Time-Varying Channel Estimation in OFDM Systems with Null Subcarriers

Channel estimation can be classified into pilot‐assisted channel estimation, blind channel estimation, and decision DDCE. This chapter focuses on pilot‐assisted channel estimation in OFDM systems. There are two main design issues for channel estimation in OFDM systems. The first one is pilot design and the second one is channel estimator design with both low complexity and accuracy. An interpolation technique should be performed to obtain a channel estimation value at each data subcarrier. Channel estimation for MIMO‐OFDM systems is more complicated than single antenna systems but the basic principle is similar to the single antenna systems. The purpose of equalizers is to find the inverse function of the channel response and eliminate an Inter‐Symbol Interference (ISI) caused by the dispersive nature of the channel. The channel estimator and the equalizer are designed according to the system requirements such as pilot assignment, antenna array, system complexity, latency, and power.

In this article, design of preamble for channel estimation and pilot symbols for pilot-assisted channel estimation in orthogonal frequency division multiplexing system with null subcarriers is studied. Both the preambles and pilot symbols are designed to minimize the l2 or the l∞ norm of the channel estimate mean-squared errors (MSE) in frequency-selective environments. We use convex optimization technique to find optimal power distribution to the preamble by casting the MSE minimization problem into a semidefinite programming problem. Then, using the designed optimal preamble as an initial value, we iteratively select the placement and optimally distribute power to the selected pilot symbols. Design examples consistent with IEEE 802.11a as well as IEEE 802.16e are provided to illustrate the superior performance of our proposed method over the equi-spaced equi-powered pilot symbols and the partially equi-spaced pilot symbols.

To solve the problem of low accuracy of channel estimation in OFDM systems in the scenario of high-speed multipath channels, it is proposed in the paper that a noise reduction scheme of channel estimation is based on DFT (Discrete Fourier Transform) algorithm. By analyzing the algorithm principles, the mathematical model of the system is built, and the performance of the scheme is analyzed. Simulation results reveal that in high-speed scenario, the scheme has effectively achieved low bit error rate and low mean square error, thus having good application value.

Pilot assisted channel tracking (PACT) has been very popular for channel estimation in OFDM systems. However, as the mobility in the system increases and one has to maintain a high accuracy in channel estimation, the pilot overhead typically has to be increased. Emerging cellular OFDM standards are expected to use about 6 - 12% pilot overhead per stream, and any possible reduction in pilot overhead would be useful. Decision directed channel tracking (DDCT) can help reduce pilot overhead, but is known to suffer from error propagation at high fade rates. In emerging broadband wireless systems promising peak bit rates of 50 Mbps or more, saving on pilot overhead by using DDCT schemes would be highly attractive provided: (a) Such a DDCT approach does not suffer from error propagation and has an error rate performance comparable to (or better than) PACT schemes even at high fade rates; (b) The computational complexity of such a DDCT approach is not significantly more than that of the MMSE based PACT scheme. In this work, we propose a low complexity DDCT method which exploits the structure of the regression matrix in conjunction with robust statistics to mitigate the effect of error propagation. It has a much lower computational complexity and a better error rate performance than the decision directed EM-Kalman and other existing robust statistics based DDCT schemes. The proposed method also outperforms a 12.5% pilot overhead based PACT scheme with only a modest increase in computational complexity.

This paper presents SLRTNet, a deep learning model designed for channel estimation in OFDM systems. SLRTNet employs a super-resolution network in combination with a transformer architecture, which features an improved encoder-decoder structure. To extract essential input information, a transformer encoder with a multi-head attention mechanism and a Feedforward Net that utilizes LRR Blocks are used. A multi-level residual network is implemented as a transformer decoder to improve the model's generalization ability. The simulation results show that SLRTNet outperforms other deep learning-based neural network schemes. Compared with the conventional LS algorithm, SLRTNet exhibits a performance gain of 0.7 to 2 dB in the low signal-to-noise ratio (SNR) regime and 5.5 to 8 dB in the high SNR regime. This indicates that SLRTNet has good performance in channel estimation for OFDM systems and improves the accuracy of channel estimation effectively.

OFDM technique uses multiple sub-carriers for the data transmission. Therefore, bit error rate increases because of inter-carrier interference caused by nonlinear high power amplifier and carrier frequency offset. Wireless OFDM transmission over multi path fading channels is characterized by small transmission gain in multiple sub-carrier frequency interval. Therefore bit error rate increases because of burst errors. Inter-leaver and convolution error control coding are effective for the reduction of this burst error. Pilot symbol is used for the channel estimation in OFDM systems. However, imperfect channel estimates in this systems degrade the performance. The performance of this convolution coding OFDM systems using inter-leaver, gauged by the bit error rate, is analyzed considering the nonlinear high power amplifier, carrier frequency offset and channel estimation error.

