Data Symbol Detection Research Articles

Joint channel estimation and data detection for high rate orthogonal time frequency space systems

SummaryThis paper proposes a new pilot pattern in the delay‐Doppler (DD) domain for the orthogonal time frequency space (OTFS) system. In contrast to the embedded‐pilot schemes, guard intervals are not used so as increase the spectral efficiency. Also, compared to the superimposed design where data symbols and pilots are arranged on the entire DD grid, in the proposed rearrangement, the number of pilots used is only spread over a subgrid of the DD grid. Hence, the interference of pilots with data symbols is reduced. Afterwards, an algorithm for channel estimation (CE) and symbol detection in the DD domain benefiting from the sparsity of the DD channel is designed. The sparse CE step is formulated as a specific marginalization of the maximum a posteriori (MAP) criterion by providing a Bayesian approach via the mean‐field approximation that involves the variational Bayesian expectation maximization (VB‐EM) algorithm. Detection of data symbols is done using a low complexity MP algorithm. We also propose an interference cancellation (IC) scheme to mitigate contamination of data by pilots that is run after each CE step. To achieve a high CE accuracy, based on the mean mutual incoherence property (MIP), a pilot optimization problem for OTFS is formulated and develop a simulated annealing‐based algorithm to solve it. Finally, simulation results show that the proposed scheme achieves a good compromise between spectral efficiency, complexity, and performance in terms of bit error rate (BER) and normalized mean square error (NMSE) when compared to literature benchmarks.

Channel Tracking and AoA Acquisition in Quantized Millimeter Wave MIMO Systems

This paper considers the channel tracking and angle of arrival (AoA) acquisition for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, in which each antenna at the base station is equipped with low-resolution analog-to-digital converters (ADCs) to quantize the received signals. We utilize the time-varying model to capture the sparsity and temporal correlation of the mmWave channel, and an offgrid model is incorporated for an accurate AoA acquisition. Essentially, the beamspace channel tracking is a quantized sparse Bayesian learning problem, which is solved under the expectation maximization (EM) framework. We first employ the Bussgang decomposition to linearize quantized signals, based on which, the Kalman filtering (KF) is adapted for the statistics' update in the expectation step. In this way, we propose a Bussgang joint channel tracking and data detection (BJ-CTDD) algorithm, in which the detected data symbols are reused to enhance the tracking without extra pilot overhead. To further reduce the computational burden caused by the KF, a variational inference joint channel tracking and data detection (VIJ-CTDD) algorithm is proposed. Finally, extensive simulations validate the superiority of the proposed BJ-CTDD and VIJ-CTDD algorithms over several existing works.

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.

Optimal Low-Complexity Orthogonal Block Based Detection of OTFS for Low-Dispersion Channels

Orthogonal time frequency space (OTFS) modulation constitutes a promising technology for high-mobility scenarios. However, the detection of OTFS systems imposes substantial complexity. Hence, we propose a novel orthogonal block (OB) based detection scheme for significantly reducing the OTFS detection complexity without any performance loss with integer Doppler shifts. This is achieved by recognizing that the received signal can be partitioned into multiple parallel orthogonal blocks. Therefore, the detection of data symbols within an orthogonal block only depends on the signals received within this orthogonal block with reduced dimension. Explicitly, we propose a graph theory based orthogonal block identification algorithm, which models the relationship between the received signal and the original information symbols as a bipartite graph, where a depth first search (DFS) algorithm is invoked for partitioning the received signals into orthogonal blocks. For each orthogonal block, the existing detection algorithms can be used. Since the size of orthogonal blocks may be much lower than that of the original received signals, the detection complexity can be significantly reduced. For example, the complexity of the OB based MMSE detector is approximately a factor 4096 lower than that of the traditional MMSE detector for a channel having two paths.

