1.2.1 CMA 2-2

The CM criterion [3,4] is usually implemented as CMA 2-2 where p,q=2. The steepest gradient descent algorithm is obtained by taking the instantaneous gradient of , which results in the CMA 2-2 equalizer update equation:

where $\ensuremath{\mathbf{f}}$ is the length-N_f equalizer coefficient vector, $\ensuremath{\mathbf{r}}(n)$ is the length-N_f receiver input vector (i.e. regressor), $\mu$ is a (small) step-size, and

is the CM error function for CMA 2-2, where $\gamma$ is chosen by $\gamma=E\{\vert s_n\vert^{4}\}/E\{\vert s_n\vert^2\}$