Models, Methods and Waveforms for Estimation and Prediction of Sparse Time-Varying Channels

Channel state information (CSI) is required at the transmitter for achieving the maximum potentials of multiple-input multiple-output (MIMO) systems. In fast time-variant vehicular communications channels high data rate feedback lines are required in a frequency division duplex (FDD) transceiver for updating the transmitter with the rapidly changing CSI. Even with high data rate feedback lines, the delay caused by channel estimation and feedback may lead to outdated CSI at the transmitter. To reduce both the feedback load and CSI delay, this paper presents a reduced rank autoregressive (AR) channel predictor based on low dimensional discrete prolate spheroidal (DPS) sequences. The new subframe-wise DPS basis expansion model (DPS-BEM) channel predictor properly exploits the channel's restriction to low dimensional subspaces for reducing the prediction error and the computational complexity. The proposed channel predictor can be applied for updating the precoding matrix in time-variant MIMO systems. Simulation results demonstrate that the proposed channel predictor outperforms the DPS based minimum energy (ME) predictor at different Doppler frequencies and has better performance than the conventional Wiener predictor for slower time-variant channels and almost similar performance for very fast time-variant channels with reduced amount of computational complexity.

Orthogonal time frequency space (OTFS) modulations are robust to time-varying frequency-selective fading channels. OTFS modulations operate in the delay-Doppler domain whereas two-dimensional (2D) orthogonal frequency division multiplexing (OFDM) modulations operate in the time-frequency domain. For 2D OFDM modulations in time-varying frequency-selective fading channels, we investigate the pilot pattern design problem, which minimizes the mean square error (MSE) of channel estimation. The MSE lower bound (LB) is theoretically derived to provide the design criterion. Based on the criterion, we show that the LB achieving design can be found by exhaustive 2D pilot location search. Exhaustive 2D search has high computational complexity. To reduce the complexity, sufficient conditions on the existence of LB achieving design are provided to decouple the 2D problem into two one-dimensional (1D) problems. For the 1D problem, we propose the LB achieving design when the number of possible pilot locations is divisible by the number of pilots. Simulation results illustrate that our proposed LB achieving design is superior to the random pilot pattern design and the bilinear interpolation channel estimation method.

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.

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.

Receive antenna selection (AS) has been shown to maintain the diversity benefits of multiple antennas while potentially reducing hardware costs. However, the promised diversity gains of receive AS depend on the assumptions of perfect channel knowledge at the receiver and slowly time-varying fading. By explicitly accounting for practical constraints imposed by the next-generation wireless standards such as training, packetization and antenna switching time, we propose a single receive AS method for time-varying fading channels. The method exploits the low training overhead and accuracy possible from the use of discrete prolate spheroidal (DPS) sequences based reduced rank subspace projection techniques. It only requires knowledge of the Doppler bandwidth, and does not require detailed correlation knowledge. Closed-form expressions for the channel prediction and estimation error as well as symbol error probability (SEP) of M-ary phase-shift keying (MPSK) for symbol-by-symbol receive AS are also derived. It is shown that the proposed AS scheme, after accounting for the practical limitations mentioned above, outperforms the ideal conventional single-input single-output (SISO) system with perfect CSI and no AS at the receiver and AS with conventional estimation based on complex exponential basis functions.

In the new generation wireless communication systems where high data rates are desired, orthogonal frequency division multiplexing (OFDM) has become the standard method because of its advantages over single carrier modulation schemes on multi-path, frequency selective fading channels. However, inter-carrier interference due to Doppler frequency shifts, and multi-path fading severely degrades the performance of OFDM systems. Estimation of channel parameters is required at the receiver. In this paper, we present a time-varying channel modeling and estimation method based on the discrete evolutionary transform that provides a time-frequency procedure to obtain a complete characterization of a multi-path, fading and frequency selective channel. Performance of the proposed method is tested on different levels of channel noise, and Doppler frequency shifts.

Multiple input-multiple output (MIMO) systems hold the potential to drastically improve the spectral effciency and link reliability in future wireless communications systems. A particularly promising candidate for next-generation fixed and mobile wireless systems is the combination of MIMO with Orthogonal Frequency Division Multiplexing (OFDM). OFDM has become the standard method because of its advantages over single carrier modulation schemes on multipath, frequency selective fading channels. In this paper, we present a time-varying channel modeling and estimation method based on the Discrete Evolutionary Transform. Performance of the proposed method is evaluated on different levels of channel noise, and Doppler frequency shifts.

Orthogonal frequency division multiplexing (OFDM) modulation, adopted by the digital video broadcasting (DVB-T) standard, has been recognized for its good performance for high data rate wireless communications. Therefore, the study of the robust transmission of multimedia data over OFDM systems has attracted extensive research interests. In the past, channel estimation, which is an important aspect in OFDM systems, has not been exploited for multimedia transmission. When using the block training based channel estimation, OFDM data blocks experience unequal decoding error rate due to the imprecision of channel estimation. We use this property to provide unequal error protection (UEP) for transmission of SPIHT coded images. Compared with the systems using pilot training channel estimation schemes, which are recommended in the DVB-T standard, the proposed scheme improves the PSNR of reconstructed images by up to 2 dB.

