Grant-free Non-orthogonal Multiple Access Research Articles

Message Passing Detectors for UAV-Based Uplink Grant-Free NOMA Systems

Utilizing unmanned aerial vehicles (UAVs) as mobile access points or base stations has emerged as a promising solution to address the excessive traffic demands in wireless networks. This paper investigates improving the detector performance at the unmanned aerial vehicle base stations (UAV-BSs) in an uplink grant-free non-orthogonal multiple access (GF-NOMA) system by considering the activity state (AS) temporal correlation of the different user equipments (UEs) in the time domain. The Bernoulli Gaussian-Markov chain (BG-MC) probability model is used for exploiting both the sparsity and slow change characteristic of the AS of the UE. The GAMP Bernoulli Gaussian-Markov chain (GAMP-BG-MC) algorithm is proposed to improve the detector performance, which can utilize the bidirectional message passing between the neighboring time slots to fully exploit the temporally correlated AS of the UE. Furthermore, the parameters of the BG-MC model can be updated adaptively during the estimation procedure with unknown system statistics. Simulation results show that the proposed algorithm can improve the detection accuracy compared to existing methods while keeping the same order complexity.

Fairness aware deep reinforcement learning for grant-free NOMA-IoT networks

Next generation networks have special areas related with the Internet of Things (IoT) to improve the performance of cellular networks in terms of throughput. Grant-free non-orthogonal multiple access (GF-NOMA) seems a feasible solution, letting machine type communication (MTC) devices transmits their packets when they ready to transmit. GF-NOMA increases the spectral efficiency by using the superimposing signals with different power levels over the same time and frequency resources. However, the main drawbacks of GF-NOMA are randomness and the management of power level selection of MTC devices. In 6G-IoT networks, the intelligence should be met to random access. It is time to design new access methods to solve the GF-NOMA issues that should be between the randomness and fully coordinated medium access. Deep-Q-Network (DQN) has become a very hot research topic in recent years that let the MTC devices to make a smart decision in an intelligent way to improve the throughput. Selfishness is an undesirable behavior of DQN for GF-NOMA system where the resources have different cost. In this study, we develop a novel learning framework for power domain GF-NOMA. The goal of our learning framework is to maximize the throughput considering fairness in power consumption which provides long-life to the IoT network. The learning algorithm push the MTC devices to exchange the resources between each other over time. The results show that the proposed method outperform the NOMA scheme with random selection in terms of throughput and increase the fairness index when the DQN with selfish behavior is employed.

An Efficient NB-IoT Compatible GF-NOMA PHY Mechanism for mMTC

The third generation partnership project (3GPP) has proposed the narrowband Internet of things (NB-IoT) standard for serving IoT users. Improvements to the NB-IoT standard are being considered to efficiently support massive machine-type communication (mMTC) IoT applications. Subsequent releases of the NB-IoT standard envision to support mMTC using different access mechanisms. In this work, a grant-free (GF) non-orthogonal multiple access (NOMA) system compatible with the current NB-IoT standard is proposed, where the resources are divided into transmission opportunities (TOs). The TOs are further divided into multiple groups based on the repetitions adopted by the users in the system. Physical (PHY) layer procedures for preamble transmission/detection, channel estimation, data transmission/decoding, and acknowledgment (ACK) transmission/reception are described in detail for the proposed GF-NOMA system. Specifically, the preamble sequences are also used as spreading sequences for data transmission and three types of sequences -Zadoff-Chu, random Gaussian and Golay sequences are explored. Results are presented for per-user success probability, latency and energy consumption considering two NB-IoT compatible settings along with repetitions and retransmissions. It is demonstrated that the proposed GF-NOMA scheme meets the mMTC requirement recommended by the 3GPP with more than 99% per-user success probability and with the energy consumption reduced by at least 80% compared to NB-IoT, while being readily compatible with the current NB-IoT standard.

Grant-Free NOMA: A Low-Complexity Power Control through User Clustering.

