In this paper, simple and complete asymptotical analysis is given for a piecewise uniform product polar quantizer (PUPPQ) with respect to mean-square error (MSE) i.e. distortion (D). PUPPQ is based on uniform product polar quantizers. PUPPQ consists of L different uniform product polar quantizers. Uniform product polar quantizer conditions for optimality and all main equations for number of phase divisions and optimal number of levels for each partition are presented. These systems, although not optimal, may have asymptotic performance close to the optimum. Furthermore, the analysis and implementation can be simpler than those of optimal systems. PUPPQ has implementation complexity between optimal nonuniform polar quantization (NPQ) and uniform product polar quantization (UPPQ). The gain of PUPPQ over optimum uniform product polar quantization is also obtained (2 dB for the rate of 8 bits/sample).