In this paper we consider a probabilistic signal-to-interference-and-noise ratio (SINR) constrained problem for transmit beamforming design in the presence of imperfect channel state information (CSI), under a multiuser multiple-input single-output (MISO) downlink scenario. In particular, we deal with outage-based quality-of-service constraints, where the probability of each user's SINR not satisfying a service requirement must not fall below a given outage probability specification. The study of solution approaches to the probabilistic SINR constrained problem is important because CSI errors are often present in practical systems and they may cause substantial SINR outages if not handled properly. However, a major technical challenge is how to process the probabilistic SINR constraints. To tackle this, we propose a novel relaxation-restriction (RAR) approach, which consists of two key ingredientssemidefinite relaxation (SDR), and analytic tools for conservatively approximating probabilistic constraints. The underlying goal is to establish approximate probabilistic SINR constrained formulations in the form of convex conic optimization problems, so that they can be readily implemented by available solvers. Using either an intuitive worst-case argument or specialized probabilistic results, we develop various conservative approximation schemes for processing probabilistic constraints with quadratic uncertainties. Consequently, we obtain several RAR alternatives for handling the probabilistic SINR constrained problem. Our techniques apply to both complex Gaussian CSI errors and i.i.d. bounded CSI errors with unknown distribution. Moreover, results obtained from our extensive simulations show that the proposed RAR methods significantly improve upon existing ones, both in terms of solution quality and computational complexity.

Multi-cell coordinated beamforming (MCBF), where multiple base stations (BSs) collaborate with each other in the beamforming design for mitigating the inter-cell interference, has been a subject drawing great attention recently. Most MCBF designs assume perfect channel state information (CSI) of mobile stations (MSs); however CSI errors are inevitable at the BSs in practice. Assuming elliptically bounded CSI errors, this paper studies the robust MCBF design problem that minimizes the weighted sum power of BSs subject to worst-case signal-to-interference-plus-noise ratio (SINR) constraints on the MSs. Our goal is to devise a distributed optimization method that can obtain the worst-case robust beamforming solutions in a decentralized fashion, with only local CSI used at each BS and little backhaul signaling for message exchange between BSs. However, the considered problem is difficult to handle even in the centralized form. We first propose an efficient approximation method in the centralized form, based on the semidefinite relaxation (SDR) technique. To obtain the robust beamforming solution in a decentralized fashion, we further propose a distributed robust MCBF algorithm, using a distributed convex optimization technique known as alternating direction method of multipliers (ADMM). We analytically show the convergence of the proposed distributed robust MCBF algorithm to the optimal centralized solution and its better bandwidth efficiency in backhaul signaling over the existing dual decomposition based algorithms. Simulation results are presented to examine the effectiveness of the proposed SDR method and the distributed robust MCBF algorithm.

Metal–organic frameworks (MOFs), constructed from organic linkers and inorganic building blocks, are well-known for their high crystallinity, high surface areas, and high component tunability. The stability of MOFs is a key prerequisite for their potential practical applications in areas including storage, separation, catalysis, and biomedicine since it is essential to guarantee the framework integrity during utilization. However, MOFs are prone to destruction under external stimuli, considerably hampering their commercialization. In this Review, we provide an overview of the situations where MOFs undergo destruction due to external stimuli such as chemical, thermal, photolytic, radiolytic, electronic, and mechanical factors and offer guidelines to avoid unwanted degradation happened to the framework. Furthermore, we discuss possible destruction mechanisms and their varying derived products. In particular, we highlight cases that utilize MOF instability to fabricate varying materials including hierarchically porous MOFs, monolayer MOF nanosheets, amorphous MOF liquids and glasses, polymers, metal nanoparticles, metal carbide nanoparticles, and carbon materials. Finally, we provide a perspective on the utilization of MOF destruction to develop advanced materials with a superior hierarchy for various applications.

This review is expected to provide a library of multi-component hierarchically porous compounds, which shall guide the state-of-the-art design of future porous materials with unprecedented tunability, synergism and precision.

Metal-organic frameworks (MOFs) have been widely employed in gas storage and separation, drug delivery, and catalysis. The design and construction of MOFs and their hierarchical assemblies play a key role in enhancing properties including guest diffusion kinetics, catalytic activity, and selectivity. This Review summarizes the most recent advances in the controlled synthesis of MOFs with tunable sizes and morphologies, discusses the programmed assembly of novel MOFs with hierarchical structures, and highlights the vital roles of composition, morphology, and the hierarchically porous structure in applications, including delivery and catalysis. A short review of programmable assembly of MOF superstructures and composites with hierarchically arranged functionalities is provided. Taken together, this Review is expected to supply synthetic guidance for developing MOFs and their hierarchical assemblies, which shall in turn guide the state-of-the-art design of sophisticated materials with unprecedented tunability for various applications.

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The defect concentration in the prototypical metal–organic framework UiO-66 can be well controlled during synthesis, leading to precisely tunable physicochemical properties for this structure. However, there has been a long-standing debate regarding the nature of the compensating species present at the defective sites. Here, we present unambiguous spectroscopic evidence that the missing-linker defect sites in an ambient environment are compensated with both carboxylate and water (bound through intermolecular hydrogen bonding), which is further supported by ab initio calculations. In contrast to the prevailing assumption that the monocarboxylate groups (COO–) of the modulators form bidentate bonding with two Zr4+ sites, COO– is found to coordinate to an open Zr4+ site in an unidentate mode. The neighboring Zr4+ site is terminated by a coordinating H2O molecule, which helps to stabilize the COO– group. This finding not only provides a new understanding of defect termination in UiO-66, but also sheds light on the origin of its catalytic activity.