line-of-sight (LOS) and non-LOS (NLOS) propagation conditions. We propose a reference channel model assuming that the scatterers are uniformly distributed in the two-dimensional (2D) horizontal space of a room. We derive analytical expressions for the probability density function (PDF) of the angle-of-arrival (AOA), the Doppler power spectral density (PSD), and the temporal autocorrelation function (ACF). We derive a sum-of-cisoids (SOC) channel simulator from the reference model. It is shown by numerical results that the statistical properties of the SOC channel simulator match very closely with the ones of the reference model. It turns out that our indoor reference model can be approximated by an SOC channel simulator with reduced realization expenditure. The resulting SOC channel simulator allows us to evaluate the performance of mobile communication systems in indoor environments by simulations. It is demonstrated that the generalized method of equal areas (GMEA) and the basic Riemann sum method (BRSM) are efficient parameter computation methods for the design of SOC indoor channel simulators.

This paper deals with the performance analysis of Alamouti coded orthogonal frequency division multiplexing (OFDM) systems over time-varying multipath Rayleigh fading channels. In our analysis, we consider a physically more realistic channel, which can be correlated either in time or in space or even in both domains. We derive an analytical expression for the bit error probability (BEP), which describes the performance of an Alamouti coded OFDM system over fading channels correlated in space and time. It is shown that the derived BEP can be reduced to the known BEP obtained over fading channels correlated in time or space. The correctness of all theoretical results is validated by system simulations. The knowledge of the obtained theoretical results makes the BEP evaluation more straightforward and less time-consuming compared to simulations. Moreover, it allows us to discuss the effect of the maximum Doppler frequency and the antenna spacing on the system performance.

In this article, we present a detailed study on the statistical properties of the channel capacity of vehicle-to-vehicle (V2V) fading channels with equal gain combining (EGC). Assuming perfect channel state information (CSI) at the receiver, we have modeled the received signal envelope at the output of the equal gain (EG) combiner as a sum of double Rayleigh processes. These double Rayleigh processes are assumed to be independent but not necessarily identical processes. It is illustrated that the probability density function (PDF) of this sum process can efficiently be approximated using the gamma distribution. Furthermore, exploiting the properties of the gamma distribution, other statistical properties of the sum process are also evaluated. Thus, given the analytical approximations for the statistical properties of the received signal envelope at the output of the EG combiner, the theoretical results associated the statistics of the channel capacity just involves transformation of random variables. Here, simple and closed-form analytical approximations for the PDF, the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the channel capacity are derived. The correctness of the theoretical results is validated by simulations. The presented results can be utilized to optimize the performance of spatial diversity receivers employed in the forthcoming V2V multiple-input multiple-output (MIMO) wireless communication systems.

This article analyzes the statistical properties of narrowband mobile-to-mobile (M2M) fading channels with equal gain combining (EGC) under line-of-sight (LOS) propagation conditions. Here, we study a dual-hop amplify-and-forward (AF)relay network. It is assumed that there can exist LOS components in the transmission links between the source mobile station and the destination mobile station via K mobile relays. In order to cater for asymmetric fading conditions in the relay links, the received signal envelope at the output of the equal gain (EG) combiner is thus modeled as a sum of K double Rice processes. These processes are considered to be independent but not necessarily identically distributed. Simple and closed-form analytical approximations are derived for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the sum process by exploiting the properties of gamma processes. The correctness of the derived analytical approximations is verified by simulations. The presented results are easily utilizable in the system performance analysis and optimization of relay-based cooperative networks, where EGC is deployed at the destination mobile station.

This paper analyzes the performance of space-time block coded orthogonal frequency division multiplexing (OFDM) systems. In our analysis, we abandon the usually made assumption of quasi-static channel conditions. Instead of this, we consider the more general and realistic case that the channel envelope changes during two consecutive transmission time slots. In addition, we take the spatial correlation between sub-channels into account. We first present a general formal expression for the bit error probability (BEP), from which we find analytical solutions for the BEP not only for temporally fading channels but also for spatially correlated channels. The knowledge of the obtained analytical solutions makes the determination of the BEP less time-consuming compared with system simulations. Moreover, they give a deep insight into the impact of the Doppler effect and the antenna spacing on the system performance.

In this letter, we introduce the Riemann sum method (RSM) as an effective tool for the design of sum-of-cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels under non-isotropic scattering conditions. We compare the performance of the RSM with that of the generalized method of equal areas (GMEA) and the Lp-norm method (LPNM), which were until now the only methods available for the design of SOC simulators for non-isotropic scattering channels. The obtained results indicate that the RSM is better suited than the GMEA and the LPNM to emulate the channel's autocorrelation function (ACF), whereas the latter two methods are more precise regarding the approximation of the envelope distribution. The results also show that the benefits of increasing the number of cisoids are more significant in the case of the RSM than in the case of the GMEA and LPNM. Owing to its simplicity and good performance, the RSM can be used to design flexible simulation platforms for the laboratory analysis of mobile communication systems operating in non-isotropic scattering environments.

Abstract In this paper, we extend the geometrical one‐ring multiple‐input multiple‐output (MIMO) channel model with respect to frequency selectivity. Our approach enables the design of efficient and accurate simulation models for wideband space‐time MIMO channels under isotropic scattering conditions. Two methods will be provided to compute the parameters of the simulation model. Especially, the temporal, frequency and spatial correlation properties of the proposed wideband space‐time MIMO channel simulator are studied analytically. It is shown that any given specified or measured discrete power delay profile (PDP) can be incorporated into the simulation model. The high accuracy of the simulation model is demonstrated by comparing its statistical properties with those of the underlying reference model with specified correlation properties in the time, frequency and spatial domain. As an application example of the new MIMO frequency‐selective fading channel model, we study the influence of various channel model parameters on the system performance of a space‐time coded orthogonal frequency division multiplexing (OFDM) system. For example, we investigate the influence of the antenna element spacings of the base station (BS) antenna as well as the mobile station (MS) antenna. It turns out that an increasing of the antenna element spacing at the BS side results in a higher diversity gain than an increasing of the antenna element spacing at the MS side. Furthermore, the diversity gain brought in by space‐time block coding schemes is investigated by simulation. Our results show that transmitter diversity can significantly reduce the symbol error rate (SER) of multiple antenna systems. Finally, the influence of the Doppler effect and the impact of imperfect channel state information (CSI) on the system performance is also investigated. Copyright © 2009 John Wiley & Sons, Ltd.

