Unmodulated continuous wave (UCW) radar has been shown to have many unique features. With the recent development, UCW radar network has become an attractive platform for target tracking. In practice, to achieve better tracking performance, UCW radars are supposed to maximize their transmitted power, which may be in contradiction with the limited energy resources of themselves. Therefore, a performancedriven power allocation algorithm for Doppler-only target tracking in a UCW radar network is proposed. This algorithm can be viewed as a reaction of the cognitive transmitter to the environment perceived by the receiver to minimize the target state estimation mean square error with a given total power budget. The Bayesian Cramér-Rao lower bound gives a measure of the achievable optimum performance for target tracking and, importantly, it can be calculated predictively. Therefore, it is derived and utilized as an optimization criterion for the power allocation algorithm. The resulting optimization problem is proved to be convex, and hence, can be solved by gradient projection method. Numerical results show that the target tracking accuracy can be efficiently improved by the proposed algorithm.Index Terms-Bayesian Cramér-Rao lower bound (BCRLB), convex optimization, power allocation, target tracking, unmodulated continuous wave (UCW) radar.