In this study, we consider the application of deep learning (DL) to tabu search (TS) detection in large multiple-input multiple-output (MIMO) systems. First, we propose a deep neural network (DNN) ...architecture for symbol detection, termed the fast-convergence sparsely connected detection network (FS-Net), which is obtained by optimizing the prior detection networks called DetNet and ScNet. Then, we propose the DL-aided TS algorithm, in which the initial solution is approximated by the proposed FS-Net. Furthermore, in this algorithm, an adaptive early termination (ET) algorithm and a modified searching process are performed based on the predicted approximation error, which is determined from the FS-Net-based initial solution, so that the optimal solution can be reached earlier. The simulation results show that the proposed algorithm achieves approximately 90% complexity reduction for a <inline-formula> <tex-math notation="LaTeX">32 \times 32 </tex-math></inline-formula> MIMO system with QPSK with respect to the existing TS algorithms, while maintaining almost the same performance.
Although the sphere decoder (SD) is a powerful detector for multiple-input multiple-output (MIMO) systems, it has become computationally prohibitive in massive MIMO systems, where a large number of ...antennas are employed. To overcome this challenge, we propose fast deep learning (DL)-aided SD (FDL-SD) and fast DL-aided <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula>-best SD (KSD, FDL-KSD) algorithms. Therein, the major application of DL is to generate a highly reliable initial candidate to accelerate the search in SD and KSD in conjunction with candidate/layer ordering and early rejection. Compared to existing DL-aided SD schemes, our proposed schemes are more advantageous in both offline training and online application phases. Specifically, unlike existing DL-aided SD schemes, they do not require performing the conventional SD in the training phase. For a <inline-formula> <tex-math notation="LaTeX">24 \times 24 </tex-math></inline-formula> MIMO system with QPSK, the proposed FDL-SD achieves a complexity reduction of more than 90% without any performance loss compared to conventional SD schemes. For a <inline-formula> <tex-math notation="LaTeX">32 \times 32 </tex-math></inline-formula> MIMO system with QPSK, the proposed FDL-KSD only requires <inline-formula> <tex-math notation="LaTeX">K = 32 </tex-math></inline-formula> to attain the performance of the conventional KSD with <inline-formula> <tex-math notation="LaTeX">K=256 </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula> is the number of survival paths in KSD. This implies a dramatic improvement in the performance-complexity tradeoff of the proposed FDL-KSD scheme.
In this work, we investigate hybrid analog-digital beamforming (HBF) architectures for uplink cell-free (CF) millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. We first ...propose two HBF schemes, namely, decentralized HBF (D-HBF) and semi-centralized HBF (SC-HBF). In the former, both the digital and analog beamformers are generated independently at each AP based on the local channel state information (CSI). In contrast, in the latter, only the digital beamformer is obtained locally at the access point (AP), whereas the analog beamforming matrix is generated at the central processing unit (CPU) based on the global CSI received from all APs. We show that the analog beamformers generated in these two HBF schemes provide approximately the same achievable rates despite the lower complexity of D-HBF and its lack of CSI requirement. Furthermore, to reduce the power consumption, we propose a novel adaptive radio frequency (RF) chain-activation (ARFA) scheme, which dynamically activates/deactivates RF chains and their connected analog-to-digital converters (ADCs) and phase shifters (PSs) at the APs based on the CSI. For the activation of RF chains, low-complexity algorithms are proposed, which can achieve significant improvement in energy efficiency (EE) with only a marginal loss in the total achievable rate.
A variety of hybrid analog-digital beamforming architectures have recently been proposed for massive multiple-input multiple-output (MIMO) systems to reduce energy consumption and the cost of ...implementation. In the analog processing network of these architectures, the practical sub-connected structure requires lower power consumption and hardware complexity than the fully connected structure but cannot fully exploit the beamforming gains, which leads to a loss in overall performance. In this work, we propose a novel unequal sub-connected architecture for hybrid combining at the receiver of a massive MIMO system that employs unequal numbers of antennas in sub-antenna arrays. The optimal design of the proposed architecture is analytically derived, and includes antenna allocation and channel ordering schemes. Simulation results show that an enhancement of up to 10% can be attained in the total achievable rate by unequally assigning antennas to sub-arrays in the sub-connected system at the cost of a marginal increase in power consumption. Furthermore, in order to reduce the computational complexity involved in finding the optimal number of antennas connected to each radio frequency (RF) chain, we propose three low-complexity antenna allocation algorithms. The simulation results show that they can yield a significant reduction in complexity while achieving near-optimal performance.
Reconfigurable intelligentsurface (RIS) has emerged as a cost- and energy-efficient solution to enhance the wireless communications capacity. However, recent studies show that a very large surface is ...required for a RIS-assisted communications system; otherwise, they may be outperformed by the conventional relay. Furthermore, the performance gain of a RIS can be considerably degraded by hardware impairments such as limited-resolution phase shifters. To overcome those challenges, we propose a hybrid relay-reflecting intelligent surface (HR-RIS) architecture, in which a single or few elements serve as active relays, while the remaining only reflect the incident signals. We propose two HR-RIS architectures, namely, the fixed and dynamic HR-RIS. The joint transmit beamforming at the base station and hybrid relay-reflecting at the HR-RIS are designed based on alternating optimization and successive convex approximation methods. The simulation results for a <inline-formula><tex-math notation="LaTeX">4 \times 2</tex-math></inline-formula> multiple-input multiple-output system show that the proposed HR-RIS with only a single active element can achieve about 40% and 25% improvement in spectral efficiency and energy efficiency, respectively, with respect to the conventional RIS-aided system. The results also show that the HR-RIS can outperform the conventional relaying scheme in most of the considered scenarios.