In this paper, we propose a method for designing measurement-based stochastic models for simulating wideband multiple-input multiple-output (MIMO) wireless channels. The proposed method allows synthesizing channel transfer functions with the spatial-temporal-frequency correlation properties approximating those of real-world radio channels. The parameters of a channel simulator are determined by fitting the space-time-frequency cross-correlation matrix of the simulation model to the estimated space-time-frequency cross-correlation matrix of a physical channel. For this purpose, an iterative parameter computation algorithm has been developed. The proposed design method is verified by creating stochastic channel simulators based on the time-variant frequency responses (TVFRs) of real-world channels measured in different propagation environments.

In this article, we propose a new test to determine the intervals of stationarity for wireless communication channels. The intervals of stationarity are identified by comparing the delay power spectral density (PSD) estimated at different time instances. The performance of the proposed stationarity test has been evaluated based on the synthetic data generated using a channel simulator. The analysis of the stationarity intervals for two radio communication channels measured in different propagation scenarios reveals that the number and the length of the stationarity intervals decrease as the dimensions of the channel matrix increase.

This paper investigates the effects of channel estimation errors on the symbol-error-rate (SER) performance of a cooperative communication system operating in an amplify-and- forward (AF) mode. A pilot symbol assisted modulation scheme with linear minimum mean square estimation (LMMSE) is used for the channel estimation. An accurate and easy-to-evaluate SER expression is presented for uncoded cooperative communication systems with quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations. Numerical simulations are conducted to verify the correctness of the proposed analytical formulation. It is shown that the performance loss caused by channel estimation errors increases mainly with the normalized maximum Doppler frequency.

It is well known that a frequency-nonselective multipath fading channel can be modeled by a sum of complex sinusoids, also called sum-of-cisoids (SOC). By using the SOC, we can efficiently model the scattered component of the received signal in non-isotropic scattering environments. Such SOC-based multipath channel models provide the flexibility of having correlated in-phase and quadrature phase components of the received signal. This paper presents the derivation and analysis of the statistical properties of the capacity of multipath fading channels under LOS conditions. As an appropriate stochastic model for the multipath fading channel, we have adopted the SOC model. We have derived the exact analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity. The statistical behavior of the channel capacity is studied for different values of the number of multipaths (cisoids) in the SOC model and the results are compared with the reference model which can be obtained by using an infinite number of cisoids. It is shown that the SOC model with ten cisoids produces results very close to the reference model. The validity of all the theoretical expressions is tested with the help of simulations.

In this paper, we study the impact of fixed and moving clusters of scatterers on the statistics of multiple- input multiple-output (MIMO) vehicle-to-vehicle (V2V) channels. Double-bounce scattering is assumed for fixed scatterers, while single-bounce scattering is considered for moving scatterers. Starting from the geometrical street model, an analytical expression is derived for the channel gain taking into account the contributions of fixed and moving scatterers in a multiple-cluster scattering scenario. The statistical properties of the proposed channel model are studied. Analytical solutions are provided for the three-dimensional (3D) space-time cross-correlation function (CCF), the 2D space CCF, and the temporal autocorrelation function (ACF). All theoretical results are validated by simulations.

In this paper, we analyze the performance of a wideband sum-of-cisoids (SOC) channel simulator w.r.t. the bit error probability (BEP) of differential phase-shift keying (DPSK) orthogonal frequency division multiplexing (OFDM) systems. Analytical BEP expressions are derived for coherent and noncoherent DPSK OFDM simulation systems in the presence of a wideband SOC channel simulator. We also study the degradations of the BEP introduced by an imperfect channel simulator. Using the deviation of the BEP as an appropriate measure, we evaluate the performance of three parameter computation methods, known as the method of exact Doppler spread (MEDS), the randomized MEDS (R-MEDS), and the Monte Carlo method (MCM). For coherent DPSK OFDM systems, it turns out that these three methods are equivalent. For noncoherent DPSK OFDM systems, it is theoretically shown that both the MEDS and the R-MEDS outperform the MCM. The correctness of all theoretical results are validated by simulations.

This paper deals with the analysis of statistical properties of the capacity of spatially uncorrelated orthogonal space-time block coded (OSTBC) Nakagami-m multiple-input multiple-output (MIMO) channels. We have derived exact closed-form expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity. We have also investigated the statistical properties of the approximated capacity of spatially correlated OSTBC Nakagami-m MIMO channels. The results are studied for different values of the fading parameter m, corresponding to different fading conditions. It is observed that an increase in the MIMO dimension1 or a decrease in the severity of fading increases the mean channel capacity. While, a significant decrease in the mean channel capacity is observed with an increase in the spatial correlation. The correctness of theoretical results is confirmed by simulations.