Channel estimation and detection with space–time transmission scheme in colocated multiple‐input and multiple‐output system

AbstractIn this study, a space–time transmission scheme is proposed to tackle the limitations of channel estimation with orthogonal pilot information in colocated multiple‐input multiple‐output systems with several transmitting and receiving antennas. Channel information is obtained using orthogonal pilots. Channel estimation introduces pilot heads required to estimate a channel. This leads to bandwidth insufficiency. As a result, trade‐offs exist between the number of pilots required to estimate a channel versus spectral efficiency. The detection of data symbols is performed using the maximum likelihood decoding method as it provides a consistent approach to parameter estimation problems. The moment‐generating function of the instantaneous signal‐to‐noise ratio is used to drive an approximate expression of the symbol error rate for the proposed scheme. Furthermore, the order of diversity is less by one than the number of receiver antennas used in the proposed scheme. The effect of the length of a pilot sequence on the proposed scheme's performance is also investigated.

Coded Assisted Transmit and Receive IQ Mismatch Compensation With Channel Estimation for AF Cooperative OFDM Systems

Amplify-and-forward (AF) orthogonal frequency division multiplexing (OFDM) transmissions encounter a significant difficulty in the form of in-phase and quadrature phase (IQ) mismatch. Previous reports on this problem have solely been discussed in the context of uncoded transmissions. In addition, in these precedent studies, IQ equalization must be conducted following the estimation stage for accurate detection of data symbols. This research delves into the issue of the IQ mismatch between transmission and reception in AF-OFDM systems in the context of channel coding. We design a magnificent code-aided approach to predict the overall channel impulse responses (CIRs), which encompass the actual CIRs and IQ mismatch originating at the source, relay, and destination. Instead of using a collection of algorithms, the proposed approach can be utilized to estimate nine parameters simultaneously. Due to the impractical nature of the precise maximum-likelihood (ML) strategy to this situation, we instead utilize an expectation-maximization (EM) process as a low complexity strategy to predict the parameters under consideration. The suggested estimation approach uses an iterative process to improve predictions exploiting the a priori knowledge gained from the soft information supplied by the channel decoder. In addition, we demonstrate how to carry out data detection by making use of the estimated parameters. The simulation results verify the effectiveness of the proposed estimator and detector for usage in real-world settings, with superiority over the conventional ones.

A Low-Complexity Algorithm for a Reinforcement Learning-Based Channel Estimator for MIMO Systems.

This paper proposes a low-complexity algorithm for a reinforcement learning-based channel estimator for multiple-input multiple-output systems. The proposed channel estimator utilizes detected symbols to reduce the channel estimation error. However, the detected data symbols may include errors at the receiver owing to the characteristics of the wireless channels. Thus, the detected data symbols are selectively used as additional pilot symbols. To this end, a Markov decision process (MDP) problem is defined to optimize the selection of the detected data symbols. Subsequently, a reinforcement learning algorithm is developed to solve the MDP problem with computational efficiency. The developed algorithm derives the optimal policy in a closed form by introducing backup samples and data subblocks, to reduce latency and complexity. Simulations are conducted, and the results show that the proposed channel estimator significantly reduces the minimum-mean square error of the channel estimates, thus improving the block error rate compared to the conventional channel estimation.

Near-Optimal BEM OTFS Receiver With Low Pilot Overhead for High-Mobility Communications

In this paper, a new receiver design based on basis expansion model (BEM) orthogonal time frequency space (OTFS) is presented for high-mobility communications with Doppler-spread channel. By deriving an analytical BEM OTFS system model, a low-order generalized complex exponential BEM (GCE-BEM) aided rough channel estimation is proposed at the initial stage with low pilot overhead, followed by equalization. Then, the refinement of channel estimation and equalization is conducted iteratively, in which a high-resolution GCE-BEM model with a large BEM order is adopted and the detected data symbols are exploited as pseudo-pilots, leading to higher estimation accuracy. Simulation results show that the proposed BEM OTFS receiver significantly outperforms the existing OTFS receivers in terms of the mean square error (MSE) of channel estimation and bit error rate (BER), while featuring low pilot overhead. Results also show the near-optimal performance of the novel solution, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , achieved BER is very close to the case of perfect channel estimation. The theoretical lower bound on MSE of channel estimation is derived to verify the effectiveness of the proposed BEM OTFS receiver, which is shown to be close to simulation results.

