Carrier phase estimation based on single-axis constant modulus cost criterion and Bussgang criteria

Apparatus for carrier phase detection in a demodulated signal formed from a data-modulated carrier, the apparatus comprising:

• a carrier tracking loop configured to generate, from the signal, an estimate of an angle between the carrier and a locally generated reference based on a stochastic gradient of a single-axis (SA) cost function, the cost function being a Bussgang-class cost function;
• and
• a rotation combiner adapted to adjust at least one of the frequency and phase of the demodulated signal based on the angle such that the magnitude of the angle is driven toward a predetermined value, wherein:
• the carrier tracking loop comprises:
• a1) a phase detector adapted to calculate an SA cost function error term based on the demodulated signal, wherein the single-axis cost function is a single-axis constant modulus criterion JCM;
• a2) a first circuit configured to form an approximation of a derivative of the demodulated signal with respect to the angle;
• and
• a3) a rotation combiner configured to combine the SA cost function error term with the approximation to form a phase error;
• and
• a4) a second circuit configured to generate the angle from the phase error:
• and
• the phase error is the stochastic gradient of the single-axis constant modulus criterion JCM (dJCM/dθ) given by:
• dJCM/dθ=4eSA-CM[n]DT[n],
• where eSA-CM is the SA cost function error term defined by (Re{yn(θ)}2−ρ2)Re{yn(θ)}, yn(θ) is input data based on the demodulated signal, and DT[n]approximates a derivative of the demodulated signal with respect to the angle θ (d(yn(θ))/dθ).

A computer-readable medium having stored thereon a plurality of instructions, the plurality of instructions including instructions which, when executed by a processor, cause the processor to implement a method for carrier phase detection in a demodulated signal formed from a data-modulated carrier, the method comprising:

• a) generating, from the signal, an estimate of an angle between the carrier and a locally generated reference based on a stochastic gradient of a single-axis cost function, the cost function being a Bussgang-class cost function;
• and
• b) adjusting at least one of the frequency and phase of the demodulated signal based on the angle such that the magnitude of the angle is driven toward a predetermined value, wherein:
• step a) generates the estimate by:
• a1) calculating an SA cost function error term based on the demodulated signal, wherein the single-axis cost function is a single-axis constant modulus criterion JCM;
• a2) forming an approximation of a derivative of the demodulated signal with respect to the angle:
• and
• a3) combining the SA cost function error term with the approximation to form a phase error:
• and
• a4) generating the angle from the phase error:
• and
• for step a3), the phase error is the stochastic gradient of the single-axis constant modulus criterion JCM (dJCM/dθ) given by:
• dJCM/dθ=4eSA-CM[n]DT[n],
• where eSA-CM is the SA cost function error term defined by (Re{yn(θ)}2−ρ2)Re{yn(θ)}, yn(θ) is input data based on the demodulated signal, and DT[n]approximates a derivative of the demodulated signal with respect to the angle θ (d(yn(θ))/dθ).

A method of carrier phase detection in a demodulated signal formed from a data-modulated carrier, the method comprising:

• a) generating, from the signal, an estimate of an angle between the carrier and a locally generated reference based on an estimate of a gradient of a single-axis cost function, the cost function being a Bussgang-class cost function;
• and
• b) adjusting at least one of the frequency and phase of the demodulated signal based on the angle such that the magnitude of the angle is driven toward a predetermined value, wherein:
• step a) generates the estimate by:
• a1) calculating an SA cost function error term based on the demodulated signal, wherein the single-axis cost function is a single-axis constant modulus criterion JCM;
• a2) forming an approximation of a derivative of the demodulated signal with respect to the angle;
• and
• a3) combining the SA cost function error term with the approximation to form a phase error;
• and
• a4) generating the angle from the phase error;
• and
• for step a3), the phase error is a stochastic gradient of the single-axis constant modulus criterion JCM(dJCM/dθ) given by:
• dJCM/dθ=4eSA-CM[n]DT[n],
• where eSA-CM is the SA cost function error term defined by (Re{yn(θ)}2−ρ2)Re{yn(θ)}, yn(θ) is input data based on the demodulated signal, and DT[n] approximates a derivative of the demodulated signal with respect to the angle θ (d(yn(θ))/dθ).

A method of carrier phase detection in a demodulated signal formed from a data-modulated carrier, the method comprising:

• a) generating, from the signal, an estimate of an angle between the carrier and a locally generated reference based on a stochastic gradient of a single-axis (SA) cost function, the cost function being a Bussgang-class cost function, wherein step a) generates the estimate by:
• a1) calculating an SA cost function error term based on the demodulated signal;
• a2) forming an approximation of a derivative of the demodulated signal with respect to the angle;
• and
• a3) combining the SA cost function error term with the approximation to form a phase error;
• and
• a4) generating the angle from the phase error;
• and
• b) adjusting at least one of the frequency and phase of the demodulated signal based on the angle such that the magnitude of the angle is driven toward a predetermined value;
• c) generating a signal quality measure (SQM) from the received signal;
• and
• d) generating at least one other cost error term based on a corresponding cost criterion, and wherein step a) generates the angle based on the SQM.

Apparatus for carrier phase detection in a demodulated signal formed from a data-modulated carrier, the apparatus comprising:

• a carrier tracking loop configured to generate, from the signal, an estimate of an angle between the carrier and a locally generated reference based on a stochastic gradient of a single-axis (SA) cost function, the cost function being a Bussgang-class cost function, wherein the carrier tracking loop comprises:
• a1) a phase detector adapted to calculate an SA cost function error term based on the demodulated signal;
• a2) a first circuit configured to form an approximation of a derivative of the demodulated signal with respect to the angle;
• and
• a3) a rotation combiner configured to combine the SA cost function error term with the approximation to form a phase error;
• and
• a4) a second circuit configured to generate the angle from the phase error;
• a rotation combiner adapted to adjust at least one of the frequency and phase of the demodulated signal based on the angle such that the magnitude of the angle is driven toward a predetermined value;
• a signal quality measure processor configured to generate a signal quality measure (SQM) from the demodulated signal;
• and
• at least one other phase detector, each phase detector configured to generate a corresponding cost function error term based on a corresponding cost criterion, wherein the carrier tracking loop is adapted to generate the angle based on the SQM.