Nonstationary Wireless Channels Research Articles

A Novel SAGE Algorithm for Estimating Parameters of Wideband Spatial Nonstationary Wireless Channels With Antenna Polarization

A Novel SAGE Algorithm for Estimating Parameters of Wideband Spatial Nonstationary Wireless Channels With Antenna Polarization

Joint Spatio-Temporal Precoding for Practical Non-Stationary Wireless Channels

The high mobility, density and multi-path evident in modern wireless systems makes the channel highly non-stationary. This causes temporal variation in the channel distribution that leads to the existence of time-varying joint interference across multiple degrees of freedom (DoF, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e.g</i> ., users, antennas, frequency and symbols), which renders conventional precoding sub-optimal in practice. In this work, we derive a High-Order Generalization of Mercer’s Theorem (HOGMT), which decomposes the multi-user non-stationary channel into two (dual) sets of jointly orthogonal subchannels (eigenfunctions), that result in the other set when one set is transmitted through the channel. This duality and joint orthogonality of eigenfuntions ensure transmission over independently flat-fading subchannels. Consequently, transmitting these eigenfunctions with optimally derived coefficients eventually mitigates any interference across its degrees of freedoms and forms the foundation of the proposed joint spatio-temporal precoding. The transferred dual eigenfuntions and coefficients directly reconstruct the data symbols at the receiver upon demodulation, thereby significantly reducing its computational burden, by alleviating the need for any complementary post-coding. Additionally, the eigenfunctions decomposed from the time-frequency delay-Doppler channel kernel are paramount to extracting the second-order channel statistics, and therefore completely characterize the underlying channel. We evaluate this using a realistic non-stationary channel framework built in Matlab and show that our precoding achieves ⩾4 orders of reduction in BER at SNR⩾15dB in OFDM systems for higher-order modulations and less complexity compared to the state-of-the-art precoding.

Joint Pilot Spacing and Power Optimization Scheme for Nonstationary Wireless Channel: A Deep Reinforcement Learning Approach

Pilot-assisted channel estimation techniques are essential for wireless communication systems. Most studies focus on the estimation algorithms and interpolation techniques. However, the design of pilot pattern is often neglected. In this letter, we propose a joint pilot spacing and power optimization scheme based on deep reinforcement learning (DRL) to address the mismatch problem of pilot configuration for nonstationary wireless channel. First, we model the adaptive pilot design decision-making process as a Markov Decision Process (MDP) to reduce pilot overhead and power loss. Then a deep Q-network (DQN) based learning algorithm is proposed to optimize the spacing and power of pilots so as to maximize estimation performance while reducing system cost. Simulation results show that the performance of the proposed approach is better than conventional pilot configuration algorithms. Moreover, we analyze the key factors that affect the performance of the proposed scheme.

Multi Direction-of-Arrival Tracking Using Rigid and Flexible Antenna Arrays

This paper is concerned with the problem of simultaneously tracking the direction-of-arrival (DOA) of far-field multiple moving sources/users in wireless communications using the vector-signal received by an antenna array of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> elements. The antenna array can be rigid (fixed array locations) or flexible (time-varying array locations), and it is used in conjunction with a “manifold extender”, a spatiotemporal state-space model and a Kalman-type tracking approach for non-stationary wireless channels. In particular, two tracking approaches are proposed. The first is based on an arrayed Extended Kalman Filter (arrayed-EKF) algorithm and the second on an arrayed Unscented Kalman Filter (arrayed-UKF) algorithm. Furthermore, if the array is rigid the spatiotemporal state-space model incorporates the DOAs and the angular velocities of the sources, while if it is flexible it also includes the array locations in the set of state-variables. The performance of the two approaches using both rigid and flexible arrays is evaluated using computer simulation studies and compared with a subspace tracking algorithm and a particle filter method under the same conditions. The results show that the arrayed-UKF and the arrayed-EKF show superior tracking performance, especially for low SNRs.

