Time-correlated Fading Channels Research Articles

On Distributed Detection in EH-WSNs With Finite-State Markov Channel and Limited Feedback

We consider a network of N sensors, tasked with solving binary distributed detection, a fusion center (FC), and a feedback channel from the FC to sensors. Each sensor is capable of harvesting energy and is equipped with a finite-size battery to store randomly arrived energy. Sensors process their observations and transmit their symbols to the FC over orthogonal and Markovian time correlated fading channels. The FC fuses the received symbols and makes a global binary decision. We aim at developing adaptive channel-dependent transmit power control policies such that J-divergence based detection metric is maximized at the FC, subject to total transmit power constraint. Modeling quantized fading channel, energy arrival, and battery dynamics as time-homogeneous finite-state Markov chains, and the network lifetime as a geometric random variable, we formulate our power control optimization problem as a discounted infinite-horizon constrained Markov decision process (MDP) problem, where sensors’ transmit powers are functions of the battery states, quantized channel gains, and the arrived energies. We utilize stochastic dynamic programming and Lagrangian approach to find the optimal and sub-optimal power control policies. We demonstrate that our sub-optimal policy provides a close-to-optimal performance with a reduced computational complexity and without imposing signaling overhead on sensors.

Age-Optimal Low-Power Status Update Over Time-Correlated Fading Channel

In this paper, we consider transmission scheduling in a status update system, where updates are generated periodically and transmitted over a Gilbert-Elliott fading channel. The goal is to minimize the long-run average age of information (AoI) under a long-run average energy constraint. We consider two practical cases to obtain channel state information (CSI): (i) without channel sensing and (ii) with delayed channel sensing. For (i), CSI is revealed by the feedback (ACK/NACK) of a transmission, but when no transmission occurs, CSI is not revealed. Thus, we have to balance tradeoffs across energy, AoI, channel exploration, and channel exploitation. The problem is formulated as a constrained partially observable Markov decision process (POMDP). We show that the optimal policy is a randomized mixture of no more than two stationary deterministic policies each of which is of a threshold-type in the belief on the channel. For (ii), (delayed) CSI is available via channel sensing. Then, the tradeoff is only between the AoI and energy. The problem is formulated as a constrained MDP. The optimal policy is shown to have a similar structure as in (i) but with an AoI associated threshold. With these, we develop an optimal structure-aware algorithm for each case.

Dynamic event-triggered fault estimation for complex networks with time-correlated fading channels

In this paper, the problem of dynamic event-based finite-horizon H∞ fault estimation is studied for a class of discrete-time complex networks with fading channels. In the communication from sensor to estimator, the channel fading phenomenon is considered, which is a dynamic process and reflects the actual situation. Moreover, the dynamic event-triggered mechanism is implemented to schedule the signal transmissions. This paper plans to design a fault estimator to meet the predetermined H∞ performance requirements. First, sufficient conditions are established to ensure the existence of the desired H∞ fault estimator. Then, the gain of the H∞ fault estimator is derived in terms of the solution to a set of recursive matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of our developed fault estimation approach.

Distributed fusion filtering for multi-sensor systems under time-correlated fading channels and energy harvesters

In this paper, the distributed fusion filtering issue is investigated for multi-sensor systems with the constraints from both time-correlated fading channels and energy harvesters. A specific scenario is considered where the sensors can harvest energy from the natural environment and may consume a certain amount of energy when transmitting measurements to the filters. In order to properly deal with the energy supply relationship between a battery and multiple sensors, a dynamic energy-allocated rule is proposed in this paper, i.e., the storage battery provides energy to sensors in order of different sensors’ priorities. Additionally, the channel fading phenomenon is also taken into consideration and the fading coefficient is described by a dynamic process. In this paper, we are committed to designing a local filter such that, under the effects of the time-correlated fading channels and energy harvesters, an upper bound on the local filtering error covariance is firstly derived by using the mathematical induction and then the upper bound is minimized by designing the local filter gain. Next, the covariance intersection approach is employed to obtain the fusion estimates. Finally, a simulation is provided to verify that the presented filtering strategy is feasible and effective.

