Performance Analysis of Joint Active User Detection and Channel Estimation for Massive Connectivity

Massive machine-type communication (mMTC) is a newly introduced service category in 5G wireless communication systems to support a variety of Internet-of-Things (IoT) applications. In recovering sparsely represented multi-user vectors, compressed sensing based multi-user detection (CS-MUD) can be used. CS-MUD is a feasible solution to the grant-free uplink non-orthogonal multiple access (NOMA) environments. In CS-MUD, active user detection (AUD) and channel estimation (CE) should be performed before data detection. In this paper, we propose the expectation propagation based joint AUD and CE (EP-AUD/CE) technique for mMTC networks. The expectation propagation (EP) algorithm is a Bayesian framework that approximates a computationally intractable probability distribution to an easily tractable distribution. The proposed technique finds the best approximation of the posterior distribution of the sparse channel vector. Using the approximate distribution, AUD and CE are jointly performed. We show by numerical simulations that the proposed technique substantially enhances AUD and CE performances over competing algorithms.

In 5G wireless communication network, massive machine type communication (mMTC) is an emerging research topic. For mMTC, non-orthogonal multiple access (NOMA) has been proposed to support its large-scale connectivity. Due to the sparsity of mMTC, compressed sensing based algorithms can be used to identify the active users and recover the sparse channel state information (CSI) vector. In this paper, we propose a Bayesian message passing algorithm based on expectation propagation (EP) for joint active user detection (AUD) and channel estimation (CE) in NOMA. The proposed method approximates the complicated target distribution with a Gaussian distribution to achieve linear complexity. Simulations demonstrate that the EP-based algorithm achieves better performance in joint AUD and CE than the exiting algorithms, especially in the low SNR regime.

Cell-free massive multiple-input multiple-output (CFmMIMO) is one of the key enabling technologies for massive machine type communications (mMTC). While CFmMIMO can achieve a macro diversity gain in mMTC, its fronthaul link capacity severely limits system performance. To balance fronthaul overhead and detection/estimation performance, in this paper we investigate joint user activity detection and channel estimation (JADCE) and develop a framework for uplink grant-free CFmMIMO systems based on mixed-quantization fronthaul compression. First, we model the JADCE problem as a mixed-quantization compressing sensing problem, making use of sporadic transmission nature of devices in mMTC. A multiple measurement vector (MMV) generalized approximate message passing (GAMP) algorithm is proposed to improve the performance of activity detection and channel estimation. Unknown priori parameters of the GAMP algorithm can be estimated by an expectation-maximization algorithm. In addition, we design a threshold detection rule at central processing unit (CPU) side and derive a lower bound of active user detection performance in a centralized CFmMIMO system. Numerical results reveal that the proposed mixed-quantization scheme can strike a good balance between fronthaul overhead and detection/estimation performance, verifying that a CFmMIMO with mixed-quantization scheme can perform well in activity detection and channel estimation by selecting an appropriate number of quantization bits.

In the massive grant-free orthogonal frequency division multiple access (OFDMA), the timing offsets between users impose new challenges on joint active user detection (AUD) and channel estimation (CE) for the subsequent data recovery. In the asynchronous OFDMA, the timing offset effects can be modeled as the phase-shifting on the pilot matrix. As such, by constructing the measurement matrix with timing offsets, the joint estimation problem can be formulated as a generalized multiple measurement vector (MMV) recovery problem with structured sparsity. However, such a structured sparsity cannot be tackled by the existing compressed sensing (CS) techniques. To address this issue, we develop an efficient structured generalized approximate message passing (S-GAMP) algorithm, which includes the parallel AMP-MMV algorithm as a particular case. Simulation results confirm the superiority of the proposed algorithm in grant-free OFDMA in the presence of timing offset.

This paper studies the user activity detection and channel estimation problem in a temporally-correlated massive access system where a very large number of users communicate with a base station sporadically and each user once activated can transmit with a large probability over multiple consecutive frames. We formulate the problem as a dynamic compressed sensing (DCS) problem to exploit both the sparsity and the temporal correlation of user activity. By leveraging the hybrid generalized approximate message passing (HyGAMP) framework, we design a computationally efficient algorithm, HyGAMP-DCS, to solve this problem. In contrast to only exploiting the historical estimations, the proposed algorithm performs bidirectional message passing between the neighboring frames for activity likelihood update to fully exploit the temporally-correlated user activities. Furthermore, we develop an expectation maximization HyGAMP-DCS (EM-HyGAMP-DCS) algorithm to adaptively learn the hyperparameters during the estimation procedure when the system statistics are unknown. In particular, we propose to utilize the analysis tool of state evolution to find the appropriate hyperparameter initialization of EM-HyGAMP-DCS. Simulation results demonstrate that our proposed algorithms can significantly improve the user activity detection accuracy and reduce the channel estimation error.

