Converts the received complex symbols \(\tilde{a}[k]\) into decimal symbol decisions \(\hat{s}[k]\) and complex symbol decisions \(\hat{a}[k]\) using maximum-likelihood estimation (MLE).

Parameters:¶

a_tilde: ArrayLike¶

The received complex symbols \(\tilde{a}[k]\).

Returns:¶

• The decimal symbol decisions \(\hat{s}[k]\), \(0\) to \(M-1\).

• The complex symbol decisions \(\hat{a}[k]\).