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.

Deep Learning Noncoherent UWB Receiver Design

Ultrawideband (UWB) is a promising technology for positioning and wireless communications in Internet-of-things (IoT) applications. However, UWB system's performance is limited by multiple interferences for low complexity noncoherent signal detection methods. Further, deep learning (DL)-based solutions have been envisioned for wireless communications in inaccurate system modeling scenarios. In this letter, we propose a deep learning noncoherent (DLN) UWB receiver to overcome the effect of various interferences such as multiuser interference (MUI), narrowband interference (NBI), and intersymbol-interference (ISI). The DLN is trained offline using the UWB channel statistics, and then, it is used online for data symbol detection. The proposed DLN efficiently learns a nonlinear relationship between input and output in an interference scenario and gives highly accurate data symbol detection, even for training data obtained in a very short period. Numerical results clearly show the proposed DLN UWB receiver's superiority, especially MUI, NBI, and ISI scenarios, over the conventional noncoherent detection method.

Semi-Blind Channel Estimation and Data Detection for Multi-Cell Massive MIMO Systems on Time-Varying Channels

We study the problem of semi-blind channel estimation and symbol detection in the uplink of multi-cell massive MIMO systems with spatially correlated time-varying channels. An algorithm based on expectation propagation (EP) is developed to iteratively approximate the joint a posteriori distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. This distribution is then used for direct estimation of the channel matrix and detection of data symbols. A modified version of the popular Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize the EP-based algorithm. Performance of the Kalman smoothing algorithm followed by KF-M is also examined. Simulation results demonstrate that channel estimation error and the symbol error rate (SER) of the semi-blind KF-M, KS-M, and EP-based algorithms improve with the increase in the number of base station antennas and the length of the transmitted frame. It is shown that the EP-based algorithm significantly outperforms KF-M and KS-M algorithms in channel estimation and symbol detection. Finally, our results show that when applied to time-varying channels, these algorithms outperform the algorithms that are developed for block-fading channel models.

Joint Channel and Phase Noise Estimation and Data Detection for GFDM

Generalized frequency division multiplexing (GFDM), an enabler of beyond-5G wireless networks, can be critically impaired due to radio frequency (RF) phase noise. However, joint channel estimation and phase noise compensation for GFDM systems have not been addressed before. Hence, we tackle this problem. To this end, we propose an iterative algorithm for joint channel and phase noise estimation and two algorithms for joint data detection and phase noise compensation. These algorithms use linear and non-linear least-squares (NLS) methods and employ block-type and comb-type pilots. The complexity of these algorithms is also analyzed. Moreover, to reduce their complexity, interpolation techniques are deployed to decrease the number of unknowns. We also analyze the signal-to-interference-plus noise ratio (SINR) and sum-rate of GFDM contaminated with phase noise. Furthermore, the accuracy of the channel and phase noise estimates is established via Cramer-Rao lower bounds (CRLBs). The simulation results illustrate that the mean-squared error (MSE) performance of the proposed joint channel and phase noise estimator reaches the CRLB. Moreover, the proposed joint data symbol detection and phase noise compensation algorithms nearly eliminate the impacts of phase noise in GFDM systems.

Molecular Signal Detection Using Nonlinear Mapping

In diffusion-based molecular communications (MC), information exchange occurs using chemical signaling with diffused molecules following a random trajectory. This random propagation of molecules leads to severe inter-symbol interference (ISI) in MC. In this letter, we propose a nonlinear mapping based low complexity data symbol detection method in MC, by reducing delay profile of the diffusing channel tail to mitigate ISI at the receiver. Further, we optimize the proposed nonlinear mapping method to minimize the ISI. The proposed method is analyzed and compared with the existing methods for ISI mitigation. Numerical analysis of the proposed method is carried out for various MC system’s parameters such as diffusion coefficient and distance. The proposed signal detection can be used on MC-based Internet of bio-nanothings with higher channel capacity and/or lower bit error rate.

