A New Approach of Channel Modeling in HAPS Based Networks and Their System Performance Analysis

This paper concerns channel modeling for High Altitude Platform Systems (HAPS) and the performance evaluation of Hybrid_ARQ in the WiMAX network provided by HAPS. The stratospheric platform or HAPS is currently a new proposal for WiMAX technology. Firstly we study the HAPS channel behavior as a Finite State Markov Channel (FSMC). In this way, the range of magnitude of the fading channel gain is partitioned into a finite number of states; then based on level crossing rates, the state transition probabilities are derived. The validity of the proposed model is evaluated by theoretical and link level simulation results. Next, we use the derived state transition probabilities as channel model parameters in OPNET simulator for HAPS-WiMAX to calculate HARQ system level measures. The paper compares the performance obtained using two different models in fading effects, i.e. AWGN and our HAPS channel model. In addition, the influence of parameters is analyzed through comparison between our model and the Stanford University Interim (SUI) channel models, in terms of the Bit Error Rate (BER).     

噪声功率时变的瑞利慢衰落信道有限状态Markov模型

对衰落信道的准确建模对于自适应无线通信、认知无线电等应用中的信道预测具有重要意义。针对噪声功率存在时变特性的无线通信应用环境,提出了一种新的瑞利衰落信道的有限状态Markov模型。通过将接收信号的衰落电平进行离散化处理,建立了衰落电平区间与Markov模型状态之间的一一对应关系,推导了门限电平与状态转移概率和状态分布概率之间的理论关系式,并在此基础上提出了一种易于实现的基于等概率的信道模型。理论分析与仿真结果表明:在噪声功率时变的条件下,已有的基于信噪比的模型失效,而该模型能准确反映信道的衰落特性,最大相对误差小于7%。      

A Markov model for the mobile propagation channel

A finite-state Markov model is fitted to the mobile propagation channel by the use of contingency tables. Narrow-band Rayleigh and Ricean fading are considered in detail, but the techniques extend to other types of fading. Several criteria may indicate that a first-order finite-state Markov model sufficiently characterizes the channel behavior. The parameters of the model are obtained both from theoretical analysis and simulation. Functional dependence between the transition probabilities and the steady-state probabilities is found in the slow fading case     

Novel Approach for Modeling Wireless Fading Channels Using a Finite State Markov Chain

Empirical modeling of wireless fading channels using common schemes such as autoregression and the finite state Markov chain (FSMC) is investigated. The conceptual background of both channel structures and the establishment of their mutual dependence in a confined manner are presented. The novel contribution lies in the proposal of a new approach for deriving the state transition probabilities borrowed from economic disciplines, which has not been studied so far with respect to the modeling of FSMC wireless fading channels. The proposed approach is based on equal portioning of the received signal‐to‐noise ratio, realized by using an alternative probability construction that was initially highlighted by Tauchen. The associated statistical procedure shows that a first‐order FSMC with a limited number of channel states can satisfactorily approximate fading. The computational overheads of the proposed technique are analyzed and proven to be less demanding compared to the conventional FSMC approach based on the level crossing rate. Simulations confirm the analytical results and promising performance of the new channel model based on the Tauchen approach without extra complexity costs.     

Modeling End-to-End Wireless Lossy Channels: A Finite-State Markov Approach

In this paper, we present a model for wireless losses in packet transmission data networks. The model provides information about the wireless channel status that can be used in congestion control schemes. A Finite State Markov Channel (FSMC) approach is implemented to model the wireless slow fading for different modulation schemes. The arrival process statistics of the packet traces determine the channel state transition probabilities, where the statistics of both error-free and erroneous bursts are captured. Later, we establish SNR partitioning scheme that uses the transition probabilities as a basis for the state margins. The crossover probability associated with each state is calculated accordingly. We also propose an end-to-end approach to loss discrimination based on the channel state estimation at the receiver. Finally, we present a scheme for finding the channel optimal number of states as a function of the SNR. The presented FSMC approach does not restrict the state transitions to the adjacent states, nor does impose constant state duration as compared to some literature studies. We validate our model by experimental packet traces. Our simulation results show the feasibility of building a fading channel model for better wireless-loss awareness.     

