Semi-blind Receiver Research Articles

Tensor Based Semi-Blind Channel Estimation for Reconfigurable Intelligent Surface-Aided Multiple-Input Multiple-Output Communication Systems

Reconfigurable intelligent surfaces (RISs) are a promising technology for sixth-generation (6G) wireless networks. However, a fully passive RIS cannot independently process signals. Wireless systems equipped with it often encounter the challenge of large channel matrix dimensions when acquiring channel state information using pilot-assisted algorithms, resulting in high pilot overhead. To address this issue, this article proposes a semi-blind joint channel and symbol estimation receiver without a pilot training stage for RIS-aided multiple-input multiple-output (MIMO) (including massive MIMO) communication systems. In a semi-blind system, a transmission symbol matrix and two channel matrices are coupled within the received signals at the base station (BS). We decouple them by building two parallel factor (PARAFAC) tensor models. Leveraging PARAFAC tensor decomposition, we transform the joint channel and symbol estimation problem into least square (LS) problems, which can be solved by Alternating Least Squares (ALSs). Our proposed scheme allows duplex communication. Compared to recently proposed pilot-based methods and semi-blind receivers, our results demonstrate the superior performance of our proposed algorithm in estimation accuracy and speed.

Overview of Tensor-Based Cooperative MIMO Communication Systems-Part 1: Tensor Modeling.

Due to increasingly strong and varied performance requirements, cooperative wireless communication systems today occupy a prominent place in both academic research and industrial development. The technological and economic challenges for future sixth-generation (6G) wireless systems are considerable, with the objectives of improving coverage, data rate, latency, reliability, mobile connectivity and energy efficiency. Over the past decade, new technologies have emerged, such as massive multiple-input multiple-output (MIMO) relay systems, intelligent reflecting surfaces (IRS), unmanned aerial vehicular (UAV)-assisted communications, dual-polarized (DP) antenna arrays, three dimensional (3D) polarized channel modeling, and millimeter-wave (mmW) communication. The objective of this paper is to provide an overview of tensor-based MIMO cooperative communication systems. Indeed, during the last two decades, tensors have been the subject of many applications in signal processing, especially for digital communications, and more broadly for big data processing. After a brief reminder of basic tensor operations and decompositions, we present the main characteristics allowing to classify cooperative systems, illustrated by means of different architectures. A review of main codings used for cooperative systems is provided before a didactic and comprehensive presentation of two-hop systems, highlighting different tensor models. In a companion paper currently in preparation, we will show how these tensor models can be exploited to develop semi-blind receivers to jointly estimate transmitted information symbols and communication channels.

Semi-Blind Receivers for Two-Hop MIMO Relay Systems with a Combined TSTF-MSMKron Coding.

Due to the increase in the number of mobile stations in recent years, cooperative relaying systems have emerged as a promising technique for improving the quality of fifth-generation (5G) wireless networks with an extension of the coverage area. In this paper, we propose a two-hop orthogonal frequency division multiplexing and code-division multiple-access (OFDM-CDMA) multiple-input multiple-output (MIMO) relay system, which combines, both at the source and relay nodes, a tensor space-time-frequency (TSTF) coding with a multiple symbol matrices Kronecker product (MSMKron), called TSTF-MSMKron coding, aiming to increase the diversity gain. It is first established that the signals received at the relay and the destination satisfy generalized Tucker models whose core tensors are the coding tensors. Assuming the coding tensors are known at both nodes, tensor models are exploited to derive two semi-blind receivers, composed of two steps, to jointly estimate symbol matrices and individual channels. Necessary conditions for parameter identifiability with each receiver are established. Extensive Monte Carlo simulation results are provided to show the impact of design parameters on the symbol error rate (SER) performance, using the zero-forcing (ZF) receiver. Next, Monte Carlo simulations illustrate the effectiveness of the proposed TSTF-MSMKron coding and semi-blind receivers, highlighting the benefit of exploiting the new coding to increase the diversity gain.