Iterative Signal Detection for Diffusion-Based Molecular Communications

Inter-symbol interference (ISI) due to slow-moving molecules is one of the key limitations affecting throughput of a diffusion based molecular communication (MC). In this paper, we propose novel ISI mitigation approaches for diffusion based MC systems. The first approach uses weighted sum (WS) to enhance the received signal-to-ISI plus noise ratio (SINR) by exploiting the apriori characteristics of the diffusion channel impulse response. In the second approach, an iterative method estimates the ISI in a frame using the block-wise data symbol detection and subtracts this estimated ISI before the signal detection. Both the proposed methods improve the MC system’s performance as compared to the conventional signal detection method. Further, we have analyzed the combined WS and iterative method, resulting in further improvement in the performance. Furthermore, the effect of various system parameters such as frame duration, diffusion coefficient, and the distance between transmitter and receiver is analyzed.

Interference Cancellation, Channel Estimation, and Symbol Detection for Communications on Overlapping Channels

In this paper, we propose the joint interference cancellation, fast fading channel estimation, and data symbol detection for a general interference setting where the interfering source and the interfered receiver are unsynchronized and occupy overlapping channels of different bandwidths. The interference must be canceled before the channel estimation and data symbol detection of the desired communication are performed. To this end, we have to estimate the Effective Interference Coefficients (EICs) and then the desired fast fading channel coefficients. We construct a two-phase framework where the EICs and desired channel coefficients are estimated using the joint maximum likelihood-maximum a posteriori probability (JML-MAP) criteria in the first phase; and the MAP based data symbol detection is performed in the second phase. Based on this two-phase framework, we also propose an iterative algorithm for interference cancellation, channel estimation and data detection. We analyze the channel estimation error, residual interference, symbol error rate (SER) achieved by the proposed framework. We then discuss how to optimize the pilot density to achieve the maximum throughput. Via numerical studies, we show that our design can effectively mitigate the interference for a wide range of SNR values, our proposed channel estimation and symbol detection design can achieve better performances compared to the existing method. Moreover, we demonstrate the improved performance of the iterative algorithm with respect to the non-iterative counterpart.

Thresholdless Detection of Symbols in Nano-Communication Systems

Molecular communication (MC) can play an indispensable role in nanonetworking and internet of bio-nano things based applications. In most MC receivers, the detection of data symbols requires the optimal threshold, which depends on the accurate diffusion channel impulse response (DCIR), and statistics of noise and interference (SNI). In order to estimate these parameters, a training phase must be carried out. Further, DCIR and SNI can change due to diffusion, drift, temperature and interference variation in the MC system, which results in complex training or sub-optimal MC performance. In this paper, we propose a coded modulation scheme (CMS) for MC, which does not require threshold estimation at the receiver. Hence, the proposed CMS is completely free from any training, and also independent of noise and interferences variation in MC systems. The proposed CMS has optimal system performance with negligible system complexity as verified through the numerical results. Further, the impact of various parameters such as diffusion coefficient, transmission distance, symbol duration, etc. are also examined for CMS.

Supervised-Learning for Multi-Hop MU-MIMO Communications With One-Bit Transceivers

This paper considers a nonlinear multi-hop multi-user multiple-input multiple-output (MU-MIMO) relay channel, in which multiple users send information symbols to a multi-antenna base station (BS) with one-bit analog-to-digital converters via intermediate relays, each with one-bit transceiver. To understand the fundamental limit of the detection performance, the optimal maximum-likelihood (ML) detector is proposed with the assumption of perfect and global channel state information (CSI) at the BS. This multi-user detector, however, is not practical due to the unrealistic CSI assumption and the overwhelming detection complexity. These limitations are addressed by presenting a novel detection framework inspired by supervised-learning. The key idea is to model the complicated multihop MU-MIMO channel as a simplified channel with much fewer and learnable parameters. One major finding is that, even using the simplified channel model, a near ML detection performance is achievable with a reasonable amount of pilot overheads in a certain condition. In addition, an online supervised-learning detector is proposed, which adaptively tracks channel variations. The idea is to update the model parameters with a reliably detected data symbol by treating it as a new training (labelled) data. Lastly, a multi-user detector using a deep neural network is proposed. Unlike the model-based approaches, this model-free approach enables to remove the errors in the simplified channel model, while increasing the computational complexity for parameter learning. Via simulations, the detection performances of classical, model-based, and model-free detectors are thoroughly compared to demonstrate the effectiveness of the supervised-learning approaches in this channel.