Two-Layer multistate Markov model for modeling a 1.8 GHz narrow-band wireless propagation channel in urban Taipei city

An accurate propagation channel model is crucial for evaluating the performance of a communication system. A propagation channel can be described by a Markov model with a finite number of states, each of which is considered to be quasi-stationary over a short period. This work proposes a two-layer multistate Markov model. Instead of a large Markov transition matrix used in a conventional single-layer Markov model, two small Markov transition matrices are employed by a two-layer Markov model to reduce the computational complexity of the model without increasing the memory requirements. The proposed approach characterizes the multiplicative processes of a propagation channel as shadowing and fast fading. Each type of fading is considered as several channel states and each of the states corresponds to a specific mixed Rayleigh-lognormal distribution. Numerical results reveal that the statistical properties of the simulated data are quite close to those obtained from the measurements; indeed, the proposed two-layer Markov model is more accurate and less complex, and requires less memory than the single-layer Markov model. Furthermore, the proposed two-layer Markov model enables the fading statistics and error probability performance of a quadrature phase-shift keying modulation scheme in a typical urban Taipei environment to be more accurately predicted. Besides, it can easily be applied to similar environmental scenarios.     

Optimizing the transmit power for slow fading channels

We consider the design of power-adaptive systems for minimizing the average bit-error rate over flat fading channels. Channel state information, obtained through estimation at the receiver, is sent to the transmitter over a feedback channel, where it is used to optimally adapt the transmit power. We consider finite-state optimal policies to reflect the limitations of the feedback channel. We develop an iterative algorithm that determines the optimal finite-state power control policy given the probability density function (PDF) of the fading. Next, we present a discretized formulation of the problem and obtain a suboptimal solution via standard dynamic programming techniques. The discretization of the problem enables us to obtain a suboptimal policy for arbitrary fading channels for which the analytic expression of the fading probability density function is not available. Simulation results are used to draw conclusions regarding the effects of limited feedback channel capacity, delay and number of states on the bit-error rate performance of the proposed policies under slow and moderate fading conditions     

Shape-gain vector quantization for noisy channels with applicationsto image coding

A new design procedure for shape-gain vector quantizers (SGVQs) which leads to substantially improved robustness against channel errors without increasing the computational complexity is proposed. This aim is achieved by including the channel transition probabilities in the design procedure, leading to an improved assignment of binary codewords to the coding regions as well as a change of partition and centroids. In contrast to conventional design, negative gain values are also permitted. The new design procedure is applied to adaptive transform image coding. Simulation results are compared with those obtained by the conventional design procedure. The new algorithm is particularly useful for heavily distorted or fading channels     

ARQ error control for fading mobile radio channels

In this paper, we study the correlation properties of the fading mobile radio channel. Based on these studies, we model the channel as a one-step Markov process whose transition probabilities are a function of the channel characteristics. Then we present the throughput performance of the Go-Back-N and selective-repeat automatic repeat request (ARQ) protocols with timer control, using the Markov model for both forward and feedback channels. This approximation is found to be very good, as confirmed by simulation results     

Finite-state Markov channel-a useful model for radio communicationchannels

The authors first study the behavior of a finite-state channel where a binary symmetric channel is associated with each state and Markov transitions between states are assumed. Such a channel is referred to as a finite-state Markov channel (FSMC). By partitioning the range of the received signal-to-noise ratio into a finite number of intervals, FSMC models can be constructed for Rayleigh fading channels. A theoretical approach is conducted to show the usefulness of FSMCs compared to that of two-state Gilbert-Elliott channels. The crossover probabilities of the binary symmetric channels associated with its states are calculated. The authors use the second-order statistics of the received SNR to approximate the Markov transition probabilities. The validity and accuracy of the model are confirmed by the state equilibrium equations and computer simulation     

POMDP-Based Coding Rate Adaptation for Type-I Hybrid ARQ Systems over Fading Channels with Memory

