System and method for synchronizing digital bits in a data stream

A method for identifying a main peak value in an array of peak values where a plot of the peak values against the offsets corresponding to each peak value shows a peak value having a largest magnitude between peak values on either side of the largest peak value and substantially linear patterns formed by the peak values right and left of the largest peak value, the method comprising:

• generating a right line by a first order curve fit using at least one peak value to the right of the largest peak value and the largest peak value, the right line having a right slope and a right intercept;
• generating a left line by a first order curve fit using at least one peak value to the left of the largest peak value and the largest peak value, the left line having a left slope and a left intercept;
• identifying a predicted peak value by identifying an intersection point on a timeline formed by the offsets at which the right line intersects the left line;
• and
• identifying the largest peak value as the main peak value if the predicted peak value is within a predefined interval around the largest peak value.

A method for identifying a main peak value in an array of peak values where a plot of the peak values against the offsets corresponding to each peak value shows a peak value having a largest magnitude between peak values on either side of the largest peak value and substantially linear patterns formed by the peak values right and left of the largest peak value, the method comprising:

• generating a second array of peak values by:
• calculating respective differences between the largest peak value and each other peak value in the array of peak values and combining the respective difference to generate an average difference value, DiffAVE, between successive peak values in the array of peak values;
• generating a set of ideal right peak values using:
• peak_right_n=largest peak value−n*DiffAVE, where n=an integer number of offsets from the offset of the largest peak value;
• generating a set of ideal left peak values using:
• peak_left_n=largest peak value−n*DiffAVE, where n=an integer number of offsets from the offset of the largest peak value;
• calculating a sum of the differences, Diff_SUM, using:
• Diff_Sum=(right—1−peak_right—1)+(right—2−peak_right—2)+ . . . +(right—n−peak_right_n)+(left—1−peak_left—1)+(left—2−peak_left—2)+ . . . +(left—n−peak—n),
• where right_n is the peak value n offsets to the right of the largest peak value and left_n is the peak value n offsets to the left of the largest peak value;
• calculating a sum of squares, SUM_SQ, using:
• SUM_SQ=(right—1−p_right—1)2+(right—2−p_right—2)2+ . . . +(right—n−p_right—n)2+(left—1−p_left—1)2+(left—2−p_left—2)2+ . . . +(left—n−p_left—n)2
• calculating a standard deviation, STD;
• and
• indicating that the largest peak value is the main peak value if DiffAVE/STD is not less than a predetermined metric threshold.

A method for synchronizing a receiver of a bit stream to the bit stream by identifying a location of a transition in the bit stream, the method comprising:

• correlating a time sequence stream of values from a finite sample of received bits with a known sequence stream of values to generate a correlated sequence of values,
• accumulating a plurality of offset accumulation values, each corresponding to an offset in a series of time intervals within the correlated sequence, starting with a first time period, each accumulation value accumulating a number of values equal to a number of samples in a bit period, the number of values accumulated by each accumulator of the plurality of offset accumulators being a set of values in the correlated sequence starting with a value at the offset corresponding to the accumulator;
• calculating respective magnitude values for each of the calculated accumulation values;
• calculating a plurality of non-coherent summation values each corresponding to one of the offsets, the plurality of non-coherent summation values being respective sums of the magnitude values received for each offset in each bit period for all of the N bits;
• and
• analyzing the total sum of magnitudes for each offset for the highest sum of magnitudes, such that the offset corresponding to the non-coherent summer with the highest sum of magnitudes represents the location of the bit transition in the bit period.

A method for synchronizing a receiver of a bit stream to the bit stream by identifying a bit transition in a bit period, the method comprising:

• generating a correlated sequence of values by correlating a time sequence stream of values from a finite sample of received bits with a known sequence stream of values;
• accumulating a plurality of offset accumulation values, each corresponding to an offset in a series of time intervals within the correlated sequence, starting with a first time period, by accumulating a number of values equal to a number of samples in a bit period, the number of values accumulated to form each accumulation value being a set of values in the correlated sequence starting with the value at the offset corresponding to the offset accumulation value;
• calculating a plurality of power magnitude values from respective ones of the plurality of offset accumulation values;
• non-coherently summing the plurality of power magnitude values to provide respective sum-of-magnitude values, each sum-of-magnitude value corresponding to a respective offset;
• and
• analyzing the plurality of sum-of-magnitude values for a highest sum of magnitude value, such that the offset corresponding to the highest sum of magnitude value represents the location of the bit transition in the bit period.