Recursive filtering for complex networks with time-correlated fading channels: An outlier-resistant approach

In this paper, the outlier-resistant recursive filtering problem is fully discussed for complex networks with time-correlated fading channels. Each sensor is able to communicate with its corresponding filter within a set of time-correlated fading channels, and the channel coefficient is assumed to be governed by certain dynamical process. In order to alleviate undesired effects (e.g. performance degradation or even divergence of the filtering error) from possible measurement outliers, a certain saturation structure is introduced in our constructed filter. The purpose is at estimating network states with satisfactory error dynamics with not only time-correlated fading channels but also measurement outliers. First, an augmented model is constructed in order to combine network dynamic evolutions along with channel coefficients. Subsequently, by means of the inductive method, upper covariance bounds are first given and later minimized by properly parameterizing filter gains. Finally, two example are given for effectiveness validation.

Fusion estimation for stochastic uncertain systems with time-correlated rician fading channels

In this article, a fusion estimation scheme is proposed for stochastic uncertain systems with time-correlated fading channels (TFCs). A batch of random variables obeying Gaussian distributions is employed to describe the parameter uncertainties. The sensor communicates with the local filter through a TFC where the evolution of the channel coefficient is characterized by a certain dynamic process with one-step correlated noises. For further analyzing the effects of TFCs, a class of additional variables is first introduced by augmenting the dynamics of channel coefficients and the concerned system. Then, a new group of modified local filters is developed and the unbiasedness of local filters is examined by means of inductive method. Furthermore, the filter gains which minimize the local filtering error covariances are designed for the modified local filters in the simultaneous presence of stochastic uncertainties and TFCs. Subsequently, the cross-covariances among local estimates are computed iteratively and, based on the obtained cross-covariances as well as the unbiased local estimates and their corresponding filtering error covariances, a fusion estimate is obtained by using weighted least square fusion method. Finally, the effectiveness of the proposed fusion estimation scheme is verified by two examples.

Recursive Quadratic Filtering for Linear Discrete Non-Gaussian Systems Over Time-Correlated Fading Channels

Recursive Quadratic Filtering for Linear Discrete Non-Gaussian Systems Over Time-Correlated Fading Channels

Optimal linear filtering for networked control systems under time correlated fading channel and noise

In this paper, the optimal filtering problem for discrete-time networked control systems affected by fading channels is investigated where both the fading channel and channel noise are time-correlated. Each fading channel is modeled as a scalar uncertain stochastic discrete-time system, and the channel noise is described by a discrete-time linear system perturbed by white noise. By using multiple recursive terms and the correlations of the signals in the systems, an optimal linear filter is proposed such that it is implemented in a recursive manner. The optimal filter designed has time independent computation structure, hence is easier to be implemented in practice. A vehicle tracking example is provided to illustrate the effectiveness and performance of the theoretic results obtained.

Robust Recursive Filtering for Stochastic Systems With Time-Correlated Fading Channels

This article is concerned with the robust recursive filtering (RF) problem for a class of stochastic uncertain systems subject to time-correlated fading channels. The measurement received by the sensor is transmitted to the remote filter through the time-correlated fading channel where the channel coefficient evolves according to a certain dynamics and hence exhibits a time-correlated nature. The parameter uncertainties of the system are described by norm-bounded unknown matrices. By introducing a class of auxiliary variables, an augmented system is constructed to reflect the dynamics of the fading coefficient and state simultaneously. Then, a recursive filter is designed which is capable of online computation. Furthermore, an upper bound is guaranteed for the filtering error covariance (FEC) for the possible parameter uncertainties as well as the time-correlated fading channels. With the help of the completing-the-squares technique, filter gains are parameterized by minimizing the obtained upper bound. Finally, two examples are employed to verify the effectiveness of the proposed robust RF method.

