Time-varying Flat Fading Channels Research Articles

A PHY/MAC cross-layer design with transmit antenna selection and power adaptation for receiver blocking problem in dense VANETs

The medium access control (MAC) protocol of IEEE 802.11p dedicated to vehicular ad hoc networks (VANETs) employs carrier sense multiple access with collision avoidance (CSMA/CA) with distributed coordination function (DCF) which prohibits simultaneous transmissions in the same detection area in order to avoid possible interference and collision between neighboring vehicles. This prohibition results in temporary blocking of data reception, which reduces the average network throughput. To solve this problem, we propose a physical (PHY)/MAC cross-layer design based on transmit antenna selection (TAS) and transmit power adaptation (TPA). We consider spatial multiplexing zero-forcing Bell-labs layered space-time (ZF-VBLAST) over multiple-input and multiple-output (MIMO) time-varying flat fading channel to be implemented in vehicle-to-vehicle (V2V) communication. The cross-layer approach is implemented to get the maximal network throughput on the MAC layer by using the channel state information (CSI) obtained from the PHY layer, while the MIMO spatial multiplexing technique is used to increase the spectral efficiency. This design helps transmitters to select the best combination of transmitting antennas to maximize throughput and also to choose the adequate transmit power level to minimize neighbors' interference and collision. Also, this solution comes with a multi-user interference cancellation method that allows simultaneous transmissions as long as the sum of transmit antennas within the same radio range does not exceed the number of receive antennas. This paper evaluates the proposed cross-layer architecture by calculating the average network throughput per V2V links concerning different network parameters such as the number of vehicles and antennas. The simulation results show that this solution allows more vehicles to communicate simultaneously and thus significantly improves the average network throughput compared to 802.11p MAC standard, in particular for VANETs with high density.

Multi-Node ML Time and Frequency Synchronization for Distributed MIMO-Relay Beamforming Over Time-Varying Flat-Fading Channels

In this paper, we investigate maximum likelihood (ML) time delay (TD) and carrier frequency offset (CFO) synchronization in multi-node decode-and-forward cooperative relaying systems operating over time-varying channels. This new synchronization scheme is embedded into a distributed multiple input multiple output (MIMO)-relay beamforming transceiver structure to avoid the drawbacks of multidimensional ML estimation at the destination and to minimize the overhead cost. By accounting for a perfect Doppler spread value, the new synchronization solution delivers accurate TD and CFO estimates. For real-world operation, however, this new technique can be jointly implemented with any Doppler spread estimator in a new iterative scheme using a time-constant channel (TCC)-based synchronization method at the initialization step. The resulting TD and CFO estimates along with the channel estimates are then fed into a distributed MIMO-relay beamforming transceiver of $K$ single-antenna nodes, for pre-compensation at each node of the transmitted signals, to ensure constructive maximum ratio combining (MRC) at the destination. Simulation results show significant synchronization accuracy improvement over previous distributed multi-node synchronization techniques assuming TCCs. The latter translates into noticeable gains in terms of useful link-level throughput, more so at higher Doppler or with more relaying nodes.

High-Rate STBC Communication System Using Imperfect CSI Under Time-Selective Flat-Fading Environment

In this paper, a high-rate space-time block-coded (STBC) mobile communication system using imperfect channel-state-information (CSI) is presented, which is working over the time-selective flat-fading wireless channels. In the work, a flat-fading channel is modelled as a first-order Markov-process, taking into account Doppler shifts and carrier frequency offsets. The STBC data-rate 5/4 with two-transmitter antennas is attained by maximizing the coding gain and by minimizing the transmitted signal peak-to-minimum-power-ratio, while using the selective power scaling in combination with quadrature-phase-shift-keying digital modulation technique. The time-selective nature of underlying channel leads to reduction in the diversity gain, though optimum power scaling factor is incorporated. However, imperfect CSI usually arises due to the availability of noisy channel estimates at the receiver, which causes system performance degradation. Simulation results are presented to illustrate that the effective throughput in terms of frame-error-rate or symbol-error-rate of the presented data-rate $${5 \mathord{\left/ {\vphantom {5 4}} \right. \kern-0pt} 4}$$ STBC system is adversely affected because of the noisy channel estimates. But, an efficient channel estimator helps in combating the time-selectivity of channel, and in turn results in effective throughput improvement under the high signal-to-noise-ratio (SNR) conditions only. Subsequently, the data-rate $${9 \mathord{\left/ {\vphantom {9 8}} \right. \kern-0pt} 8}$$ STBC system with four-transmitter antennas is explored using similar strategy working over the time-nonselective (time-varying) flat-fading channels, which performs well under the high SNR and low channel estimation noise/error conditions.

