Wide-sense Stationary Uncorrelated Scattering Research Articles

Channel Emulator Framework for Underwater Acoustic Communications

In this paper, we develop a tractable mathematical model and an emulation framework for communicating information through water using acoustic signals. Water is considered one of the most complex media to model due to its vastness and variety of characteristics, which depend on the scenario, the type of water body (lakes, rivers, tanks, sea, etc.), and the geographical location of the water body being considered. Our proposed mathematical model involves the concept of damped harmonic oscillators to represent the medium (water); Milne’s oscillator technique is used to map the interaction between the acoustic signal and water. Wave equations formulated for acoustic pressure and acoustic wave velocity are employed to characterise the travelling acoustic signal. The signal strength, phase shift, and time delay generated from the mathematical model are then inputted into a Simulink-based emulator framework to generate channel samples and channel impulse responses. The emulator utilises the wide sense stationary uncorrelated scattering (WSSUS) assumption and a finite sum-of-sinusoids (SOS) approach with a uniformly distributed phase to generate the channel samples. By utilising this emulator platform, it becomes feasible to generate profiles for amplitude variation, the Doppler shift, and spread experienced by any travelling signal in various underwater communication scenarios. Such a platform can be employed to simulate different communication scenarios, underwater network topologies, and data for training various learning models. Additionally, it can predict the performance of different modulation, multiplexing, error correction, and multi-access techniques for underwater acoustic communication (UWAC) systems.

On the Stationarity Time of a Vehicle-to-Infrastructure Massive Radio Channel in a Line-of-Sight Suburban Environment.

Massive multiple-input multiple-output (mMIMO) communication systems are a pillar technology for 5G. However, the wireless radio channel models relying on the assumption of wide-sense stationary uncorrelated scattering (WSSUS) may not always be valid for dynamic scenarios. Nonetheless, an analysis of the stationarity time that validates this hypothesis for mMIMO vehicular channels as well as a clear relationship with the scattering properties is missing in the literature. Here, time-varying single-user mMIMO radio channels were measured in a suburban environment at the 5.89 GHz vehicular band with a strong Line-of-Sight (LOS) to study the non-WSSUS and large scale characteristics of the vehicle-to-infrastructure (V2I) link. The generalized local scattering function (GLSF), computed from the sampled channels, was used to derive (1) the spatial distribution of the stationarity time using the channel correlation function (CCF) and empirical collinearity methods and (2) the root mean square delay/angular spread and coherence time/bandwidth values from the projected power delay profile (PDP) and Doppler power spectra (DPS). The results highlight the high degree of correlation between the spatial distribution of the stationarity time and the scattering properties along the measurement route.

A Fair SINR Performance Comparison of FBMC/OQAM and FBMC/QAM Multicarrier Communication Systems in the Discrete-Time Framework

In the last couple of decades, multicarrier modulations have witnessed a considerable interest in wireless communication networks due to their ability to fight against multipath fading and offer multiple access with flexible resource sharing. One of the well known multicarrier modulation systems is filter-bank multi-carrier with an offset quadrature amplitude modulation (FBMC/OQAM), which was proposed as a powerful solution during the standardization of 5G. In this paper, we derive a closed-form expression of the signal to interference plus noise ratio (SINR) for FBMC/OQAM systems in the discrete-time context, for arbitrary wide sense stationary uncorrelated scattering (WSSUS) channels as well as transmitter (Tx) and receiver (Rx) waveforms. We quantify the potential gains in SINR brought by FBMC/OQAM, which exclusively operates on critical lattice density, with respect to FBMC/QAM, which have the flexibility to operate on critical or non-critical lattice densities. For completeness, we compare the performance of FBMC/OQAM in the discrete-time context, sweeping the discrete space of waveforms supports, with that of FBMC/OQAM in the continuous-time context, using the Hermite functions, and show how they perform similarly. Simulation results prove that FBMC/OQAM optimization algorithm, performing with the ping-pong optimized pulse shaping (POPS) paradigm, converges rapidly to excellent SINR values, even with small supports durations, in discrete-time context, which is equivalent to a reduced number of Hermite functions, in the continuous-time context.