A Resilient Approach to Recursive Distributed Filtering for Multirate Systems Over Sensor Networks With Time-Correlated Fading Channels

This paper addresses the resilient distributed filtering problem for a class of time-varying multirate systems over sensor networks subject to time-correlated fading channels. The time-correlated fading channel, whose fading coefficient is described by a dynamical process, is introduced to better capture the time-correlation property of the wireless channels. Moreover, the phenomenon of stochastic gain fluctuations is taken into account to accommodate the potential implementation errors, thereby achieving resilient filtering performance. The lifting technique is employed to cast the underlying multirate system into a general signal-rate one, and then an augmented system is formulated to account for the dynamics from both the plant and the fading coefficients. Our aim is to design a distributed filter such that certain upper bound is first guaranteed on the filtering error covariance and then minimized at each sampling instant.With the help of trace operations, the gain parameters of the desired distributed filter are obtained in terms of the solutions to two sets of recursive equations. Finally, the effectiveness of the developed filtering algorithm is verified via an illustrative example.

On the Impact of Time-Correlated Fading for Downlink NOMA

This paper investigates the performance of non-orthogonal multiple access (NOMA) systems over time-correlated Rayleigh fading channels, where the users have heterogeneous quality of service requirements, e.g., a latency-critical user with a low target rate and a delay-tolerant user with a large target rate. In order to meet the different requirements of the users, two partial hybrid automatic repeat request (HARQ) schemes, including partial HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR), are proposed. The closed-form expressions of outage probabilities for NOMA with and without re-transmission are derived. With the developed outage probabilities, a condition on the superiority of NOMA to orthogonal multiple access (OMA) is obtained. In particular, the condition is characterized by the transmit powers for NOMA without re-transmission and is obtained by using the bisection method in the case with re-transmission. To further improve the performance of the HARQ enabled NOMA schemes, we consider an average transmit power minimization problem by optimizing the transmit power among different transmission rounds with outage constraints. However, due to the complexity of the developed outage probabilities, the formulated problem is non-convex and challenging to solve. Then we approximate the original problem by deriving the upper-bound approximations of the outage probabilities and solve it by using the geometric programming method. Simulation results demonstrate the accuracy of the developed analytical results. It is shown that the performance of NOMA is superior to OMA, only when the obtained condition is satisfied. HARQ-CC and HARQ-IR can enhance the outage performance of NOMA over time-correlated fading channels and the HARQ-IR has excellent performance in terms of energy efficiency.

Optimal linear filtering for networked control systems with time-correlated fading channels

In this paper, the problem of filtering for discrete-time networked control systems with time-correlated fading channels is considered where each time-correlated fading channel is described by a one-dimensional discrete-time uncertain linear system model with random disturbance. Using the innovation analysis approach and optimal estimates for the products of channel gain and system state obtained, an optimal linear recursive filter is proposed, that has time-independent complexity, and does not increase computation and storage load with time. An example and simulation are provided to show the effectiveness and potential of the proposed new design technique.

Energy-Efficient Optimization for HARQ Schemes Over Time-Correlated Fading Channels

Energy efficiency of three common hybrid automatic repeat request (HARQ) schemes, including Type I HARQ, HARQ with chase combining (HARQ-CC) and HARQ with incremental redundancy (HARQ-IR), is analyzed and joint power allocation and rate selection to maximize the energy efficiency is investigated in this paper. Unlike prior literature, time-correlated fading channels are considered and two widely concerned quality of service (QoS) constraints, i.e., outage and goodput constraints, are also considered in the optimization, which further differentiates this paper from prior ones. Using a unified expression of asymptotic outage probabilities, optimal transmission powers and optimal rate are derived in closed forms to maximize the energy efficiency while satisfying the QoS constraints. These closed-form solutions then enable a thorough analysis of the maximal energy efficiencies of various HARQ schemes. It is revealed that with low-outage constraint, the maximal energy efficiency achieved by Type I HARQ is $\frac{1}{4\ln 2}$ b/J, while HARQ-CC and HARQ-IR can achieve the same maximal energy efficiency as $\frac{\kappa _\infty }{4\ln 2}$ b/J, where $\kappa _\infty = 1.6617$ . Moreover, time correlation in the fading channels has a negative impact on the energy efficiency, whereas large maximal allowable number of transmissions is favorable for the improvement of energy efficiency. The effectiveness of the energy-efficient optimization is verified by extensive simulations and the results also show that HARQ-CC can achieve the best tradeoff between energy efficiency and spectral efficiency among the three HARQ schemes.

