M&M Carrier Recovery Algorithm

The M&M carrier recovery algorithm is a classical method in digital communications used to correct carrier phase deviations in received signals. Proposed by Mueller and Müller, this algorithm is renowned for its high efficiency and low computational complexity. It analyzes phase relationships between adjacent symbols to progressively adjust the local oscillator phase, ultimately achieving precise carrier synchronization.

The core principle of the M&M algorithm involves utilizing phase differences between symbols to estimate phase errors. By comparing the phase difference between current and previous symbols, it generates error signals that drive adjustments through loop filters and numerically controlled oscillators. This closed-loop feedback mechanism effectively suppresses noise interference and is suitable for various modulation schemes including QPSK and QAM.

In MATLAB implementation, key components typically include: error detector design (calculating phase differences using dot products or cross-products), loop filter parameter configuration (proportional-integral filters for smooth phase adjustment), and phase compensation realization through complex multiplication. The algorithm's precision is influenced by loop bandwidth selection—wider bandwidth enables faster convergence but reduced stability, while narrower bandwidth provides better stability at the cost of slower convergence. This implementation has been verified to meet phase synchronization requirements for conventional communication systems, with critical functions involving signal phase rotation using complex exponential operations and error calculation through symbol correlation techniques.