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In this study, a nano-displacement measurement system is proposed and demonstrated both theoretically and experimentally, which was based on a modified Mach-Zehnder (M-Z) interferometer using two conjugated orbital angular momentum (OAM) beams. In contrast to the previous M-Z-based OAM interferometer, a reflection module is inserted into the reference arm instead of a simple mirror. As a result, the effect of the transverse position-dependence phase-shift caused by the dove prism can be clearly eliminated and a stable and robust (off-axis insensitive) petal-like interference pattern can be obtained successfully. More importantly, a significant rotation angle of the petal-like pattern vs. the tiny displacement of the tested object can be clearly observed. In accordance with the modified measurement setup, a novel phase-demodulation method enabling to quickly and accurately characterize the rotation angle of the petal-like interference-patterns is proposed and demonstrated also. A tiny displacement ranging from 50 to 800 nm with resolution of $\sim 50$ pm has been measured successfully. The proposed approach may find applications in not only the ultra-high precision displacement sensor, but also the temperature, strain, and refractive index sensors. [ABSTRACT FROM AUTHOR]

In this paper, we concentrate on the robust multi-objective optimization (MOO) for the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in device-to-device (D2D) communications underlaying heterogeneous networks (HetNets). Different from traditional resource optimization, we focus on finding robust Pareto optimal solutions for spectrum allocation and power coordination in D2D communications underlaying HetNets with the consideration of interference channel uncertainties. The problem is formulated as an uncertain MOO problem to maximize EE and SE of cellular users (CUs) simultaneously while guaranteeing the minimum rate requirements of both CUs and D2D pairs. With the aid of $\varepsilon$ -constraint method and strict robustness, we propose a general framework to transform the uncertain MOO problem into a deterministic single-objective optimization problem. As exponential computational complexity is required to solve this highly non-convex problem, the power coordination and the spectrum allocation problems are solved separately, and an effective two-stage iterative algorithm is developed. Finally, simulation results validate that our proposed robust scheme converges fast and significantly outperforms the non-robust scheme in terms of the effective EE-SE tradeoff and the quality of service satisfying probability of D2D pairs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general framework to study the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in massive multiple-input-multiple-output-enabled heterogenous networks while ensuring proportional rate fairness among users and taking into account the backhaul capacity constraint. We aim at jointly optimizing user association, spectrum allocation, power coordination, and the number of activated antennas, which is formulated as a multi-objective optimization problem maximizing EE and SE simultaneously. With the help of weighted Tchebycheff method, it is then transformed into a single-objective optimization problem, which is a mixed-integer non-convex problem and requires unaffordable computational complexity to find the optimum. Hence, a low-complexity effective algorithm is developed based on primal decomposition, where we solve the power coordination and number of antenna optimization problem and the user association and spectrum allocation problem separately. Both theoretical analysis and numerical results demonstrate that our proposed algorithm can fast converge within several iterations and significantly improve both the EE-SE tradeoff performance and rate fairness among users compared with other algorithms. [ABSTRACT FROM AUTHOR]

In this letter, we investigate the tradeoff between energy efficiency (EE) and spectral efficiency (SE) while ensuring proportional rate fairness in massive multiple-input multiple-output enabled heterogenous networks, where user association and power coordination are jointly considered. It is first formulated as a multi-objective optimization problem, and then transformed into a single-objective optimization problem. To solve this mixed-integer non-convex problem, an effective algorithm is developed, where the original problem is separated into lower level power coordination problem and master user association problem. Simulation results verify that our proposed algorithm can significantly improve the performance of EE–SE tradeoff and obtain higher rate fairness compared with other algorithms. [ABSTRACT FROM PUBLISHER]