Exact ML criterion based on semidefinite relaxation for MIMO systems

In this letter, we propose an exact maximum likelihood (ML) criterion based on semidefinite relaxation (SDR) in multiple-input multiple-output systems. Although a conventional SDR criterion for determining whether a symbol is the ML solution exists, its results cannot be guaranteed when noise is present. In place of the conventional criterion's positive semidefinite (PSD) discriminant, we propose a new, exact ML criterion based on the condition that all diagonal values are positive (PDV), a simple characteristic and necessary condition of PSD. The proposed criterion has a lower calculation complexity for testing than does a PSD and can ensure that the ML solution is always satisfactory.