Blind equalization of multilevel turbo coded‐continuous phase frequency shift keying over MIMO channels

In this paper, multilevel turbo coded‐continuous phase frequency shift keying (MLTC‐CPFSK) is introduced and its bit error performance in multiple input multiple output (MIMO) fading channels are investigated considering a blind maximum likelihood channel estimation. Multilevel turbo coded signals with continuous phase modulation (CPM) provides low spectral occupancy and is suitable for power and bandwidth‐limited channels. Besides, antenna diversity is one of the best method to combat with multipath fading effects. The performance of 2LTC for 4‐ary CPFSK over AWGN, Rician (for Rician channel parameter K=10 dB) and Rayleigh channels are given for 1Tx–1Rx, 2Tx–1Rx and 2Tx–2Rx antenna configurations. Channel capacities of 2LTC‐4CPFSK signals are obtained as ?5.26, ?7.65 and ?7.14 dB for 1Tx–1Rx, 2Tx–1Rx and 2Tx–2Rx antenna configurations, respectively. Baum–Welch (BW) algorithm is used to estimate the channel parameters. Bit error probabilities of 2 level turbo coded 4 CPFSK (2LTC‐4CPFSK) are drawn in the cases of no channel state information (CSI), BW estimation, and perfect CSI. Approximately 0.1 and 0.75 dB gains in E_s/N₀ are obtained using BW channel estimator for Rician and Rayleigh channels, respectively. Therefore, MLTC‐CPFSK with BW channel estimator has excellent performance in MIMO fading channels. Copyright © 2006 John Wiley & Sons, Ltd.     

Genetic Grey Wolf Optimizer Based Channel Estimation in Wireless Communication System

Various methods are available for channel estimation in the orthogonal frequency division multiplexing and orthogonal frequency and code division multiplexing (OFCDM) based wireless communication schemes. Along with this, the most utilized techniques are namely the minimum mean square error (MMSE) and least square (LS). The process of LS channel estimation method is simple but it occupies a very high mean square error. On the other hand, the performance of MMSE is better than LS in terms of SNR, though it shows high computational complexity. Compared to MMSE and LS based techniques, the combination of MMSE and LS techniques using evolutionary programming reduces the error significantly to receive exact signal. In this study, we propose a hybrid method namely GGWO that includes grey wolf optimization (GWO) and genetic algorithms (GA) for estimate the channel in MIMO–OFCDM schemes. At first, the best channel is estimated using GWO and afterwards, the MMSE and LS are hybridized through GA for calculating the best channel to decrease error. Overall, the GWO and GA contribute in fine tuning the obtained channel scheme so that the channel model is derived further to correlate with the ideal scheme. Our results demonstrate that the proposed scheme is superior to conventional MMSE and LS in terms of BER and SNR.     

Sparse channel estimation and tracking for cyclic delay diversity orthogonal frequency division multiplexing systems

In cyclic delay diversity orthogonal frequency division multiplexing systems, the excessive channel delay spread and corresponding high frequency selectivity makes channel estimation a challenging task. In this paper, we propose a two‐stage scheme to estimate and track the highly frequency selective channel. At the preamble reception stage, least squares channel estimation with L₀ norm regularization is proposed to exploit the channel sparsity. At the data demodulation stage, an expectation–maximization algorithm with the most significant tap selection is developed to track channel variations by using the channel order obtained from the first stage. Compared with other estimation methods, the proposed scheme requires no prerequisite knowledge of delay parameter settings, which leads to more flexibility. Furthermore, the scheme can exploit the channel sparse structure by detecting the nonzero taps and, consequently, has better mean squared error performance. Simulation results show that the proposed estimation scheme can retain the provided diversity gain of cyclic delay diversity effectively in time‐varying fading channels. Copyright © 2011 John Wiley & Sons, Ltd.     

