FPGA-Based Time-Domain Channel Estimation in Gaussian Mixture Model

Accurate channel estimation is essential for achieving the performance gains offered by reconfigurable intelligent surface (RIS)-aided wireless communications. A variety of channel estimation methods have been proposed for such systems; however, none of the existing methods takes into account the effect of synchronization errors such as carrier frequency offset (CFO). In general, CFO can significantly degrade the channel estimation performance of orthogonal frequency division multiplexing (OFDM) systems. Motivated by this, we investigate the effect of CFO on channel estimation for RIS-aided OFDM systems. Furthermore, we propose a joint CFO and channel impulse response (CIR) estimation method for these systems. Simulation results demonstrate the effectiveness of our proposed method, and also demonstrate that the use of time-domain rather than frequency-domain estimation in this context results in an improvement in the mean-squared error (MSE) performance of channel estimation as well as in a significantly lower overall computational complexity.

Orthogonal frequency division multiplexing (OFDM) is adopted in most wireless communication systems, and the performance of OFDM is affected by impulse noise (IN). Better channel estimation (CE) performance is required to detect the channel information on the receiving side. The OFDM system is considered with the number of subcarriers carrying the data and pilot symbols. In the OFDM modulator, the symbols of the frequency domain are transformed into the signals of the time domain using inverse discrete Fourier transformation (IDFT). Effective impulsive noise mitigation is crucial for improving the effectiveness of OFDM communication systems, and it improves the signal-to-noise ratio (SNR) at the receiver. A cyclic prefix is then appended before transmission through the channel. In the receiver noise, the effect of IN is mitigated jointly with CE using the Bayesian matching pursuit (BMP) and Moth-flame algorithm (MFA). In this approach, the IN and channel information is considered as a sparse vector. Here, the data symbols used are considered an unknown parameter. The approach incorporating all subcarriers has a lower mean square error (MSE) of IN estimate for impulsive noise reduction. The MFA algorithm is used to optimize the sensor matrix in BMP. The sparsity of the channel and the impulse response are observed in the time domain to represent the channel and IN together. It exactly recovers the sparse signal for finding the convex objectives of the sparse minimizer, and the sparse solution is obtained with fixed point updates. The proposed BMP algorithm improves the CE by explicitly considering the existence of IN. The BMP is a greedy algorithm that selects the most correlated residuals at each column. Under mutual incoherence, it recovers the signal with a higher probability. The simulated outcomes proved that the proposed CE and noise mitigation model achieved better performance based on the bit error rate (BER), throughput and MSE.

Multipath channels often exhibit sparse structures in multicarrier underwater acoustic (MC-UWA) communication systems. Conventional linear channel estimators, such as least squares (LS) and minimum mean square error (MMSE) are considered as optimal solutions under the assumption of rich multipath. However, they often result in low spectral efficiency due to neglect of the sparsity in multipath channels. In this paper, we propose a novel sparse channel estimation method with compressive sensing. The proposed estimator has better estimation performance and low complexity when compared with the LS estimator. Simulations verified the proposed method with respect to the mean square error (MSE) and the computational complexity. Key words: Underwater acoustic (UWA), orthogonal frequency division multiplexing (OFDM), sparse multipath, compressive sensing (CS), sparse channel estimator.

This paper is concerned with a challenging problem of channel estimation for amplify-and-forward cooperative relay based orthogonal frequency division multiplexing (OFDM) systems in the presence of sparse underwater acoustic channels and of the correlative non-Gaussian noise. We exploit the sparse structure of the channel impulse response to improve the performance of the channel estimation algorithm, due to the reduced number of taps to be estimated. The resulting novel algorithm initially estimates the overall sparse channel taps from the source to the destination as well as their locations using the matching pursuit (MP) approach. The correlated non-Gaussian effective noise is modeled as a Gaussian mixture. Based on the Gaussian mixture model, an efficient and low complexity algorithm is developed based on the combinations of the MP and the space-alternating generalized expectation-maximization (SAGE) technique, to improve the estimates of the channel taps and their location as well as the noise distribution parameters in an iterative way. The proposed SAGE algorithm is designed in such a way that, by choosing the admissible hidden data properly on which the SAGE algorithm relies, a subset of parameters is updated for analytical tractability and the remaining parameters for faster convergence Computer simulations show that underwater acoustic (UWA) channel is estimated very effectively and the proposed algorithm has excellent symbol error rate and channel estimation performance.

The development of internet related applications and their increasing demands have led to advancement in high speed communication systems. For the accomplishment of these increasing demands MIMO channels with multiple transmitting and receiving antennas have been devised. MIMO systems enhance the capacity using spatial multiplexing and interference reduction through spatial dimensioning. Furthermore, MIMO systems mutual with orthogonal frequency division multiplexing (MIMO-OFDM) improves system capacity and mitigation against fading. These systems are the basis of 4G and beyond wireless communication standards. This research work focus on improvement in channel estimation performance using various techniques on standard communication models. Semi blind channel estimation technique is employed for channel estimation, which includes use of training sequence in form of pilots. Block type arrangement is being used, since it’s based on frequency selective channels. LSE and MMSE estimations are the two basic estimation techniques which can be efficiently used to estimate channels in OFDM systems. For MMSE implementation information of noise variance and channel covariance is required. Furthermore it is extremely complex than LSE estimator. DFT and DCT based channel estimation methods are employed to increase the performance and diminish the complexity. Different interpolation methods are been used and analyzed for better performance. Number of subcarriers which also have an impact on estimation performance has also been discussed. Overall channel estimation performance have been examined for both large and small scale fading channel models.