Validation of cloud‐radio access network control unit with intra‐PHY architecture: Hardware‐in‐the‐loop framework based on frequency‐domain channel models

AbstractIn this article, a signal processing framework for hardware‐in‐the‐loop (HIL) validation of the cloud‐radio access network (C‐RAN) control unit (CU) with a crosshaul intra‐PHY architecture split is evaluated. The framework is based on the assumption that data exchanged over the crosshaul interface between the lower and higher parts of the physical layer have the form of frequency‐domain orthogonal frequency division multiplexing (OFDM) subcarriers. Therefore, it is proposed to simulate the effects of a wireless fading channel directly in the frequency domain, instead of the conventionally selected time domain. This approach leads to complexity reduction of the channel simulation model by minimizing the number of required FFT/IFFT operations, at the cost of simulation accuracy in high‐mobility and high‐delay spread scenarios. Analysis of bit error ratio (BER) and block error ratio (BLER) metrics obtained using both time‐ and frequency‐domain channel models is presented in order to validate the proposal and evaluate the accuracy loss caused by the usage of nonideal frequency‐domain models. The frequency‐domain methods are compared against the conventional wide sense stationary uncorrelated scattering (WSSUS) model implementation based on the tapped delay line (TDL). It is shown that the utilization of improved frequency‐domain models instead of the block‐fading model substantially decreases the BER/BLER prediction error in specific scenarios.

Dual mode spectroscopic biomedical sensor: Technical considerations for the wireless testbed* *This work has been partly supported by the German Academic Exchange Service (Deutsche Akademische Austausch Dienst (DAAD)) and the University of Kassel.

A real time implementation of a spectroscopy based dual mode sensor necessitates a timely and reliable transmission of information to and from the sensor. This becomes one of the pivotal roles of the sensor as the wireless transmission must be timely, accurate and reliable. For this purpose, our project aims to use a Gabor expansion model with a single-tap time-frequency channel model. This protocol has been planned to be used in a biomedical sensor system that aims for the detection of human breath for patients above 60. For this mechanism to work in dispersive channels, error introduced by this model needs to be minimized by optimizing Gabor prototype frames. We attempt to reduce this error via Newton method for a Wide-Sense Stationary Uncorrelated Scattering (WSSUS) environment. Therefore, numerous factors need to be considered, and have been presented. The sensitivity of this sensor setup in terms of least amount of discernible absorption coefficient is , and we attempt to maintain this value via our wireless approach. The suggested solution provides an error within a threshold of 1 to 2% in case of our results. In this manner, the sanctity of information going to and from the human body is tantamount to be highly accurate that highlights the efficiency of this scheme in our biomedical sensor.

Assessment of Wide-Sense Stationarity of an Underwater Acoustic Channel Based on a Pseudo-Random Binary Sequence Probe Signal

The performances of Underwater Acoustic Communication (UAC) systems are strongly related to the specific propagation conditions of the underwater channel. Designing the physical layer of a reliable data transmission system requires a knowledge of channel characteristics in terms of the specific parameters of the stochastic model. The Wide-Sense Stationary Uncorrelated Scattering (WSSUS) assumption simplifies the stochastic description of the channel, and thus the estimation of its transmission parameters. However, shallow underwater channels may not meet the WSSUS assumption. This paper proposes a method for testing the Wide-Sense Stationary (WSS) part of the WSSUS feature of a UAC channel on the basis of the complex envelope of a received probe Pseudo-Random Binary Sequence (PRBS) signal. Two correlation coefficients are calculated that can be interpreted, together, as a measure that determines whether the channel is WSS or not. A similar wide-sense stationarity assessment can be performed on the basis of the Time-Varying Impulse Response (TVIR) of a UAC channel. However, the method proposed in this paper requires fewer computational operations in the receiver of a UAC system. PRBS signal transmission tests were conducted in the UAC channel simulator and in real conditions during an inland water experiment. The correlation coefficient values obtained using the method based on the envelope of a probe signal and the method of analysing the TVIR estimates are compared. The results are similar, and thus, it is possible to assess if the UAC channel can be modelled as a WSS stochastic process without the need for TVIR estimation.

Performance Analysis of a Multicarrier Spread Spectrum System in Doubly Dispersive Channels With Emphasis on HF Communications

In this paper, we present a bit error rate (BER) analysis of a multicarrier spread spectrum (MC-SS) system that accounts for several non-ideal factors that exist in actual systems; specifically, channel estimation error, correlated subcarriers, and frequency selectivity over each subcarrier frequency band. The particular MC-SS system that is addressed makes use of filter banks to keep subcarrier bands non-overlapping. In this analysis, the time varying multipath channel is modeled using the wide-sense stationary uncorrelated scattering (WSSUS) channel model, and the channel is estimated using a pilot symbol assisted modulation (PSAM) method. Numerical results that demonstrate the accuracy of the developed theoretical results when applied to design transceivers for high frequency (HF) skywave communications show the usefulness of the developed theory in a practical case study.

