Phase rotation estimation

Apparatus, systems, and methods are described that implement techniques for estimating a relative rotation between a first complex signal and a second complex signal. In apparatus form, a rotation-estimation circuit includes a first quadrant detector and receives the first and second complex signals and produces an estimate of the relative rotation between the complex signals. A variable rotator receives the estimate of the relative rotation and rotates at least one of the first and second complex signals using the estimate of the relative rotation. In method form, a first quadrant estimate is calculated that corresponds to the relative rotation between the first and second complex signals, and at least one of the first and second complex signals is rotated using the quadrant estimate of the relative rotation.

BACKGROUND

The following disclosure relates to electrical circuits and signal processing.

Aligning the phases of two or more signals in a communication system can be useful. The signals can be information signals at multiple points in a signal path. For example, in a communications system that uses feedback, the phase of a feedback signal may need to be aligned with the phase of a forward path signal for the system to operate correctly or efficiently. Aligning two signals is equivalent to making the relative rotation between the signals substantially zero.

A relative rotation (for example, between two complex signals) can have several causes. In a conventional application, a first complex signal can be used to modulate a radio-frequency (RF) carrier. The modulated carrier, an RF signal, undergoes analog processing, after which the modulated carrier can be demodulated. A second complex signal results from the demodulation. Any difference in phase between the modulated carrier before the processing and the modulated carrier after the processing is manifested as a relative rotation between baseband constellations corresponding to the first and second complex signals.

An example of a component in a communications system that uses feedback is a Cartesian feedback transmitter. In a conventional Cartesian feedback transmitter, a complex feedback signal is subtracted from a complex input signal to produce a complex error signal. The complex error signal is amplified and filtered to produce an intermediate signal, which is then modulated for transmission. The modulated signal is also demodulated in the transmitter to produce the complex feedback signal. Using Cartesian feedback in a transmitter improves the linearity of the transmitter, but properly aligning the phases of the complex intermediate signal and the complex feedback signal is important for stable operation.

The complex feedback signal typically has a different phase than the complex intermediate signal because of, for example, delays in the RF signal path or a phase difference between the oscillator signal used during modulation and the oscillator signal used during demodulation. A change in output power level or a change in carrier frequency can also cause a relative rotation between the complex intermediate signal and the complex feedback signal. The phase of the complex intermediate signal can be adjusted (e.g., by using a rotator circuit) to align the complex intermediate signal and the complex feedback signal. The adjustment of the phase of the complex intermediate signal can be controlled based on, for example, an estimate of the relative rotation between the complex intermediate signal and the complex feedback signal.

One technique that can be used to estimate the phase difference between the complex intermediate signal and the complex feedback signal is to multiply the in-phase component of the complex intermediate signal (Ifwd) by the quadrature component of the complex feedback signal (Qfb) and to multiply the quadrature component of the complex intermediate signal (Qfwd) by the in-phase component of the complex feedback signal (Ifb), all multiplication being done in the analog domain. The second product (QfwdIfb) is then subtracted from the first product (IfwdQfb), and the result is integrated. A rotator circuit can use the integrated result to rotate the phase of the complex intermediate signal with respect to the complex feedback signal.

SUMMARY

Apparatus, systems, and methods are described that implement techniques for estimating a relative rotation between a first complex signal and a secon complex signal.

In apparatus form, a rotation-estimation circuit includes a first quadrant detector and receives the first and second complex signals and produces an estimate of the relative rotation between the complex signals. A variable rotator receives the estimate of the relative rotation and rotates at least one of the first and second complex signals using the estimate of the relative rotation.

In method form, a first quadrant estimate is calculated that corresponds to the relative rotation between the first and second complex signals, and at least one of the first and second complex signals is rotated using the quadrant estimate of the relative rotation.

The techniques described herein can be implemented to realize one or more of the following advantages. A phase difference between two complex signals is estimated quickly and accurately. The output of the technique can be used as a preset for a conventional phase alignment loop. The technique simplifies hardware and/or arithmetic operations used for fast and accurate phase estimation.

These general and specific aspects may be implemented using an apparatus, a method, a system, or any combination of apparatus, methods, and systems.