Spectrum Sensing for Cognitive Radios With Unknown Noise Variance and Time-variant Fading Channels

The unknown noise variance and time-variant fading channels make the spectrum sensing design a challenging task for cognitive radios. Most existing sensing methods suffer from the information uncertainty and can hardly acquire promising performances in the adverse situations. To address this challenge, in this paper, we first formulate a dynamic state-space model for spectrum sensing, in which the unknown noise variance and time-variant flat fading channels are all taken into considerations. The dynamic behaviors of both primary user states and fading channels are characterized by two discrete state Markov chains. Based on this model, a novel spectrum sensing scheme is designed to recursively estimate the occupancy state of primary users, by estimating the time-variant fading channel gain and noise parameters jointly. The joint estimation is primarily premised on a maximum a posteriori probability criterion and the marginal particle filtering schemes. Simulation results are provided to demonstrate the advantages of our proposed method, which can significantly improve the sensing performance over time-variant flat fading channels, even with unknown noise variance.

Joint detection scheme for cooperative spectrum sensing in cognitive radio network

In this paper, a new architecture of cognitive radio network (CRN) is presented for future dynamic spectrum sharing in time-variant flat fading (TVFF) channels. We consider a practical scenario where secondary users (SUs) are able to access the idle spectrum by secondary user routers (SU_Rs). Managed by a fusion center (FC), SU_Rs can work together to capture the idle spectrum, and then assign to the SUs. Besides, it is imperative to guarantee the wireless communication quality between primary base station (P_BS) and SU_Rs. Therefore, a new cooperative spectrum sensing (CSS) algorithm is suggested to recursively estimate the channel state information (CSI) while capturing the idle licensed band. The united mathematics model relies on a dynamic state-space model (DSM) and a Bernoulli filters (BF) algorithm. TVFF channels are modeled as finite-state Markov channel (FSMC). In order to reduce complexity of CSS, the particles are manipulated and reconstructed. Experimental simulations demonstrate that, by exploiting dynamic CSI, sensing performance of the new CSS algorithm will surpass the traditional schemes and this new architecture can be used in a realistic spectrum sharing system.

Data‐assisted channel estimation and performance analysis for two‐way amplify‐and‐forward relay networks with M ‐ary frequency shift keying modulation

In this study, a new method is proposed for channel estimation and symbol detection in amplify-and-forward two-way relay networks with frequency shift keying signalling, over block fading as well as time-varying Rayleigh flat fading channels. It relies solely on information symbols to estimate reciprocal and non-reciprocal channels without pilot symbols assistance. To achieve this goal, users apply known periodic phase shifts to their transmit symbols and adopt maximum likelihood or linear minimum mean square error criteria to discriminate and estimate the two composite channels. Optimal and suboptimal phase shifts are designed to minimise the mean square error (MSE). Minimum distance receiver is then used for symbol detection. An approximate upper bound for the resulting bit error rate (BER) is derived and the effect of channel variation rate on the MSE and BER is studied. Finally, simulation results are provided to verify the effectiveness of the suggested method.

Spectrum Sensing for Self-Organizing Network in the Presence of Time-Variant Multipath Flat Fading Channels and Unknown Noise Variance

Cognitive radio, as an important means of implementing spectrum-awareness and dynamic sharing, is of great significance to the future deployment of self-organizing networks. Given its practical application, cognitive radio technology may operate in various adverse self-organizing networks environments. For example, in wireless mobile communication, the multipath propagation with time-varying fading coefficients and unknown noise variance becomes inevitable. Unfortunately, most existing spectrum sensing methods could hardly acquire good performance in this adverse situation. To overcome this difficulty, in this paper we present a novel spectrum sensing algorithm in realistic cognitive radio applications. Firstly, we establish a dynamic state-space model which gives full consideration to the evolution characteristics of primary user's state and time-variant multipath flat fading channel, while the received signal processed by matched filtering is viewed as the observation. On this basis, spectrum sensing is realized by estimating the primary user's state, multipath channel impulse response and noise variance jointly and iteratively. This formulated problem is solved based on maximum a posteriori probability criterion and marginal particle filtering technology. Simulations demonstrate that the sensing performance achieved by proposed algorithm is satisfactory and at the same time, the channel response and noise variance are estimated accurately.

Joint detection scheme for spectrum sensing over time‐variant flat fading channels

As the application scope of cognitive radio grows continuously, time-variant flat fading (TVFF) channels become common in practical spectrum sensing scenarios. Unfortunately, most existing spectrum sensing methods which are designed for time-invariant propagation channels could hardly obtain good performance when they operate in realistic TVFF channels. To combat this difficulty, in this investigation the authors design a promising spectrum sensing method. Firstly, a novel dynamic state-space model is proposed in which a two-state Markov chain is employed to abstract the evolution of primary user states and a finite-state Markov channel model is utilised to characterise the TVFF channel. Secondly, based on the maximum a posteriori probability criteria and the particle filtering mechanic, a joint estimation algorithm of the time-dependent fading channel gain and the state of primary user is presented. Experimental simulations verify the performance superiority of the authors presented joint detection scheme, which could be properly applied to spectrum sensing in realistic TVFF channels.