Analytic Expressions for Radar Sea Clutter WSSUS Scattering Functions

Bello’s stochastic linear time-varying system theory has been widely used in the wireless communications literature to characterize multipath fading channel statistics. In the context of radar backscatter, this formulation allows for statistical characterization of distributed radar targets in range and Doppler using wide-sense stationary uncorrelated scattering (WSSUS) models. WSSUS models separate the channel from the effect of the waveform and receive filter, making it an ideal formulation for waveform design problems. Of particular interest in the radar waveform design community is the ability to suppress unwanted backscatter from the earth’s surface, known as clutter. Various methods for estimating WSSUS system functions have been studied in the literature, but to date no analytic expressions for radar surface clutter range-Doppler scattering functions exist. In this work we derive a frequency-selective generalization of the Jakes Doppler spectrum model, which is widely used in the wireless communications literature, adapt it for use in radar problems, and show how the maximum entropy method can be used to extend this model to account for internal clutter motion. Validation of the spectral and stationarity properties of the proposed model against a subset of the Australian Ingara sea clutter database is performed, and good agreement is shown.

Exploiting WSSUS Multipath for GNSS Ranging

We propose a low-dimensional parameter estimation scheme for satellite-based ranging in the presence of an attenuated line-of-sight (LOS) signal and a time-varying number of multipath signals. This is of interest for landmobile users of global navigation satellite systems in diverse scattering environments with limited satellite visibility (e.g., a car moving through an urban canyon). Conventional ranging techniques, which rely solely on estimation of LOS parameters, ignore or suppress multipath and thus sacrifice available information; on the other hand, exhaustive approaches involving detection and estimation of each time-variant echo are too cumbersome in terms of parameter dimension. We suggest an unconditional maximum likelihood estimator (U-MLE) for joint estimation of LOS synchronization parameters and a small set of multipath distribution parameters. Our key assumptions are Gaussian wide-sense stationary uncorrelated scattering (WSSUS) and a known structure of the power delay profile. The proposed estimator uses as input data only a few complex-valued correlator outputs, which are provided by conventional navigation receivers, and its complexity is independent of the actual number of present echoes. Simulations demonstrate that the U-MLE improves accuracy and robustness of LOS synchronization for various model-matched and -mismatched multipath settings, including standardized and approved urban scenarios.

Maximum-Likelihood Blind Synchronization for GFDM Systems

Generalized frequency-division multiplexing (GFDM) inherits the cyclic-prefixed (CP) block signaling structure from orthogonal frequency-division multiplexing (OFDM). The feasibility of CP-based maximum-likelihood (ML) blind synchronization for GFDM systems, however, has not been assessed in the literature. We find that such synchronization is complicated by the covariance structure of the signal which, due to nonorthogonal pulse shaping, possesses a time-varying signal power and some weak self-induced interference. Neglecting the latter and approximating the former by the average power enable us to obtain an approximate-ML solution based on a recent result on OFDM synchronization in wide-sense stationary uncorrelated scattering (WSSUS) channels. Simulations show that the resulting method for GFDM yields comparable performance, under commonly considered pulse-shaping filters, to its kin for OFDM.

Spatial Stationarity of Ultrawideband and Millimeter Wave Radio Channels

For radio channels with broad bandwidth resource, such as those often used for ultrawideband (UWB) and millimeter wave (mmwave) systems, the Wide-Sense Stationary Uncorrelated Scattering (WSSUS) and spatial stationary assumptions are more critical than typical cellular channels with very limited bandwidth resource. This paper studies spatial stationarity and bandwidth dependency of the Multipath Component (MPC) parameters, and the concept of local region of stationarity (LRS) is used as the measure of the physical stationarity region. LRS calculation results based on channel measurements show that the size of LRS is bandwidth dependent in all measured bands, 2–4 GHz, 14–16 GHz, and 28–30 GHz. The results in this paper point out that an inappropriate choice of bandwidth in channel parameter estimation could violate spatial stationary assumptions. The paper indicates LRS sizes for different bandwidths in the three bands.

