Efficient Methods and Architectures for Mean and Variance Estimations of QAM Symbols

In this paper, we design efficient methods for the mean and variance estimations of QAM symbols with applications to iterative receivers. The proposed methods for optimal estimations enable scalable hardware implementations for any Gray mapped PAM or QAM with less circuitries. For variance estimations, the proposed method reduces the complexity from $O((\log_{2}N)^{2})$ in the existing method to $O(\log_{2}N)$ for an N-QAM. Two suboptimal methods are also proposed to avoid the multiplications in the hardware implementations. The presented approximation approaches provide similar or better performance than the existing methods but with simpler implementation and less logical circuitries. In addition, based on the proposed architecture, we present novel unit module designs with disassembled estimation components and the schematics to virtualize the estimation hardware. With efficient design of unit module and control unit, maximized parallelization can be achieved.