Method and circuitry for symbol timing and frequency offset estimation in time division multiple access radio systems

A method for obtaining a symbol timing estimate in the processing of a digital phase modulated radio signal consisting of sequential bursts of symbols, comprising the steps of:

• digitizing an intermediate frequency (IF) signal at a plurality of sampling times per symbol at a sampling rate which is a multiple of the symbol timing rate by at least a factor of four;
• processing the digitized signal to obtain in-phase and in-quadrature signals;
• converting said in-phase and in-quadrature signals to phase values at each sampling time;
• obtaining differential phase values from said phase values by introducing at least a one symbol delay and taking differences between delayed phase values and corresponding present phase values;
• collapsing said differential phase values into values between 0 and 90 degrees in the phase plane;
• expanding said collapsed differential phase values into values between 0 and 360 degrees in the phase plane;
• forming the vector sums in the phase plane of the collapsed and expanded differential phase values separately for each sampling time and substantially over the entire burst;
• and
• obtaining symbol timing by selecting from amongst the set of sampling times the particular sampling time at which the vector sum of the collapsed and expanded differential phase values has the largest magnitude.

A method of determining symbol timing in the processing of a digital phase modulated radio signal transmission consisting of sequential bursts of symbols, comprising the steps of:

• converting an intermediate frequency (IF) radio signal from a modulated sinusoid into phase values after sampling said IF radio signal at a plurality of sampling times per symbol at a rate which is a multiple of the symbol rate by at least a factor of four;
• obtaining differential phase values at each sampling time from said phase values by introducing at least a one symbol delay and taking differences between delayed phase values and corresponding present phase values;
• collapsing said differential phase values into polar values between 0 and 90 degrees in the phase plane;
• expanding said collapsed differential polar phase values into polar values between 0 and 360 degrees in the phase plane;
• converting the polar values of said expanded and collapsed differential phase values into Cartesian coordinates;
• summing separately for each sampling time and substantially over the entire burst the X Cartesian coordinates of the expanded and collapsed differential phase values, and summing separately for each sampling time and substantially over the entire burst the Y Cartesian coordinates of the expanded and collapsed differential phase values;
• for each sampling time squaring the sum of the X coordinates and squaring the sum of the Y coordinates,
• for each sampling time adding the square of the sum of the X coordinates and the square of the sum of the Y coordinates;
• and
• determining at which sampling time the sum of the square of the sum of the X coordinates and the square of the sum of the Y coordinates has the largest magnitude and using that sampling time as the time for symbol timing.

A circuit for providing a symbol timing estimate in the processing of a digital phase modulated radio signal transmission consisting of sequential bursts of symbols, comprising:

• means for digitizing an intermediate frequency (IF) signal at a plurality of sampling times per symbol at a sampling rate which is a multiple of the symbol rate by at least a factor of four;
• means for processing the digitized signal to obtain in-phase and in-quadrature signals;
• means for converting the in-phase and in-quadrature signals to phase values at each sampling time;
• delay and differencing means for introducing at least a one symbol delay and taking differences between delayed phase values and corresponding present phase values to form differential phase values;
• means for collapsing said differential phase values into values between 0 and 90 degrees in the phase plane;
• means for expanding said collapsed differential phase values into values between 0 and 360 degrees in the phase plane;
• means for forming the vector sums in the phase plane of the collapsed and expanded differential phase values separately for each sampling time and substantially over the entire burst;
• means for determining the vector sum with the largest magnitude;
• and
• means for obtaining symbol timing by selecting amongst the set of sampling times the sampling time associated with the vector sum having the largest magnitude.

A circuit for providing a symbol timing estimate in the processing of a digital phase modulated radio signal transmission consisting of sequential bursts of symbols, comprising:

• means for converting an intermediate frequency (IF) radio signal from a modulated sinusoid into phase values at a plurality of sampling times per symbol at a sampling rate which is a multiple of the symbol rate by at least a factor of four;
• delay and differencing means for introducing at least a one symbol delay and taking differences between delayed phase values and corresponding present phase values;
• means for collapsing said differential phase values into one quadrant in the phase plane;
• means for expanding said collapsed differential phase values into a full 360 degree polar phase plane;
• means for forming the vector sums in the phase plane of the collapsed and expanded differential phase values separately for each sampling time and substantially over the entire burst;
• means for determining the vector sum with the largest magnitude;
• and
• means for obtaining symbol timing by selecting amongst the set of sampling times the sampling time associated with the vector sum having the largest magnitude.

A circuit for determining symbol timing in the processing of a digital phase modulated radio signal transmission consisting of sequential bursts of symbols, comprising:

• means for converting an intermediate frequency (IF) radio signal from a modulated sinusoid into phase values after sampling said IF radio signal at a plurality of sampling times per symbol at a rate which is a multiple of the symbol rate by at least a factor of four;
• delay and differencing means for introducing at least a one symbol delay and taking differences between delayed phase values and corresponding present phase values;
• means for collapsing said differential phase values into polar phase values between 0 and 90 degrees in the phase plane;
• means for expanding said collapsed differential phase values into polar values between 0 and 360 degrees in the phase plane;
• means for converting the polar values of said expanded and collapsed differential phase values into Cartesian coordinates;
• first summing means for summing separately for each sampling time and substantially over the entire burst the X Cartesian coordinates of the expanded and collapsed differential phase values [.SIGMA.X];
• second summing means for summing separately for each sampling time and substantially over the entire burst the Y Cartesian coordinates of the expanded and collapsed differential phase values [.SIGMA.Y];
• first squaring means for squaring for each sampling time the sum of the X coordinates [(.SIGMA.X).sup.2 ];
• second squaring means for squaring for each sampling time the sum of the Y coordinates [(.SIGMA.Y).sup.2 ];
• adding means for forming a vector sum for each sampling time by adding the square of the sum of the X coordinates and the square of the sum of the Y coordinates [(.SIGMA.X).sup.2 +(.SIGMA.Y).sup.2 ];
• means for determining which vector sum has the largest magnitude;
• means for determining symbol timing as that sample time associated with the vector sum with the largest magnitude.