Non-orthogonal multiple access (NOMA) has emerged as a promising solution to support multiple devices on the same network resources, improving spectral efficiency and enabling massive connectivity required by ever-increasing Internet of Things devices. However, traditional NOMA schemes operate in a grant-based fashion and require channel-state information and power control, which hinders its implementation for massive machine-type communications. Accordingly, this paper proposes synchronous grant-free NOMA (GF-NOMA) frameworks that effectively integrate user equipment (UE) clustering and low-complexity power control to facilitate the power-reception disparity required by the power-domain NOMA. Although single-level GF-NOMA (SGF-NOMA) designates an identical transmit power for all UEs, multi-level GF-NOMA (MGF-NOMA) groups UEs into partitions based on the sounding reference signals strength and assigns partitions with different identical power levels. Based on the objective of interest (e.g., max-sum or max-min rate), the proposed UE clustering scheme iteratively admits UEs to form clusters whose size is dynamically determined based on the number of UEs and available resource blocks (RBs). Once the UEs are acknowledged with power levels and allocated RBs through random-access response (RAR) messages, UEs can transmit anytime without grant acquisition. Numerical results show that the proposed GF-NOMA frameworks can compute clusters in the order of milliseconds for hundreds of UEs. The MGF-NOMA can reach up to 96-99% of the optimal benchmark max-sum rate, and the SGF-NOMA reaches 87% of the optimal benchmark max-sum rate at the same power consumption. Since the MGF-NOMA and optimal benchmark enforce the strongest and weakest channel UEs to transmit at maximum and minimum transmit powers, respectively, the SGF-NOMA also offers a significantly higher energy consumption fairness and network lifetime as all UEs consume equal transmit powers. Although the MGF-NOMA delivers an inferior max-min rate performance, the SGF-NOMA is shown to reach 3e6 MbpJ energy efficiency compared to the 1e7 MbpJ benchmark.

RIS-Assisted Grant-Free NOMA: User Pairing, RIS Assignment, and Phase Shift Alignment

This paper introduces a reconfigurable intelligent surface (RIS)-assisted grant-free non-orthogonal multiple access (GF-NOMA) scheme. We propose a joint user equipment (UE) clustering and RIS assignment/alignment approach that jointly ensures the power reception disparity required by the power domain NOMA (PD-NOMA). The proposed approach maximizes the network sum rate by judiciously pairing UE with distinct channel gains and assigning RISs to proper clusters. To alleviate the computational complexity of the joint approach, we decouple UE clustering and RIS assignment/alignment subproblems, which reduces run times 80 times while attaining almost the same performance. Once the proposed approaches acknowledge UEs with the cluster index, UEs are allowed to access corresponding resource blocks (RBs) at any time requiring neither further grant acquisitions from the base station (BS) nor power control as all UEs are requested to transmit at the same power. In addition to passive RISs containing only passive elements and giving an 18% better performance, an active RIS structure that enhances the performance by 37% is also used to overcome the double path loss problem. The numerical results also investigate the impact of UE density, RIS deployment, RIS hardware specifications, and the fairness among the UEs in terms of bit-per-joule energy efficiency.

Constructions of Low/Zero Correlation Zone Sequence Sets and Their Application in Grant-Free Non-Orthogonal Multiple Access System

Constructions of Low/Zero Correlation Zone Sequence Sets and Their Application in Grant-Free Non-Orthogonal Multiple Access System

Deep Learning-Based User Activity Detection and Channel Estimation in Grant-Free NOMA