ABSTRACTDeep‐learning (DL) methods have shown promising performance in pioneering studies on orthogonal frequency division multiplexing (OFDM) channel estimation challenges. Unlike typical DL‐based channel estimation methods that mainly rely on separate real and imaginary inputs while ignoring the inherent correlation between the two streams, this paper proposes AE‐DENet, a novel autoencoder (AE)‐based data enhancement network to achieve robust channel estimation for OFDM systems. AE‐DENet employs the classic least square (LS) channel estimation as input and proposes a data enhancement method to extract the interaction features from the real and imaginary parts of the complex channel estimation matrix, which are joined with the original real and imaginary streams to generate an enhanced input for better channel inference. Experimental findings in terms of the mean square error (MSE) results for a range of representative DL‐based channel estimation methods demonstrate that the proposed AE‐DENet‐enhanced channel estimation framework achieves state‐of‐the‐art channel estimation performance with trivial added computational complexity. Furthermore, the input dimensions of the DL‐based channel estimation models can be adaptively adjusted to accommodate the dimension of the enhanced LS input. The proposed approach is also shown to be robust to channel variations and high user mobility.

In this paper, OFDM data-aided channel estimation based on the decimation of the Channel Impulse Response (CIR) through the selection of the Most Significant Samples (MSS) is addressed. Our aim is to approach the Minimum Mean Square Error (MMSE) channel estimation performance, while avoiding the need for a-priori knowledge of channel statistics (KCS). The optimal set of samples is defined in the instantaneous and average senses. We derive lower bounds on the estimation mean-square error (MSE) performance for any MSS selection strategy. We show how MSS-based channel estimation can approach these MSE lower bounds. We introduce novel MSS strategies oriented towards instantaneous decimation (Instantaneous Energy Selection - IES), and windowed decimation (Average Energy Selection - AES). We also consider decimation via Threshold Crossing Selection (TCS), which we characterize analytically, to derive the optimum threshold in the minimum MSE sense. We also propose a sub-optimal method for threshold setting that does not require KCS. Finally, we provide numerical results in terms of both MSE estimation performance and Bit Error Rate (BER) of a coded OFDM system using the proposed channel estimators, to show that they indeed approach MMSE performance.

In this paper, exponentially-weighted recursive least squared (EW-RLS) channel estimation for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems is investigated. Channel estimation in time-domain (TD) as well as frequency-domain (FD) is investigated through exploiting preambles and pilot symbols inserted in TD and FD, respectively. The channel is assumed to be slowly time-varying frequency-selective, constant during one OFDM symbol but changing from symbol to symbol. Simulation results show that the TD EW-RLS estimator has better estimation performance in terms of the mean-squares error (MSE) and bit-error rate (BER), compared to FD EW-RLS estimation approach. The computational complexity is significantly reduced by recursively updating the channel estimates and by applying the matrix inversion lemma.

In spread multi-carrier systems with a code-multiplexed pilot channel, variations of the channel within the spreading block impact channel estimation and data demodulation through the loss of orthogonality of the spreading codes. In this paper the mean-squared error (MSE) between the true channel and a channel estimate obtained through simple despreading of the pilot code is derived. The closed-form MSE expression is a function of the channel fading statistics, the currently employed spreading codes, and the powers of the different users. By evaluating the MSE for a time-spread orthogonal frequency-division multiplexed (OFDM) system, it is observed that while spreading in time will have little impact in a pico-cell system scenario, a wide-area cell system experiences significant degradation in channel estimation performance at moderate Doppler frequencies. The impact on data demodulation is evaluated through simulations with the data users employing a turbo code.

This work examines the use of two-way training to efficiently discriminate the channel estimation performances at a legitimate receiver (LR) and an unauthorized receiver (UR) in a multiple-input multiple-output (MIMO) wireless system. This work improves upon the original discriminatory channel estimation (DCE) scheme proposed by Chang where multiple stages of feedback and retraining were used. While most studies on physical layer secrecy are under the information-theoretic framework and focus directly on the data transmission phase, studies on DCE focus on the training phase and aim to provide a practical signal processing technique to discriminate between the channel estimation performances (and, thus, the effective received signal qualities) at LR and UR. A key feature of DCE designs is the insertion of artificial noise (AN) in the training signal to degrade the channel estimation performance at UR. To do so, AN must be placed in a carefully chosen subspace, based on the transmitter's knowledge of LR's channel, in order to minimize its effect on LR. In this paper, we adopt the idea of two-way training that allows both the transmitter and LR to send training signals to facilitate channel estimation at both ends. Both reciprocal and nonreciprocal channels are considered and a two-way DCE scheme is proposed for each scenario. For mathematical tractability, we assume that all terminals employ the linear minimum mean square error criterion for channel estimation. Based on the mean square error (MSE) of the channel estimates at all terminals, we formulate and solve an optimization problem where the optimal power allocation between the training signal and AN is found by minimizing the MSE of LR's channel estimate subject to a constraint on the MSE achievable at UR. Numerical results show that the proposed DCE schemes can effectively discriminate between the channel estimation and, hence, the data detection performances at LR and UR.

