Multiuser detection algorithm based on an efficient Laplacian scale mixture prior

With the rapid evolution of fifth-generation (5G) mobile communication technologies, massive machine-type communication (mMTC) has become a pivotal application scenario in modern networks. This paradigm shift presents significant challenges in multiuser detection, particularly due to the exponential growth in user connections and heightened signal activity. Traditional orthogonal multiple access schemes, while ensuring minimal interuser interference, inherently limit the number of supported users by relying on orthogonal resource allocation, thereby failing to meet the scalability demands of mMTC. Consequently, grant-free nonorthogonal multiple access has emerged as a key enabler for Internet of Things communications, allowing nonorthogonal data superposition on limited resource blocks to enhance access capacity. However, existing sparse Bayesian learning (SBL) algorithms—although capable of achieving optimal sparse solutions—suffer from high computational complexity, primarily due to matrix inversion operations during expectation-maximization iterations. This complexity impedes real-time deployment in large-scale mMTC systems. To address this gap, this work proposes a novel SBL framework leveraging an efficient Laplace scale mixture (ELSM) prior, aiming to simultaneously enhance detection performance, reduce computational overhead, and adapt to dynamic multimeasurement scenarios.

This paper proposes an ELSM-SBL algorithm to overcome the limitations of conventional SBL methods. First, a hierarchical Bayesian model is constructed using a Laplace scale mixture prior, which leverages the sharp peaks and heavy-tailed properties of Laplace distributions to promote sparsity and robustness against outliers. To avoid computationally expensive matrix inversions, a surrogate function is introduced to approximate the Gaussian likelihood function. This approximation is optimized within a majorization-minimization (MM) framework, where a block coordinate descent (BCD) algorithm solves the resulting nonconvex optimization problem. For single measurement vector (SMV) scenarios, the ELSM-SBL-SMV algorithm optimizes hyperparameters via evidence maximization, while an MM framework with BCD resolves nonconvexity in the joint cost function. For multiple measurement vector (MMV) scenarios, the ELSM-SBL-MMV scheme exploits temporal correlations among active user sets across consecutive time slots by sharing sparsity-controlling hyperparameters, thereby enhancing reconstruction performance.

Extensive simulations were conducted under mMTC settings with a total user count of K=108, subcarriers N=72, and active users M=12 using BPSK modulation and repeated over 1, 000 trials. For MMV scenarios, the number of measurement vectors was set to T=7. Compared with state-of-the-art SBL algorithms (e.g., GIG-SBL, BGIG-SBL, and LSM-SBL), the proposed ELSM-SBL-SMV algorithm can achieve a performance gain of about 2 dB, while the ELSM-SBL-MMV algorithm can achieve a gain of 3 dB. Meanwhile, the computational complexity of ELSM-SBL-SMV is $\mathcal{O}$(K²), which is superior to existing SBL algorithms, demonstrating the superiority of the proposed algorithm in terms of performance and efficiency.

The ELSM-SBL algorithm approximates the Gaussian likelihood function of the model by introducing a surrogate function, avoiding matrix inversion and reducing algorithm complexity, thereby considerably improving multiuser detection in mMTC systems. The SMV and MMV extensions demonstrate robust performance gains of 2 and 3 dB, respectively, while achieving $\mathcal{O}$(K²) complexity, which is optimal for large-scale deployments. The experimental results confirm the algorithm's superiority in terms of BER, AER, and runtime, making it a viable solution for 5G and beyond-5G networks. Future work will explore real-time hardware implementations and extensions to massive Multiple-Input Multiple-Output scenarios to further enhance applicability in dynamic wireless environments.