In the uplink machine-type communication (MTC) system, a combination of grant-free transmission and non-orthogonal multiple access (NOMA) emerges to reduce the control overhead and transmission latency. In the grant-free scenario, the base station needs to identify the active devices and estimate the channel state information before the data detection. However, due to the lack of a scheduling process, the user activity detection (UAD) and channel estimation (CE) are both challenging, especially when short non-orthogonal preambles are adopted. In this paper, by exploiting the framework of the compressive sensing-based algorithm, we propose a novel deep learning architecture, namely UAD and CE Neural Network (UAD-CE-NN), to effectively solve the joint UAD and CE problem for grant-free NOMA. In the proposed scheme, the user activity and channel state information hidden in the received data signals are also exploited to aid the preamble for higher detection accuracy. Specifically, UAD-CE-NN is composed of two stages: we first build a preamble detection neural network for a tentative UAD-CE; a data detection neural network is then deployed to exploit the data signals. Compared with the conventional schemes, the proposed scheme obtains much higher accuracy for both the UAD and CE, especially when short preamble sequences are employed.

Temporal Correlation Enhanced Multiuser Detection for Uplink Grant-Free NOMA

Compressed sensing has been identified as a good candidate for user detection in grant-free non-orthogonal multiple access (NOMA) by exploiting the inherent sparsity of user activity. However, most of the existing works do not fully utilize the temporal correlation in NOMA and rely heavily on the unrealistic assumption that the number of active users is known in advance. To address these issues, we propose a temporal correlation enhanced multiuser detection scheme to achieve efficient and practical multiuser detection. Firstly, using 1 bit memory to piggyback the information whether the active users still have data to transmit, the base station can realize whether the active users in current time slot will turn to be silent or remain active. Then, to make explicit use of the temporal correlation of active user sets, a cross validation based adaptive subspace pursuit (CVASP) algorithm, is developed by utilizing the reported information on prior active users. The proposed CVASP is a highly practical algorithm that does not require any prior knowledge of the user sparsity level, as the cross validation technique could properly determine the stopping condition. Extensive simulation results demonstrate that the proposed mechanism could achieve a superier performance without requiring any prior knowledge.

Active Terminal Identification, Channel Estimation, and Signal Detection for Grant-Free NOMA-OTFS in LEO Satellite Internet-of-Things

This paper investigates the massive connectivity of low Earth orbit (LEO) satellite-based Internet-of-Things (IoT) for seamless global coverage. We propose to integrate the grant-free non-orthogonal multiple access (GF-NOMA) paradigm with the emerging orthogonal time frequency space (OTFS) modulation to accommodate the massive IoT access, and mitigate the long round-trip latency and severe Doppler effect of terrestrial–satellite links (TSLs). On this basis, we put forward a two-stage successive active terminal identification (ATI) and channel estimation (CE) scheme as well as a low-complexity multi-user signal detection (SD) method. Specifically, at the first stage, the proposed training sequence aided OTFS (TS-OTFS) data frame structure facilitates the joint ATI and coarse CE, whereby both the traffic sparsity of terrestrial IoT terminals and the sparse channel impulse response are leveraged for enhanced performance. Moreover, based on the single Doppler shift property for each TSL and sparsity of delay-Doppler domain channel, we develop a parametric approach to further refine the CE performance. Finally, a least square based parallel time domain SD method is developed to detect the OTFS signals with relatively low complexity. Simulation results demonstrate the superiority of the proposed methods over the state-of-the-art solutions in terms of ATI, CE, and SD performance confronted with the long round-trip latency and severe Doppler effect.

A Hybrid Grant NOMA Random Access for Massive MTC Service

Nonorthogonal multiple access (NOMA) is classified into grant-based (GB) random access (RA) and grant-free (GF) RA in 5G systems. GF NOMA RA allows user equipments (UE) to directly transmit data packet over uplink resources without grant information so that the signaling overhead is substantially reduced. This approach is suitable for small-size data packet IoT services. However, power collision interference resulting from uncoordinated resource selection leads to serious transmission failure in massive MTC scenarios. As a result, the number of transmissions and access delay are sharply increased. In this article, we make the best of the advantages of both GB RA and GF RA and propose a hybrid grant (HG) NOMA RA scheme to address the signaling overhead and power collision issues. The objective of the proposed scheme is to achieve an acceptable tradeoff among signaling overhead, access failure probability, and access delay. The UE selects the access resource without uplink grant, and the BS assists to avoid inter-NOMA power collision by limited interference resolution (IR) signaling. To comprehensively analyze the performance, the closed-form expression of outage probability is derived by adopting the order statistic theory and the sum of independent exponential distributions, and the maximum number of transmissions and access delay are theoretical analyzed. A Monte Carlo simulation framework is built to verify the theoretical analysis. Finally, the analytical and simulation results show that HG NOMA RA outperforms GB NOMA RA and GF NOMA RA in massive access scenarios.