Non-Stationary Wireless Channel Modeling Approach Based on Extreme Value Theory for Ultra-Reliable Communications

A proper channel modeling methodology that characterizes the statistics of extreme events is key in the design of a system at an ultra-reliable regime of operation. The strict constraint of ultra-reliability corresponds to the packet error rate (PER) in the range of $10^{-9}-10^{-5}$ within the acceptable latency on the order of milliseconds. Extreme value theory (EVT) is a robust framework for modeling the statistical behavior of extreme events in the channel data. In this paper, we propose a methodology based on EVT to model the extreme events of a non-stationary wireless channel for the ultra-reliable regime of operation. This methodology includes techniques for splitting the channel data sequence into multiple groups concerning the environmental factors causing non-stationarity, and fitting the lower tail distribution of the received power in each group to the generalized Pareto distribution (GPD). The proposed approach also consists of optimally determining the time-varying threshold over which the tail statistics are derived as a function of time, and assessing the validity of the derived Pareto model. Finally, the proposed approach chooses the best model with minimum complexity that represents the time variation behavior of the non-stationary channel data sequence. Based on the data collected within the engine compartment of Fiat Linea under various engine vibrations and driving scenarios, we demonstrate the capability of the proposed methodology in providing the best fit to the extremes of the non-stationary data. The proposed approach significantly outperforms the channel modeling approach using the stationary channel assumption in characterizing the extreme events.

A Novel B5G Frequency Nonstationary Wireless Channel Model

Frequency nonstationarity is an important statistical property of beyond fifth generation wireless communication channels due to extremely large bandwidths used in millimeter wave (mmWave) and teraherz communications. In this article, a general averaged power delay profile method is first introduced as a metric to determine the stationarity regions of wireless channels in the time, frequency, and spatial domains. Then, we apply this method to determine the frequency stationarity regions (FSRs) of channel measurements in a sub-6-GHz frequency band (2-4 GHz) and two mmWave frequency bands (14-16 GHz and 28-30 GHz). Frequency nonstationary (FnS) properties are found from all of the three bands. A novel FnS channel model is then proposed to model wireless channels in all frequency bands. We first split a FnS channel into a few frequency stationary (FS) subband channels and model them one by one, which are finally combined as an FnS channel model considering the cluster evolution in the frequency domain and the frequency consistency of subband channels. Simulation results show that the frequency correlation functions of the proposed FnS channel model fit well those of the measured FnS channels.

A General 3D Non-Stationary Wireless Channel Model for 5G and Beyond

In this paper, a novel three-dimensional (3D) non-stationary geometry-based stochastic model (GBSM) for the fifth generation (5G) and beyond 5G (B5G) systems is proposed. The proposed B5G channel model (B5GCM) is designed to capture various channel characteristics in (B)5G systems such as space-time-frequency (STF) non-stationarity, spherical wavefront (SWF), high delay resolution, time-variant velocities and directions of motion of the transmitter, receiver, and scatterers, spatial consistency, etc. By combining different channel properties into a general channel model framework, the proposed B5GCM is able to be applied to multiple frequency bands and multiple scenarios, including massive multiple-input multiple-output (MIMO), vehicle-to-vehicle (V2V), high-speed train (HST), and millimeter wave-terahertz (mmWave-THz) communication scenarios. Key statistics of the proposed B5GCM are obtained and compared with those of standard 5G channel models and corresponding measurement data, showing the generalization and usefulness of the proposed model.

Real-time Prediction of Non-stationary Wireless Channels

Modern wireless systems are increasingly dense and dynamic that makes the channel highly non-stationary, rendering conventional receivers sub-optimal in practice. Predicting the channel characteristics for non-stationary channels has the distinct advantage of pre-conditioning the waveform at the transmitter to match the expected fading profile. The difficulty lies in extracting an accurate model for the channel, especially if the underlying variables are uncorrelated, unobserved and immeasurable. Our work implements this prescience by assimilating the Channel State Information (CSI), obtained as feedback from the receiver, over time and space to adjust the modulation vectors such that the channel impairments are significantly diminished at the receiver, improving the Bit Error Rate (BER). We design a channel recommender, in which an adaptive smoother is used to filter the noise in CSI, while a tensor factorization & completion approach is used to track the ephemeral changes in non-stationary channel statistics by observing the changes in certain measurable parameters. V2X communication is used as an example of non-stationary channels to shows the efficacy of this approach. Overall, the system is shown to operate with a prediction accuracy of 10−3 MSE even in dense scattering environments over space and time, improving the BER at the receiver by 90% for higher-order modulations.