DETAILED DESCRIPTION

FIG. 1shows a feedback transmitter200, hereafter referred to as transmitter200. Transmitter200receives a complex input signal201from, for example, a baseband circuit and subtracts a complex feedback signal202from complex input signal201. A summer210subtracts an in-phase component204of complex feedback signal202from an in-phase component206of complex input signal201to produce an in-phase component203of a complex error signal207. A summer215subtracts a quadrature component212of complex feedback signal202from a quadrature component214of complex input signal201to produce a quadrature component205of complex error signal207. Filter218filters in-phase component203of complex error signal207to produce an in-phase component208of a complex forward path signal209and filter219filters quadrature component205of complex error signal207to produce a quadrature component216of complex forward path signal209. Filters218and219provide a gain to complex error signal207. Any of complex input signal201, complex feedback signal202, complex error signal207, and complex forward path signal209can be a continuous-time signal or a discrete-time signal.

A signal path rotator230receives in-phase component208and quadrature component216of complex forward path signal209and rotates complex forward path signal209responsive to a rotation signal222, which is an estimate of the relative rotation between complex feedback signal202and complex forward path signal209, to produce a complex rotated signal211. Rotator230can rotate the phase of complex forward path signal209by computing an in-phase component232of complex rotated signal211and a quadrature component234of complex rotated signal211as weighted sums of in-phase component208and quadrature component216of complex forward path signal209. In one implementation, rotator230rotates the phase of complex forward path signal209by shifting the phase of first local-oscillator signals236and238relative to the phase of second local-oscillator signals262and266. In another implementation, rotator230rotates the phase of complex feedback signal202by shifting the phase of second local-oscillator signals262and266relative to the phase of first local-oscillator signals236and238. In one implementation, rotator230is placed in the feedback path of transmitter200(e.g., between summers210and215and mixers260and266), and rotator230rotates complex feedback signal202instead of complex forward path signal209. Alternatively, in one implementation, rotator230can be placed anywhere in the baseband signal path to the right of or below summers210and215.

A mixer240mixes in-phase component232of complex rotated signal211with a first in-phase local-oscillator signal236and a mixer245mixes quadrature component234of complex rotated signal211with a first quadrature local-oscillator signal238to produce a modulated signal247. Modulated signal247is amplified by a power amplifier250and is transmitted by antenna255. A mixer260receives a modulated signal258that corresponds to the signal transmitted by antenna255. Mixer260mixes modulated signal258with a second in-phase local-oscillator signal262to produce in-phase component204of the complex feedback signal202. A mixer265also receives modulated signal258and mixes modulated signal258with a second quadrature local-oscillator signal266to produce quadrature component212of complex feedback signal202. Complex feedback signal202typically has a different phase than complex rotated signal211because of, for example, delays in the signal path (e.g., the signal path between the outputs of mixers240and245and the inputs of mixers260and265) or a phase difference between the local-oscillator signals (i.e., first local-oscillation signals236and238) provided to mixers240and245and the local-oscillator signals (i.e., second local-oscillator signals262and266) provided to mixers260and265. All sources of relative rotation between complex feedback signal202and complex rotates signal211can be modeled (e.g., by the phase φ in second local-oscillator signals262and and266) as being caused by a phase difference between first local-oscillator signals236and238and second local-oscillator signal262and266. Complex feedback signal202is provided to summers210and215.

A rotation estimator270receives in-phase component204and quadrature component212of complex feedback signal202and in-phase component208and quadrature component216of complex forward path signal209and generates rotation signal222, which is an estimate of the relative rotation between complex feedback signal202and complex forward path signal209. Generating rotation signal222quickly and accurately is beneficial. A preset circuit can preset the value of rotation signal222to increase the speed and accuracy of rotation estimator270.

As shown inFIG. 2, rotation estimator270includes a phase aligner272and a preset circuit274. Phase aligner272includes a multiplier276that receives in-phase component204and quadrature component212of complex feedback signal202and in-phase component208and quadrature component216of complex forward path signal209. Multiplier276generates combination signals278and279and provides combination signals278and279to a combiner280. Combination signal278results from multiplying quadrature component212of complex feedback signal202and in-phase component208of complex forward path signal209. Combination signal279results from multiplying in-phase component204of complex feedback signal202and quadrature component216of complex forward path signal209. Combiner280subtracts combination signal279from combination signal278to produce a phase error signal281(IfwdQfb−QfwdIfb). A gain block282amplifies the phase error signal281and provides the amplified signal283to an integrator284. Integrator284integrates amplified signal283and generates rotation signal222, which is a representation of the relative rotation between complex feedback signal202and complex forward path signal209. Integrator284receives a preset signal288and an enable signal291from the preset circuit274.

