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In multiuser MIMO systems, the Channel Inversion Regularization (CIR) precoding outperforms Zero-Forcing (ZF) in the case of a small number of users and low SNR. However, unlike the zero-interference ZF, the optimal power allocation issue using CIR is a nonconvex optimization problem which will become more intractable with nonconvex QoS constraints. In this paper we focus on the challenging QoS-aware optimal power allocation problem, aiming to maximize the system sum rate and guarantee the users' minimum data rates. As a result, an "Iterative Geometric Programming" (IGP) strategy is proposed which transforms the underlying problem to a series of tractable Geometric Programming (GP) problems through an iterative convex approximation. Extensive simulations have been conducted and the results indicate that IGP is quite suitable to tackle the problem, which can achieve a good balance between the system sum rate and the individual QoS requirements.