Semi-blind receivers based on a coupled nested Tucker-PARAFAC model for dual-polarized MIMO systems using combined TST and MSMKron codings

Over the past two decades, tensor-based approaches have generated ever-increasing interest for designing multiple-input multiple-output (MIMO) communication systems. In this paper, we propose a new double directional dual-polarized (DD-DP) MIMO system, equipped with uniform rectangular arrays (URAs) at both ends of the link, which combines a multiple Kronecker product of symbol matrices with a tensor space-time (TST) coding, called TST-MSMKron coding. It is first shown that the channel tensor is represented by a fifth-order PARAFAC decomposition, separated into two parts associated with vertically and horizontally polarized receive antennas, respectively. Then, it is established that the tensor of received signals satisfies a new coupled nested Tucker-PARAFAC model whose core tensor is the coding tensor. Capitalizing on this tensor modeling and assuming the tensor coding is known at the reception, two semi-blind receivers composed of two stages are derived for estimating the transmitted symbols and channel parameters (directions of departure (DoD) and arrival (DoA) angles, path loss coefficients). A new rectification method is proposed to ensure the Vandermonde structure of the estimated steering matrices. Parameter identifiability and computational complexity are analyzed for each receiver. Monte Carlo simulation results are provided to illustrate the effectiveness of the proposed TST-MSMKron coding and semi-blind receivers, in terms of symbol error rate (SER) and channel parameters estimation.

Semi-Blind Joint Channel and Symbol Estimation for IRS-Assisted MIMO Systems

Intelligent reflecting surface (IRS) is a promising technology for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$6^\mathrm{th}$</tex-math></inline-formula> generation of wireless systems, realizing the smart radio environment concept. This paper presents a novel tensor-based receiver for IRS-assisted multiple-input multipleoutput communications capable of jointly estimating the channels and the transmitted data streams in a semi-blind fashion. Assuming a fully passive IRS architecture and introducing a simple space-time coding scheme at the transmitter, the received signal model can be advantageously built using the PARATUCK tensor model, which can be seen as a hybrid of parallel factor analysis and Tucker models. A semi-blind receiver is derived by exploiting the algebraic structure of the PARATUCK tensor model. We first formulate a semi-blind receiver based on a trilinear alternating least squares method that iteratively estimates the two involved-IRS-base station and user terminal-IRS-communication channels and the transmitted symbol matrix. We discuss identifiability conditions that ensure the joint semi-blind recovery of the involved channel and symbol matrices and propose a joint design of the coding and IRS reflection matrices to optimize the receiver performance. We also formulate an enhanced two-stage semiblind receiver that efficiently exploits the direct link to refine the channel and symbol estimates iteratively. In particular, we discuss the impact of an imperfect IRS absorption (residual reflection) on the performance of the proposed receiver. Numerical results are proposed for performance evaluation in several system settings in terms of the normalized mean squared error of the estimated channels and the achieved symbol error rate, corroborating the merits of the proposed semi-blind receiver in comparison to competing methods.

A Semiblind Receiver for a Two-Way UAV-Aided PIC System Based on the PARAFAC Model

In this paper, we consider a two-way communication system using the unmanned aerial vehicle (UAV) as a relay (UAV-aided). This system eliminates impulse interference through an adaptive filter based on the least mean square (LMS) and uses the received signal transmitted by the UAVs to construct a parallel factor (PARAFAC) model. Based on the identifiability condition of the PARAFAC model, a pulse interference cancellation orthogonal pilot tensor (PIC-OPT) receiver without iteration is proposed. Our algorithm is also used in millimeter-wave to achieve the acquisition of channel information. Compared with the least squares method, the simulation results demonstrate the superiority of the proposed semiblind receiver in terms of the relative mean square error and bit error rate.

Semi-Blind Joint Channel and Symbol Estimation in IRS-Assisted Multiuser MIMO Networks

Intelligent reflecting surface (IRS) is a promising technology for beyond of the wireless communications. In fully passive IRS-assisted systems, channel estimation is challenging and should be carried out only at the base station or at the terminals since the elements of the IRS are incapable of processing signals. In this letter, we formulate a tensor-based semi-blind receiver that solves the joint channel and symbol estimation problem in an IRS-assisted multi-user multiple-input multiple-output system. The proposed approach relies on a generalized PARATUCK tensor model of the signals reflected by the IRS, based on a two-stage closed-form semi-blind receiver using Khatri-Rao and Kronecker factorizations. Simulation results demonstrate the superior performance of the proposed semi-blind receiver, in terms of the normalized mean squared error and symbol error rate, as well as a lower computational complexity, compared to recently proposed parallel factor analysis-based receivers.

