Data-aided Channel Estimation Research Articles

Optimal pilot pattern for data‐aided channel estimation for MIMO‐OFDM wireless systems

AbstractThis article presents an optimal pilot pattern for the data‐aided channel estimation (DACE) scheme for both single‐input single‐output (SISO) and multiple‐input multiple‐output orthogonal frequency division multiplexing (MIMO‐OFDM) wireless systems. The research evaluates the performance of the DACE scheme using different comb‐type pilot patterns for both least square (LS) and linear minimum mean square error (LMMSE) channel estimators. In this regard, it is found that pilot spacing significantly influences system performance. Inserting pilot symbols in consecutive subcarriers cannot compensate for increased pilot spacing. Hence, the solution to this problem is to place pilot symbols at appropriate locations within the given spectrum. Moreover, data symbols which are reliably detected at the receiver are used as additional pilot signals to further enhance system performance. However, reliable data symbols need to be determined carefully because wrong detection results in severe performance degradation. In this respect, the proposed comb‐type pilot pattern using a single pilot subcarrier extracts the maximum number of reliable data symbols for the DACE scheme, improves channel estimation accuracy, and provides bandwidth optimization for MIMO‐OFDM systems. Furthermore, it outperforms all other pilot patterns in terms of system mean square error (MSE) and bit‐error‐rate (BER) performance.

Data-Aided Channel Estimation and Combining for Cell-Free Massive MIMO With Low-Resolution ADCs

Data-Aided Channel Estimation and Combining for Cell-Free Massive MIMO With Low-Resolution ADCs

Iterative channel estimation and data detection algorithm for MIMO-OTFS systems

Channel estimation in high-mobility environments is a challenging problem for advanced mobile communication systems (5G and beyond). In this manuscript, we first propose an iterative algorithm for channel estimation and data detection in the delay-Doppler domain for multiple-input multiple-output orthogonal time frequency space system. Then, in order to increase the spectral efficiency of the system, we use a superimposed pilot pattern. The proposed algorithm takes advantage from the sparse nature of the channel in the delay-Doppler domain and iterates between message passing-aided data detection and data-aided channel estimation. For channel estimation, we propose two algorithms. The first one consists in estimating all channel parameters, including the number of path gains, delay taps, Doppler taps, and channel gains by using a mean-field approximation and the variational Bayesian expectation maximization algorithm. The second one, based on the fact that delay and Doppler taps remain unchanged for a rather long period of time, uses an MMSE approach combined with Cholesky decomposition to only estimate channel gains in each transmitted frame. For data detection, we adapt the message-passing algorithm proposed in the literature. We also derive a lower bound on the signal-to-interference-plus-noise ratio of the proposed scheme, and maximize it by optimally allocating power between pilots and data symbols. Finally, we compare the complexity and the performance in terms of normalized mean square error, bit error rate, and spectral efficiency against existing methods. Simulation results, conducted in high-mobility scenarios show that the proposed algorithm achieves a good compromise between complexity and performance.

Semi-Data-Aided Channel Estimation for MIMO Systems via Reinforcement Learning

Data-aided channel estimation is a promising solution to improve channel estimation accuracy by exploiting data symbols as pilot signals for updating an initial channel estimate. In this paper, we propose a semi-data-aided channel estimator for multiple-input multiple-output communication systems. Our strategy is to leverage reinforcement learning (RL) for selecting reliable detected symbols, then update the channel estimate by utilizing only the selected symbols as additional pilot signals. Towards this end, we first define a Markov decision process (MDP) which sequentially decides whether to use each detected symbol as an additional pilot signal. We then develop an RL algorithm to find an effective policy of the MDP based on a Monte Carlo tree search approach. In this algorithm, we exploit the a-posteriori probability for approximating both the optimal future actions and the corresponding state transitions of the MDP and derive a closed-form expression for the optimal policy under the approximations. A key advantage of the proposed channel estimator is that it requires less computational complexity than conventional iterative data-aided channel estimators. Simulation results demonstrate that the proposed channel estimator effectively mitigates both channel estimation error and detection performance loss caused by insufficient pilot signals.

Reinforcement Learning-Aided Channel Estimator in Time-Varying MIMO Systems.