We address the issue of optimal coding rate scheduling for adaptive type-I hybrid automatic repeat request wireless systems. In this scheme, the coding rate is varied depending on channel, buffer and incoming traffic conditions. In general, we consider the hidden Markov model for both time-varying flat fading channel and bursty correlated incoming traffic. It is shown that the appropriate framework for computing the optimal coding rate allocation policies is partially observable Markov decision process (POMDP). In this framework, the optimal coding rate allocation policy maximizes the reward function, which is a weighted sum of throughput and buffer occupancy with appropriate sign. Since polynomial amount of space is needed to calculate the optimal policy even for a simple POMDP problem, we investigate maximum-likelihood, voting and Q-MDP policy heuristic approaches for the purpose of efficient and real-time solution. Our results show that three heuristics perform close to completely observable system state case if the fading and/or traffic state mixing rate is slow. On the other hand, when the channel fading is fast, Q-MDP heuristic is the most throughput-efficient among considered heuristics. Also, its performance is close to the optimal coding rate allocation policy of fully observable system state case. We also explore the performances of the proposed heuristics in the bursty correlated traffic case and show that maximum-likelihood and voting heuristics consistently outperform the non-adaptive case     

Bayesian blind turbo receiver for coded OFDM systems with frequencyoffset and frequency-selective fading

The design of a blind receiver for coded orthogonal frequency-division multiplexing communication systems in the presence of frequency offset and frequency-selective fading is investigated. The proposed blind receiver iterates between a Bayesian demodulation stage and a maximum a posteriori channel decoding stage. The extrinsic a posteriori probabilities of data symbols are iteratively exchanged between these two stages to achieve successively improved performance. The Bayesian demodulator computes the a posteriori data symbol probabilities, based on the received signals (without knowing or explicitly estimating the frequency offset and the fading channel states), by using Markov chain Monte Carlo (MCMC) techniques. In particular, two MCMC methods-the Metropolis-Hastings algorithm and the Gibbs sampler-are studied for this purpose. Computer simulation results show that the proposed Bayesian blind turbo receiver can achieve good performance and is robust against modeling mismatch     

Achievable Rates with Imperfect Transmitter Side Information Using a Broadcast Transmission Strategy

rdquoWe investigate the performance of the broadcast approach for various fading distributions, which correspond to different models of partial transmit channel state information (CSI). The first model considered is the quantized limited feedback. In this model, the receiver can send as feedback only a finite number of bits describing the fading gain. We derive the optimal power allocation for the broadcast approach for the quantized feedback model. For a Rayleigh fading channel, numerical results here show that if the feedback word can be longer than one bit, the broadcasting gain becomes negligible, due to diminished channel uncertainty. The second partial transmit CSI model is a stochastic Gaussian model with mean and variance information, which is commonly used for modeling the channel estimation error. In a single-input single-output (SISO) channel, this model also corresponds to the Ricean fading distribution, for which we derive maximal achievable broadcasting rates. We further consider a multiple-input single-output (MISO) channel, and derive the optimal power allocation strategy in a broadcast approach. Numerical results here show that uniform power allocation is preferable over beamforming power allocation in the region where broadcasting gain over single level coding is non-negligible.     

Cross-Layer Rate and Power Adaptation Strategies for IR-HARQ Systems over Fading Channels with Memory: A SMDP-Based Approach

Incremental-redundancy hybrid automatic repeatrequest (IR-HARQ) schemes are proposed in several wireless standards for increased throughput-efficiency and greater reliability. We investigate transmit power and modulation order adaptation strategies for the IR-HARQ schemes over correlated Rayleigh fading channels using semi-Markov decision processbased model. In order to jointly analyze physical layer and link layer, transmitter model incorporates a finite-size buffer that receives randomly varying traffic from a higher layer application. It is assumed that channel variations can be modeled with a firstorder Markov chain. We show that the optimal transmission power and rate adaptation laws under buffering delay and packet overflow constraints can be obtained using the framework of semi-Markov decision process. We discuss three different adaptation models for the IR-HARQ schemes and compare their performances with the non-adaptive scheme. It is shown that unique optimal policy exists for each case and it can be computed using linear programming approach. This optimal policy is then applied for realistic channel fading and incoming traffic samples to evaluate its performance for both hard-decision and softdecision decoding. Simulation results in general point out that substantial power savings can be achieved using adaptation and also if the transmission-delay requirements are relaxed.     

Analysis of Go-Back-N ARQ in Block Fading Channels

This work analyzes the throughput of Go-Back-N (GBN) in block fading, a model frequently used for slow fading wireless channels. We devise hidden Markov models and block transition probabilities for the block fading channel, allowing us to calculate the throughput of GBN with reliable feedback, as well as unreliable feedback. The advantages of this approach include generality: it applies to two-state as well as multi-state models for forward and reverse channels. Also, the results for both reliable and unreliable feedback are expressed in terms of probability matrices, which can be used as convenient building blocks in the analysis and simulation of larger systems. Simulations verify our analysis.     