Spectrum Sensing for Cognitive Radios in Time-Variant Flat-Fading Channels: A Joint Estimation Approach

Most of the existing spectrum sensing schemes utilize only the statistical property of fading channels, which unfortunately fails to cope with the time-varying fading channel that has disastrous effects on sensing performance. As a consequence, such sensing schemes may not be applicable to distributed cognitive radio networks. In this paper, we develop a promising spectrum sensing algorithm for time-variant flat-fading (TVFF) channels. We first formulate a dynamic state-space model (DSM) to characterize the evolution behaviors of two hidden states, i.e., the primary user (PU) state and the fading gain, by utilizing a two-state Markov process and another finite-state Markov chain, respectively. The summed energy, which serves as the observation of DSM, is employed for the ease of implementation. Relying on a Bayesian statistical inference framework, the sequential importance sampling based particle filtering is then exploited to numerically and recursively estimate the involved posterior probability, and thus, the PU state and the fading gain are jointly estimated in time. The estimations of two states are soft-outputs, which are successively refined with a designed iterative approach. Simulation results demonstrate that the new scheme can significantly improve the sensing performance in TVFF channels, which, in turn, provides particular promise to realistic applications.

Blind Estimation of PN Sequence of DS-CDMA Signals over Time Varying Flat Fading Channel

Blind Estimation of PN Sequence of DS-CDMA Signals over Time Varying Flat Fading Channel

Robust estimation in flat fading channels under bounded channel uncertainties

We investigate channel equalization problem for time-varying flat fading channels under bounded channel uncertainties. We analyze three robust methods to estimate an unknown signal transmitted through a time-varying flat fading channel. These methods are based on minimizing certain mean-square error criteria that incorporate the channel uncertainties into their problem formulations instead of directly using the inaccurate channel information that is available. We present closed-form solutions to the channel equalization problems for each method and for both zero mean and nonzero mean signals. We illustrate the performances of the equalization methods through simulations.

Fading model for antenna array receiver for a ring-type cluster of scatterers

This correspondence presents an alternate method for simulating the time-varying flat fading wireless channels for the antenna array receivers, in which the discrete ring of scatterers is incorporated around the mobile transmitter to model the spreading of azimuth. The ring-type cluster of scatterers continuously changes due to the movement of the mobile unit. Under this time-varying environment, each scatterer, at successive stages of the ring, is correlated with the scatterers at preceding stages of the ring using the second-order Markov modelling. The correlation of fading waveforms generated with the proposed paradigm is compared with the expected analytical correlation, which clearly depicts that the simulation results are consistent with the findings based on Jakes’ model.

Finite-state Markov channel modelling under jointly varying amplitude and phase in time-varying flat fading channels

In this study, the authors investigate the first-order finite-state Markov chain modelling of time-varying flat fading channels. The scope of this work is to consider the joint effects of unknown channel phase and amplitude on the received signal. Performance measures such as level crossing rate, steady-state probability, state transition probability and state time duration of the fading models are derived, plotted and analysed. Comparison of the performance measures are made for Rician, Lognormal and Weibull fading distributions.

On the Capacity of MIMO Channels with Outdated Channel State Information

A Multiple-input multiple-output (MIMO) time-varying flat fading channel is considered. The transmitter obtained the channel state information (CSI) relying on the reciprocity principle or by the feedback from the receiver. Thus, channel state information at the transmitter (CSIT) is outdated due to the delay between the estimation of the channel and the transmission of the data. In order to achieve the maximum channel capacity, the transmitter linearly precoded the signal before transmission based on the outdated CSIT. Under the assumptions of wide-sense stationary uncorrelated scattering Rayleigh fading channels and Jake’s model, the instantaneous mutual information and ergodic capacity is derived for MIMO channels with outdated CSIT. The information outage probability of MIMO channel with outdated CSIT is also presented.

