Robust carrier phase and frequency tracking for M-QAM demodulation

A non-transitory computer-readable medium having instructions stored thereon that when executed by a processor, cause the processor to perform operations of first and second methods, comprising:

• the first method is for determining coarse carrier phase and frequency offsets of an initial block of a series of blocks of received symbols modulated using an M quadrature amplitude modulation (M-QAM) symbol map that includes the operations of:
• creating a grid of discrete candidate phase offset values;
• for each candidate phase offset value in the grid:
• applying the candidate phase offset value to each of the M-QAM symbols;
• applying a respective hard decision from the symbol map to each of the candidate phase offset value-applied M-QAM symbols;
• and
• computing a figure of merit for the candidate phase offset value based on the candidate phase offset value-applied M-QAM symbols and their respective hard decisions;
• selecting the discrete candidate phase offset value from the grid having the best figure of merit as an initial phase offset estimate;
• and
• computing an initial frequency offset estimate using the M-QAM symbols updated with the initial phase offset estimate, their respective hard decisions, and an approximation of the complex exponential function;
• and
• the second method is for tracking carrier phase and frequency offsets associated with subsequent blocks of the series of blocks after the initial block that includes the operations of:
• for each M-QAM symbol of a current block of the subsequent blocks:
• setting a binary trust weight for the M-QAM symbol based on comparison of a computed parameter with a threshold;
• and
• using the binary trust weights to compute a phase offset error and a frequency offset error associated with the current block, wherein each of the M-QAM symbols having a zero-valued binary trust weight is non-contributory in the computation of the phase and frequency offset errors.

A radio frequency device that tracks carrier phase and frequency offsets associated with a series of blocks of received symbols modulated using an M quadrature amplitude modulation (M-QAM) symbol map, comprising:

• a processor configured to:
• determine coarse carrier phase and frequency offsets of an initial block of the series of blocks by:
• creating a grid of discrete candidate phase offset values;
• for each candidate phase offset value in the grid:
• applying the candidate phase offset value to each of the M-QAM symbols of the initial block;
• applying a respective hard decision from the symbol map to each of the candidate phase offset value-applied M-QAM symbols of the initial block;
• and
• computing a figure of merit for the candidate phase offset value based on the candidate phase offset value-applied M-QAM symbols of the initial block and their respective hard decisions;
• selecting the discrete candidate phase offset value from the grid having the best figure of merit as an initial phase offset estimate;
• and
• computing an initial frequency offset estimate using the M-QAM symbols of the initial block updated with the initial phase offset estimate, their respective hard decisions, and an approximation of the complex exponential function;
• and
• for each M-QAM symbol of a current block of the series of blocks subsequent to the initial block:
• set a binary trust weight for the M-QAM symbol based on comparison of a computed parameter with a threshold, wherein each binary trust weight has a value of either zero or one;
• and
• use the binary trust weights to compute a phase offset error and a frequency offset error associated with the current block, wherein each of the M-QAM symbols having a zero-valued binary trust weight is non-contributory in the computation of the phase and frequency offset errors.