A Parafac-Based Semi-Blind Receiver for a Multiway Relay System with Software Defined Radio (SDR) Experimentation

A Parafac-Based Semi-Blind Receiver for a Multiway Relay System with Software Defined Radio (SDR) Experimentation

Semi-blind joint symbols and multipath parameters estimation of MIMO systems using KRST/MKRSM coding

In this paper, we propose a new MIMO communication system in a time-varying multipath environment, using a Khatri-Rao space-time (KRST) coding combined with a multiple Khatri-Rao product of symbol matrices (MKRSM). It is shown the signals received at the receiver form a tensor which satisfies a (M+2)-order nested PARAFAC model, where (M−1) denotes the number of symbol matrices considered for MKRSM coding. Such a generalization of the nested PARAFAC model to (M+N)-order tensors is first studied from a general point of view, with the discussion of some parameter estimation methods depending on the a priori knowledge on the model. Then, a semi-blind receiver composed of three stages, is developed for jointly estimating the transmitted symbols and the multipath parameters.In the first stage, the transmitted symbols and a matrix unfolding of the effective channel including the fading coefficients and the steering matrices, are estimated using closed-form algorithms based on Khatri-Rao factorizations. In the second one, the channel estimation is refined by means of a simplified least-squares algorithm which takes the column orthonormality assumption on the coding matrix into account. In the third one, an alternating least-squares algorithm, combined with a rectification for the Vandermonde factors containing the spatial steering vectors at the transmitter and receiver sides, is applied to estimate the multipath parameters from the estimated channel. A complexity analysis is made for the receivers, and an expected Cramer-Rao bound related to channel estimation is established. Extensive Monte Carlo simulation results show that the semi-blind receiver which combines the channel estimation refinement with the rectification technique exhibit very interesting performance.

Semi-Blind Receivers for UAV M-KRST Coding MIMO Systems Based on Nested Tensor Models

In this letter, we consider the dual-hop and three-hop multiple-input multiple-output (MIMO) sensor systems using multiple Khatri-Rao space-time (M-KRST) coding at the unmanned aerial vehicles and sensor nodes. According to the tensor structure of the communication links, the signals received at the fusion center form two separate nested tensors, which satisfy a nested parallel factor (PARAFAC) model and a nested parallel Tucker2 (PARATUCK2) model. Exploiting this nested structure, two semi-blind receivers based on an alternating least squares algorithm are formulated for a joint estimation of symbols and channels. Compared with the two-stage training method, simulation results demonstrate the superiority of the proposed semi-blind receivers in terms of normalized mean square error and bit error rate.

Space-Time-Frequency Coding for MIMO Relay System Based on Tensor Decomposition

Space-time-frequency (STF) coding can obtain the diversity gain from three dimensions (space, time and frequency) to effectively improve the transmission performance of the multi-input multi-output (MIMO) relay system. In this study, a MIMO one-way two-hop amplify-and-forward (AF) relay communication system is presented by means of triple Khatri–Rao space-time-frequency (KRSTF) coding, which forms a five-dimensional tensor at the destination node that satisfies a new multi-dimensional tensor decomposition approach called asymmetric nested PARAFAC decomposition (ANPD). Then based on this model, a semi-blind receiver is derived to perform the joint channel and symbol estimation in terms of three-step alternating least squares (ALS) algorithm. Compared with the existing two-hop symmetry methods, the proposed scheme uses an asymmetric nested model to obtain additional frequency coding diversity, which significantly improves the performance of the system in parameter estimation accuracy as demonstrated by simulation results.

Semi-Blind Receivers for Multi-User Massive MIMO Relay Systems Based on Block Tucker2-PARAFAC Tensor Model

Massive multiple-input multiple-output (MIMO) relay can significantly improve the capacity and throughput of wireless networks, thus has been a sought-after technique for future communication systems. However, the development of massive MIMO relay systems faces several major challenges. For example, the knowledge of instantaneous channel state information (CSI) is needed to estimate signals and optimize systems. Traditional estimation schemes need to transmit pilot sequences, which occupy the spectrum resources. In this paper, we propose a tensor-based method for joint signal and channel estimation for multi-user massive MIMO relay systems without using pilot sequences, and develop two tensor-based semi-blind receivers. Through multidimensional signaling scheme, the signals received by each user are formulated as the block Tucker2-PARAFAC (TP) tensor model. Then, two semi-blind receivers are proposed to jointly estimate the information signals and channel matrices. One is based on the tensor-based closed-form receiver, the other is based on the tensor-based iterative receiver. The proposed closed-form approach can also be used to initialize the iterative receiver for improving the convergence speed. In particular, the proposed schemes are practicable for both time division duplexing (TDD) and frequency division duplexing (FDD) modes. Uniqueness, identifiability and complexity are analyzed for our receivers. Compared with existing receivers, our receivers offer superior bit error rate (BER) and normalized mean square error (NMSE) performance. Numerical examples are shown to demonstrate the effectiveness of the proposed tensor-based receivers.