Joint Symbol and ToA Estimation for Iterative Transmitted Reference Pulse Cluster UWB System

In the impulse radio ultra-wideband (UWB) literature, a transmitted reference pulse cluster (TRPC)-based non-coherent receiver is proposed to avoid the requirement of a wideband analog delay-line-based receiver. However, the TRPC receiver is effected by inter-pulse interference (IPI) and reduced energy transmission efficiency due to the transmission of reference pulses. In this paper, we propose an iterative TRPC (ITRPC) receiver to improve the performance of a conventional TRPC receiver by considering a blockwise data symbol detection. The ITRPC receiver estimates a new reference signal from the data pulses of the block. The estimated new reference signal in the ITRPC receiver reduces the effect of noise and IPI, which results in the improved performance. Furthermore, the single reference pulse either in a frame or a whole data symbol block is transmitted in the proposed ITRPC structure, which enhances the data rate and energy transmission efficiency of the system. The performance of the ITRPC receiver is analyzed for the binary-phase-shift-keying-modulated UWB system in standard IEEE 802.15.4a channels in the presence of additive white Gaussian noise.

Multiuser Interference Cancellation for GFDM With Timing and Frequency Offsets

In uplink multiuser systems, different timing offset (TO) and/or carrier frequency offset (CFO) of multiple users cause multiuser interference (MUI) to a desired user. In this paper, we propose two different MUI cancellation methods, namely weighted parallel interference cancellation (WPIC) and adaptive interference cancellation filter (AICF), for uplink transmission with generalized frequency division multiplexing (GFDM) waveform over Rayleigh fading channel given the existence of TO and CFO of multiple users. The proposed WPIC performs MUI estimation using the detected data symbol of other users and obtains the optimal weight to maximize the signal-to-interference ratio (SIR) of the desired user. We also propose the AICF that aims to maximize the SIR of the desired user. Based on our SIR expression derived in closed-form in the presence of TO and CFO, the AICF is obtained by solving the Rayleigh quotient problem. Lastly, the impact of multiple antennas at the receiver on MUI cancellation is also analyzed to improve reliability. The simulation results show that the proposed WPIC and AICF effectively eliminate MUI and that the AICF can outperform the WPIC in terms of the SIR and spectral efficiency. In addition, the multiple receiver antennas effectively cancel MUI as the number of antennas goes to infinity.

One-Bit OFDM Receivers via Deep Learning

This paper develops novel deep learning-based architectures and design methodologies for an orthogonal frequency division multiplexing (OFDM) receiver under the constraint of one-bit complex quantization. Single bit quantization reduces greatly the complexity and power consumption but makes accurate channel estimation and data detection difficult. This is particularly true for multicarrier waveforms that have high peak-to-average power ratio in the time domain and fragile subcarrier orthogonality in the frequency domain. The severe distortion for one-bit quantization typically results in an error floor even at moderately low signal-to-noise-ratio (SNR) such as 5 dB. For channel estimation (using pilots), we design a novel generative supervised deep neural network that can be trained with a reasonable number of pilots. After channel estimation, a neural network-based receiver—specifically, an autoencoder—jointly learns a precoder and decoder for data symbol detection. Since quantization prevents end-to-end training, we propose a two-step sequential training policy for this model. With synthetic data, our deep learning-based channel estimation can outperform least squares channel estimation for unquantized (full-resolution) OFDM at average SNRs up to 14 dB. For data detection, our proposed design achieves lower bit error rate (BER) in fading than unquantized OFDM at average SNRs up to 10 dB.