A Novel 3D Non-Stationary Wireless MIMO Channel Simulator and Hardware Emulator

In this paper, a new WINNER+-based 3-D non-stationary geometry-based stochastic model (GBSM) for multiple-input multiple-output channels is proposed, as well as extended evolving algorithms of time-variant channel parameters. Meanwhile, important statistical properties of the channel model, i.e., time-variant autocorrelation function, time-variant cross-correlation function, and time-variant Doppler power spectrum density are derived and analyzed. Moreover, we propose an efficient hardware implementation method, namely, sum-of-frequency-modulation (SoFM) method, to generate non-stationary channel coefficients. By utilizing compact hardware architecture with SoFM modules, the proposed 3-D non-stationary GBSM is realized on a field-programmable gate array hardware platform. Simulations and hardware measurement results demonstrate that our proposed channel simulator and emulator can get more accurate and realistic Doppler frequency than those of the existing models. In addition, hardware measurements of statistical properties are also well consistent with the corresponding theoretical ones, which verify the correctness of both the hardware emulation scheme and theoretical derivations.

Learning in Wireless Control Systems Over Nonstationary Channels

This paper considers a set of multiple independent control systems that are each connected over a non-stationary wireless channel. The goal is to maximize control performance over all the systems through the allocation of transmitting power within a fixed budget. This can be formulated as a constrained optimization problem examined using Lagrangian duality. By taking samples of the unknown wireless channel at every time instance, the resulting problem takes on the form of empirical risk minimization, a well-studied problem in machine learning. Due to the non-stationarity of wireless channels, optimal allocations must be continuously learned and updated as the channel evolves. The quadratic convergence property of Newton's method motivates its use in learning approximately optimal power allocation policies over the sampled dual function as the channel evolves over time. Conditions are established under which Newton's method learns approximate solutions with a single update, and the subsequent sub-optimality of the control problem is further characterized. Numerical simulations illustrate the near-optimal performance of the method and resulting stability on a wireless control problem.

Adaptive Pilot Patterns for CA-OFDM Systems in Nonstationary Wireless Channels

In this paper, we investigate the performance gains of adapting pilot spacing and power for carrier aggregation orthogonal frequency-division multiplexing (CA-OFDM) systems in nonstationary wireless channels. In current multiband CA-OFDM wireless networks, all component carriers use the same pilot density, which is designed for poor channel environments. This leads to unnecessary pilot overhead in good channel conditions and performance degradation in the worst channel conditions. We propose adaptation of pilot spacing and power using a codebook-based approach, where the transmitter and the receiver exchange information about the fading characteristics of the channel over a short period of time, which are stored as entries in a channel profile codebook. We present a heuristic algorithm that maximizes the achievable rate by finding the optimal pilot spacing and power from a set of candidate pilot configurations. We also analyze the computational complexity of our proposed algorithm and the feedback overhead. We describe methods to minimize the computation and feedback requirements for our algorithm in multiband CA scenarios and present simulation results in typical terrestrial and air-to-ground/air-to-air nonstationary channels. Our results show that significant performance gains can be achieved when adopting adaptive pilot spacing and power allocation in nonstationary channels. We also discuss important practical considerations and provide guidelines to implement adaptive pilot spacing in CA-OFDM systems.

Receding Horizon Control for an Online Cross-Layer Design of Wireless Networks Over Time-Varying Stochastic Channels

In this paper, we formulate a network utility maximization (NUM) problem, targeting an optimal cross-layer network operation, while considering time-varying and random possibly non-stationary wireless channels. As indicated in the literature, this problem imposes scalability constraints when the time horizon of the network control increases, impeding an online (i.e., real-time) application of its solution during the network operation. To achieve an online network control, in this paper, we leverage on model predictive control (MPC) or receding horizon control (RHC) for the solution of the NUM problem. Furthermore, MPC/RHC allows for the adaptation of the optimal controls in dynamic and evolving network conditions, in our case with respect to the wireless channels, the modeling parameters of which are estimated in an online fashion. We present and analyze the NUM problem, while we appropriately reformulate it for applying MPC/RHC. Then, we describe the MPC/RHC-based algorithmic solution, which determines the decisions for the online network control including power control, scheduling, routing, and congestion control, while we discuss stability and optimality issues. Finally, we evaluate the proposed methodology via numerical results and we show that the performance lies very close to the optimal one even for relatively small receding horizon lengths that significantly reduce the computational time complexity.

