In this letter, we investigate the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in device-todevice (D2D) communications underlaying cellular networks with uplink channel reuse. The resource allocation problem is modeled as a noncooperative game, in which each user equipment (UE) is self-interested and wants to maximize its own EE. Given the SE requirement and maximum transmission power constraints, a distributed energy-efficient resource allocation algorithm is proposed by exploiting the properties of the nonlinear fractional programming. The relationships between the EE and SE tradeoff of the proposed algorithm and system parameters are analyzed and verified through computer simulations. Index Terms-EE and SE tradeoff, D2D communication, noncooperative game, nonlinear fractional programming.

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In multi-objective evolutionary algorithms (MOEAs), the diversity of Pareto front (PF) is significant. For good diversity can provide more reasonable choices to decision-makers. The diversity of PF includes the span and the uniformity. In this paper, we proposed a dynamic crowding distance (DCD) based diversity maintenance strategy (DMS) (DCD-DMS), in which individual's DCD are computed based on the difference degree between the crowding distances of different objectives. The proposed strategy computes individuals' DCD dynamically during the process of population maintenance. Through experiments on 9 test problems, the results demonstrate that DCD can improve diversity at a high level compared with two popular MOEAs: NSGA-II and ε-MOEA.

Abstract-The pole-sensitivity approach is employed to investigate the stability issue of the discrete-time control system, where a digital controller, implemented with finite word length (FWL), is used. A new stability related measure is derived, which is more accurate in estimating the closed-loop stability robustness of an FWL implemented controller than some existing measures for the pole-sensitivity analysis. This improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output-feedback and observer-based controllers. A numerical example is used to verify the theoretical analysis and to illustrate the design procedure.Index Terms-Closed-loop stability, digital controller, finite word length, optimization.