Multi carrier modulation is Orthogonal Frequency Division Multiplexing (OFDM), dividing the large band spectrum into small (narrow) band spectrum.OFDM offers flexibility in adaptation to time varying channel condition by adopting the parameters at each subcarrier accurately.Due to the multipath effect the OFDM system suffers Inter Symbol Interference (ISI).ISI can be reduced by introducing the guard band (cyclic prefix).Time-varying channel estimation is an important activity in next generation wireless communication.Channel estimation is required mainly for the significant signal processing operation in multiple input multiple output MIMO-OFDM systems.In this project DFT -based channel estimation based on block type arrangement is implemented in MAT Lab.The bit error rate (BER) of DFT (Discrete Fourier Transform)based channel estimation is less than the BER of LS (Least Square) and MMSE (Minimum Mean Square Error) based channel estimation with same signal to noise ratio (SNR).

We derive an approximate analytic model for the eigenfunctions of underspread LTV channels which plays a fundamental role in the analysis/synthesis of the optimal precoding that maximizes the information rate in transmissions over linear time-varying (LTV) channels. We assume that channel status information is available to both receiver and transmitter and that the channel impulse response can be predicted exactly, within a finite duration interval, from its past evolution. More specifically, we use our analytic model to prove that the optimal precoding is equivalent to applying the water-filling principle in the time-frequency domain and to simplify the computation of the optimal precoder. We include numerical results to support the validity of our model.

In high‐mobility scenarios, the time variation of mobile radio channels leads to a loss of orthogonality among subcarriers in orthogonal frequency division multiplexing (OFDM) systems, resulting in intercarrier interference (ICI) and performance deterioration. Conventional channel estimation schemes are usually based on pilot tones, which are distributed in each OFDM symbol to estimate the channel variation. Hence, the channel estimator itself suffers from ICI. In this study, a new estimation scheme, which does not suffer from ICI, is proposed to estimate the channel variation within OFDM symbols. The main idea is to zero‐pad (ZP) the OFDM symbol in the time domain. Then, in the middle of the ZP interval, an impulse signal is inserted as a pilot sample, which is used to estimate the channel at the pilot signal in the OFDM symbol. Finally, a linear model is used to estimate the channel variation over an OFDM symbol. Additionally, we derive the mean squared error (MSE) of the proposed estimation technique under the constraint that the channel varies linearly within OFDM symbols. Simulation results show that our scheme can achieve a substantial improvement in the bit error rate (BER) performance of OFDM, in spite of the OFDM symbol length being increased. Moreover, in many cases, the new scheme can achieve the same BER performance as the perfect knowledge of channel state information (CSI). Theoretical analysis and numerical simulations show that our scheme achieves excellent performance with much lower computational complexity.

This article proposes an uplink transmission scheme for cell-free (CF) massive multiple-input-multiple-output (MIMO) systems in high-speed railway communications to mitigate the negative effects of fast time-varying multipath channels with fewer antennas and insufficient angular resolution. To enhance the estimation performance by utilizing the possible similarity of the relatively slow time-varying channel parameters, the Dirichlet process (DP) is introduced to construct the probabilistic model of the doubly selective multiparameter channel estimation problem, which is solved by adopting the expectation-maximization (EM) framework. Furthermore, by introducing successive approximation, an enhanced channel estimation scheme is proposed. Finally, for the data transmission utilizing the orthogonal frequency-division multiplexing (OFDM) modulation, based on estimated channel parameters, a distributed intercarrier interference (ICI) elimination algorithm with local channel quality-based combining is proposed, and the performance of the system under different architectures and ICI elimination algorithms is analyzed. Simulation results show that DP can improve estimation performance by utilizing implicit similarity, the combination of first-order Taylor expansion and successive approximation can effectively improve estimation performance at higher speeds under relatively higher pilot power, and compared to centralized processing, the proposed distributed ICI elimination algorithm with local channel quality-based combining has a relatively small performance loss.

The aim of the paper is to compare multicarrier and single carrier modulation schemes for radio communication systems. In both cases the fast Fourier transform (FFT) and its inverse are utilized. In the case of OFDM (orthogonal frequency division multiplexing), the inverse FFT transforms the complex amplitudes of the individual subcarriers at the transmitter into the time domain. At the receiver the inverse operation is carried out. In the case of single carrier modulation, the FFT and its inverse are used at the input and output of the frequency domain equalizer in the receiver. Different single carrier and multicarrier transmission systems are simulated with time-variant transfer functions measured with a wideband channel sounder. In the case of OFDM, the individual subcarriers are modulated with fixed and adaptive signal alphabets. Furthermore, a frequency-independent as well as the optimum power distribution are used.

In this paper, the performance of time division duplex (TDD) orthogonal frequency division multiplexing (OFDM) systems over slow Rayleigh channels with phase and amplitude and phase pre-equalization are analyzed. The hit error rate (BER) formulas of binary phase-shift keying (BPSK) modulated TDD OFDM systems using ideal and nonideal pre-equalization are provided. Computer simulations are performed and the results verify corresponding formulas. The system performance of phase pre-equalization is decided by E/sub b//N/sub 0/ and channel estimation(CE) error. With the diminishing of CE error, system performance will reach towards the theoretical performance of a BPSK system in Rayleigh channels. In amplitude and phase pre-equalization systems, appropriate pre-equalization factor should he selected carefully to avoid the boost effect of transmission power and CE error on those subcarriers suffering deep fading. The corresponding BER formulas are presented, which base upon the E/sub b//N/sub 0/, mean square error (MSE) and pre-equalization factor.

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.