We propose an iterative channel estimation algorithm based on the Least Square Estimation (LSE) and Sparse Message Passing (SMP) algorithm for the Millimeter Wave (mmWave) MIMO systems. The channel coefficients of the mmWave MIMO are approximately modeled as a Bernoulli-Gaussian distribution and the channel matrix is sparse with only a few non-zero entries. By leveraging the advantage of sparseness, we propose an algorithm that iteratively detects the exact locations and values of non-zero entries of the sparse channel matrix. At each iteration, the locations are detected by the SMP, and values are estimated with the LSE. We also analyze the Cramér-Rao Lower Bound (CLRB), and show that the proposed algorithm is a minimum variance unbiased estimator under the assumption that we have the partial priori knowledge of the channel. Furthermore, we employ the Gaussian approximation for message densities under density evolution to simplify the analysis of the algorithm, which provides a simple method to predict the performance of the proposed algorithm. Numerical experiments show that the proposed algorithm has much better performance than the existing sparse estimators, especially when the channel is sparse. In addition, our proposed algorithm converges to the CRLB of the genie-aided estimation of sparse channels with only five turbo iterations.

With recent advances on the dense low-earth orbit (LEO) constellation, LEO satellite network has become one promising solution to providing global coverage for Internet-of-Things (IoT) services. Confronted with the sporadic transmission from randomly activated IoT devices, we consider the random access (RA) mechanism, and propose a grant-free RA (GF-RA) scheme to reduce the access delay to the mobile LEO satellites. A Bernoulli-Rician message passing with expectation maximization (BR-MP-EM) algorithm is proposed for this terrestrial-satellite GF-RA system to address the user activity detection (UAD) and channel estimation (CE) problem. This BR-MP-EM algorithm is divided into two stages. In the inner iterations, the Bernoulli messages and Rician messages are updated for the joint UAD and CE problem. Based on the output of the inner iterations, the expectation maximization (EM) method is employed in the outer iterations to update the hyper-parameters related to the channel impairments. Finally, simulation results show the UAD and CE accuracy of the proposed BR-MP-EM algorithm, as well as the robustness against the channel impairments.

Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable (e.g., perform poorly or even diverge) for other matrix ensembles, especially for ill-conditioned ones. To solve this issue, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP (BO-OAMP/VAMP) requires a high-complexity linear minimum mean square error (MMSE) estimator. This prevents OAMP/VAMP from being used in large-scale systems. To address the drawbacks of AMP and BO-OAMP/VAMP, this paper offers a memory AMP (MAMP) framework based on the orthogonality principle, which ensures that estimation errors in MAMP are asymptotically IID Gaussian. To realize the required orthogonality for MAMP, we provide an orthogonalization procedure for the local memory estimators. In addition, we propose a Bayes-optimal MAMP (BO-MAMP), in which a long-memory matched filter is used for interference suppression. The complexity of BO-MAMP is comparable to AMP. To asymptotically characterize the performance of BO-MAMP, a state evolution is derived. The relaxation parameters and damping vector in BO-MAMP are optimized based on state evolution. Most crucially, the state evolution of the optimized BO-MAMP converges to the same fixed point as that of the high-complexity BO-OAMP/VAMP for all right-unitarily-invariant matrices, and achieves the Bayes optimal MSE predicted by the replica method if its state evolution has a unique fixed point. Finally, simulations are provided to verify the theoretical results’ validity and accuracy.

This paper considers a low-complexity Gaussian Message Passing (GMP) scheme for a coded massive Multiple- Input Multiple-Output (MIMO) systems with Non-Orthogonal Multiple Access (massive MIMO-NOMA), in which a base station with Ns antennas serves Nu sources simultaneously in the same frequency. Both Nu and Ns are large numbers, and we consider the overloaded cases with Nu > Ns. The GMP forMIMO-NOMA is a message passing algorithm operating on a fully-connected loopy factor graph, which is well understood to fail to converge due to the correlation problem. In this paper, we utilize the largescale property of the system to simplify the convergence analysis of the GMP under the overloaded condition. First, we prove that the variances of the GMP definitely converge to the mean square error (MSE) of Linear Minimum Mean Square Error (LMMSE) multi-user detection. Secondly, the means of the traditional GMP will fail to converge when Nu/Ns < (√2 - 1)-2 ≈ 5.83. Therefore, we propose and derive a new convergent GMP called scale-and-add GMP (SA-GMP), which always converges to the LMMSE multi-user detection performance for any Nu/Ns > 1, and show that it has a faster convergence speed than the traditional GMP with the same complexity. Finally, numerical results are provided to verify the validity and accuracy of the theoretical results presented.

We address the joint device activity detection and channel estimation (JACE) problem in a massive MIMO connectivity scenario in which a large number of mobile devices are connected to a base station (BS), while only a small portion are active at any given time. The main objective is to provide an efficient transmission and detection scheme with both spatial and temporal correlations. We formulate JACE as a multiple measurement vector (MMV) problem with correlated entries in the vectors to be estimated. We propose an MMV form of the orthogonal approximate message passing algorithm (OAMP-MMV). We derive a group Gram-Schmidt orthogonalization (GGSO) procedure for the realization of OAMP-MMV. We outline a state evolution (SE) procedure for OAMP-MMV and examine its accuracy using numerical results. We also compare OAMP-MMV with existing alternatives, including AMP-MMV and GTurbo-MMV. We show that OAMP-MMV outperforms AMP-MMV when pilot sequences are generated using Hadamard pilot matrices. Such a pilot design is attractive due to the low-cost signal processing technique using the fast Hadamard transform (FHT). We also show that OAMP-MMV outperforms GTurbo-MMV in correlated channels.