Multi-cell Optimal Downlink Beamforming Algorithm with Per-base Station Power Constraints

We consider a problem of optimizing multi-cell downlink throughput in multiple-input single-output (MISO) beamforming with single user per sub-channel in the wireless communication system. Previous work based on the generalization of uplink-downlink duality has already reformulated the maximum achievable downlink throughput into dual uplink throughput maximization problem. Since the dual uplink problem is nonconvex, it is difficult to find its optimal solution. The main contribution of this paper is a novel practical algorithm based on heuristic to find the solution of beamforer design satisfying the necessary optimality conditions of the dual uplink problem. Meanwhile the converged beamforming vectors can in turn improve the system sum rate significantly. As the dual problem is a mixed optimization, we also provide algorithms for its two sub-optimal problems. Simulation results validate the convergence and the efficiency of proposed algorithms.     

One Pot Synthesis of Octahydroquinazolinone Derivatives Using (Me (Im)<Superscript>12</Superscript>) H<Subscript>4</Subscript>CuPW<Subscript>11</Subscript>O<Subscript>39</Subscript> as a Surfactant Type Catalyst

This study is aimed at proposing a practical green procedure for the synthesis of octahydroquinazolinone derivatives using benzaldehyde, dimedone and urea under microwave irradiation in water. A surfactant type polyoxometalate-based organic–inorganic hybrid was able to efficiently catalyze this synthesis. The catalyst was prepared and characterized by Fourier transform infrared, UV–Vis, X-ray diffraction, and thermogravimetric analysis. The employed catalyst exerted a synergistic effect; the anion part acted as a catalyst while the cation part acted as a surfactant in order to increase the concentration of organic reactants in water. The main advantage of this method is its remarkable yield in short reaction periods, which results in the rendering of products with high purity. Moreover, this heterocatalyst is capable of being easily recovered and reused several times. The influences of reaction conditions were studied systematically, and a possible catalysis mechanism was proposed for understanding the highly efficient heterogeneous catalytic behavior.