The problem that the computational complexity of the detection algorithm increases exponentially with the number of modes. This paper analyzes the maximum likelihood detection algorithm for channel sorting and QR decomposition (CR-QRM-MLD) for sub-optimal detection algorithm to improve and process the ML detection algorithm and to apply to the mode division and multiplexing system. Simulation results show that the QR matrix decomposition simplifies the computational process and the interception of the candidate emission symbol detection vector reduces the computational complexity of the detection algorithm. Studying the performance of the sub-optimal detection algorithm in the mode division multiplexing (MDM) system, it can reduce the complexity of the system.
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