This paper deals with the modeling and analysis of narrowband multiple-input multiple-output (MIMO) mobile-to-mobile (M2M) fading channels in relay-based cooperative networks. Non-line-of-sight (NLOS) propagation conditions are assumed in the transmission links from the source mobile station to the destination mobile station via the mobile relay. A stochastic narrowband MIMO M2M reference channel model is derived from the geometrical three-ring scattering model, where it is assumed that an infinite number of local scatterers surround the source mobile station, the mobile relay, and the destination mobile station. The complex channel gains associated with the new reference channel model are derived and their temporal as well as spatial correlation properties are explored. General analytical solutions are presented for the four-dimensional (4-D) space-time cross-correlation function (CCF), the three-dimensional spatial CCF, the two-dimensional (2-D) transmit (relay, receive) correlation function (CF), and the temporal autocorrelation function (ACF). Closed-formed expressions for different CCFs under isotropic scattering conditions are also provided in this paper. The proposed reference channel model can be used as a starting point to develop stochastic and deterministic channel simulators. Such channel simulators are not only important for analyzing the dynamic behavior of the MIMO M2M channel capacity but also for the development of future MIMO M2M cooperative communication systems.

A new method is proposed for estimating the velocity of wideband mobile stations (MSs) equipped with multiple antennas. The MS speed is determined using the well-known relationship between the direction-of-arrivals (DOAs) and the Doppler frequency shifts experienced by the multipath signal components. The method is based on the assumption that the multipath signal components with the DOAs confined to a small angular interval are clustered in the delay domain. Additionally, we assume that different intervals of the DOAs correspond to different intervals of the propagation delays. The performance of the proposed method is assessed by simulations. The algorithm has a low computational cost and is therefore suitable for realtime implementations.

Cooperative diversity is a promising technology for future wireless networks. In this paper, we consider a cooperative communication system operating in an amplify-and-forward (AF) mode with an imperfectly-known relay fading channel. It is assumed that a pilot symbol assisted modulation (PSAM) scheme with linear minimum mean square estimator (LMMSE) is used for the channel estimation. A simple and easy-to-evaluate asymptotical upper bound (AUB) of the symbol-error-rate (SER) is derived for uncoded AF cooperative systems with quadrature amplitude modulation (QAM) constellations. Based on the AUB, we propose a criterion for the choice of parameters in the PSAM scheme, i.e., the pilot spacing and the Wiener filter length. We also formulate an optimum power allocation problem for the considered system. The optimum power allocation can be found by means of a gradient search over a continuous range. Numerical simulations are presented to verify the correctness of the theoretical results and the benefits of the parameter optimization.

This paper deals with the design of a set of multiple uncorrelated Rayleigh fading waveforms. The Rayleigh fading waveforms are mutually uncorrelated, but each waveform is correlated in time. The waveforms are generated by using the deterministic sum-of-sinusoids (SOS) channel modeling principle. Two new closed-form solutions are presented for the computation of the model parameters. Analytical and numerical results show that the resulting deterministic SOS-based channel simulator fulfills all main requirements imposed by the reference model with given correlation properties derived under two-dimensional isotropic scattering conditions. The proposed methods are useful for the design of simulation models for diversity-combined Rayleigh fading channels, relay fading channels, frequency-selective channels, and multiple-input multiple-output (MIMO) channels.

Abstract This paper analyzes the validity and statistical behavior of symbol‐spaced tapped‐delay‐line (SSTDL) models for wide‐sense stationary uncorrelated scattering (WSSUS) mobile radio channels. SSTDL models are obtained by sampling the channel impulse response (CIR) in delay domain at a rate equal to the reciprocal of the symbol duration. They were proposed more than four decades ago as canonical channel models for band‐limited time‐variant linear (TVL) systems, and are nowadays widely in use for assessing the performance of several wireless communication systems. The applicability of these tapped‐delay‐line (TDL) models seems to be unquestionable, as they were developed in the framework of the sampling theorem. Nonetheless, we show here that SSTDL models should be used with care to model WSSUS channels, because the channel's uncorrelated scattering (US) condition might easily be violated. Furthermore, we show that SSTDL models suffer from strong limitations in emulating the channel frequency correlation function (FCF). This drawback leads to an inaccurate performance evaluation of wireless communication systems sensitive to the FCF. To cope with this problem, we present a simple solution by doubling the channel's sampling rate. The benefits of this solution are demonstrated with some exemplary simulation results. Copyright © 2008 John Wiley & Sons, Ltd.

This paper deals with the study of the statistical properties of the capacity of Nakagami-lognormal (NLN) channels for various fading environments. Specifically, the impact of shadowing and the severity of fading on the channel capacity is investigated. We have derived analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity. These results are analyzed for different levels of shadowing and for various fading conditions, corresponding to different terrestrial environments. It is observed that the severity of fading and shadowing has a significant influence on the spread and the maximum value of the PDF and LCR of the channel capacity. Moreover, it is also observed that if the fading gets less severe as compared to the Rayleigh fading, the mean channel capacity increases. However, the shadowing effect has no impact on the mean channel capacity. The validity of all analytical results is confirmed by simulations.

This paper studies the fading behavior of mobile- to-mobile (M2M) fading channels in relay-based cooperative networks under line-of-sight (LOS) conditions. Here, we assume that LOS components exist in both the direct link between the source mobile station (SMS) and the destination mobile station (DMS) as well as in the link via the mobile relay (MR). In such a propagation environment, the fading channel is referred to as the multiple-LOS second-order scattering (MLSS) channel. The fading behavior of MLSS channels is studied by analyzing the level-crossing rate (LCR) and the average duration of fades (ADF) of the received envelope. We have derived analytical expressions for the LCR, ADF, and cumulative distribution function (CDF) of the envelope of MLSS channels. It is shown that MLSS channels include various other channel models as special cases, e.g., double Rayleigh channels, double Rice channels, single-LOS double-scattering (SLDS) channels, non-line-of-sight (NLOS) second-order scattering (NLSS) channels, and the single- LOS second-order scattering (SLSS) channels. The correctness of all theoretical results is confirmed by simulations. Our studies regarding the fading behavior of MLSS channels are useful for the development and performance evaluation of relay-based cooperative wireless networks in different M2M propagation environments.