This paper proposes a reinforcement learning-aided channel estimator for time-varying multi-input multi-output systems. The basic concept of the proposed channel estimator is the selection of the detected data symbol in the data-aided channel estimation. To achieve the selection successfully, we first formulate an optimization problem to minimize the data-aided channel estimation error. However, in time-varying channels, the optimal solution is difficult to derive because of its computational complexity and the time-varying nature of the channel. To address these difficulties, we consider a sequential selection for the detected symbols and a refinement for the selected symbols. A Markov decision process is formulated for sequential selection, and a reinforcement learning algorithm that efficiently computes the optimal policy is proposed with state element refinement. Simulation results demonstrate that the proposed channel estimator outperforms conventional channel estimators by efficiently capturing the variation of the channels.

Alternative threshold-based channel estimation and message-passing-based symbol detection in MIMO-OTFS systems using superimposed pilots

In this work, we investigate the challenging problem of channel estimation in high-mobility environments for advanced mobile communication systems (5G and beyond). First, we propose an iterative algorithm for channel estimation and symbol detection in the delay-Doppler domain for multiple-input multiple-output orthogonal time–frequency space (OTFS) system. The proposed algorithm is based on a superimposed pilot pattern to improve the spectral efficiency of the system. It iterates between data-aided channel estimation and message-passing-aided data detection. The channel estimation step is based on a threshold method. This step considers interference-plus-noise caused by the data symbols and the additive noise to adapt the threshold at each iteration. The data detection step is based on an adapted version of the message-passing algorithm proposed in the literature for uncoded OTFS. Then, to improve the channel estimation efficiency, we suggest an interference cancellation scheme executed at each iteration of the proposed algorithm. Finally, we compare the computational complexity and the achieved performance in terms of normalized mean square error of channel estimation, bit error rate, and spectral efficiency against five state-of the-art methods.

Data Aided Channel Estimation for MIMO-OFDM Wireless Systems Using Reliable Carriers

Wireless channel estimation is one of the challenging problems in Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) wireless systems. The MIMO-OFDM exploits the spatial resources and increases the reliability and capacity of wireless systems. However, the performance of these systems depends on accurate channel estimation since the receivers require perfect Channel State Information (CSI) for coherent signal detection. Thus, wireless channel estimation is a necessary component of OFDM systems. In this article, we have proposed an algorithm for MIMO-OFDM systems that combines pilot symbols with reliable data symbols for channel estimation. The reliable data symbols serve as virtual pilots and enhance the spectral efficiency. The proposed Data Aided Channel Estimation (DACE) algorithm eliminates the requirement of any additional resources such as excessive number of training symbols to attain the desired performance. Also, it outperforms the traditional Least Square (LS) and Linear Minimum Mean Square Error (LMMSE) methods for channel estimation in terms of Mean Square Error (MSE) and Bit Error Rate (BER) performance of the system.

Single-Channel Blind Separation of Unsynchronized Multiuser PSK Signals With Non-Identical Sampling Frequency Offsets

Single-channel blind source separation (SCBSS) of uncoordinated, non-spread, co-frequency interfering multi-user signals is a challenging task. When the multi-user signals have sampling frequency offset (SFO) due to the imperfection of the local oscillator (LO), this problem becomes even more difficult to be solved. In this letter, a select-stitch data-aided channel estimation (CE) initialized per-survivor processing (SS-DCE-PSP) algorithm is proposed for SCBSS of multi-user signals with SFOs caused by imperfect LOs. By dividing a long sequence into a number of segments and selecting the segments with highest detection reliability to stitch together, the time slip and symbol slip due to the non-identical SFOs can be resolved. The data-aided CE in SS-DCE-PSP further enhances the performance of PSP, especially for the initial symbols. Simulation results show that the proposed SS-DCE-PSP algorithm is robust to the normalized SFO up to 10−4, and the BERs obtained by the SS-DCE-PSP algorithm are close (within 0.5dB) to the BERs obtained for multi-user signals without SFOs.