Preset circuit274includes a segment detector286that receives the in-phase and quadrature components of the complex forward path signal209and the complex feedback signal202. Segment detector286receives an enable signal292and generates a timer signal294and preset signal288. Enable signal292can be controlled by an external controller (not shown) that controls the operation of segment detector286. Preset signal288allows integrator284to be preset to a specific value, which in turn causes rotation signal222to have a specific value. Timer signal294can be used to keep phase aligner272idle while preset circuit274is activated to generate preset signal288. After the segment estimation is complete and preset signal288is generated, timer signal294is de-asserted, and phase aligner272can be operated while preset circuit274is kept idle.

As shown inFIG. 3, segment detector286includes control-path rotators302(1)-302(N), quadrant detectors304(1)-304(N) and a fine phase detector306. Each control-path rotator302(1)-302(N) receives complex forward path signal209and can receive a rotation angle signal303(1)-303(N). Each control-path rotator302(1)-302(N) generates a rotated forward path signal308(1)-308(N) that is rotated by an angle set by the corresponding rotation angle signal303(1)-303(N). In one implementation, each control-path rotator302(1)-302(N) rotates complex forward path signal209by a preset angle, and control-path rotators302(1)-302(N) do not receive rotation angle signals303(1)-303(N). In another implementation, each control-path rotator302(1)-302(N) rotates complex feedback path signal202instead of complex forward path signal209. The number of control-path rotators can range from one to an arbitrarily large number. The rotation angle of each control-path rotator302(1)-302(N) typically is unique (that is, no two control-path rotators have the same rotation angle). The rotation angle (θi) of each control-path rotators302(1)-302(N) can be an arbitrary angle such that (θmin)≦θi≦(θmin+2π) radians. The value of θmincan be, for example, π/(2N). For certain values of θi, such as 0, π/2, π, and 3π/2, rotation can be achieved by a simple wire connection.

Rotated forward path signals308(1)-308(N) and complex feedback path signal202optionally can be filtered by filters312(1)-312(N),314(1)-314(N),316, and318. Filters312(1)-312(N) and314(1)-314(N),316, and318can, for example, remove a direct-current (DC) component or noise from the corresponding signal. Quadrant detectors304(1)-304(N) received (filtered) rotated forward path signals308(1)-308(N) and (filtered) complex feedback signal202. Enable signal292and a timer signal326are combined by AND gate324and provided to quadrant detectors304(1)-304(N) as an enable signal322. Timer signal326is also directly provided to quadrant detectors304(1)-304(N). Quadrant detectors304(1)-304(N) create quadrant estimates320(1)-320(N) and provide the quadrant estimates to fine phase detector306. Quadrant estimates320(1)-320(N) indicate the rotation between rotated forward path signals308(1)-308(N) and feedback signal202with a resolution of π/2 radians. The rotation between the signals is given by φ−θi, and each of quadrant estimates320(1)-320(N) can be:0 if {0≦φ−θi≦π/2},1 if {π/2≦φ−θi≦π},2 if {π≦φ−θi≦3π/2}, and3 if {3π/2≦φ−θi≦2π}.

Segment detector286can be implemented with just one (N=1) quadrant detector304(1), which can produce a quadrant estimate320(1) of the rotation between the complex forward path signal209and the complex feedback signal202. Segment detector286can also be implemented with one control-path rotator302(1) having a non-zero rotation angle coupled to one quadrant detector304(1).

Fine phase detector306creates an error signal330and the preset signal288, which is a segment estimate of the relative rotation between complex feedback signal202and forward path signal209. Fine phase detector306can identify a common overlap segment of the N rotated forward path signals308(1)-308(N). Fine phase detector306can receive rotation angle signals303(1)-303(N) and can be implemented as a lookup table. For example, if two quadrant detectors are used, fine phase detector306can identify a common overlap segment SD using the following table:

SD ValueQd2= 0Qd2= 1Qd2= 2Qd2= 3Qd1= 012errorerrorQd1= 1error34errorQd1= 2errorerror56Qd1= 30errorerror7
The preset signal288can be calculated as φ′=(SD=0.5)*π/4. The “error” conditions in the table represent non-overlapping quadrant estimates, and fine phase detector306can assert error signal330when a non-overlapping set of quadrant estimates is observed. Error signal330can be used to re-initiate the segment estimation operation, or can be used to trigger a default safe mode of operation.

