On the Limitation of Linear MMSE Detection

This correspondence highlights the performance limitation of linear minimum mean-squared error (mmse) detection in underdetermined vector Gaussian channels (as in overloaded code-division multiple-access (CDMA) systems) where the number of symbols (users) exceeds the signal space dimension (spread factor). It is shown that for such a simple receiver it is not possible to construct signal sets (or spreading codes) to even satisfy the basic requirement that every user´s symbol error probability decays exponentially as noise power vanishes. This result holds for arbitrary received energies, modulation schemes, and any strictly underdetermined system with a finite signal space dimension and a finite number of users