In this work, we propose the multichannel two- dimensional (2D) autoregressive (AR) model for multiple-input multiple-output (MIMO) wideband mobile wireless channels. The parameters of the proposed model can be estimated from the real- world measurement data. For this purpose, we suggest using a straightforward extension of the prediction error minimization (PEM) algorithm. We also address the problem of possible instability of the multichannel 2D AR model. A model stabilization procedure based on numerical optimization techniques is proposed. The performance of the multichannel 2D AR model has been evaluated based on the synthetic data generated using two different channel simulators.

In this paper, we extend the geometrical street multiple-input multiple-output (MIMO) mobile-to-mobile (M2M) channel model with respect to multiple clusters of scatterers as well as to frequency selectivity. The statistical properties of the proposed reference model are studied. Analytical solutions are provided for the three-dimensional (3D) space-time cross-correlation function (CCF), the temporal autocorrelation function (ACF), the 2D space CCF, and the frequency correlation function (FCF). The correlation properties are studied under the assumption of non-isotropic scattering conditions. The proposed reference model can be used as a starting point for the derivation of a wideband MIMO M2M channel simulator. The latter is very useful for the design and analysis of future wideband MIMO M2M communication systems.

Mobile-to-mobile (M2M) fading channels in cooperative networks can efficiently be modeled using the multiple scattering concept. In this paper, we propose a new second-order scattering channel model for M2M fading channels in amplify-and-forward relay links under line-of-sight (LOS) conditions, where the received signal comprises only of the single and double scattered components. In the proposed model, LOS components exist in the direct link between the source mobile station (SMS) and the destination mobile station (DMS) as well as the link via the mobile relay (MR). Analytical expressions are derived for the probability density function (PDF) of the envelope and phase of M2M fading channels. It is shown mathematically that the proposed model includes as special cases double Rayleigh, double Rice, single-LOS double-scattering (SLDS), non-line-of-site (NLOS) second-order scattering (NLSS), and single-LOS second-order scattering (SLSS) processes. The validity of all theoretical results is confirmed by simulations. Our novel M2M channel model is important for the investigation of the overall system performance in different M2M fading environments under LOS conditions.

A finite sum of complex harmonic functions, also known as a sum-of-cisoids (SOC), has been widely applied in the literature for the modeling and simulation of mobile fading channels. In this paper, we focus on the analysis of the stationarity of SOC-based mobile fading channel simulators. An SOC model depends on three kinds of parameters, namely, the gains, the frequencies, and the phases, where each of which can be a collection of random variables or constants. Hence, there exist altogether eight classes of SOC models. Each individual class will systematically be investigated with respect to its stationary properties.

In this paper, we present a wideband one-ring multiple-input multiple-output (MIMO) channel model for non-isotropic scattering environments. The model is designed in such a way that the delay power spectral density (PSD) of the resulting reference channel model is identical to a given delay PSD. Furthermore, we present an efficient deterministic channel simulation model obtained by using the principle of deterministic channel modeling. The statistical properties of both the reference model and the simulation model are also studied. Analytical expressions will be presented for the temporal autocorrelation function (ACF), the two-dimensional (2D) space cross-correlation function (CCF), and the frequency correlation function (FCF). We show that the statistical properties of the deterministic simulation model can be brought into astonishingly good agreement with those of the reference model. The resulting deterministic simulation model enables the performance evaluation of wideband MIMO communication systems by simulation, which is shown exemplarily by studying the system performance of a space-time coded MIMO orthogonal frequency division multiplexing (OFDM) system.

For the modelling and simulation of mobile radio channels, one often uses a sum of complex sinusoids (cisoids). This paper analyses in detail the level-crossing rate (LCR), the average duration of the fades (ADF), and the cumulative distribution function (CDF) of the envelope of a sum-of-cisoids (SOC). For these statistical quantities, exact and simple approximate solutions are derived by taking into account that the inphase and quadrature components of SOC models are generally correlated. The correctness of all theoretical results is confirmed by simulations. The results are not only important for getting a better fundamental understanding of the statistical behaviour of SOC models, but also for the performance evaluation of SOC-based mobile radio channel simulators.

This paper studies the statistical properties of the channel capacity of spatially correlated Nakagami-m multiple- input multiple-output (MIMO) channels. We have derived closed- form expressions for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the lower bound on the channel capacity. In order to study the impact of the spatial correlation on the channel capacity, the analysis of the statistical properties of the channel capacity is carried out for different receiver antenna spacings. It is observed that the antenna spacing has a significant influence on the spread and maximum value of the PDF and LCR. The proposed method can be employed to study the statistical properties of the capacity of MIMO channels in different fading environments. The correctness of the analytical expressions is confirmed by simulations.

In this article, we analyze different ways to estimate the temporal autocorrelation function (TACF) and the frequency correlation function (FCF) of wideband mobile radio channels from real-world channel measurements. The way the TACF and FCF are estimated depends on whether the measured channel is autocorrelation-ergodic with respect to time and/or frequency. In either case, it is shown that double averaging, i.e., averaging of measurement snapshots over time and frequency, improves the estimates of the TACF and FCF. We provide two examples of applying the iterative nonlinear least squares approximation (INLSA) algorithm to determine the parameters of measurement- based channel simulators from the estimated TACF and FCF. The presented examples correspond to real-world outdoor and indoor propagation environments. The distinctive feature of the designed channel simulators is that their temporal and frequency correlation characteristics are sufficiently close to those that have been estimated from the measurement data. For comparison reasons, we also show the corresponding results obtained by applying the well-known subspace-alternating generalized expectation-maximization (SAGE) algorithm.

