On scheduling a multifunction radar with duty cycle budget QU Zheng 1 , Philippe Baptiste 2 , Frédéric Barbaresco 3 1 :X2006, École Polytechnique, 91128, Palaiseau, France 2 :LIX, CNRS, École Polytechnique, 91128, Palaiseau,France 3 :Thales Air Systems, Hameau de Roussigny, F-91470 Limours, France Abstract : The radar performs two operations per job or signal : the transmission and reception. In order to increase the utilization of radar and also to improve its performance in case of overload, we want to use waiting intervals to run more of possible tasks. The scheduling problem is a real time problem. An additional constraint : the duty cycle constraint has been added to the problem. Our goal is to interlace coupled tasks as many as possible while satisfying the constraints of duty cycle budget for application in advanced cognitive & agile multifunction radars [7]. Keywords :Scheduling, Local Search, Linear programming, Strong duality 1. Introduction Radar works similarly to sonar. Radar electromagnetic pulse travels in free air space at the speed of light (300, 000km/s). The pulse is reflected from a target object and an echo is returned. The radar determines the distance to the reflector by measuring the time from emission of a pulse to reception. The target location is determined by the direction in which radar antenna points when it emits radio signals. Multi-function radar (MFR) performs three types of tasks : surveillance, confirmation and tracking. We will consider the tasks of tracking and surveillance. Surveillance task provides surveillance of the specified areas while tracking task track the detected target. A target i is completely characterized by the distance R i (km), the elevation α i ( ◦ ) and the azimuth β i ( ◦ ). The emission time a i , reception time b i , waiting time L i and the period T i of the target tracking task are functions of (R i ,α i ,β i ). However we don’t take into account the periodicity because our horizon is small than the usual period 1s. We can consider the radar tasks as coupled tasks. The first subtask is the emission of electromagnetic wave, the second subtask is the reception wave. For a tracking task, the proportion between the active period (reception period plus emission period) and the inactive period is sometimes below 20%, which encourages us to make use of waiting periods to perform more tasks. During an adequate period (no loss of target), we know approximately the target’s position, so we can greatly reduce the interval of idle time. We can then try to interlace coupled tasks. But this kind of interlacing is not always possible due to the constraint of duty cycle budget, which limits the accumulated emission time in a given time interval. 2. Model 2.1 Notations The following notations are used : a i : emission time b i : reception time L i : idle time r i : release time d i : deadline p i : duration of the task i D i =[r i ,d i ] : execution window T i : period w i : weight i t i : starting time x i : 1 if the task i is executed in [r i ,d i ], 0 otherwise n : number of coupled tasks H : horizon 2.2 Objective function In reality, if the target tracking is not finished before the deadline, we consider it as a target loss. The loss being very expensive, we will try to perform as many COGIS 2009 _ COGNITIVE SYSTEMS WITH INTERACTIVE SENSORS