信道估计误差下的深度人工噪声预编码生成方法

基于人工噪声的物理层安全通信系统，传统人工噪声通常采用推导得到的闭式表达式或最优化方法数值求解生成，要求输入准确的传输信道矩阵信息，才能保证通信系统的保密性。但实际环境中存在的信道估计误差会导致人工噪声预编码误差，从而降低通信系统保密容量。为此提出一种基于深度学习的人工噪声预编码生成方法，通过将有误差的信道估计信息作为输入，与无估计误差情况下传统数值求解得到的预编码矩阵进行拟合，训练得到可适应信道估计误差的深度神经网络。仿真表明，该方法在信道估计有误差时的保密性能与鲁棒性优于传统人工噪声生成系统；相比于其他深度学习方法在物理层安全的应用，所提方法具有更快的收敛速度。     

Kalman filter‐based channel estimation and ICI suppression for high‐mobility OFDM systems

The use of orthogonal frequency division multiplexing (OFDM) in frequency‐selective fading environments has been well explored. However, OFDM is more prone to time‐selective fading compared with single‐carrier systems. Rapid time variations destroy the subcarrier orthogonality and introduce inter‐carrier interference (ICI). Besides this, obtaining reliable channel estimates for receiver equalization is a non‐trivial task in rapidly fading systems. Our work addresses the problem of channel estimation and ICI suppression by viewing the system as a state‐space model. The Kalman filter is employed to estimate the channel; this is followed by a time‐domain ICI mitigation filter that maximizes the signal‐to‐interference plus noise ratio (SINR) at the receiver. This method is seen to provide good estimation performance apart from significant SINR gain with low training overhead. Suitable bounds on the performance of the system are described; bit error rate (BER) performance over a time‐invariant Rayleigh fading channel serves as the lower bound, whereas BER performance over a doubly selective system with ICI as the dominant impairment provides the upper bound. Copyright © 2008 John Wiley & Sons, Ltd.     

Iterative interference cancellation and channel estimation in multibeam satellite systems

This paper deals with the use of non‐linear multiuser detection techniques to mitigate co‐channel interference on the reverse link of multibeam satellite systems. These techniques allow more capacity efficient frequency reuse strategies than classical ones, as they make possible to cope with lower C/I. The considered system takes as a starting point the DVB‐RCS standard, with the use of convolutional coding, and the use of the Ka‐band. We propose different iterative interference cancellation schemes, which operate at the beamformer outputs, and which use information from decoders. The proposed receivers assume an initial single‐user synchronization step: frame synchronization and timing recovery, and then perform channel estimation: beamformer coefficients; signal carrier phases and signal amplitudes. In a first step, these receivers are evaluated by simulation in terms of bit error rate and of channel estimation error on two interference configurations. For one of these receivers, sensitivity to imperfect timing recovery and to low‐frequency offsets from user terminals is evaluated. In a second step, since the receiver performances highly depend on the interference configuration, we propose an approach to evaluate performances on a multibeam coverage (by taking into account the variability of interference configurations on the coverage). This method is used to compare different receivers on an example based on a coverage designed on a digital focal array feed reflector antenna. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis and design of joint CFO/channel estimate techniques for a cooperative STBC‐OFDM system

This paper studies the joint estimation technique of carrier frequency offset (CFO) and channel information for a distributed decode‐and‐forward (DF) cooperative space‐time block‐coded (STBC) orthogonal frequency division multiplexing (OFDM) system. For the considered relay system, we provide theoretical analysis of the effects upon the output signal‐to‐noise ratio (SNR), which is caused by the CFO/channel estimation error. Based on the provided analytical results, a joint CFO/channel estimation scheme is then developed, where the CFO estimate is achieved by a multiple‐dimensional linear search algorithm. Furthermore, we propose an alternative estimation solution with iteration approach being designed for the CFO estimation prior to the channel estimation. In contrast to the former estimator, the iterative method enjoys the advantage of the substantially reduced implementation complexity without sacrificing the estimate performance. The conducted computer simulation results verify the effectiveness of the proposed schemes.     

Channel‐estimate‐based frequency‐domain equalization (CE‐FDE) for broadband single‐carrier transmission

A channel‐estimate‐based frequency‐domain equalization (CE‐FDE) scheme for wireless broadband single‐carrier communications over time‐varying frequency‐selective fading channels is proposed. Adaptive updating of the FDE coefficients are based on the timely estimate of channel impulse response (CIR) to avoid error propagation that is a major source of performance degradation in adaptive equalizers using least mean square (LMS) or recursive least square (RLS) algorithms. Various time‐domain and frequency‐domain techniques for initial channel estimation and adaptive updating are discussed and evaluated in terms of performance and complexity. Performance of uncoded and coded systems using the proposed CE‐FDE with diversity combining in different time‐varying, multi‐path fading channels is evaluated. Analytical and simulation results show the good performance of the proposed scheme suitable for broadband wireless communications. For channels with high‐Doppler frequency, diversity combining substantially improves the system performance. For channels with sparse multi‐path propagation, a tap‐selection strategy used with the CE‐FDE systems can significantly reduce the complexity without sacrificing the performance. Copyright © 2004 John Wiley & Sons, Ltd.     