Capacity Bounds Under Imperfect Polarization Tracking

In optical fiber communication, due to the random variation of the environment, the state of polarization (SOP) fluctuates randomly with time leading to distortion and performance degradation. The memory-less SOP fluctuations can be regarded as a two-by-two random unitary matrix. In this paper, for what we believe to be the first time, the capacity of the polarization drift channel under an average power constraint with imperfect channel knowledge is characterized. An achievable information rate (AIR) is derived when imperfect channel knowledge is available and is shown to be highly dependent on the channel estimation technique. It is also shown that a tighter lower bound can be achieved when a unitary estimation of the channel is available. However, the conventional estimation algorithms do not guarantee a unitary channel estimation. Therefore, by considering the unitary constraint of the channel, a data-aided channel estimator based on the Kabsch algorithm is proposed, and its performance is numerically evaluated in terms of AIR. Monte Carlo simulations show that Kabsch outperforms the least-square error algorithm. In particular, with complex, Gaussian inputs and eight pilot symbols per block, Kabsch improves the AIR by 0.20 to 0.30 bits/symbol throughout the range of studied signal-to-noise ratios.

Low-Resolution Precoding for Multi-Antenna Downlink Channels and OFDM.

Downlink precoding is considered for multi-path multi-input single-output channels where the base station uses orthogonal frequency-division multiplexing and low-resolution signaling. A quantized coordinate minimization (QCM) algorithm is proposed and its performance is compared to other precoding algorithms including squared infinity-norm relaxation (SQUID), multi-antenna greedy iterative quantization (MAGIQ), and maximum safety margin precoding. MAGIQ and QCM achieve the highest information rates and QCM has the lowest complexity measured in the number of multiplications. The information rates are computed for pilot-aided channel estimation and a blind detector that performs joint data and channel estimation. Bit error rates for a 5G low-density parity-check code confirm the information-theoretic calculations. Simulations with imperfect channel knowledge at the transmitter show that the performance of QCM and SQUID degrades in a similar fashion as zero-forcing precoding with high resolution quantizers.

Massive MIMO-OFDM Systems with Low Resolution ADCs: Cramér-Rao Bound, Sparse Channel Estimation, and Soft Symbol Decoding

We consider the delay-domain sparse channel estimation and data detection/decoding problems in a massive multiple-input-multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) wireless communication system with low-resolution analog-to-digital converters (ADCs). The high non-linear distortion due to coarse quantization leads to severe performance degradation in conventional OFDM receivers, which necessitates novel receiver techniques. Firstly, we derive the Bayesian Cramr-Rao-lower-bound (CRLB) on the mean squared error (MSE) in recovering jointly compressible vectors from quantized noisy underdetermined measurements. Secondly, we formulate the pilot-assisted channel estimation as a multiple measurement vector (MMV) sparse recovery problem, and propose a variational Bayes (VB) algorithm to infer the posterior distribution of the channel. We benchmark the MSE performance of our algorithm with that of the CRLB, and numerically show that the VB algorithm meets the CRLB. Thirdly, we propose a soft symbol decoding algorithm that infers the posterior distributions of the data symbols given the quantized observations. We utilize the posterior statistics of the detected data symbols as virtual pilots, and propose an iterative soft symbol decoding and data-aided channel estimation procedure. Finally, we propose a variant of the iterative algorithm that utilizes the output bit log-likelihood ratios of the channel decoder to adapt the data prior to further improve the performance. We provide interesting insights into the impact of the various system parameters on the MSE and bit error rate of the proposed algorithms, and benchmark them against the state-of-the-art.

Data-Aided Channel Estimation for OTFS Systems With a Superimposed Pilot and Data Transmission Scheme

The recently developed orthogonal time frequency space (OTFS) modulation has shown its capability of coping with the fast time-varying channels in high-mobility environments. In particular, OTFS modulation gives rise to the sparse representation of the delay-Doppler (DD) domain channel model. Hence, one can an enjoy accurate channel estimation by adopting only one pilot symbol. However, conventional OTFS channel estimation schemes require the deployment of guard space to avoid data-pilot interference, which inevitably sacrifices the spectral efficiency. In this letter, we develop a data-aided channel estimation algorithm for a superimposed pilot and data transmission scheme, which can improve the spectral efficiency. To accurately estimate the channel and detect the data symbols, we coarsely estimate the channel based on the pilot symbol, followed by an iterative process which detects the data symbols and refines the channel estimates. Simulation results show that the bit error rate (BER) performance based on the proposed method can approach the baseline scheme with perfect channel estimation.