Saturation throughput analysis of IEEE 802.11 in the presence of non ideal transmission channel and capture effects

In this paper, we provide a saturation throughput analysis of the IEEE 802.11 protocol at the data link layer by including the impact of both transmission channel and capture effects in Rayleigh fading environment. Impacts of both non-ideal channel and capture effects, specially in an environment of high interference, become important in terms of the actual observed throughput. As far as the 4-way handshaking mechanism is concerned, we extend the multi-dimensional Markovian state transition model characterizing the behavior at the MAC layer by including transmission states that account for packet transmission failures due to errors caused by propagation through the channel. This way, any channel model characterizing the physical transmission medium can be accommodated, including AWGN and fading channels. We also extend the Markov model in order to consider the behavior of the contention window when employing the basic 2-way handshaking mechanism. Under the usual assumptions regarding the traffic generated per node and independence of packet collisions, we solve for the stationary probabilities of the Markov chain and develop expressions for the saturation throughput as a function of the number of terminals, packet sizes, raw channel error rates, capture probability, and other key system parameters. The theoretical derivations are then compared to simulation results confirming the effectiveness of the proposed models.     

Karhunen-Loeve expansion of the WSSUS channel output and itsapplication to efficient simulation

This paper derives a Karhunen-Loeve (K-L) expansion of the time-varying output of a multipath Rayleigh fading wide-sense-stationary uncorrelated-scattering (WSSUS) channel. It is shown that under the same mean-squared error condition, the number of terms required by the truncated K-L expansion is less than that of the series expansion obtained by using the discrete-path approximation of the channel so that simulation using the K-L expansion is more efficient. This computational advantage becomes more significant as higher simulation accuracy is required. The derived K-L expansion is applied to develop an efficient simulation technique for digital transmission over a multipath Rayleigh fading WSSUS channel using an optimum receiver. We show that the proposed technique requires shorter computation time than two other known simulation techniques     

Discrete Rayleigh fading channel modeling

In order to understand the behaviour of upper‐layer protocols and to design or fine tune their parameters over wireless networks, it is common to assume that the underlying channel is a flat Rayleigh fading channel. Such channels are commonly modeled as finite state Markov chains. Recently, hidden Markov models have also been employed to characterize these channels. In this paper, we study the different models that have been proposed along with the analysis of their validity. We start by presenting some preliminary concepts related to the modeling of the wireless communications channel. We then proceed to introduce finite state Markov channel models (FSMCs) along with the relations between them and the modulation schemes, error control protocols and channel coding. We propose and study the effects of taking into account the fading process in its characterization. We finish with a discussion on hidden Markov models for Rayleigh fading channel modeling. Copyright © 2004 John Wiley & Sons, Ltd.     

Effects of Nonzero-Centroid and Skewness of Fading Spectrum on Incoherent FSK and DPSK Error Probabilities

The effects of nonzero-centroid and skewness of a fading spectrum are shown to influence the binary error probabilities of incoherent FSK and differentially coherent phase-reversal (DPSK) matched-filter receivers. It is also shown that for incoherent FSK, the skewness or nonzero centroid in the fading spectrum causes different error probabilities for binary signals, resulting in a binary asymmetric channel. The difference in error probabilities for binary signals can be used as a criterion for aligning the transmitter and receiver antennas coupled through a fading channel.     

An average error probability evaluation in a fading environment using finite state Markov channel for LEO satellite communication system

Recent research shows that fading channels have a much larger capacity than anticipated with traditional approaches. This modern view on fading channels encouraged us to characterize these channels more precisely for better identification and use of wireless channel capacity.Since the Markov model is a natural way to approximate a channel with memory, many people have considered finite state first-order Markov modeling for describing a wireless communication channel.In this paper, we first introduce the relationship between a physical fading channel and the corresponding finite state Markov Model (FSMC) in case of low earth orbit (LEO) satellite communication system, which can be used for performance evaluation in an M-order quadrature amplitude-modulation (MQAM) transmission scheme by deriving an analytical expression of average bit error rate in Rayleigh fading channel. By establishing the FSMC, we show that the FSMC is accurate enough to evaluate the performance of MQAM modulation scheme to be implemented on board a LEO satellite communication system.