This paper addresses the problem of operating parameter assignment to multiple real-time tasks in a phased array radar system. The objective is to maximize the resulting system utility while ensuring the schedulability of all tasks with the assigned operating parameters. For this, we propose a novel framework by integrating the existing resource management framework called QRAM (QoS-based Resource Allocation Model) with the notion of "schedulability envelope". The schedulability envelope designed offline hides the complex details of phased array antenna scheduling and provides a linear formula as its quantitative abstraction. This abstraction allows QRAM to find the optimal resource assignment without concerning the details of complex scheduling. Our experimental results show that the proposed framework can achieve significantly improved system utility compared to the existing techniques.