Deep Reinforcement Learning-Based Grant-Free NOMA Optimization for mURLLC

Grant-free non-orthogonal multiple access (GF-NOMA) is a potential technique to support massive Ultra-Reliable and Low-Latency Communication (mURLLC) service. However, the dynamic resource configuration in GF-NOMA systems is challenging due to random traffics and collisions, that are unknown at the base station (BS). Meanwhile, joint consideration of the latency and reliability requirements makes the resource configuration of GF-NOMA for mURLLC more complex. To address this problem, we develop a novel learning framework for signature-based GF-NOMA in mURLLC service taking into account the multiple access signature collision, the UE detection, as well as the data decoding procedures for the K-repetition GF and the Proactive GF schemes. The goal of our learning framework is to maximize the long-term average number of successfully served users (UEs) under the latency constraint. We first perform a real-time repetition value configuration based on a double deep Q-Network (DDQN) and then propose a Cooperative Multi-Agent learning technique based DQN (CMA-DQN) to optimize the configuration of both the repetition values and the contention-transmission unit (CTU) numbers. Our results show the superior performance of CMA-DQN over the conventional load estimation-based uplink resource configuration approach (LE-URC) in heavy traffic and demonstrate its capability in dynamically configuring in long term for mURLLC service. In addition, with our learning optimization, the Proactive scheme always outperforms the K-repetition scheme in terms of the number of successfully served UEs, especially under the high backlog traffic scenario.

Multitype Services Coexistence in Uplink NOMA for Dual-Layer LEO Satellite Constellation

The upcoming mega low-earth orbit (LEO) high-throughput satellite constellation is regarded as an emerging paradigm shift in the fifth-generation-advance (5GA) networks. In this article, we propose a multitype services coexistence handover (MSCH) nonorthogonal multiple access (NOMA) scheme for a dual-layer mega LEO satellite constellation, which can simultaneously and efficiently provide uplink NOMA for three types of fifth-generation user equipments (UEs): 1) mission-critical communications (MCCs) UEs (CUs); 2) massive machine-type communications (mMTCs) UEs (MUs); and 3) enhanced mobile broadband (eMBB) UEs (EUs). The EUs are mainly served in the higher layer satellites for longer service duration and may handover to the lower layer satellites to coexist with CUs or MUs. Moreover, the CUs and MUs perform grant-based (GB) and grant-free (GF) NOMA on resource blocks (RBs) in the lower layer satellites, respectively. Then, we derive the closed-form expressions of three specific key performance indicators (KPIs), i.e., outage probability (OP), system throughput (ST), and ergodic capacity (EC) in the MSCH NOMA scheme, and design five corresponding NOMA algorithms. Simulation results verify the accuracy of our theoretical derivations and show that the proposed NOMA schemes can achieve a better KPI performance than the state-of-the-art ones.

