On the optimal Constant Norm Algorithm, in respect to the EMSE, for blind QAM equalization

During the last Eusipco conference [1] we proposed a new class of algorithm, called Constant Norm Algorithm (CNA), which contains the well-known CMA. From this class, two new cost functions well designed for QAM modulation, were derived. The first, named CQA for Constant sQuare Algorithm, is better adapted for QAM than the classical CMA. It results in a lower algorithm's noise without an increase of complexity. This algorithm was derived thanks to the infinite norm which was intuitively better adapted for square mapping modulation than the norm 2 of the CMA. In the same period [4] we proposed a geometrical derivation for computing the Excess Mean Square Error for Bussgang algorithm. Then in respect to this derivation, we prove in this paper that the optimal norm which minimizes the EMSE for QAM modulation is not the infinite norm (even it gives a lower EMSE than the norm 2) but it is the norm 6.