This paper' deals with the modeling, analysis, and simulation of multiple-input multiple-output (MIMO) narrowband fading channels for mobile-to-mobile communications. A stochastic MIMO mobile-to-mobile reference channel model is derived from the geometrical two-ring scattering model under the assumption that both the transmitter and the receiver are surrounded by an infinite number of local scatterers. Using a wave propagation model, the complex channel gains are derived and their statistical properties are studied. General analytical solutions are provided for the three-dimensional (3-D) space-time cross-correlation function (CCF). We show that this function can be expressed as the product of two 2D space-time cross-correlation function (CFs), called the transmit and receive CF. From the non-realizable reference model, a stochastic and a deterministic simulation model are derived using a double sum of complex exponential functions. It is shown how the parameters of the simulation model can be determined for any given distribution of the angle of departure (AOD) and angle of arrival (AOA). In case of isotropic scattering, we present a closed-form solution for the parameter computation problem and illustrate some numerical results concerning the transmit CF. The proposed procedure provides an important framework for designers of future mobile-to-mobile communication systems to verify new transmission concepts employing MIMO techniques under realistic propagation conditions.

Abstract In this paper, we present a reference model for a wideband multiple‐input multiple‐output (MIMO) channel based on the geometric elliptical scattering model. The model takes into account the exact relationship between the angle of departure (AOD) and the angle of arrival (AOA). Based on this relationship, the statistical properties of the reference model are studied. Analytical solutions are presented for the three‐dimensional (3D) space‐time cross‐correlation function (CCF), the temporal autocorrelation function (ACF), the 2D space CCF, and finally the frequency correlation function (FCF). The correlation properties are studied and visualized under the assumption of isotropic as well as non‐isotropic scattering conditions. The proposed reference model can be used as a starting point for the derivation of a frequency‐selective space‐time MIMO channel simulator enabling the performance evaluation of multi‐antenna wideband communication systems. The reference model is also quite useful for studying the MIMO channel capacity under various propagation conditions imposed by the geometry of the underlying scattering model. Copyright © 2007 John Wiley & Sons, Ltd.

This paper presents a modified version of the method of equal areas (MEA) for designing simulation models for frequency non-selective mobile fading channels under non- isotropic scattering conditions. The proposed method, called modified MEA (MMEA), is well suited for channel simulators based on a finite sum of complex sinusoids. The combination of the MMEA with the principle of set partitioning is also proposed here as an efficient way to improve the performance of the simulator and to reduce the computational costs. Such a combination results in a new parameter computation method called MMEA with set partitioning (MMEA-SP). The MMEA and the MMEA-SP are quite general and can be applied on any given distribution of the angle of arrival (AOA). However, to exemplify the good performance of both methods, it is assumed that the AOA follows the von Mises distribution. The obtained results demonstrate that the two proposed methods approximate the autocorrelation function (ACF) of non-isotropic scattering channels with high precision.

This paper reviews the pertinence and statistical behavior of symbol-spaced tapped-delay-line (TDL) models which are widely used to model wide-sense stationary uncorrelated scattering (WSSUS) channels. Symbol-spaced TDL models are obtained by sampling the channel impulse response (CIR) at a rate equal to the reciprocal of the symbol duration. They were proposed more than three decades ago within the context of band-limited systems and their applicability seems to be unquestionable. Nonetheless, we show here that these TDL models should be used with care to model WSSUS channels within such a context, because that would violate the channel's uncorrelated scattering (US) condition. We also show that symbol-spaced TDL models suffer from strong limitations in emulating the channel frequency correlation function (FCF). It is shown that this drawback leads to an inaccurate performance evaluation of wireless communication systems sensitive to the FCF. We discuss a simple solution to this problem by doubling the channel's sampling rate. The advantages of this solution will be demonstrated by some numerical examples.

This paper deals with some important statistical properties of the multiple-input multiple-output (MIMO) channel capacity. We assume that all the subchannels are uncorrelated. In case of single-input multiple-output (SIMO) and multiple-input single-output (MISO) channels, exact closed-form expressions are derived for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the channel capacity. Furthermore, these exact closed-form expressions are extended to characterize the statistical properties of the maximum MIMO channel capacity. The correctness of the derived closed-form expressions is confirmed by simulations.

Simulating wideband fading channels, multiple-input multiple-output (MIMO) channels, and diversity-combined fading channels often demands the generation of multiple uncorrelated Rayleigh fading waveforms. In this letter, two appropriate parameter computation methods, namely the method of exact Doppler spread (MEDS) and Lp-norm method (LPNM), for deterministic sum-of-sinusoids (SoS) channel simulators are investigated to guarantee the uncorrelatedness between different simulated Rayleigh fading processes. Numerical and simulation results show that the resulting deterministic SoS channel simulator can accurately and efficiently reproduce all the desired statistical properties of the reference model.

In this paper, we extend the geometrical one-ring multi-input multi-output (MIMO) channel model with respect to frequency-selectivity. Our approach enables the design of efficient and accurate simulation models for wideband space-time MIMO channels under isotropic scattering conditions. Two methods will be provided to compute the parameters of the simulation model. Especially, the space, time, and frequency correlation properties of the proposed wideband space-time MIMO channel simulator are studied analytically. It is shown that any given discrete or continuous power delay profile (PDP) can be incorporated in the simulation model. The high accuracy of the simulation model is demonstrated by comparing its statistical properties with those of the underlying reference model. Our procedure provides an important framework for developers of future wideband mobile communication systems to test and to verify new high data rate transmission concepts employing, e.g., space-time coded MIMO orthogonal frequency division multiplexing (OFDM) techniques.

This paper deals with the design of a set of multiple uncorrelated Rayleigh fading waveforms. The Rayleigh fading waveforms are mutually uncorrelated, but each waveform is correlated in time. The waveforms are generated by using the sum-of-sinusoids principle. Two new closed-form solutions are presented for the computation of the model parameters. Analytical and numerical results show that the resulting sum-of-sinusoids-based channel simulator fulfills all main requirements imposed by the reference model with given correlation properties derived under two-dimensional isotropic scattering conditions. The proposed methods are useful for the design of simulation models for diversity-combined Rayleigh fading channels, frequency-selective channels, and multiple-input multiple-output (MIMO) channels.