Generalized Approximate Message Passing Based Bayesian Learning Detectors for Uplink Grant-Free NOMA

The existing sparse Bayesian learning (SBL) and pattern coupled sparse Bayesian learning (PCSBL) multiuser detection (MUD) algorithms for grant-free non-orthogonal multiple access (GF-NOMA) have high computational complexity, i.e. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N{K^{2}})$</tex-math></inline-formula> , considering mainly the calculation of posterior distribution of the transmitted signals. In this paper, we embed generalized approximate message passing (GAMP) to SBL and PCSBL, and develop two efficient Bayesian learning algorithms for GF-NOMA systems, that is, generalized approximate message passing sparse Bayesian learning (GAMP-SBL) and generalized approximate message passing pattern coupled sparse Bayesian learning (GAMP-PCSBL). It is shown that the Bayesian algorithms can significantly reduce the computational complexity from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(N{K^{2}})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {O}(NK)$</tex-math></inline-formula> . Simulation results show that these two low complexity detectors still have superior recovery performance than the conventional MUD methods, and nearly have the same performance compared with SBL and PCSBL.

Block Sparse Bayesian Learning Based Joint User Activity Detection and Channel Estimation in Grant-Free MIMO-NOMA

In the massive machine type of communication (mMTC), grant-free non-orthogonal multiple access (NOMA) is receiving more and more attention because it can skip the complex grant process to allocate non-orthogonal resources to serve more users. To address the limited wireless resources and substantial connection challenges, combining grant-free NOMA and multiple-input multiple-output (MIMO) is crucial to further improve the system’s capacity. In the grant-free MIMO-NOMA system, the base station should obtain the relevant information of the user before data detection. Thus, user activity detection (UAD) and channel estimation (CE) are two problems that should be solved urgently. In this paper, we fully consider the sparse characteristics of signals and the spatial correlation between multiple antennas in the grant-free MIMO-NOMA system. Then, we propose a spatial correlation block sparse Bayesian learning (SC-BSBL) algorithm to address the joint UAD and CE problems. First, by fully mining the block sparsity of signals in the grant-free MIMO-NOMA system, we model the joint UAD and CE problem as a three-dimensional block sparse signal recovery problem. Second, we derive the cost function based on the hierarchical Bayesian theory and spatial correlation. Finally, to estimate the channel and the set of active users, we optimize the cost function with fast marginal likelihood maximization. The simulation results indicate that, compared with the existing algorithms, SC-BSBL can always fully use the signal sparsity and spatial correlation to accurately complete UAD and CE under various user activation probabilities, SNRs, and the number of antennas. The normalized mean square error of CE can be reduced to 0.01, and the UAD error rate can be less than 10−5.

Grant-Free Non-Orthogonal Multiple Access in Single-Carrier Frequency-Selective Fading Channels

Grant-free (GF) access is one key technology for massive machine-type communication (mMTC) in Internet-of-things. Single-carrier (SC) modulation has higher power-efficiency than multicarrier modulation such as orthogonal frequency division multiplexing, due to lower peak-to-average power ratio, and thus is specifically suitable for low-power-supply machine-type devices. In this paper, we study both the coherent and non-coherent grant-free non-orthogonal multiple access (GF-NOMA) schemes where SC modulation is employed in frequency selective fading channels. For coherent SC-GF-NOMA, the linear input-output relation is first presented, and two user-activity detection (UAD) algorithms, block covariance-based maximum-likelihood detection (CB-MLD) and turbo approximated message passing (Turbo AMP), are proposed. In block CB-MLD, a block update strategy is introduced in the coordinate descent iteration to utilize the special block-sparsity signal property inherent in coherent SC-GF-NOMA. Moreover, Turbo AMP consists of two components, AMP and message passing (MP), and turbo iteration between them. Concretely, AMP is designed for UAD-CE with fixed active user probability, and MP is designed to update the active user probability by utilizing the block sparsity. Moreover, the performance of Turbo AMP is analyzed by state-evolution (SE) formalism. For non-coherent SC-GF-NOMA, the linear input-output relation is first derived from which the hierarchical block-sparsity signal property is observed, and then block CB-MLD-based UAD algorithm is presented to utilize this signal property. Finally, computer simulation results are given to demonstrate the effectiveness of the proposed algorithms in both coherent and non-coherent SC-GF-NOMA.