Joint carrier frequency offset and channel estimation for OFDM systems with two receive antennas

Carrier frequency offset (CFO) in OFDM systems results in loss of channel orthogonality and hence degrades the system's performance. In this paper, we propose a new method for joint CFO/channel estimation for OFDM systems with two receive antennas. Our method avoids the complexity of full search methods in one or two dimensions. Using one training OFDM symbol and utilizing the knowledge of the structure of the inter‐channel interference that results from CFO, we develop a two‐stage estimation procedure. The first stage derives an initial CFO/channel estimate based on a one shot minimization step. The second stage refines this joint estimate by conducting a small CFO search in the vicinity of the initial estimate. This procedure provides CFO estimates over a full range of −N /2–N /2, (N : number of subcarriers), as well as the channel estimates. Computer simulations show an excellent performance that is very close to the Cramer–Rao lower bound and superior to some existing methods. The effect of antenna correlation on performance is also investigated through computer simulations, showing small performance degradation even at medium correlation coefficients (0.3–0.6). Copyright © 2015 John Wiley & Sons, Ltd.     

Accurate direction‐of‐arrival estimation of multiple sources using a genetic approach

In this paper, we present an accurate direction‐of‐arrival (DOA) estimation method, which is based on the maximum likelihood (ML) principle and implemented using a modified and refined genetic algorithm (GA). With the newly introduced features—intelligent initialization and the emperor‐selective (EMS) mating scheme, carefully selected crossover and mutation operators and fine‐tuned parameters such as the population size, the probability of crossover and mutation etc., the GA‐ML estimator achieves fast global convergence. A GA operator and parameter standard is suggested for this application, which is independent of the source and array configurations except the number of sources. Simulation results demonstrate that in general scenarios, the proposed estimator is the most efficient in computation and its statistical performance is the best among all popular ML‐based DOA estimation methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Least Square Channel Estimation for Two‐Way Relay MIMO OFDM Systems

This letter considers the channel estimation for two‐way relay MIMO OFDM systems. A least square (LS) channel estimation algorithm under block‐based training is proposed. The mean square error (MSE) of the LS channel estimate is computed, and the optimal training sequences with respect to this MSE are derived. Some numerical examples are presented to evaluate the performance of the proposed channel estimation method.     

Sparse least mean mixed‐norm adaptive filtering algorithms for sparse channel estimation applications

Sparse least‐mean mixed‐norm (LMMN) algorithms are developed to improve the estimation performance for sparse channel estimation applications. Both the benefits of the least mean fourth and least mean square algorithms are utilized to exploit a type of sparse LMMN algorithms. The proposed sparse‐aware LMMN algorithms are implemented by integrating an l ₁‐norm or log‐sum function into the cost function of traditional LMMN algorithm so that they can exploit the sparse properties of the broadband multi‐path channel and achieve better channel estimation performance. The proposed sparse LMMN algorithms are equal to adding an amazing zero‐attractor in the update equation of the traditional LMMN algorithm, which aim to speed up the convergence. The channel estimation performance of the proposed sparse LMMN algorithms are evaluated over a sparse broadband multi‐path channel to verify their effectiveness. Simulation results depict that the sparse LMMN algorithms are superior to the previously reported sparse‐aware least mean square/fourth, least mean fourth and least mean square and their corresponding sparse‐aware algorithms in terms of both the convergence and steady‐state behavior when the broadband multi‐path channel is sparse. Copyright © 2016 John Wiley & Sons, Ltd.     