On Maximum-Likelihood Blind Synchronization Over WSSUS Channels for OFDM Systems

Various blind synchronization methods built on the maximum likelihood (ML) principle have been proposed, where the addressed scenarios include additive white Gaussian noise (AWGN), single-path fading, and multipath fading channels. We consider ML blind synchronization over wide-sense stationary uncorrelated scattering (WSSUS) channels. Different from existing studies, we exploit a more complete signal correlation function and find the carrier frequency offset estimate to be the solution of a quartic equation, rather than the phase angle of a complex number. As the truly ML synchronizer (dubbed MLE) is very complicated, we also derive a reduced-complexity alternative (dubbed RCE). It is found that the RCE yields indistinguishable performance from the MLE, at a somewhat lower complexity than an existing rival. We also present an in-depth theoretical analysis and comparison of the performance of various methods. Simulations show that the proposed methods yield rather robust performance in modeling errors of the fading rate and the channel power-delay profile (PDP).

Prolate Spheroidal Coordinates for Modeling Mobile-to-Mobile Channels

Often, the choice of an appropriate coordinate system permits a simpler solution to a problem. In this letter, it is shown that in certain cases a prolate spheroidal coordinate system can be advantageous when calculating the delay-dependent Doppler probability density functions (pdfs) for mobile-to-mobile wireless channels. Recently, it was demonstrated how a geometry-based approach can be utilized to compute delay-dependent Doppler pdfs for vehicle-to-vehicle channels that violate the wide-sense stationary uncorrelated scattering (WSSUS) assumption. However, the corresponding pdfs required quite extensive numerical evaluations. When considering the same modeling problem in prolate spheroidal coordinates, it becomes possible to obtain analytical representations in some special, yet practically relevant cases, and thus simplify the computations of the resulting density functions significantly. Furthermore, it becomes possible to calculate the characteristic function for such a scenario. Thus, we are able to determine the mean Doppler and Doppler spread.

Estimation of Non-WSSUS Channel for OFDM Systems in High Speed Railway Environment Using Compressive Sensing

Non Wide Sense Stationary Uncorrelated Scattering (Non-WSSUS) is one of characteristics for high-speed railway wireless channels. In this paper, estimation of Non-WSSUS Channel for OFDM Systems is considered by using Compressive Sensing (CS) method. Given sufficiently wide transmission bandwidth, wireless channels encountered here tend to exhibit a sparse multipath structure. Then a sparse Non-WSSUS channel estimation approach is proposed based on the delay-Doppler-spread function representation of the channel. This approach includes two steps. First, the delay-Doppler-spread function is estimated by the Compressive Sensing (CS) method utilizing the delay-Doppler basis. Then, the channel is tracked by a reduced order Kalman filter in the sparse delay-Doppler domain, and then estimated sequentially. Simulation results under LTE-R standard demonstrate that the proposed algorithm significantly improves the performance of channel estimation, comparing with the conventional Least Square (LS) and regular CS methods.

On the Sensitivity of Continuous-Time Noncoherent Fading Channel Capacity

The noncoherent capacity of stationary discrete-time fading channels is known to be very sensitive to the fine details of the channel model. More specifically, the measure of the support of the fading-process power spectral density (PSD) determines if noncoherent capacity grows logarithmically with the signal-to-noise ratio (SNR) or slower than logarithmically. Such a result is unsatisfactory from an engineering point of view, as the support of the PSD cannot be determined through measurements. The aim of this paper is to assess whether, for general continuous-time Rayleigh-fading channels, this sensitivity has a noticeable impact on capacity at SNR values of practical interest. To this end, we consider the general class of band-limited continuous-time Rayleigh-fading channels that satisfy the wide-sense stationary uncorrelated-scattering (WSSUS) assumption and are, in addition, under spread. We show that, for all SNR values of practical interest, the noncoherent capacity of every channel in this class is close to the capacity of an additive white Gaussian noise channel with the same SNR and bandwidth, independently of the measure of the support of the scattering function (the 2-D channel PSD). Our result is based on a lower bound on noncoherent capacity, which is built on a discretization of the channel input-output relation induced by projecting onto Weyl-Heisenberg sets. This approach is interesting in its own right as it yields a mathematically tractable way of dealing with the mutual information between certain continuous-time random signals.