Channel estimation and synchronization are considered the most challenging issues in Orthogonal Frequency Division Multiplexing (OFDM) system. OFDM is highly affected by synchronization errors that cause reduction in subcarriers orthogonality, leading to significant performance degradation. The synchronization errors cause two issues: Symbol Time Offset (STO), which produces inter symbol interference (ISI) and Carrier Frequency Offset (CFO), which results in inter carrier interference (ICI). The aim of the research is to simulate Comb type pilot based channel estimation for OFDM system showing the effect of pilot numbers on the channel estimation performance and propose a modified estimation method for STO with less number of pilot to mitigate ISI effect. Channel estimation is simulated for different pilot number with 16QAM modulation in Ped-A Rayleigh channel. The STO effect assumed less than the cyclic prefix length to minimize ISI and maintain the orthogonality between subcarriers. The simulation results show that the high number of pilots are needed to achieve good channel estimation in case no synchronization used while similar results are achieved with smaller number of pilots if the propose modification on the synchronization method are used aligned with the channel estimation. The proposed system is evaluated in terms of BER and SNR.

Optimization on semi-blind channel estimation for MIMO-OFDM systems

Background: To resist the time-variant underwater acoustic (UWA) channel, large amounts of channel estimation algorithms for the UWA orthogonal frequency division multiplexing (OFDM) are presented. An updated review of the recent UWA OFDM channel estimators is suggested in this article. Objective: The goal of this work is to review and conclude the development of different types of channel estimators. The possible perspectives about the future UWA channel estimator design are also discussed. Methodology: The principles and performances of the linear channel estimators, the compressed sensing (CS)-based channel estimators, and the neural network (NN)-based channel estimators are reviewed and discussed. Simulations are conducted to compare the typical implementations of the different methods. Conclusion: To take more channel state characteristics into account, the data-driven methods have been applied in the channel estimator design. Compared with the linear and CS-based methods, the NN-based channel estimator shows the higher performance, robustness and lower complexity, which is promising to be applied with the proper structure and training sets.

Orthogonal frequency-division multiplexing (OFDM) is widely used to mitigate inter-symbol interference (ISI) from multipath fading. However, the open nature of wireless OFDM systems makes them vulnerable to jamming attacks. In this context, pilot jamming is critical as it focuses on corrupting the symbols used for channel estimation and equalization, degrading the system performance. Although neural networks (NNs) can improve channel estimation and mitigate pilot jamming penalty, they are also themselves susceptible to malicious perturbations known as adversarial examples. If the jamming attack is crafted in order to fool the NN, it represents an adversarial example that impairs the proper behavior of OFDM systems. In this work, we explore two machine learning (ML)-based jamming strategies that are especially intended to degrade the performance of ML-based channel estimators, in addition to a traditional Additive White Gaussian Noise (AWGN) jamming attack. These ML-based attacks create noise patterns designed to reduce the precision of the channel estimation process, thereby compromising the reliability and robustness of the communication system. We highlight the vulnerabilities of wireless communication systems to ML-based pilot jamming attacks that corrupts symbols used for channel estimation, leading to system performance degradation. To mitigate these threats, this paper proposes an adversarial training defense mechanism desined to counter jamming attacks. The effectiveness of this defense is validated through simulation results, demonstrating improved channel estimation performance in the presence of jamming attacks. The proposed defense methods aim to enhance the resilience of OFDM systems against pilot jamming attacks, ensuring more robust communication in wireless environments.

SummaryThis paper introduces the concept of spatial and media‐based modulated (SMBM) orthogonal frequency division multiplexing (OFDM) as a potential candidate for highly mobile next generation beyond 5G (B5G) wireless communications. The proposed SMBM‐OFDM technique utilizes not only the transmit antenna and channel state indices but also OFDM subcarriers to improve the system performance under high mobility. In addition, this study sheds light on challenging fast time‐varying channel estimation problem of MBM‐based systems by using the linear minimum mean square error (LMMSE) approach due to its optimality to investigate the achievable system performance with the aid of basis expansion modeling. The minimum lower bound on the channel estimation error (Bayesian Cramer–Rao bound) is derived theoretically and shown to be attainable by the considered LMMSE estimator. Moreover, symbol detection performance is provided for different modulation types and higher mobile velocities. Simulation results demonstrate that SMBM‐OFDM system under high mobility is able to provide around 12‐dB performance gains in terms of both channel estimation and symbol detection error compared to conventional spatial modulation (SM)‐OFDM systems without MBM. The presented framework is important due to addressing the high mobility support of SMBM‐OFDM systems for B5G wireless communications in terms of achievable channel estimation and data detection performance.