In one implementation, fine phase detector306is implemented using arithmetic and logic operations such as comparisons, addition, subtraction, multiplication, and division. If only one quadrant detector304(1) is used, fine phase detector306can be omitted, and the quadrant estimate320(1) of quadrant detector304(1) can be used directly as the preset signal288.

FIG. 4shows a digital implementation of a quadrant detector400(e.g., one of quadrant detectors304[1]-304[N] fromFIG. 3). An in-phase component313of a rotated version of complex forward path signal209(e.g., signal308[1]) is provided to a comparator410, and a quadrature component315of the rotated version of complex forward path signal209is provided to a comparator414. The (filtered) in-phase component317of the complex feedback signal202is provided to a comparator416, and the (filtered) quadrature component319of the complex feedback signal202is provided to a comparator412. In one implementation, comparators410,412,414, and416compare the respective input signals to ground and output synchronous one-bit quantized representations of the input signals. The outputs of comparators410,412,414, and416represent the signs of the respective input signals. Hereafter, when the output from comparators410,412,414, or416is discussed, a positive output will be referred to as a 1, and a negative output will be referred to as a −1. In an alterative implementation, the components313,315,317, and319are quantized with higher resolution than one bit, and other components in quadrant detector400are correspondingly more complex.

A quantized in-phase component of the rotated forward path signal418aand a quantized quadrature component of the feedback signal418dare provided to an exclusive-OR (XOR) gate420. A quantized quadrature component of the rotated forward path signal418band a quantized in-phase component of the feedback signal418care provided to an XOR gate425. The quantized in-phase component of the forward path signal418aand the quantized in-phase component of the feedback signal418care also provided to an XOR gate450, while the quantized quadrature component of the forward path signal418band the quantized quadrature component of the feedback signal418dare provided to an XOR gate455. XOR gates420,425,450, and455perform an exclusive-OR logic operation on their respective input signals. The input signals can have a positive value (1) or a negative value (−1). The outputs of each of XOR gates420,425,450, and455in the sign-inverted, scaled, and shifted product of the two respective input signals. For example, when both input signals to an XOR gate are 1 or both are −1, the output of the XOR gate is low (0). When one input signal is −1 and one input signal is 1, the output of the XOR gate is high (1).

The output signal422of XOR gate420is provided to an integrator470, and the output signal423of XOR gate425is scaled by −1 and provided to integrator470. The output signals452and457of XOR gates450and455are provided to an AND gate460and an AND gate465. The inputs of AND gate460are both inverting inputs. The output signal462of AND gate460is provided to an integrator472, and the output signal466of AND gate465is scaled by −1 and provided to integrator472.

Integrator470receives output signals422and423and an enable signal322and produces an integrated signal474representing the sine of the angle between the rotated version of complex forward path signal209and complex feedback signal202. The sine of the angle is given by the equation sin(φ−θr)=(IrQfb−QrIfb), where φ is the angle between complex forward path signal209and complex feedback signal202, and θris the angle of rotation (relative to complex forward path signal209) of the rotated version of complex forward path signal209that is provided to comparators410and414. Integrator472receives output signals462and466and enable signal322and produces an integrated signal476representing the cosine of the angle between the rotated version of complex forward path signal209and complex feedback signal202: cos(φ−θr)=(IrIfb+QrQfb). When timer signal326is deasserted, the most significant bits (the sign bits) of integrated signal474and integrated signal476are provided to a look up table478. Look up table478produces quadrant estimate480. In a noiseless system, the integrators470and472can be omitted, and an instantaneous quadrant estimate can be formed by taking the signs of the sine and the cosine of the angle between the rotated version of complex forward path signal209and complex feedback signal202: sgn(sin(φ−θr)) and sgn(cos(φ−θr)).

A quadrant detector can also be implemented using analog circuitry. Analog multipliers, summers, and/or integrators can be used to produce a quadrant estimate.