Differential Data-Aided Channel Estimation for Up-Link Massive SIMO-OFDM

Pilot symbol assisted modulation (PSAM) is widely used to obtain the channel state information (CSI) needed for coherent demodulation. It allows the density of pilot symbols to be dynamically chosen depending on the channel conditions. However, the insertion of pilots reduces the spectral efficiency, more severely when the channel is highly time-variant and/or frequency-selective. In these cases a significant amount of pilots is required to properly track the channel variations in both time and frequency dimensions. Alternatively, non-coherent demodulation does not require any CSI for the demodulation independently of the channel conditions. For the particular case of up-link (UL) based on massive single input - multiple output (SIMO) combined with orthogonal frequency division multiplexing (OFDM), we propose to replace the traditional reference signals of PSAM by a new differentially-encoded data stream that can be non-coherently detected. The latter can be demodulated without the knowledge of the CSI and subsequently used for the channel estimation. We denote our proposal as hybrid demodulation scheme (HDS) because it exploits both the benefits of a coherent demodulation scheme (CDS) and a non-coherent demodulation scheme (NCDS) to increase the spectral efficiency. The mean squared error (MSE) of the channel estimation, bit error rate (BER), achieved throughput and complexity are analyzed to highlight the benefits of this differential data-aided channel estimation as compared to other approaches. We show that the channel estimation is almost as good as PSAM, while the BER performance and throughput are improved for different channel conditions with a very small complexity increase.

Data-Aided Channel Estimation for Multiple-Antenna Users in Massive MIMO Systems

In this paper, we study the performance of large-scale MIMO network where the base station has a large number of antennas and performs semi-blind channel estimation. We show that one can increase the number of antennas at the user side without increasing the overhead imposed by the channel estimation linearly with the number of user antennas. Specifically, we propose a simple data-aided channel estimation scheme which exploits the quasi-orthogonality of the channel vectors and takes advantage of the conventional pilot-aided channel estimation performed for the first antenna at each user. Two schemes are then analyzed using the extra antenna(s) at the users: data-multiplexing and interference alignment. We obtain achievable rates for the proposed uplink multi-cell MIMO system in both schemes. The rate bounds are tight and the system performance is also analyzed in terms of the outage probability to study the effect of the data length used for channel estimation scheme.

Optimal number of user antennas in a constrained pilot‐length massive MIMO system

In this study, the authors analyse the performance of a massive multiple-input multiple-output network with N-antenna users. Equipping the user terminal (UT) with a multiple of antennas is usually challenging since it increases the overhead of the channel estimation process (linearly with N). In this study, the authors use semi-blind (data-aided) channel estimation that significantly reduces the pilot overhead and analytically obtains the optimal number of antennas that can be mounted at the UT. The proposed channel estimation algorithm is especially useful in cases where a UT can be assigned a single, or generally a few numbers of, pilot sequence(s) although it might have a number of antennas greater than the number of sequences (as the case of 5G proposed solutions); therefore the network does not have to assign more pilots to the user in order to estimate the additional antennas. The authors also characterise the user outage performance when a part of its data is used for the blind channel estimation.

Semi-Blind, Training, and Data-Aided Channel Estimation Schemes for MIMO-FBMC-OQAM Systems

This paper considers and analyzes the performance of semiblind, training, and data-aided channel estimation schemes for multiple-input multiple-output (MIMO) filter bank multicarrier (FBMC) systems with offset quadrature amplitude modulation. A semiblind MIMO-FBMC (SB-MF) channel estimator is developed that exploits both the training symbols and second-order statistical properties of the data symbols, which leads to a significant decrease in the mean squared error (MSE) with respect to its conventional training-based counterpart. Its performance is compared with that of the interference approximation method-based least squares MIMO-FBMC (LS-MF) channel estimator, wherein the channel is estimated using exclusively training symbols. The Cramér-Rao lower bounds are derived to characterize the MSE of the proposed and LS-MF estimators, which interestingly demonstrate that while the MSE per parameter of the proposed scheme decreases with the number of receive antennas, it remains constant for the training-based scheme. The resulting bit error rates are derived for the proposed SB-MF and LS-MF channel estimators. An expectation maximization-based data-aided MIMO-FBMC channel estimator is also investigated that performs iterative maximum a posteriori channel estimation in the E-step followed by data detection in the M-step. A comparative analysis is presented for the computational complexities of the various schemes. Simulation results with practical channel models demonstrate that the proposed semiblind scheme significantly outperforms the training-based and data-aided schemes.