We demonstrate a super-quasi-orthogonal space- time (ST) trellis code for four transmit antennas with rectangular signal constellations for wireless communications with a spectral efficiency of 5bits/s/Hz, thus larger than only 4 bits/s/Hz as shown in our previous conference paper. Considering a mobile wireless communications system with four transmit antennas, we form an 8D signal constellation as Cartesian product of four 2D rectangular signal sets, an 8D point being transmitted by the first antenna as four concatenated 2D points in four consecutive channel uses. The 2D symbols transmitted by the other three antennas are not independent, but so chosen as to form, together with the symbols transmitted by the first antenna, the entries of a 4times4 quasi-orthogonal matrix. The union of two sets of quasi-orthogonal matrices forms a super-quasi-orthogonal signal set. With 4x4 quasi-orthogonal matrices, we then label the state transitions of a trellis diagram describing the operation of the encoder. The frame error rate (FER) and the bit error rate (BER) performance results show an excellent behavior of our proposed super-quasi-orthogonal ST trellis codes.

We demonstrate a super-quasi-orthogonal space- time (ST) trellis code for four transmit antennas with rectangular signal constellations for wireless communications with a spectral efficiency of 4 bits/s/Hz. Considering a mobile wireless communications system with four transmit antennas, we form an 8D signal constellation as Cartesian product of four 2D rectangular signal sets, an 8D point being transmitted by the first antenna as four concatenated 2D points in four consecutive channel uses. The 2D symbols transmitted by the other three antennas are not independent, but so chosen as to form, together with the symbols transmitted by the first antenna, the entries of a 4 times 4 quasi- orthogonal matrix. The union of two sets of quasi-orthogonal matrices forms a super-quasi-orthogonal signal set. With 4times4 quasi-orthogonal matrices, we then label the state transitions of a trellis diagram describing the operation of the encoder. The frame error rate (FER) and the bit error rate (BER) performance results show an excellent behavior of our proposed super-quasi- orthogonal ST trellis codes.

We suggest applying constellation shaping to reduce the peak and average power of orthogonal frequency division multiplexing (OFDM) signals using quadrature amplitude modulation (QAM) in all subcarriers without clipping or reducing the data rate. Adopting the successful shell mapping algorithm for high data rate transmission over telephone channels, as described in the V.34 Recommendation of ITU-T, we build a shell mapping algorithm for multidimensional constellation in the frequency domain for OFDM communication systems with N subcarriers. We give closed-form expressions of the functions needed to apply the constellation shaping algorithm for any N being a power of two. No side information needs to be transmitted and the data rate remains the same as for the basic OFDM system. Our simulation results show that we are able to reduce the peak and mean power by about 1 dB for OFDM signals with N = 16. For a higher number of subcarriers, we expect that we obtain more freedom in power minimization and the resulting gain will be higher. The only price to be paid is the enhanced complexity of the system by an amount that is rather acceptable.

We consider the problem of creating signal constellations for trellis-coded unitary space–time communication links, where neither the transmitter nor the receiver knows the fading gains of the channel. Our study includes design techniques for trellis-coded schemes with and without parallel paths, which allows us to find a tradeoff between low complexity and high performance. We present a new formulation of the constellation design problem for trellis-coded unitary space–time modulation schemes. The two key differences in our approach against those of other authors are that we not only combine the constellation design and mapping by set partitioning into one step, but we also use directly the Chernoff bound of the pairwise error probability as a design metric. By novelly employing a theorem for the Clarke subdifferential of the sum of the$k$largest singular values of the unitary matrix, we also present a numerical optimization procedure for finding signal constellations resulting in high-performance communications systems. To demonstrate the advantages of our new design method, we report the best constellations found for trellis-coded unitary space–time modulation systems. Simulation results show that these constellations achieve 1 dB coding gain against the usually used constellations.

We consider the problem of creating signal constellations for trellis-coded unitary space-time communication links, where neither the transmitter nor the receiver knows the fading gains of the channel. Our study includes constellation-design techniques for trellis-coded schemes with and without parallel paths, which allows us to find a tradeoff between low complexity and high performance. We present a new formulation of the constellation design problem for trellis-coded unitary space-time modulation (TCUSTM) schemes. The two key differences in our approach against those of other authors are that we not only combine the constellation design and mapping by set partitioning into one step, but we also use directly the Chernoff bound of the pairwise error probability as a design metric. By novelly employing a theorem for the Clarke subdifferential of the sum of the k largest singular values of the unitary matrix, we also present a numerical optimization procedure for finding signal constellations resulting in high-performance communications systems. To demonstrate the advantages of our new design method, we report the best constellations found for TCUSTM systems. Simulation results show that these constellations achieve a 1-dB coding gain at a bit-error rate of 10-4against usually used constellations

We demonstrate super-orthogonal space-time (ST) trellis codes with rectangular signal constellations for wireless communications with a spectral efficiency of 4 bits/s/Hz. Considering a mobile wireless communications system with two transmit antennas, we form a 4D signal constellation as Cartesian product of two 2D rectangular signal sets, a 4D point being transmitted by the first antenna as two concatenated 2D points in two consecutive channel uses. The 2D symbols transmitted by the second antenna are not independent, but so chosen as to form, together with the symbols transmitted by the first antenna, the entries of a 2 times 2 orthogonal matrix. This can be done in four different ways, resulting in four sets of 2 times 2 orthogonal matrices. To obtain a higher data rate, the union of two of them forms a super-orthogonal signal set. With 2 times 2 orthogonal matrices, we then label the state transitions of a trellis diagram describing the operation of the encoder. We perform simulations using a model that takes into account the Doppler effect as well as the effect of spatial antenna correlation at both the base station (BS) and at the mobile station (MS). The frame error rate (FER) and the bit error rate (BER) performance results show an excellent behaviour of our proposed super-orthogonal ST trellis code, which clearly outperforms all known simple ST trellis codes of same spectral efficiency using 16QAM or 16PSK

In this paper, we present a new formulation of the problem of signal design for trellis-coded unitary space-time communication systems. Our approach differs from other methods in that we not only combine the constellation design and set partitioning process together, we also use directly the Chernoff bound of the pairwise probability of error as design metric, which is a better figure of merit than the previously used chordal distance, for unitary constellation design. By novelly employing a theorem regarding the Clarke subdifferential of the sum of the k largest singular values of the unitary matrix, we present a numerical optimization procedure for finding good constellations and report the best signal constellations found. Simulation results show that these constellations achieve 1 dB gain against the previously used constellations of unitary space-time signals.