This paper studies a new gradient regularity in Lorentz spaces for solutions to a class of quasilinear divergence form elliptic equations with nonhomogeneous Dirichlet boundary ...conditions:{div(A(x,∇u))=div(|F|p−2F)inΩ,u=σon∂Ω, where Ω⊂Rn (n≥2), the nonlinearity A is a monotone Carathéodory vector valued function defined on W01,p(Ω) for p>1 and the p-capacity uniform thickness condition is imposed on the complement of our bounded domain Ω. Moreover, for given data F∈Lp(Ω;Rn), the problem is set up with general Dirichlet boundary data σ∈W1,p(Ω). In this paper, the optimal good-λ type bounds technique is applied to prove some results of fractional maximal estimates for gradient of solutions. And the main ingredients are the action of the cut-off fractional maximal functions and some local interior and boundary comparison estimates developed in previous works 45,52,53 and references therein.
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In the conventional tabu search (TS) detection algorithm for multiple-input multiple-output (MIMO) systems, the cost metrics of all neighboring vectors are computed to determine the best neighbor. ...This can require an excessively high computational complexity, especially in large MIMO systems because the number of neighboring vectors and the dimension per vector are large. In this study, we propose an improved TS algorithm based on the QR decomposition of the channel matrix (QR-TS), which allows for finding the best neighbor with a significantly lower complexity compared with the conventional TS algorithm. Specifically, QR-TS does not compute all metrics by early rejecting unpromising neighbors, which reduces the computational load of TS without causing any performance loss. To further optimize the QR-TS algorithm, we investigate novel ordering schemes, namely the transmit-ordering (Tx-ordering) and receive-ordering (Rx-ordering), which can considerably reduce the complexity of QR-TS. Simulation results show that QR-TS reduces the complexity approximately by a factor of two compared with the conventional TS. Furthermore, when both Tx-ordering and Rx-ordering are applied, QR-TS requires approximately <inline-formula><tex-math notation="LaTeX">60\%\text{ -- }90\%</tex-math></inline-formula> less complexity compared with the conventional TS scheme. The proposed algorithms are suitable for both low-order and high-order modulation, and can achieve a significant complexity reduction compared to the Schnorr-Euchner and <inline-formula><tex-math notation="LaTeX">K\text{-}</tex-math></inline-formula>best sphere decoders in large MIMO systems.
The aim of this paper is to establish an abstract theory based on the so-called fractional-maximal distribution functions (FMDs). From the basic ideas introduced in 1, we develop and prove some ...abstract results related to the level-set inequalities and norm-comparisons by using the language of such FMDs. Particularly interesting is the applicability of our approach that has been shown in regularity and Calderón-Zygmund type estimates. In this paper, due to our research experience, we will establish global regularity estimates for two types of general quasilinear problems (problems with divergence form and double obstacles), via fractional-maximal operators and FMDs. The range of applications of these abstract results is large. Apart from these two examples of the regularity theory for elliptic equations discussed, it is also promising to indicate further possible applications of our approach for other special topics.
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In the conventional tabu search (TS) detection algorithm for multiple-input multiple-output (MIMO) systems, the metrics of all neighboring vectors are computed to determine the best one to move to. ...This strategy requires high computational complexity, especially in large MIMO systems with high-order modulation schemes such as 16- and 64-QAM signaling. This paper proposes a novel reduced-complexity TS detection algorithm called neighbor-grouped TS (NG-TS), which divides the neighbors into groups and finds the best neighbor by using a simplified cost function. Furthermore, based on the complexity analysis of NG-TS, we propose a channel ordering scheme that further reduces its complexity. Simulation results show that the proposed NG-TS with channel ordering can achieve up to 85% complexity reduction with respect to the conventional TS algorithm with no performance loss in both low- and higher-order modulation schemes.
This paper continues the development of regularity results for quasilinear elliptic equations −div(A(x,∇u))=μinΩ,andu=0on∂Ω,in Lorentz and Lorentz–Morrey spaces, where Ω⊂Rn (n≥2); A is a monotone ...Carathéodory vector valued operator acting between W01,p(Ω) and its dual W−1,p′(Ω); and μ is a datum in some Lebesgue space Lm(Ω), for m<p′. It emphasizes that in this paper, we restrict our study to the case of ‘very singular’ when 1<p≤3n−22n−1, and under mild assumption that the p-capacity uniform thickness condition is imposed on the complement of domain Ω. There are two main results obtained in our study pertaining to the global gradient estimates of solutions in Lorentz and Lorentz–Morrey spaces involving the use of maximal and fractional maximal operators. The idea for writing this working paper comes directly from the recent results by others in the same research topic, where global estimates for gradient of solutions for the ‘very singular’ case still remains a challenge, specifically related to Lorentz and Lorentz–Morrey spaces.
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