Data-Aided SNR Estimation in Time-Variant Rayleigh Fading Channels

This paper addresses the data-aided (DA) signal-to-noise ratio (SNR) estimation for constant modulus modulations over time-variant flat Rayleigh fading channels. The time-variant fading channel is modeled by considering the Jakes' model and the first order autoregressive (AR1) model. Closed-form expressions of the Cramer-Rao bound (CRB) for DA SNR estimation are derived for known and unknown fast fading Rayleigh channels parameters cases. As special cases, the CRBs over slow and uncorrelated fading Rayleigh channels are derived. Analytical approximate expressions for the CRBs are derived for low and high SNR. These expressions that enable the derivation of a number of properties that describe the bound's dependence on key parameters such as SNR, channel correlation and sample number. Since the exact maximum likelihood (ML) estimator is computationally intensive in the case of fast-fading channels, two approximate ML estimator solutions are proposed for high and low SNR cases in the case of known channel parameters. The performances of theses estimators are examined analytically in terms of means and variances. In the presence of unknown channel parameters, a high SNR ML estimator based on the AR1 correlation model is derived. It is shown that the ML estimates of the SNR parameter and unknown channel parameters may be obtained in a separable form. Finally, simulation results illustrate the performance of the estimator and confirm the validity of the theoretical analysis.

On Information Rates of Time-Varying Fading Channels Modeled as Finite-State Markov Channels

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT lsim 0.01.

Minimum-Energy Band-Limited Predictor With Dynamic Subspace Selection for Time-Variant Flat-Fading Channels

In this paper, we develop and analyze the basic methodology for minimum-energy (ME) band-limited prediction of sampled time-variant flat-fading channels. This predictor is based on a subspace spanned by time-concentrated and band-limited sequences. The time-concentration of these sequences is matched to the length of the observation interval and the band-limitation is determined by the support of the Doppler power spectral density of the fading process. Slepian showed that discrete prolate spheroidal (DPS) sequences can be used to calculate the ME band-limited continuation of a finite sequence. We utilize this property to perform channel prediction. We generalize the concept of time-concentrated and band-limited sequences to a band-limiting region consisting of disjoint intervals. For a fading process with constant spectrum over its possibly discontiguous support we prove that the ME band-limited predictor is identical to a reduced-rank maximum-likelihood predictor which is a close approximation of a Wiener predictor. In current cellular communication systems the time-selective fading process is highly oversampled. The essential dimension of the subspace spanned by time-concentrated and band-limited sequences is in the order of two to five only. The prediction error mainly depends on the support of the Doppler spectrum. We exploit this fact to propose low-complexity time-variant flat-fading channel predictors using dynamically selected predefined subspaces. The subspace selection is based on a probabilistic bound on the reconstruction error. We compare the performance of the ME band-limited predictor with a predictor based on complex exponentials. For a prediction horizon of one eights of a wavelength the numerical simulation results show that the ME band-limited predictor with dynamic subspace selection performs better than, or similar to, a predictor based on complex exponentials with perfectly known frequencies. For a prediction horizons of three eights of a wavelength the performance of the ME band-limited predictor approaches that of a Wiener predictor with perfectly known Doppler bandwidth.

Orthogonal Space–Time Block Code Over Time-Varying Flat-Fading Channels: Channel Estimation, Detection, and Performance Analysis

This paper studies the channel estimation, detection and performance analysis of mobile wireless communication systems employing space-time block codes (STBC), where the channels exhibit flat Rayleigh fading with a significant amount of Doppler spread. Pilot-symbol-assisted modulation (PSAM) is developed to estimate the channels. The performance of the channel estimation is evaluated. Maximum-likelihood (ML) detection is first formulated. A linear detector, called the symmetric linear (SL) detector, is proposed. An interference cancellation (IC) detector is also developed to improve the performance of the SL detector. We derive the closed-form analytical expressions for the bit-error rate (BER) or symbol-error rate (SER) of pilot-sequence-assisted STBC with binary phase-shift keying (PSK), quaternary PSK, 16-quadrature amplitude modulation (QAM) and 64-QAM, when the SL and IC detectors are used. Some important design issues in the pilot-sequence-assisted STBC systems, including the selection of pilot spacing and interpolator size, are discussed. Simulation results are presented that verify our analytical results. The tradeoffs between the performance and complexity for ML, SL, and IC detection are also discussed

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

Capacity Analysis for Finite-State Markov Mapping of Flat-Fading Channels

In this paper, time-varying flat-fading channels are modeled as first-order finite-state Markov channels (FSMC). The effect of this modeling on the channel information capacity is addressed. The approximation accuracy of the first-order memory assumption in the Markov model is validated by comparing the FSMC capacity with the channel capacity assuming perfect state information at the receiver side. The results indicate that the first-order Markovian assumption is accurate for normalized Doppler frequencies f/sub d/T /spl lsim/ 0.01, in amplitude-only quantization of the channel gain for noncoherent binary signaling. In phase-only and joint phase and amplitude quantization of the channel gain for coherent binary signaling, the first-order Markovian assumption is accurate for f/sub d/T /spl lsim/ 0.001. Furthermore, the effect of channel quantization thresholds on the FSMC capacity is studied. In high signal-to-noise ratio (SNR) conditions, nonuniform two-level amplitude quantization scheme outperforms equiprobable quantization method by 0.8-1.5 dB.