In this paper, we investigate the performance of cell-free massive MIMO systems with massive connectivity. With the generalized approximate message passing (GAMP) algorithm, we obtain the minimum mean-squared error (MMSE) estimate of the effective channel coefficients from all users to all access points (APs) in order to perform joint user activity detection and channel estimation. Subsequently, using the decoupling properties of MMSE estimation for large linear systems and state evolution equations of the GAMP algorithm, we obtain the variances of both the estimated channel coefficients and the corresponding channel estimation error. Finally, we study the achievable uplink rates with zero-forcing (ZF) detector at the central processing unit (CPU) of the cell-free massive MIMO system. With numerical results, we analyze the impact of the number of pilots used for joint activity detection and channel estimation, the number of APs, and signal-to-noise ratio (SNR) on the achievable rates.

In this paper, the grant-free non-orthogonal multiple access over universal filtered multicarrier (GF-UFMC) is studied. Note that the even-component of frequency domain (FD) received signal suffers from neither inter-sub-band interference nor inter-sub carrier interference while the odd-component suffers from both. A two-stage joint active user detection (AUD) and channel estimation (CE) is proposed. In the first stage, the cross-validation aided block sparsity adaptive subspace pursuit is employed to perform the AUD and CE by utilizing only the even-component. In the second stage, the unreliable estimates by the first-stage are further refined by utilizing additional odd-component. Specifically, a proper reliability metric defined as the second order variation rate of cross validation error is presented. Finally, simulation results are given to demonstrate the performance of the proposed method.

This letter considers a joint user activity, channel and data estimation problem in an uplink grant-free massive MIMO systems with low-precision analog-to-digital converters (ADCs). This joint estimation is firstly formalized as a non-overlapping group sparse problem, in which the components of compound channel follow independent conditional distribution. To address this problem, a new algorithm consists of the celebrated bilinear generalized approximate message passing (BiG-AMP) and loop belief propagation (LBP) is then proposed, where the strong connection of compound channel can be decoupled in LBP part. By exchanging the information between BiG-AMP part and LBP part, the proposed algorithm improves the performance of channel estimation compared with HyGAMP based method, in which the estimated payload data of proposed algorithm are utilized to aid channel estimation and it leads to relatively few pilot symbols to achieve equivalent channel and data estimation performances. The simulation results confirm that our proposed joint estimation algorithm improves the performance of the existing works in terms of user activity, channel and data estimation.

The paper presents a method for joint channel and data estimation for transmission over frequency-selective and time-variant channels. Hereby, fast time-variant channels can be tracked, which is important for mobile communications at very high velocities. We approach the problem by estimating the scattering function, which is assumed to be limited in delay and Doppler frequency. At the transmitter, a short training sequence is inserted at the beginning of the data block. This sequence is used for initializing a Kalman filter, which carries out the joint channel and data estimation adaptively. After the training sequence, hypothetical data symbols are considered to extend the persecuted paths in the data tree.

Joint channel estimation and data detection under fading on reconfigurable fabric

In this paper, we study how to efficiently and reliably detect active devices and estimate their channels in a multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) based grant-free non-orthogonal multiple access (NOMA) system to enable massive machine-type communications (mMTC). First, by exploiting the correlation of the channel frequency responses in narrow-band mMTC, we propose a block-wise linear channel model. Specifically, the continuous OFDM subcarriers in the narrow-band are divided into several sub-blocks and a linear function with only two variables (mean and slope) is used to approximate the frequency-selective channel in each sub-block. This significantly reduces the number of variables to be determined in channel estimation and the sub-block number can be adjusted to reliably compensate the channel frequency-selectivity. Second, we formulate the joint active device detection and channel estimation in the block-wise linear system as a Bayesian inference problem. By exploiting the block-sparsity of the channel matrix, we develop an efficient turbo message passing (Turbo-MP) algorithm to resolve the Bayesian inference problem with near-linear complexity. We further incorporate machine learning approaches into Turbo-MP to learn unknown prior parameters. Numerical results demonstrate the superior performance of the proposed algorithm over state-of-the-art algorithms.

