Patent US 9,942,004

This invention discloses apparatus and methods for detecting transmit symbols from the receiving waveform samples at the receiver side for communications systems. The receiving waveform samples are corrupted by channel and noise effects and the detection is carried out with a maximum likelihood optimality criterion. This invention utilizes a successive linear constraint exchange scheme that formulates a sequence of linearly constrained minimization subproblems to allow the solutions to these subproblems, combined with certain quantization and mapping operations, to converge to the optimal maximum likelihood estimate. This invention is applicable to any digitally modulated communications systems, including but not limited to Multiple Input Multiple Output (MIMO) communications systems.