Differential pulse‐amplitude modulation signalling for free‐space optical communications

To improve the bandwidth efficiency of free-space optical systems and at the same time to reduce the impact of the background noise, a differential M -ary pulse-amplitude modulation ( M -PAM) signalling scheme that uses two laser transmitters is proposed. The authors first consider the condition that the receiver perfectly knows the instantaneous channel coefficient and compare the performance of the proposed differential PAM with the conventional PAM signalling and show the improved performance when the background noise level is relatively high. Second , the practical situation where the receiver has to estimate the channel for signal detection is considered. The authors propose an estimation scheme based on the characteristics of the differential PAM signalling while requiring no pilot symbol transmission. The proposed data-aided channel estimation is performed on a sequence of received PAM symbols. The authors also show that for a sufficiently large observation window, the proposed estimation method allows achieving a performance close to the perfect channel knowledge.

Deep Learning-Based Channel Estimation for Massive MIMO Systems

In this letter, we propose a deep learning (DL)-based channel estimation scheme for the massive multiple-input multiple-output (MIMO) system. Unlike existing studies, we develop the channel estimation scheme for the case that the pilot length is smaller than the number of transmit antennas. The proposed scheme takes a two-stage estimation process: 1) a DL-based pilot-aided channel estimation and 2) a DL-based data-aided channel estimation. In the first stage, the pilot itself and the channel estimator are jointly designed by using both a two-layer neural network (TNN) and a deep neural network (DNN). In the second stage, the accuracy of channel estimation is further enhanced by using another DNN in an iterative manner. The simulation results demonstrate that the proposed channel estimation scheme has much better performance than the conventional channel estimation scheme. We also derive a useful insight into the optimal pilot length given the number of transmit antennas.

Secure Transmission in Multi-Cell Multi-User Massive MIMO Systems With an Active Eavesdropper

In this letter, we investigate secure transmission for multi-cell multi-user massive multiple-input multiple-output systems with an active eavesdropper. During the uplink (UL) training, the eavesdropper can attack the training phase to cause pilot contamination. To resist such pilot contamination attack (PCA), we propose a secure transmission that does not require statistical information of the channels. In the proposed transmission strategy, we first detect PCA by a simple method. If the PCA is not detected, we then estimate the UL data of the users by a semi-blind method based on an asynchronous protocol. After that, we perform the data-aided channel estimation and design the corresponding precoder. Simulation results demonstrate that the proposed transmission can effectively resist the PCA even when the PCA detection method fails.

A Data-Aided Channel Estimation Scheme for Decoupled Systems in Heterogeneous Networks

Uplink/downlink (UL/DL) decoupling promises more flexible cell association and higher throughput in heterogeneous networks (HetNets), however, it hampers the acquisition of DL channel state information (CSI) in time-division-duplex (TDD) systems due to different base stations (BSs) connected in UL/DL. In this paper, we propose a novel data-aided (DA) channel estimation scheme to address this problem by utilizing decoded UL data to exploit CSI from received UL data signal in decoupled HetNets where a massive multiple-input multiple-output BS and dense small cell BSs are deployed. We analytically estimate BER performance of UL decoded data, which are used to derive an approximated normalized mean square error (NMSE) expression of the DA minimum mean square error (MMSE) estimator. Compared with the conventional least square (LS) and MMSE, it is shown that NMSE performances of all estimators are determined by their signal-to-noise ratio (SNR)-like terms and there is an increment consisting of UL data power, UL data length and BER values in the SNR-like term of DA method, which suggests DA method outperforms the conventional ones in any scenarios. Higher UL data power, longer UL data length and better BER performance lead to more accurate estimated channels with DA method. Numerical results verify that the analytical BER and NMSE results are close to the simulated ones and a remarkable gain in both NMSE and DL rate can be achieved by DA method in multiple scenarios with different modulations.