FIG. 5is a flowchart of a process500for estimating a rotation between two complex signals, for example, a complex forward path signal and a complex feedback signal. The complex forward path signal optionally is rotated (step510) by one or more rotation angles, and the rotated signals are compared to the complex feedback signal. Rotating the complex forward path signal can change a quadrant in which the complex feedback signal falls relative to the rotated signal. That is, if a set of axes are always aligned with the rotated signal, changing the rotation angle will change the position, relative to the axes, of a vector representing the complex feedback signal. If the rotation angle is changed by more than π/2, the vector representing the complex feedback signal will fall in a different quadrant of the space defined by the axes than the quadrant in which the vector began. For example, if the complex feedback signal has a rotation of 3π/4 relative to the forward path signal, the complex feedback signal will fall in a first quadrant of a plane whose axes are aligned relative to the complex forward path signal. If the complex forward path signal is rotated by −π/2, the complex feedback signal will fall in a second quadrant of a plane whose axes are aligned relative to the rotated signal. The quadrants in which the complex feedback signal lies relative to each rotated signal and/or relative to the complex forward path signal are computed (step520).

When multiple quadrant estimates are computed, the quadrant estimates optionally can be combined into a segment estimate (530). The segment estimate can be formed, for example, by comparing the overlap of the quadrant estimate when each quadrant estimate is translated back to a plane whose axes are aligned relative to the forward path signal. If the number of quadrant estimates is large and the quadrant estimates are relatively noise-free, a very accurate estimate of the rotation between the complex forward path and complex feedback signals can be obtained. The quadrant estimates and/or segment estimate optionally can be used to preset an estimate of the rotation (step540) that is used, for example, by a phase alignment circuit to control a rotator in the forward path or the feedback path. One or both of the complex forward path signal and the complex feedback signal can be rotated by adjusting the phase of the signal using the estimate of rotation (step550). In one implementation, the quadrant estimate and/or segment estimate can be used directly as the estimate of rotation.

FIG. 6shows an alternative implementation of rotation estimator270. The rotation estimator600shown inFIG. 6reuses components to implement a phase aligner and a preset circuit. Rotation estimator600operates in either a phase alignment mode or a preset mode, depending on the state of a mode signal610, which can be controlled by a timer. A rotator block605receives components208and216of the forward path signal209and the mode signal610. When the mode signal610is high, a multiplexer655selects an angle signal657(θstart) to be used as rotation signal222. Angle signal657can be selected by a user, hardwired, or computed during the operation of rotation estimator600. If angle signal657correctly reflects the rotation between complex forward path signal209and complex feedback signal202, rotation estimator600will leave the angle signal657unaltered. If angle signal657is incorrect, rotation estimator600will calculate a correction and add the correction to the angle signal657using a combiner680. When the mode signal610is high, the phase alignment actions of rotation estimator600are disabled and rotator block605rotates complex forward path signal209by 45°. When mode signal610is high, rotation estimator600uses combiners625and630, integrators635and640, and look up table670to generate a segment estimate675. The combination of combiners625and630, integrators635and640, and look up table670functions as a quadrant detector. When mode signal61o is low, rotator block605does not rotate complex forward path signal209. When mode signal610is low, the multiplexer655selects an output645of integrator635to be used as rotation signal222, and rotation estimator600acts as a phase aligner. Rotation estimator600allows a phase alignment loop to operate with a starting preset value that is established by the sum of segment estimate675and angle signal657.

FIG. 7shows another alternative implementation of rotation estimator270. In a rotation estimator700, a segment detector705is used without a phase alignment system to generate rotation signal222. A segment estimate710is stored in a register715and is used directly as rotation signal222instead of being used as a preset for a phase alignment system. A system that requires only a coarse phase alignment can be implemented using rotation estimator700. The number (N) of rotators and quadrant detectors included in segment detector705can be chosen such that the resolution of the segment estimate710is sufficient for the application. Segment detector705can be enabled as frequently as necessary to adjust for any misalignment caused by time varying effects such as drift.

The invention and all of the functional operations described in this specification can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combination of them.

The invention has been described in terms of particular embodiments. Other embodiments are within the scope of the following claims. The described apparatus and method can be used in many different types of digital or analog systems. For example, the apparatus or method can be used in any electronic communication system whose complex signal path includes at least two points between which phase alignment is useful for operation. In addition, the apparatus can be modified and placed at various points in a communications system while still operating substantially as described.