An Analysis Framework for Buffer-Aided Relaying Under Time-Correlated Fading Channels

In this paper, we propose a framework to analyze the performance of buffer-aided (BA) relaying under time-correlated fading channels in terms of the queueing behavior of packets at the relay's buffer. Unlike independent and identically distributed (i.i.d.) fading, correlated fading brings challenges in performance analysis since the state transition probabilities of buffer occupancy become time variant. To overcome this issue, we first establish an aggregate quasi-birth-death (QBD) Markov chain integrating both the buffer occupancy process and the channel fading process, then analyze the stationary distribution of the aggregate chain, and finally extract the stationary distribution of buffer occupancy from it. Using the stationary distribution of buffer occupancy, system throughput, end-to-end delay, and outage probability are derived. Numerical results verify our analyses and show that the throughput of BA relaying under correlated fading channels can approach the one under i.i.d. fading only for loose delay constraints or high fading margins. For stringent delay constraints and low fading margins, correlated fading causes great degradation of throughput. In particular, a throughput loss of about 16% under an infinite buffer (28% under a finite buffer) is observed for the requirement of an average delay of 20 slots and a fading margin of 5 dB. This means that the designs based on i.i.d. fading are not always feasible for correlated fading. According to these observations, some insights on performance degradation and guidelines on redesigning improved policies under correlated fading are provided.

Low-Complexity Optimal Scheduling over Time-Correlated Fading Channels with ARQ Feedback

We investigate the downlink scheduling problem under Markovian ON/OFF fading channels, where the instantaneous channel state information is not directly accessible, but is revealed via ARQ-type feedback. The scheduler can exploit the temporal correlation/channel memory inherent in the Markovian channels to improve network performance. However, designing low-complexity and throughput-optimal algorithms under temporal correlation is a challenging problem. In this paper, we find that under an average number of transmissions constraint, a low-complexity index policy is throughput-optimal. The policy uses Whittle's index value, which was previously used to capture opportunistic scheduling under temporally correlated channels. Our results build on the interesting finding that, under the intricate queue length and channel memory evolutions, the importance of scheduling a user is captured by a simple multiplication of its queue length and Whittle's index value. The proposed queue-based index policy has provably low complexity. Numerical results show that significant throughput gains can be realized by exploiting the channel memory using the proposed low-complexity policy.

Inverse Moment Matching Based Analysis of Cooperative HARQ-IR over Time-Correlated Nakagami Fading Channels

This paper analyzes the performance of cooperative hybrid automatic repeat request with incremental redundancy (HARQ-IR) and proposes a new approach of outage probability approximation for performance analysis. A general time-correlated Nakagami fading channel covering fast fading and Rayleigh fading as special cases is considered here. An efficient inverse moment matching method is proposed to approximate the outage probability in a closed form. The effect of approximation degree is theoretically analyzed to ease its selection. Moreover, diversity order of cooperative HARQ-IR is analyzed. It is proved that the diversity order is irrelevant to the time correlation coefficient $\rho$ , as long as $\rho , and full diversity from both spatial and time domains can be achieved by cooperative HARQ-IR under time-correlated fading channels. The accuracy of the analytical results is verified by computer simulations, and the results reveal that cooperative HARQ-IR scheme can benefit from high fading order and low channel time correlation. Optimal rate selection to maximize the long-term average throughput given a maximum allowable outage probability is finally discussed as one application of the analytical results.

Analysis of HARQ-IR Over Time-Correlated Rayleigh Fading Channels

In this paper, performance of hybrid automatic repeat request with incremental redundancy (HARQ-IR) over Rayleigh fading channels is investigated. Different from prior analysis, time correlation in the channels is considered. Under time-correlated fading channels, the mutual information in multiple HARQ transmissions is correlated, making the analysis challenging. By using polynomial fitting technique, probability distribution function of the accumulated mutual information is derived. Three meaningful performance metrics including outage probability, average number of transmissions, and long term average throughput (LTAT) are then derived in closed-forms. Moreover, diversity order of HARQ-IR is also investigated. It is proved that full diversity can be achieved by HARQ-IR, i.e., the diversity order is equal to the number of transmissions, even under time-correlated fading channels. These analytical results are verified by simulations and enable the evaluation of the impact of various system parameters on the performance. Particularly, the results unveil the negative impact of time correlation on the outage and throughput performance. The results also show that although more transmissions would improve the outage performance, they may not be beneficial to the LTAT when time correlation is high. Optimal rate design to maximize the LTAT is finally discussed and significant LTAT improvement is demonstrated.