Tensor Communication Waveform Design With Semi-Blind Receiver in the MIMO System

A flexible mathematical framework for adaptive wireless communication waveform design is of importance for the implement of the cognitive radio-based software defined radio (CR-based SDR). As one of the popular models, the “spectrally modulated spectrally encoded” (SMSE) was proposed to tackle this problem but it cannot be trivially applied to the (massive) multiple input multiple output (MIMO) systems. In this paper, we extend the useful SMSE model into MIMO systems. Inspired by the tensor technique in signal processing and machine learning, we reformulate the desired waveforms as a higher-order tensors, of which the modes correspond to various modulation parameters such as coding chips, frequency and antennas. Beside the waveform design model, we further propose a new semi-blind receiver for the new model. Due the uniqueness of the applied tensor decomposition, we proved that the proposed receiver can jointly estimate the user symbols and channel state information without the aid of pilot sequences. Experimental results demonstrate the effectiveness of the proposed model in various communication scenes and outperforms the baseline systems. approximately 3 dB compared with the ideal receiver.

Joint DL and UL Channel Estimation for Millimeter Wave MIMO Systems Using Tensor Modeling

In this paper, we address the problem of joint downlink (DL) and uplink (UL) channel estimation for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems. Assuming a closed-loop and multifrequency-based channel training framework in which pilot signals received by multiple antenna mobile stations (MSs) are coded and spread in the frequency domain via multiple adjacent subcarriers, we propose two tensor-based semiblind receivers by capitalizing on the multilinear structure and sparse feature of the received signal at the BS equipped with a hybrid analog-digital beamforming (HB) architecture. As a first processing stage, the joint estimation of the compressed DL and UL channel matrices can be obtained in an iterative way by means of an alternating least squares (ALS) algorithm that capitalizes on a parallel factors model for the received signals. Alternatively, for more restricted scenarios, a closed-form solution is also proposed. From the estimated effective channel matrices, the users’ channel parameters such as angles of departure (AoD), angles of arrival (AoA), and path gains are then estimated in a second processing stage by solving independent compressed sensing (CS) problems (one for each MS). In contrast to the classical approach in the literature, in which the DL and UL channel estimation problems are usually considered as two separate problems, our idea is to jointly estimate both the DL and UL channels as a single problem by concentrating most of the processing burden for channel estimation at the BS side. Simulation results demonstrate that the proposed receivers achieve a performance close to the classical approach that is applied on DL and UL communication links separately, with the advantage of avoiding complex computations for channel estimation at the MS side as well as dedicated feedback channels for each MS, which are attractive features for massive MIMO systems.

Semi-blind receivers for MIMO multi-relaying systems via rank-one tensor approximations

This paper proposes two tensor-based receivers for multiple-input multiple-output (MIMO) multi-relaying systems capable of jointly estimating the channels and symbols in a semi-blind fashion. Assuming space-time coding at the source and relay stations, we propose an orthogonal design based on a parallel factor (PARAFAC) analysis of the coding structure. Exploiting the proposed tensor codes and the multi-linear structure of the resulting received signals, we show that the data model for every relay-assisted link after space-time combining/decoding has a Kronecker structure, which can be recast as a rank-one tensor corrupted by noise. The proposed receivers combine the tensor signals for the multiple cooperative links for joint channel and symbol estimation by coupling multiple rank-one tensor approximation problems. The first one is a coupled-SVD based receiver that estimates all the involved communication channels and transmitted symbols in closed form. The second one is an iterative solution based on alternating least squares. The performances of both receivers are evaluated by means of computer simulations in a variety of system configurations. Our results show the effectiveness of the proposed receivers and its good performance-complexity trade-off in comparison with competing receivers.

Tensor-Based Joint Channel Estimation and Symbol Detection for AF MIMO Relay Networks

A study on the joint channel and symbol estimation issue is provided for two hop relay networks which employ the amplify-and-forward (AF) relaying approach. The encoding scheme at the source node introduces the time-domain spreading with a time-varying linear constellation precoding. Then, a set of amplifying factors matrices is utilized by the relays to amplify and forward the received data to the destination. The received signal at the destination can be constructed as a fourth-order tensor model, which is referred to as the nested parallel factor (PARAFAC) model. And then, we present a novel Levenberg-Marquardt (LM) algorithm based on this tensor model. The proposed method does not require complex signal processing at the relay, which effectively reduces the burden of relay. As a semi-blind method, which does not require the pilot signal, the proposed receiver can jointly recover the channels and information symbols. Moreover, the proposed semi-blind receiver is robust as it can work in different wireless channel scenarios. Simulations are conducted to demonstrate the efficiency of the proposed semi-blind approach.

