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A conventional constant modulus (CM) algorithm can be applied in blind equalization to recover the data symbols of 4-QAM signals. The equalized constellation is likely to be tilted and can be aligned in real-imaginary plane with a simple rotation. This approach works also with higher order QAM signals though the modulus of the symbol sequence is no longer constant. To reduce the residual equalization imperfection, Satorius and Mulligan introduced a specialized cost function for M-QAM signals and provided an iterative gradient algorithm: rectangular constellation-based blind equalization (RECBEQ). In this paper we combine the RECBEQ-type of coefficient update with modified CM recursive least-squares (RLS) algorithm. The blind equalizer is further improved with ldquogear-shiftrdquo priming and differential QAM encoding to resolve the phase ambiguity.