A novel variable step size adjustment method based on channel output autocorrelation for the LMS training algorithm

The least mean squares (LMS) algorithm, the most commonly used channel estimation and equalization technique, converges very slowly. The convergence rate of the LMS algorithm is quite sensitive to the adjustment of the step‐size parameter used in the update equation. Therefore, many studies have concentrated on adjusting the step‐size parameter in order to improve the training speed and accuracy of the LMS algorithm. A novel approach in adjusting the step size of the LMS algorithm using the channel output autocorrelation (COA) has been proposed for application to unknown channel estimation or equalization in low‐SNR in this paper. Computer simulations have been performed to illustrate the performance of the proposed method in frequency selective Rayleigh fading channels. The obtained simulation results using HIPERLAN/1 standard have demonstrated that the proposed variable step size LMS (VSS‐LMS) algorithm has considerably better performance than conventional LMS, recursive least squares (RLS), normalized LMS (N‐LMS) and the other VSS‐LMS algorithms. Copyright © 2011 John Wiley & Sons, Ltd.     

Two‐pilot channel estimation scheme for amplify‐and‐forward relay networks

In amplify‐and‐forward relay networks, the equivalent channel to the destination node is not independent of equivalent noise and the equivalent noise does not follow a Gaussian distribution. Therefore, it is difficult to directly estimate the equivalent channel based on traditional optimal rules. In this paper, we propose a two‐pilot estimation (TPE) scheme that decomposes a non‐Gaussian noise channel estimation problem into two channel estimation problems in Gaussian noise. In TPE scheme, the relay‐destination channel is first estimated by one pilot and the other pilot is used to estimate the equivalent channel with the aid of the estimated relay‐destination channel. Simulation results show that the TPE scheme can achieve less estimation error and larger system throughput than other existing channel estimators in slow fading case. Copyright © 2012 John Wiley & Sons, Ltd.     

Time‐varying channel estimation for MIMO/OFDM systems using superimposed training and basis expansion models

An approach of superimposed training (ST)‐aided time‐varying (TV) channel estimation for multiple‐input multiple‐output orthogonal frequency division multiplexing systems is presented. By modeling the TV channel with the truncated discrete basis expansion model, a two‐step approach is adopted to estimate the TV channel. In addition, the mean square error (MSE) of the proposed channel estimation is analyzed, and its closed‐form expression is derived, which is a function of the data‐to‐ST power ratio. Using the developed channel MSE, we case the problem of ST power‐allocation by minimizing the lower bound on the average channel capacity. To enhance the performance of channel estimation, a low‐complexity decision feedback mechanism is introduced to iteratively mitigate the unknown data interference. Numerical results verify the performances of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Sub‐Nyquist rate ADC sampling‐based compressive channel estimation

To realize high‐speed communication, broadband transmission has become an indispensable technique in the next‐generation wireless communication systems. Broadband channel is often characterized by the sparse multipath channel model, and significant taps are widely separated in time, and thereby, a large delay spread exists. Accurate channel state information is required for coherent detection. Traditionally, accurate channel estimation can be achieved by sampling the received signal with large delay spread by analog‐to‐digital converter (ADC) at Nyquist rate and then estimate all of channel taps. However, as the transmission bandwidth increases, the demands of the Nyquist sampling rate already exceed the capabilities of current ADC. In addition, the high‐speed ADC is very expensive for ordinary wireless communication. In this paper, we present a novel receiver, which utilizes a sub‐Nyquist ADC that samples at much lower rate than the Nyquist one. On the basis of the sampling scheme, we propose a compressive channel estimation method using Dantzig selector algorithm. By comparing with the traditional least square channel estimation, our proposed method not only achieves robust channel estimation but also reduces the cost because low‐speed ADC is much cheaper than high‐speed one. Computer simulations confirm the effectiveness of our proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Effects of imperfect channel sensing and estimation on the performance of cognitive radio systems

In realistic scenarios of cognitive radio (CR) systems, imperfect channel sensing may occur due to false alarms and miss detections. Channel estimation between the secondary user transmitter and another secondary user receiver is another challenge in CR systems, especially for frequency‐selective fading channels. In this context, this paper presents a study of the effects of imperfect channel sensing and channel estimation on the performance of CR systems. In particular, different methods of channel estimation are analyzed under channel sensing imperfections. Initially, a CR system model with channel sensing errors is described. Then, the expectation maximization (EM) algorithm is implemented in order to learn the channel fading coefficients. By exploiting the pilot symbols and the detected symbols at the secondary user receiver, we can estimate the channel coefficients. We further compare the proposed EM estimation algorithm with different estimation algorithms such as the least squares (LS) and linear minimum mean square error (LMMSE). The expressions of channel estimates and mean squared errors (MSE) are determined, and their dependencies on channel sensing uncertainty are investigated. Finally, to reduce the complexity of EM algorithm, a sub‐optimal algorithm is also proposed. The obtained results show that the proposed sub‐optimal algorithm provides a comparable bit error rate (BER) performance with that of the optimal one yet with less computational complexity.     