Amplitude-goniometric passive location of an emitting target in the nonstationary radio channel

The further development of the concept related to passive direction finders (DFs) equipped with an energy-measurement channel is implemented. The goniometric-energy method of passive detection and ranging, according to which the slant distance to a target can be determined from its emission in the form of a constant-envelope signal, is generated as applied to the given stationary DFs. In the spatial case, the passive location problem is solved using the time-dependent behavior of the generalized radiolocation coefficient. A complex algorithm is constructed with the aim at jointly estimating the given coefficient and the detection range under the condition that rectilinear uniform motion of an emitting target is simulated on the estimation interval. The computational experiment results are presented to confirm the possibility of practical application of the proposed method.

Non-Stationary Propagation Model for Scattering Volumes With an Application to the Rural LMS Channel

The design of efficient positioning algorithms in navigation satellite systems, like GNSS, operating in land mobile environments demands for detailed models of the radio channel. On the one hand, the models need to accurately describe scattering and shadowing/obstruction caused by vegetation. On the other hand, they have to incorporate the steady change in the propagation constellation due to the receiver displacement. In this paper we propose a model of the non-stationary radio channel in a scenario where a mobile receiver drives past a scattering volume, such as a ball or a cuboid, while the transmitter is elevated, like in satellite positioning applications. Such a volume may represent the canopy of a single tree, the canopies of trees in a grove, or a small forest. Scattering by the volume is characterized by means of multiple point-source scatterers that are assumed to form a marked spatial point process. The system functions of the radio channel are given. An integral form of the time-frequency correlation function of the component in the system functions contributed by the scattering volume is obtained as a direct consequence of Campbell's Theorem. Furthermore, a closed-form approximation of this integral form is derived for time lags corresponding to displacements along the receiver trajectory for which the plane wave assumption holds. The approximation takes into account the steady change in the propagation constellation. The proposed model is validated by means of Monte Carlo simulations and by comparing its prediction capabilities with experimental data in a scenario where a mobile receiver drives past a roadside tree. A good agreement is observed, despite the simplicity of the model.

Base station identification in single-frequency network positioning system under mixed line-of-sight/non-line-of-sight condition

A base station (BS) identification algorithm which does not modify the transmitter hardware and digital terrestrial television broadcasting signal framework is proposed for single-frequency networks positioning system. Similar to the outlier detection in multi-object tracking environments, the BS identification is formulated as a data validation problem which is solved with gate construction. Compared with traditional gate algorithm, an additional mode probability parameter is introduced to describe the wireless channel condition and overcome its drawback in non-stationary wireless channel environments by the interacting multiple model approach. In the proposed algorithm, two parallel innovation statistical distribution deduction modes with line-of-sight and non-line-of-sight condition are employed to estimate the corresponding parameters, respectively. Then a combination scheme is utilised to mix the two estimated statistical parameters by the predicted mode probabilities and obtains the final innovation distribution. At last, gate parameter is calculated like traditional gate algorithm and the BS identification is achieved. Simulation results demonstrate its robustness and high performance in different scenarios.

Analysis of Scattering in Mobile Radio Channels Based on Clustered Multipath Estimates

This paper presents the results of angle and delay measurements in physically nonstationary radio channels obtained in an outdoor urban environment. The multidimensional estimation data are obtained using a recently developed 3-D high-resolution channel sounder. The estimation results are compared with results obtained from a 3-D deterministic propagation prediction tool. For a better analysis, a hierarchical clustering method is presented that can separate and group the multidimensional estimation data into clusters. Measurements performed at a fixed position as well as along a trajectory are used to characterize the angular dispersion in both azimuth and elevation. The angular dispersion in terms of the rms cluster angular spread in both elevation and azimuth of the different clusters is analyzed over space and time and related to its physical scattering sources. Compared to the measurements, a large number of multipath clusters are missing in the predictions. Furthermore, it is observed from the measurements that different objects cause different angular spread values in azimuth and elevation. The results can be very helpful for the identification, improvement and calibration of deterministic propagation prediction models.