In this paper, we propose a multiple-input multiple-output (MIMO) mobile-to-mobile channel simulation model derived from a non-realizable reference model presented in Part I of our paper. The underlying reference model is based on the geometrical two-ring scattering model, where both the transmitter and the receiver are moving. A closed-form solution is provided for the three dimensional (3-D) space-time cross-correlation function (CCF) of the simulation model. An important result is that this CCF is ergodic. Also, our results show that this 3-D function can be expressed as a product of two 2-D space-time CCF, called the transmit and the receive CCE. It is shown that the parameters of the simulation model can be determined for any given space-time CCF describing the reference model. In case of isotropic scattering, we present a closed-form solution of the model parameters and illustrate some numerical results for the transmit and receive CCF. Finally, simulation results show an excellent correspondence between the statistical and time average of the MIMO channel capacity. This supports the hypothesis that the MIMO capacity is ergodic with respect to the mean.

In this paper, we propose a muiltiple-input multiple-output (MIMO) channel model for mobile-to-mobile commmunications. This so-called MIMO mobile-to-mobile channel model is derived from the geometrical two-ring scattering model under the assumption that both the transmitter and the receiver are moving. In Part I of our paper. we focus on the reference model. which is based on the assumption that the transmitter and the receiver are surrounded by an infinite number of local scatterers. From a wave model, the complex channel gains are derived and their statistical properties are studied. General analytical solutions are provided for the three-dimenisional (3-D) space-time cross-correlation function (CCF). We show that this 3-D function cani be expressed as the product of two 2-D space-time CCFs, which are introduced as the transmit arid receive CCF. Especially for the latter CCFs, closed-form expressions and numerical results are presented in case of isotropic scattering. The procedure presented in our paper provides an important framework for designers of future mobile-to-mobile communication systems to verify new transmission concepts under certain propagation conditions.

The crossing statistics of phase processes and random frequency modulation (FM) noise are studied for Nakagami-q fading channels. Closed-form expressions are first derived for the probability density function (PDF) and the cumulative distribution function (CDF) of random FM noise. The crossing rate of the phase process is then obtained for any crossing level of the phase. Moreover, the conditional PDF of random FM noise and envelope processes-conditioned on the crossings of an arbitrary level of the phase-are investigated. Since the Rayleigh fading channel is a special case of the Nakagami-q fading channel, the derived expressions are verified by comparison with results known for Rayleigh fading channels. In addition, it is shown that the derived analytical results are in excellent agreement with those obtained by computer simulations. The presented results are useful, for example, for studying the statistics of noise spikes occurring in limiter-discriminator FM receivers and for investigating the cycle slipping phenomenon in phase-locked-loop schemes when considering the transmission over Nakagami-q mobile fading channels.

In order to evaluate the performance of wireless communication protocols and design good error control schemes for bursty channels, it is important to develop accurate and simple generative models. In this paper, a novel generative deterministic model (GDM) is proposed for the simulation of bursty error sequences encountered in digital mobile fading channels. The proposed GDM is simply a properly parameterized and sampled deterministic process followed by a threshold detector and two parallel mappers. Simulation results show that this generative model enables us to match very closely any given error-free run distribution (EFRD), gap distribution (GD), and error cluster distribution (ECD) of the underlying descriptive model.

Simulation results for the capacity of multiple-input multiple-output (MIMO) mobile radio channels are presented in this paper. Our MIMO channel simulation model is based on the so-called one-ring scattering model with two antennas at both the base station (BS) and the mobile station (MS) side. For the capacity study, we have investigated the influence of various model parameters, such as the angle spread at the MS, the mean angle of arrival (AOA), and the orientation of the antenna elements. The Doppler effect is also taken into account. Nonisotropic scattering around the MS is modelled by the von Mises distribution. The presented simulation results show an excellent correspondence between the statistical and the time average of the capacity. Furthermore, it turned out that a large distance between the antenna elements is not a guarantee for high capacity. Simulation results are also provided for the level crossing rate (LCR) and the average duration of fades (ADF) of the MIMO channel capacity.

This paper deals with the design of spatial simulation models for shadowing processes. Such processes are generally assumed to be lognormally distributed. The simulation model is derived from a reference model by using the sum-of-sinusoids principle. Analytical expressions are presented for the spatial autocorrelation function (ACF), probability density function (PDF), and the level-crossing rate (LCR) of both the reference and the simulation model. Two methods are discussed enabling the fitting of the simulation model to the reference model with respect to the PDF of the received signal strength as well as to a given spatial ACF with an exponential shape. The usefulness and the performance of the shadowing channel simulator is demonstrated by applying the proposed design method on two scenarios capturing the shadowing effects in suburban and urban areas.