An eigen‐select denoising threshold for channel estimation in OFDM systems

In reliable orthogonal frequency division multiplexing systems, channel estimator (CE) plays a crucial role. A pilot‐aided orthogonal frequency division multiplexing CE often employs denoising thresholds to identify significant and noisy channel impulse response taps. When the knowledge of channel statistics (KCS) is completely unavailable, the existing suboptimal thresholds require consistent estimation of one or more KCS parameters. In this paper, the effect of noise variance parameter estimation on CE's mean square error (MSE) performance is characterized analytically by computing threshold's tap‐detection probability. To mitigate MSE degradation due to KCS estimation, an eigen‐select threshold, which does not require any KCS estimation, is proposed. It utilizes eigen values of the auto‐covariance matrix formed by estimated channel impulse response. The proposed threshold is compared with existing state‐of‐art alternatives, for CE's MSE performance and system's BER performance, in correlated Rayleigh fading channel environments. Results reveal that, with the proposed threshold, performance plots converge to optimal solution more closely than the others. Copyright © 2015 John Wiley & Sons, Ltd.     

Jointly multi‐user detection and channel estimation with genetic algorithm

This work aims at proposing the use of the evolutionary computation methodology in order to jointly solve the multi‐user channel estimation (MuChE) and detection problems at its maximum‐likelihood, both related to the direct sequence code division multiple access (DS/CDMA). The effectiveness of the proposed heuristic approach is proven by comparing performance and complexity merit figures with that obtained by traditional methods found in literature. Simulation results considering genetic algorithm (GA) applied to multipath, DS/CDMA and MuChE and multi‐user detection (MuD) show that the proposed genetic algorithm multi‐user channel estimation (GAMuChE) yields a normalized mean square error estimation (nMSE) inferior to 11%, under slowly varying multipath fading channels, large range of Doppler frequencies and medium system load, it exhibits lower complexity when compared to both maximum likelihood multi‐user channel estimation (MLMuChE) and gradient descent method (GrdDsc). A near‐optimum multi‐user detector (MuD) based on the genetic algorithm (GAMuD), also proposed in this work, provides a significant reduction in the computational complexity when compared to the optimum multi‐user detector (OMuD). In addition, the complexity of the GAMuChE and GAMuD algorithms were (jointly) analyzed in terms of number of operations necessary to reach the convergence, and compared to other jointly MuChE and MuD strategies. The joint GAMuChE–GAMuD scheme can be regarded as a promising alternative for implementing third‐generation (3G) and fourth‐generation (4G) wireless systems in the near future. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance analysis for relay networks with hierarchical support vector machines

In this paper, we consider a cooperative relay scheme for a mobile network with MIMO technology. The channel capacity for two well‐known relaying schemes are investigated: analogue relaying (amplify and forward) and digital relaying (decode and forward) from a mobile device to the base station through a relay node. In order to further increase the channel capacity, we propose an efficient hierarchical procedure based on support vector machine, namely hierarchical support vector machines (HSVM), to estimate the wireless networks condition approximately and design two ways (matched filter and minimum mean square error filter) of increasing the channel capacity according to the estimated wireless network condition. The proposed HSVM can estimate the wireless networks condition in much shorter time compared with the traditional minimum mean square error scheme without incurring much estimation error, which is spatial, useful for delay sensitive communication. For digital relaying, the effect of imperfect channel decode is also addressed. Our numerical results demonstrate the reduction of estimation complexity by adopting HSVM and the significant improvement of network capacity by applying the matched filter weight at relay nodes according to the network estimation. Copyright © 2011 John Wiley & Sons, Ltd.