PARATUCK semi-blind receivers for relaying multi-hop MIMO systems

In this paper, two receivers are proposed for a multiple-input multiple-output (MIMO) relaying multi-hop communication system using a Khatri-Rao space-time (KRST) coding at the source and amplify-and-forward (AF) relays. It is shown that the third-order tensor of signals received at the destination satisfies a PARATUCK-(K+1) tensor model, where K is the number of relays. After formulating the system model, the expressions of the Cramér-Rao bound (CRB) for the communication channels are derived for the particular case of a two-hop system, i.e., K=1. The presented tensorial modeling enables a joint semi-blind estimation of the transmitted symbols and the channels. The first proposed estimation algorithm is a non-iterative technique based on a rearrangement of the Kronecker product, while the second proposed receiver is based on the alternating least squares (ALS) algorithm. The uniqueness of the tensor decomposition and the identifiability conditions of the proposed algorithms are discussed. The performance of these receivers is evaluated by means of Monte Carlo simulations.

A Robust Semi-Blind Receiver for Joint Symbol and Channel Parameter Estimation in Multiple-Antenna Systems

For multiple-antenna systems, the technologies of joint symbol and channel parameter estimation have been developed in recent works. However, existing technologies have a number of problems, such as performance degradation and the large cost of prior information. In this paper, a tensor space-time coding scheme in multiple-antenna systems was considered. This scheme allowed spreading, multiplexing, and allocating information symbols associated with multiple transmitted data streams. We showed that the received signal was formulated as a third-order tensor satisfying a Tucker-2 model, and then a robust semi-blind receiver was developed based on the optimized Levenberg–Marquardt (LM) algorithm. Under the assumption that the instantaneous channel state information (CSI) is unknown at the receiving end, the proposed semi-blind receiver jointly estimates the information symbol and channel parameters efficiently. The proposed receiver had a better estimation performance compared with existing semi-blind receivers, and still performed well when the channel became strongly correlated. Moreover, the proposed semi-blind receiver could be extended to the multi-user massive multiple-input multiple-output (MIMO) system for joint symbol and channel estimation. Computer simulation results were shown to demonstrate the effectiveness of the proposed receiver.

Semi‐blind receiver for two‐way MIMO relaying systems based on joint channel and symbol estimation

This study proposes a semi-blind receivers for two-way multiple-input multiple-output (MIMO) relaying systems capable of jointly estimating the channels and symbols in a direct-data approach. Resorting to a Khatri-Rao coding scheme applied at both uplink and downlink transmission phases, the authors show that the signals received at the relay and user node are third-order tensors satisfying the parallel factor (PARAFAC) and PARATUCK2 models, respectively. Combining these two tensor models, a semi-blind receiver based on an integrated alternating least squares algorithm is proposed to estimate the channels and symbols transmitted by the user nodes without training sequences. The effectiveness of the proposed semi-blind receiver is corroborated with numerical results, which show that the proposed semi-blind receiver outperforms state-of-the-art two-stage training sequence estimator, while operating close to the tensor-based channel estimator.

Fast Iterative Semi-Blind Receiver for URLLC in Short-Frame Full-Duplex Systems With CFO

We propose an iterative semi-blind (ISB) receiver structure to enable ultra-reliable low-latency communications in short-frame full-duplex (FD) systems with carrier frequency offset (CFO). To the best of our knowledge, this is the first paper to propose an integral solution to channel estimation and CFO estimation for short-frame FD systems by utilizing a single pilot. By deriving an equivalent system model with the CFO included implicitly, a subspace-based blind channel estimation is proposed at the initial stage, followed by CFO estimation and channel ambiguities elimination. Then, the refinement of channel and the CFO estimates is conducted iteratively. The integer and fractional parts of CFO in the full range are estimated as a whole and in closed-form at each iteration. The proposed ISB receiver significantly outperforms the previous methods in terms of frame error rate, mean square errors of channel estimation and CFO estimation and output signal-to-interference-and-noise ratio, while at a halved spectral overhead. Cramer–Rao lower bounds are derived to verify the effectiveness of the proposed ISB receiver structure. It also demonstrates high-computational efficiency as well as the fast convergence speed.