A distributed algorithm is presented in this technical paper under directed communication networks, which is used to solve the economic dispatch problem in fixed time in smart grid systems. A new globally fixed-time stability theory (Lemma 3) is first given in this paper, which contains a new upper bound for the estimation of the settling time. Moreover, the fixed-time convergence for the proposed algorithm is rigorously proved with the aid of convex optimization theory, the new lemma and Lyapunov stability theory under the strongly connected and weight-balanced network topology. Finally, numerical simulations show the effectiveness and advantages of the distributed fixed-time optimization algorithm.

Considering some communication or security requirements, the sensors cannot be deployed randomly. In order to improve the localization accuracy, we discuss the optimal geometry problem with some constraints: 1) the source and the sensors are restricted to be deployed inside a circular region; 2) the relative sensor-source distance must be greater than the minimum safety distance. The optimal geometry problem can be summarized as a constrained optimization problem, with D-optimality as its objective function, the deployment feasible region as constraints. To avoid complicated mathematical calculations, our primary idea is to establish equivalent and more intuitive constraints by using the introduced maximum feasible angle and optimal separation angle.

The sensor-target placement plays a pivotal role in improving the localization accuracy, the commonly used evaluation function for this problem is built by Cramer-Rao lower bound (CRLB) or Fisher information matrix (FIM). Frame theory, which was developed recently, can provide a more easily tractable evaluation function, especially for some complex cases. In this letter, we derive an evaluation function by frame theory and prove its equivalence with that by CRLB and FIM. For angle of arrival (AOA) based localization system, we present the optimal sensor augmentation problem with several fixed sensors and an arbitrary number of new sensors, and for arbitrary but fixed distances between new sensors and target. The conclusions are verified by several simulations.

Source localization is a fundamental problem in underwater wireless sensor networks. From the observability analysis, we know that the sensor placement can significantly affect the localization performance. This letter is concerned with the optimal sensor placement for underwater source localization, and a parameter is introduced into the measurement model to represent the distance-dependent noise. The evaluation criterion used to solve the optimal placement is built by the Cramer-Rao lower bound theory. Subsequently, we mainly discuss the case when the distances between the sensors and the source are fixed, and the optimal sensor placement is affected by the relative magnitude of the distances.

In recent years, the network operators have paid more attention to user experience. The design of scheduling algorithm is a great challenge in long term evolution (LTE) system to improve the overall system Quality of Experience (QoE). Many papers have been developed to solve the scheduling problem for the full buffer traffic. In this paper, a new scheduling algorithm named percent proportional fair (PPF) is proposed for the reality burst traffic. To evaluate the user experience, we introduce two measure indicators, average user perceived throughput (UPT) and user perceived throughput-cut (UPT-cut). In order to improve the average UPT with fairness guarantee, we design the scheduling priority by considering the ratio of the amount of transmitted data to the total amount of burst data. At the same time, an allocation matrix is introduced so as to avoid bandwidth waste. Finally, comparing the PPF scheduler with the classical proportional fair (PF) scheduler and fair allocation high throughput (FAHT) scheduler, the simulation results show the improvement of average UPT while ensuring fairness among the users. Besides, the performance of PPF scheduling is analyzed in various system scenarios.