A Three-Dimensional Geometry-Based Statistical Model of2×2Dual-Polarized MIMO Mobile-to-Mobile Wideband Channels

A three-dimensional (3D) model for wide-band dual-polarized (DP) multiple-input-multiple-output (MIMO) mobile-to-mobile (M2M) channels is proposed. Using geometrical scattering based on concentric spheres at the transmitter (Tx) and at the receiver (Rx), a 3D parametric reference model for2×2M2M DP multipath fading channels is developed. The channel model assumes the use of colocated half-wavelength dipole antennas for vertical and horizontal polarizations at both transmit and receive stations. Model parameters include the velocities of the Tx and Rx nodes, the distance between the nodes, the 3D antenna pattern gains, the azimuth and elevation angles of arrival and departure, the geometrical distribution of the scatterers, the Rician K-factors defining the fading envelope distributions, the maximum Doppler frequency, the scattering loss factors, the cross-polar power discrimination ratio (XPD), and the copolarization power ratio (CPR). Using the proposed model, expressions for joint time-frequency correlation functions (TFCFs) are derived which are used to investigate system behavior over different wide sense stationary uncorrelated scattering (WSSUS) channel realizations. The numerical results illustrate the sensitivities of the TFCF to simultaneous time and frequency offsets for the2×2DP-MIMO architectures.

Stochastic Replay of Non-WSSUS Underwater Acoustic Communication Channels Recorded at Sea

To fully exploit sea experiments under controlled and reproducible laboratory conditions, a channel model driven by real data is derived. This model relies on the assumption that a channel recorded at sea is a single observation of an underlying random process. From this single observation, the channel statistical properties are estimated to then feed a stochastic simulator that generates multiple realizations of the underlying process. Based on the analysis of data collected in the Atlantic Ocean and the Mediterranean Sea, we fully relax the usual wide-sense stationary uncorrelated scattering (WSSUS) assumption. We show thanks to the empirical mode decomposition that a trend stationary model suits the analyzed underwater acoustic communication channels very well. Scatterers with different path delays are also assumed to be potentially correlated so that the true second-order statistics of the channel are taken into account by our model. Test cases illustrate the benefits of channel stochastic replay to communication system design and validation. The Matlab code corresponding to the proposed simulator is available at http://perso.telecom- bretagne.eu/fxsocheleau/software .

Multilevel/AES-LDPCC-CPFSK with channel equalization over WSSUS multipath environment

In this paper, in order to ensure secure and robust communication, a new type of data encryption and error correction mechanism called Multilevel/Advanced Encryption Standard-Low Density Parity Check Coded-Continuous Phase Frequency Shift Keying (Multilevel/AES-LDPCC-CPFSK) is carried out. Here, we have chosen AES for data encryption, LDPC codes for error correction and CPFSK for modulation. We have evaluated error performance of this scheme over Wide-Sense Stationary Uncorrelated Scattering (WSSUS) multipath channels with channel equalization. We have simulated 5-level AES, 2-level LDPC for 4CPFSK and 16CPFSK over WSSUS channels modeled by Cooperation in the field of Science & Technology, Project #207 (COST207). We have concluded that our proposed structure has promising results compared to Turbo Codes for all SNR values in WSSUS channels.

Equivalence of VSSO and VSVO Kalman Channel Estimators in Doubly-Selective OFDM Systems—A Theoretical Perspective

Vector state-vector observation (VSVO) , and vector state-scalar observation (VSSO) are two types of Kalman estimators that can be used for channel estimation in doubly-selective OFDM systems over wide-sense stationary uncorrelated-scattering (WSSUS) channels. It was shown in that the VSSO Kalman channel estimator resulted in over 90% complexity savings compared to the VSVO Kalman channel estimator and this was achieved without any loss of performance. This inevitably raises the question whether the VSSO and VSVO Kalman channel estimators are computationally equivalent? We attempt to answer this question in this letter and theoretically show the equivalence of the VSSO and VSVO Kalman channel estimator for WSSUS channels.

Optimal and Suboptimal Differentially Coherent Reception of MDPSK in Time-Spread WSSUS Channel

A model of the wide-sense stationary uncorrelated scattering (WSSUS) channel with time-spread and additive white Gaussian noise is considered. The general expression for the symbol-by-symbol reception algorithm of M-ary differential phase shift keying (MDPSK), which realizes implicit diversity, is obtained. Depending on the type of impulse response receiver filter (demodulator kernel), the partial cases that follow from this expression are considered: optimal demodulator, conventional differentially coherent demodulator, demodulator with iterative kernel and its special cases. Relations for assessing the bit error probability of the considered demodulators in the case when signals are transmitted with binary and quadrature differential phase shift keying without taking into account intersymbol interference are derived. The performance bounds for the optimized binary and quadrature systems are determined. The results of the calculation of the bit error probability are presented.