The minimum mean-square error (MMSE) criterion is often used for channel estimation in wireless OFDM systems. The MMSE channel estimators perform better than the least-square (LS) criterion-based techniques but their computational complexity is one of the main drawbacks for practical implementation, especially when the number of subcarriers is large. To address this issue while maintaining the performance advantage, we present a new simplified MMSE channel estimator for OFDM systems in multipath fading channels. The proposed method is primarily based on the rank-reduction of the channel correlation matrix in the frequency domain. Simulation results show that the proposed method achieves almost the same performance as the full-rank MMSE method, while significantly reducing the computational complexity.

Complex Amplitudes Tracking Loop for multipath channel estimation in OFDM systems under slow to moderate fading

In this paper we address the joint estimation of the channel impulse response in orthogonal frequency division multiplexing systems with phase distortion, namely phase noise and carrier frequency offset, phase noise bandwidth and the additive noise variance. The estimation algorithm is based on an implementation of the Extended Kalman Filter within the general framework of the Expectation-Maximization algorithm. We focus on the partial training case, where the transmitted signal is not fully known. To tackle this problem, we utilize a Rao-Blackwellized Extended Kalman Filter. We also compare our results with another nonlinear filtering technique, namely Rao-Blackwellized Particle Filtering, applied to this joint estimation problem. The performance of the two filtering techniques considered in this paper is evaluated in terms of the mean square error of the channel estimates and the numerical complexity introduced by each of these techniques.

This paper considers the problem of channel estimation for OFDM systems, where the number of channel taps and their power delay profile (PDP) are unknown. Using a Bayesian approach, we construct a model in which we estimate jointly the coefficients of the channel taps, the channel order and decay rate of the PDP. In order to sample from the resulting posterior distribution we develop a novel Trans-dimensional Markov chain Monte Carlo (TDMCMC) algorithm. This is done using a Stochastic Approximation (SA) approach to develop an adaptively learning algorithm to improve mixing rates of the basic Birth-Death (B-D) Markov chain for the between model subspaces. Using simulations we assess its performance in terms of channel order estimation and bit error rate (BER). It is shown that the proposed algorithm can achieve results very close to the case where both the channel length and the PDP are known.

Channel estimation is critical for coherent detection in OFDM systems. In pilot symbol aided channel estimation methods, the LS channel estimation can be viewed as a noisy observation of the true channel frequency response, so the noise component can be compressed through signal subspace projecting. In this paper, we focus on parametric channel estimation method combined with subspace projecting. First, we estimate the signal space of the OFDM system, and then we can use ESPRIT method to estimate the multipath delay of wireless channel, finally we use subspace projecting to get more accurate channel estimation. When the channel multipath delays vary with time, the signal subspace should be tracked to keep the efficiency of channel estimation. Computer simulations show that the performance of our method is much better than traditional channel estimation methods and its nonparametric counterpart.

In OFDM systems, channel estimation is a crucial consideration for improving system performance. The channel fading effects are eliminated by the equalization of received signal, and the equalizer coefficients are determined according to the results of channel estimation. In this paper, the channel estimation of OFDM systems in time domain for fast fading channel is investigated and developed. The time-domain channel estimation scheme is achieved by inserting pseudo-noise (PN) sequences in the prefix of each OFDM symbol, and therefore the channel impulse response can be estimated. These proposed algorithms include both least-squares and maximum-likelihood estimation techniques. The proposed techniques can perform better than the conventional channel estimation with correlators. Some comparative simulations are given to illustrate the superior performance of the proposed channel estimation techniques.

We investigate a practical pilot design for indoor channels with an analysis of channel estimation for block and comb-type pilot arrangements. For the pilot design over indoor channels, the performance is determined by the tradeoff between the interpolation error by frequency selectivity of the channel and the noise reduction by the interpolator, compared to the Doppler effect. Results show that the performance of channel estimation for the comb-type pilot symbol, with respect to the derived criterion, outperforms that of the block-type pilot symbol for indoor channels, whereas it is a slow-fading environment.

A novel data-aided channel estimation for OFDM systems based on selective superimposed pilot sequences is proposed in this paper, where the receiver correlates the received signal sequence with the pilot symbol sequence, and obtains the channel estimation. However, the pilot sequence is superimposed on a data sequence and transmitted together, and thus it has a high spectral efficiency. The selective pilot sequence owns low correlation with data sequence to reduce the interference. In the case of Pilot=1 and L=31, BER of the proposed channel estimation is improved about 2%. With the increase of L and pilot, BER gets lower. So by taking advantage of the correlation between pilot sequences themselves, the proposed algorithm can achieve the good channel estimation.

In wireless communication systems, the ambient channel noise is known through experimental measurements to be decidedly non-Gaussian, due largely to impulse phenomena. It is known, too, that when data are contaminated by non-Gaussian noise, the conventional MMSE channel estimation method may perform poorly. We develop robust channel estimation algorithms to combat the impulse noise in multiple input multiple output (MIMO) systems. Simulation results show that the robust channel estimation (RCE) method offers significant performance gain with little attendant increase in computational complexity compared with the MMSE channel estimation method in non-Gaussian channels. To implement RCE in practice, we also develop two approximate robust channel estimation (ARCE) methods.