Efficient and accurate generative models are of great importance for the design and performance evaluation of wireless communication protocols as well as error control schemes. In this paper, deterministic processes are utilized to derive a new generative model for the simulation of bursty error sequences encountered in digital mobile fading channels. The proposed deterministic process based generative model (DPBGM) is simply a properly parameterized and sampled deterministic process followed by a threshold detector and two parallel mappers. The target error sequence is generated by a computer simulation of a frequency hopping (FH) convolutionally coded Gaussian minimum shift keying (GMSK) transmission system with Rayleigh fading. Simulation results show that this generative model enables us to match very closely any given gap distribution (GD), error-free run distribution (EFRD), error cluster distribution (ECD), error burst distribution (EBD), error-free burst distribution (EFBD), block error probability distribution (BEPD), and bit error correlation function (BECF) of the underlying descriptive model.

Abstract This paper introduces a general concept for the design of efficient multi‐input multi‐output (MIMO) narrowband fading channel simulators. The proposed procedure is applied on a reference model for the geometrical one‐ring scattering model consisting of an infinite number of local scatterers laying on a ring around the mobile station (MS). The statistical properties of both the reference model and the simulation model are studied. Closed‐form solutions are presented, for example for the space‐time cross‐correlation function (CCF), the time autocorrelation function (ACF) and the two‐dimensional (2‐D) space CCF. It will be shown, how the parameters of the MIMO channel simulator can be determined for any given space‐time CCF describing the reference model. The excellent performance of the proposed space‐time channel simulator is demonstrated by comparing its temporal and spatial correlation properties with those of the reference model. Moreover, it is demonstrated how the channel simulator can be used to analyze the statistics of the capacity of MIMO channels from time‐domain simulations. Copyright © 2004 John Wiley & Sons, Ltd.

Channel simulators based on Rice's sum-of-sinusoids are playing an important role in fading channel modelling. However, the parameters of the sum-of-sinusoids have to be determined carefully to fully exploit the potential that this powerful procedure has to offer. This paper presents general conditions under which the sum-of-sinusoids procedure results in a stationary and ergodic channel simulator. Moreover, with the help of the introduced conditions, several established parameter computations methods is investigated with respect to their usability to design stationary and ergodic fading channel generators. It turns out that if and only if the gains and frequencies are constant quantities and the phases are random variables, then the sum-of-sinusoids defines a stationary and ergodic process.

Generative models have significant applications in the design and performance evaluation of communication protocols as well as coding systems. In this paper, a novel deterministic process based generative model (DPBGM) is proposed for the characterization of burst errors in Rayleigh fading channels. A simple procedure has been developed for generating an error sequence with desired burst error statistics from a properly sampled and parameterized deterministic process followed by a threshold. The proposed generative model enables us to perfectly match any given error burst distribution (EBD) and error-free burst distribution (EFBD) of the underlying descriptive model. The gap distribution (GD) and the error-free run distribution (EFRD) obtained from the generated error sequence can also be fitted to those of the target error sequence with good accuracy.

For the simulation of practical diversity combined fading channels, multiple-input multiple-output (MIMO) channels, and space-time-selective fading channels, it is desirable to produce multiple Rayleigh fading processes with specified cross-correlations. Based on the deterministic sum-of-sinusoids (SOS) channel modeling approach, we have developed a simple efficient procedure for generating an arbitrary number of cross-correlated Rayleigh fading processes. It is demonstrated by numerical and simulation results that the resulting deterministic channel simulator can accurately reproduce all of the desired statistical properties, such as the autocorrelation functions (ACFs), the cross-correlation functions (CCFs), and the phase properties.

In this paper, a novel 3-D deterministic simulation model is proposed, which takes into account not only the temporal but also the spatial characteristics of mobile fading channels. Basing on given theoretical reference models, the parameters of the spatial-temporal simulation model are calculated by the so-called Lp-norm method. The simulation results show that both the temporal and the spatial properties of the simulation model fit those of the reference model very well. The proposed simulation model enables to emulate the received signal with any given probability density function (PDF) of the spatial angle of arrival (AOA).

Level crossing statistics of phase and random FM noise are studied for Nakagami-q fading channels. Closed form expression for the probability density function of random FM is first derived. Level crossing rate of the phase process is then obtained for an arbitrary crossing level of the phase. Also, conditional probability density functions of random FM and envelope processes, conditioned on crossings of an arbitrary level of the phase, are investigated. It is shown that the derived analytical results are in excellent agreement with those obtained by computer simulations. The results are useful, for example, for the study of the statistics of click noise and phase locked loop schemes when considering the trans- mission over Nakagami-q mobile fading channels.

We discuss three methods for the computation of the model parameters of spatial channel simulators basing on Rice's (1944, 1945) sum of sinusoids. Each method is universally described and can in principle be applied to the modelling of any type of scattering object with given spatial characteristics. However, examples illustrating the procedures are presented for a Laplacian scattering object only. The performance of each procedure is investigated with respect to important spatial characteristic quantities such as the spatial cross-correlation function (SCCF), the mean angle of arrival (AOA), and the angular spread.

A channel simulator that models accurately the physical channel statistics determined by the frequency separation between two carriers in frequency hopping (FH) systems is called a FH channel simulator. In this paper, we propose a novel deterministic FH simulation model for Rayleigh fading channels, which can easily be implemented and is very useful for investigating the frequency diversity gain of low speed mobiles in practical FH systems. The optimization technique based on the L/sub p/-norm method is exploited to calculate some simulation model parameters. Moreover, the performance evaluation of the proposed channel simulator is performed for typical GSM FH mobile radio data transmission scenarios. A pretty good agreement between the statistical properties of the simulation model and those of the underlying analytical model is observed in all cases.

In this paper a computer simulation model for a land mobile radio fading channel is presented. The model assumes non frequency-selective fading but takes into consideration the effects caused by shadowing. The simulation model is based on an efficient approximation of filtered white Gaussian noise by a finite sum of weighted sinusoids with equally distributed phases. Two completely different methods for the computation of the coefficients of the simulation model are discussed. The design of a fading channel model by one of the presented methods leads always to a simulation model that is completely determined for all time, and therefore, it can be considered as a deterministic model that approximates a stochastic process.