Scheduling Over Nonstationary Wireless Channels With Finite Rate Sets

We consider a wireless basestation transmitting high-speed data to multiple mobile users in a cell. The channel conditions between the basestation and the users are time-varying and user-dependent. Our objective is to design a scheduler that determines which user to schedule at each time step. Previous work on this problem has typically assumed that the channel conditions are governed by a stationary stochastic process. In this setting, a popular algorithm known as Max-Weight has been shown to have good performance. However, the stationarity assumption is not always reasonable. In this paper, we study a more general worst-case model in which the channel conditions are governed by an adversary and are not necessarily stationary. In this model, we show that the nonstationarities can cause Max-Weight to have extremely poor performance. In particular, even if the set of possible transmission rates is finite, as in the CDMA 1xEV-DO system, Max-Weight can produce queue sizes that are exponential in the number of users. On the positive side, we describe a set of tracking algorithms that aim to track the performance of a schedule maintained by the adversary. For one of these tracking algorithms, the queue sizes are only quadratic. We discuss a number of practical issues associated with the tracking algorithms. We also illustrate the performance of Max-Weight and the tracking algorithms using simulation

Communicating over nonstationary nonflat wireless channels

We develop the concept of joint time-frequency estimation of wireless channels. The motivation is to optimize channel usage by increasing the signal-to-noise ratio (SNR) after demodulation while keeping training overhead at a moderate level. This issue is important for single-input single-output (SISO) and multiple-input multiple-output (MIMO) systems but particularly so for the latter. Linear operators offer a general mathematical framework for symbol modulation in channels that vary both temporally and spectrally within the duration and bandwidth of one symbol. In particular, we present a channel model that assumes first-order temporal and spectral fluctuations within one symbol or symbol block. Discrete prolate spheroidal sequences (Slepian sequences) are used as pulse-shaping functions. The channel operator in the Slepian basis is almost tridiagonal, and the simple intersymbol interference pattern can be exploited for efficient and fast decoding using Viterbi's algorithm. To prove the concept, we use the acoustic channel as a meaningful physical analogy to the radio channel. In acoustic 2 /spl times/ 2 MIMO experiments, our method produced estimation results that are superior to first-order time-only, frequency-only, and zeroth-order models by 7.0, 9.4, and 11.6 db. In computer simulations of cellular wireless channels with realistic temporal and spectral fluctuations, time-frequency estimation gains us 12 to 18 db over constant-only estimation in terms of received SNR when signal-to-receiver-noise is 10 to 20 db. The bit error rate (BER) decreases by a factor of two for a binary constellation.

A cross-layer quality-of-service mapping architecture for video delivery in wireless networks

Providing quality-of-service (QoS) to video delivery in wireless networks has attracted intensive research over the years. A fundamental problem in this area is how to map QoS criterion at different layers and optimize QoS across the layers. In this paper, we investigate this problem and present a cross-layer mapping architecture for video transmission in wireless networks. There are several important building blocks in this architecture, among others, QoS interaction between video coding and transmission modules, QoS mapping mechanism, video quality adaptation, and source rate constraint derivation. We describe the design and algorithms for each building block, which either builds upon or extend the state-of-the-art algorithms that were developed without much considerations of other layers. Finally, we use simulation results to demonstrate the performance of the proposed architecture for progressive fine granularity scalability video transmission over time-varying and nonstationary wireless channel.

Delay and synchronization control middleware to support real-time multimedia services over wireless PCS networks

This paper presents a discussion of several middleware design issues related to the support of real-time multimedia communications over wireless personal communication services (PCS) networks. Specific interests are given to error recovery and synchronization mechanisms. A hybrid automatic repeat request (ARQ) scheme is employed for error control in the proposed system because it can efficiently adapt to nonstationary wireless channels and yield high throughput and reliability. In particular, delay and delay jitter control related to retransmissions in the error control module are addressed. An adaptive source rate control mechanism is used to handle the fluctuation of the effective channel data rate due to retransmissions. An adaptive synchronization scheme is developed to compensate for long-term delay variation caused by large-scale fading so that synchronization is preserved and end-to-end delay is kept low. Simulation results from the performance evaluation of the system are presented.