Minimum mean square error (MMSE) signal detection algorithm is nearoptimal for uplink multi-user large-scale multiple input multiple output (MIMO) systems, but involves matrix inversion with high complexity. In this letter, we firstly prove that the MMSE filtering matrix for largescale MIMO is symmetric positive definite, based on which we propose a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method to avoid the matrix inversion. The complexity can be reduced from O(K 3 ) to O(K 2 ), where K is the number of users. We also provide the convergence proof of the proposed algorithm. Simulation results show that the proposed signal detection algorithm converges fast, and achieves the near-optimal performance of the classical MMSE algorithm.Introduction: Large-scale multiple input multiple output (MIMO) employing hundreds of antennas at the base station (BS) to simultaneously serve multiple users is a promising key technology for 5G wireless communications [1]. It can achieve orders of magnitude increase in spectrum and energy efficiency, and one challenging issue to realize such goal is the low-complexity signal detection algorithm in the uplink, due to the increased dimension of large-scale MIMO systems [2]. The optimal signal detection algorithm is the maximum likelihood (ML) algorithm, but its complexity increases exponentially with the number of transmit antennas, making it impossible for large-scale MIMO. The fixedcomplexity sphere decoding (FSD) [3] and tabu search (TS) [4] algorithms have been proposed with reduced complexity, but their complexity is unfordable when the dimension of the large-scale MIMO system is large or the modulation order is high [5]. Low-complexity linear detection algorithms such as zero-forcing (ZF) and minimum mean square error (MMSE) with near-optimal performance have been investigated [2], but these algorithms have to use unfavorable matrix inversion, whose high complexity is still not acceptable for large-scale MIMO systems. Very recently, the Neumann series approximation algorithm has been proposed to approximate the matrix inversion [6], which converts the matrix inversion into a series of matrix-vector multiplications. However, only marginal complexity reduction can be achieved.In this letter, we propose a low-complexity near-optimal signal detection algorithm by exploiting the Richardson method [7] to avoid the complicated matrix inversion. We firstly prove a special property of large-scale MIMO systems that the MMSE filtering matrix is symmetric positive definite, based on which we propose to exploit the Richardson method to avoid the complicated matrix inversion. Then we prove the convergence of the proposed algorithm for any initial solution when the relaxation parameter is appropriate. Finally, we verify through simulations that the proposed signal detection algorithm can efficiently solve the matrix inversion problem in an iterative way until the desired accuracy is attained, and achieve the near-optimal performance of the MMSE algori...

Background Glial activation and neuroinflammation play a crucial role in the pathogenesis and development of Alzheimer’s disease (AD). The receptor for advanced glycation end products (RAGE)-mediated signaling pathway is related to amyloid beta (Aβ)-induced neuroinflammation. This study aimed to investigate the neuroprotective effects of tanshinone IIA (tan IIA), a natural product isolated from traditional Chinese herbal Salvia miltiorrhiza Bunge, against Aβ-induced neuroinflammation, cognitive impairment, and neurotoxicity as well as the underlying mechanisms in vivo and in vitro. Methods Open-field test, Y-maze test, and Morris water maze test were conducted to assess the cognitive function in APP/PS1 mice. Immunohistochemistry, immunofluorescence, thioflavin S (Th-S) staining, enzyme-linked immunosorbent assay (ELISA), real-time quantitative reverse-transcription polymerase chain reaction (qRT-PCR), and western blotting were performed to explore Aβ deposition, synaptic and neuronal loss, microglial and astrocytic activation, RAGE-dependent signaling, and the production of pro-inflammatory cytokines in APP/PS1 mice and cultured BV2 and U87 cells. Results Tan IIA treatment prevented spatial learning and memory deficits in APP/PS1 mice. Additionally, tan IIA attenuated Aβ accumulation, synapse-associated proteins (Syn and PSD-95) and neuronal loss, as well as peri-plaque microgliosis and astrocytosis in the cortex and hippocampus of APP/PS1 mice. Furthermore, tan IIA significantly suppressed RAGE/nuclear factor-κB (NF-κB) signaling pathway and the production of pro-inflammatory cytokines (TNF-α, IL-6, and IL-1β) in APP/PS1 mice and cultured BV2 and U87 cells. Conclusions Taken together, the present results indicated that tan IIA improves cognitive decline and neuroinflammation partly via inhibiting RAGE/NF-κB signaling pathway in vivo and in vitro. Thus, tan IIA might be a promising therapeutic drug for halting and preventing AD progression.

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It is very important to know how to allocate tolerances economically for parts in a CAD

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