Joint data and channel estimation for mobile communication receivers can be realized by employing a Viterbi detector along with channel estimators which estimate the channel impulse response. The behavior of the channel estimator has a strong impact on the overall error rate performance of the receiver. Kalman filtering is an optimum channel estimation technique which can lead to significant improvement in the receiver bit error rate (BER) performance. However, a Kalman filter is a complex algorithm and is sensitive to roundoff errors. Square-root implementation methods are required for robustness against numerical errors. Real-time computation of the Kalman estimator in a mobile communication receiver calls for parallel and pipelined structures to take advantage of the inherent parallelism in the algorithm. In this paper different implementation methods are considered for measurement update and time update equations of the Kalman filter. The unit-lower-triangular-diagonal (LD) correction algorithm is used for the time update equations, and systolic array structures are proposed for its implementation. For the overall implementation of joint data and channel estimation, parallel structures are proposed to perform both the Viterbi algorithm and channel estimation. Simulation results show the numerical stability of different implementation techniques and the number of bits required in the digital computations with different estimators.

Low earth orbit (LEO) satellite has been considered as a potential supplement for the terrestrial Internet of Things (IoT). In this paper, we consider grant-free non-orthogonal random access (GF-NORA) in the orthogonal frequency division multiplexing (OFDM) system to increase access capacity and reduce access latency for LEO satellite-IoT. We focus on the joint device activity detection (DAD) and channel estimation (CE) problem at the satellite access point. The delay and the Doppler effect of the LEO satellite channel are assumed to be partially compensated. We propose an OFDM-symbol repetition technique to better distinguish the residual Doppler frequency shifts, and present a grid-based parametric probability model to characterize channel sparsity in the delay-Doppler-user domain, as well as to characterize the relationship between the channel states and the device activity. Based on that, we develop a robust Bay esian message-passing algorithm named modified variance state propagation (MVSP) for joint DAD and CE. Moreover, to tackle the mismatch between the real channel and its on-grid representation, an expectation–maximization (EM) framework is proposed to learn the grid parameters. Simulation results demonstrate that our proposed algorithms significantly outperform the existing approaches in both activity detection probability and channel estimation accuracy.

Massive Machine-Type Communications (mMTC) features a massive number of low-cost user equipments (UEs) with sparse activity. Tailor-made for these features, grant-free random access (GF-RA) serves as an efficient access solution for mMTC. However, most existing GF-RA schemes rely on strict synchronization, which incurs excessive coordination burden for the low-cost UEs. In this work, we propose a receiver design for asynchronous GF-RA, and address the joint user activity detection (UAD) and channel estimation (CE) problem in the presence of asynchronization-induced inter-symbol interference. Specifically, the delay profile is exploited at the receiver to distinguish different UEs. However, an inherent sample correlation problem in this receiver design impedes straightforward factorization of the joint likelihood function, which complicates the UAD and CE problem. To address this correlation problem, we design a partially uni-directional (PUD) factor graph representation for the joint likelihood function. Building on this PUD factor graph, we further propose a PUD message passing based sparse Bayesian learning (SBL) algorithm for asynchronous UAD and CE (PUDMP-SBL-aUADCE). Finally, simulation results are provided to demonstrate the superior performance of the PUDMP-SBL-aUADCE algorithm.

This paper addresses joint channel and data estimation for transmission over frequency‐selective and time‐varying channels based on a Doppler‐variant channel impulse response (CIR). A discrete spreading function (DSF), which corresponds to the Doppler Fourier series of the time‐varying channel taps, is introduced. The spectral leakage associated with the Fourier series representation is reduced by oversampling in Doppler‐direction. This approach, however, requires joint channel estimation and equalisation (JCE). Therefore, a recursive least squares (RLS) algorithm for the DSF estimation is combined with the data detection in a reduced state diagram. Furthermore, an enhanced metric, previously introduced in De Broeck et al. (Proceedings of Second International Workshop on Multi‐Carrier Spread‐Spectrum, 1999; published by Kluwer Academic Publishers: Dordrecht, 2000) for time‐invariant channels, is applied here for path selection. The performance of this metric is investigated here for time‐varying and frequency‐selective (TV‐FS) channels. The performance of the proposed approach is compared with the JCE algorithm which uses RLS estimation of a CIR by simulations. Copyright © 2007 John Wiley & Sons, Ltd.