Enhanced Index Modulation-Aided Grant Free Non-Orthogonal Multiple Access Transmission

In this letter, an enhanced index modulation (IM)-aided grant-free non-orthogonal multiple access (GF-NOMA) scheme is presented in the multiple-antenna massive access system. In the IM-aided GF-NOMA, each user is allocated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> spread sequences, from which only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{a}, N_{a} &lt; N$ </tex-math></inline-formula> , sequences are activated to transmit information. In the conventional scheme, only the indexes of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{a}$ </tex-math></inline-formula> active sequences are utilized to convey information. In the proposed enhanced IM (EIM)-aided scheme, besides these indexes, constellation symbols are also utilized to convey information. Concretely, the first active spread sequence carries pilot while the others carry constellation symbols. At receiver, two multiuser detection algorithms, hybrid approximate message passing and covariance-based maximum-likelihood detection are presented. Finally, simulation results are given to demonstrate the performance of the proposed scheme.

New Constructions of Binary Golay Spreading Sequences for Uplink Grant-Free NOMA

Non-orthogonal multiple access (NOMA) is a promising technology for massive machine-type communications (mMTC). This letter focuses on constructing spreading sequences with low coherence as well as low peak-to-average power ratio (PAPR) for uplink grant-free NOMA. Recently, a framework of spreading matrices from Boolean functions was provided by Yu. Exploiting this framework, we first show that optimum coherence of the constructed spreading matrices can be achieved if the difference of any two distinct Boolean functions is a bent (or almost bent) function. With this result, explicit constructions of Boolean functions are then developed, which lead to new binary Golay spreading matrices with optimum coherence and yielding PAPR of each spreading sequence at most 2. Simulation results demonstrate that such spreading sequences are suitable for uplink grant-free access. Moreover, the proposed Golay spreading sequences are capable of accommodating up to 400% overloaded devices, which can not be achieved from the existing algebraic methods.

Multiuser Detection of GF-NOMA With Dynamic-Active Users and Temporal-Correlated Channels

In this letter, an efficient multiuser detection (MUD) is proposed for the grant-free non-orthogonal multiple access in the scenario with dynamic active users and unknown temporal-correlated channels. The proposed MUD performs active user and slot detection, channel estimation, and data detection simultaneously by iterative generalized approximate message passing (GAMP) and message passing (MP) over the joint factor graph. Concretely, GAMP is to decouple the transmissions of different users, and MP to update channel and user activity information. Finally, computer simulations are provided to validate the performance of the proposed method.

Low-Complexity Block Coordinate Descend Based Multiuser Detection for Uplink Grant-Free NOMA

Grant-free non-orthogonal multiple access (NOMA) scheme is considered as a promising candidate for the enabling of massive connectivity and reduced signalling overhead for Internet of Things (IoT) applications in massive machine-type communication (mMTC) networks. Exploiting the inherent nature of sporadic transmissions in the grant-free NOMA systems, compressed sensing based multiuser detection (CS-MUD) has been deemed as a powerful solution to user activity detection (UAD) and data detection (DD). In this paper, block coordinate descend (BCD) method is employed in CS-MUD to reduce the computational complexity. We propose two modified BCD based algorithms, called enhanced BCD (EBCD) and complexity reduction enhanced BCD (CR-EBCD), respectively. To be specific, by incorporating a novel candidate set pruning mechanism into the original BCD framework, our proposed EBCD algorithm achieves remarkable CS-MUD performance improvement. In addition, the proposed CR-EBCD algorithm further ameliorates the proposed EBCD by eliminating the redundant matrix multiplications during the iteration process. As a consequence, compared with the proposed EBCD algorithm, our proposed CR-EBCD algorithm enjoys two orders of magnitude complexity saving without any CS-MUD performance degradation, rendering it a viable solution for future mMTC scenarios. Extensive simulation results demonstrate the bound-approaching performance as well as ultra-low computational complexity.

Massive Connectivity Over MIMO-OFDM: Joint Activity Detection and Channel Estimation With Frequency Selectivity Compensation

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.