Differential Space-Time Modulation Using DAPSK Over Rician Fading Channels

This paper studies differential space-time modulation using diversity-encoded differential amplitude and phase shift keying (DAPSK) for the multiple-input multiple-output (MIMO) system over independent but not identically distributed (inid) time-correlated Rician fading channels. An asymptotic maximum likelihood (AML) receiver is developed for differentially detecting diversity-encoded DAPSK symbol signals by operating on two consecutive received symbol blocks sequentially. Based on Beaulieu's convergent series, the bit error probability (BEP) upper bound is analyzed for the AML receiver over inid time-correlated Rician fading channels. Particularly, an approximate BEP upper bound of the AML receiver is also derived for inid time-invariant Rayleigh fading channels with large received signal-to-noise power ratios. By virtue of this approximate bound, a design criterion is developed to determine the appropriate diversity encoding coefficients for the proposed DAPSK MIMO system. Numerical and simulation results show that the AML receiver for diversity-encoded DAPSK is nearly optimum when the average received signal-to-noise power ratios are high and the channel is heavily correlated fading and can provide better error performance than conventional noncoherent MIMO systems when the effect of non-ideal transmit power amplification is taken into account.

Cooperative ARQ With Relay Selection: An Analytical Framework Using Semi-Markov Processes

An important building block in cooperative diversity is relay selection, which has to ensure that a well-suited node is employed as a relay. The required coordination among nodes causes signaling overhead, which in turn can significantly devalue the performance benefits gained by cooperative diversity. A relay update policy defines when a new relay is selected; it can balance the tradeoff between performance and overhead. This tradeoff is studied using mathematical methods. We consider three relay selection schemes, i.e., permanent, reactive, and adaptive, which have different relay update rules. We develop an analytical framework using semi-Markov processes to evaluate the throughput and energy efficiency of cooperative automatic repeat request (ARQ) protocols in time-correlated multipath fading channels. Results reveal potential performance gains of different selection schemes under various conditions. The reactive and adaptive schemes make use of better suited relays due to frequent selections. If their selection overhead, however, is significant, a permanent relay can achieve higher throughput due to negligible overhead. The impact of temporal correlation of fading channels on throughput and energy efficiency is also shown. These insights can be applied for development of cooperative communication protocols.

Cooperative Strategies for Wireless Relay Networks With Cochannel Interference Over Time-Correlated Fading Channels

Practical mobile communication systems suffer from time-variant channel fading and cochannel interference, both of which give rise to challenges concerning strategy design and performance analysis in wireless relay networks. Although these two aspects have attracted concerns in recent studies, most researchers still focused on dealing with a single problem and avoided intricate joint considerations. In this paper, we investigate the cooperative strategies for the communications of two cochannel pairs over time-correlated Rayleigh channels, and the system consists of a relay-assisted pair (Pair 1) along with a direct transmission pair (Pair 2). We begin with a theoretical evaluation on a conventional relay selection (RS) algorithm that maximizes outdated signal-to-interference-plus-noise ratio (M-SINR), and then develop a more sophisticated method that involves extra statistical and interference information based on the concept of minimizing outage probability (MOP). Closed-form outage probability expressions are derived for both pairs with each RS algorithm, and the MOP-type selection is confirmed to outperform M-SINR in robustness against channel fluctuation when the network operates on medium-to-high signal-to-noise ratio (SNR). Implementation issues of the RS methods are discussed to clarify their overhead and to support their practicability. Further, an interference control scheme is proposed to guarantee Pair 2 communication quality under either RS algorithm by disqualifying the relays that probably cause severe cochannel interference to Pair 2. The interference control mechanism is carried out via a novel threshold parameter e that represents the tolerance of outage performance degradation of Pair 2 resulting from interference. The closed-form analysis validates that the given e is rational for an arbitrary network scenario, and it can balance the two pairs' outage behavior under a proper configuration. We reveal the influence of factors such as average SNR, transmit rate, and network topology on system performance to make a comprehensive comparison between diverse cooperative strategies.