Phase rotation of signals

Abstract: Phase rotation of an input digital signal is effected by applying the input signal (I,Q) to a look-up table (l2) in a memory together with a rotation control signal (R). The output of the memory (I′,Q′) is the phase rotated signal. To reduce the size of the PROM required for the look-up table advantage is taken of the symmetry of the quadrants through which the signal may be rotated. With a maximum 0° to 360° phase rotation range divided into four 90° quadrants a look-up table (l2) is only required for one quadrant. Thus the quadrant which the input signal is in is determined and the input signal transformed to correspond to the one quadrant by simple logic (l0,ll,l3,l4,l5) external to the PROM (l2).

Description: This invention relates to a method and means for effecting phase rotation of signals and is especially useful in electronic navigation systems. A recent development in navigation is a system known as NAVSTAR, utilising a number of earth satellites. The complete Navstar system is planned to consist of 18 satellites arranged in nearly circular orbits with radii of 26,600Km, and an inclination to the earth's equatorial plane of 55°. Each satellite transmits two navigation signals, designated L1 and L2 and centred on 1575 and 1228 MHz respectively. Both signals convey ranging information by means of modulations which are locked in time to atomic standards. The forms of these modulations (which are known as pseudorandom codes because they appear random but are nevertheless well defined) are unique to each satellite. By measuring the phases of the received codes against a clock in the receiver, together with the Doppler shifts of the radio frequency carriers, a user can calculate the range and range rate to a particular satellite by monitoring four satellites. By decoding data about their motions which are also modulated onto the transmitted signals, the user may solve equations to determine his three-dimensional position and velocity and also apply corrections to his clock, making it conform to satellite time. Two pseudorandom codes are in fact transmitted by each satellite. The first of these is used to aid acquisition of the satellite signals and to provide coarse navigation, and hence is called the Coarse/Acquisition (C/A) code. The second has a 10-times higher modulation rate which yields the full navigational accuracy of the system, and is designated the Precision (P) code. A basic Navstar receiver typically contains a low-noise amplifier and down-converter to a convenient IF, followed by one or more code and carrier tracking channels, each capable of tracking the transmissions from any satellite. There are also associated range and range-rate measurement circuits. The purpose of the code tracking loop is to keep a code generator in the receiver in step with a received pseudorandom sequence, and hence provide information on the range to the satellite being tracked. One implementation of a Navstar receiver, as disclosed in British patent specification GB-A-2 131 177, includes amplification of the received r.f. signals and down conversion to i.f. frequencies to produce quadrature signals; analogue-to-digital converters to digitise separately the quadrature signals; local digital code generating means; means for correlating the digitised quadrature signals separately with the same locally generated digital codes; channel processing means to which the outputs of the correlation means are applied, the processing means being arranged to control the code and carrier tracking of the receiver; and correction means responsive to control signals generated in the processing means to effect phase rotation of the baseband signal phasor represented by the quadrature signals to effect Doppler tracking in the receiver loop. Any Doppler shift will cause the phasor to rotate and by removing this rotation the Doppler shift can be tracked. To remove the phase rotation from a signal vector the latter must be multiplied by a counter-rotating unit vector. Attention is directed to European patent publication No. EP-A-0 155 776 which discusses this aspect in greater detail. The above referred to receiver implementation further includes a digital data memory means loaded with data in the form of "look-up" tables incorporating combinations of signal input combinations, means for applying the digitised quadrature signals as partial address signals for the memory means, and means for generating additional address signals for the memory means in response to control signals whereby phase rotation correction is effected by accessing the memory means in accordance with the address signals to produce an output signal for the channel signal processing means. In European patent publication No. EP-A-0 196 179 there is described a method and apparatus for effecting phase rotation which involves a transformation on the digitised I and Q vectors in order to overcome accuracy problems arising because of the compressions and truncation involved in rotating a uniformally arranged square grid of points within a square grid of requantisation boundaries. This can be implemented by incorporating a modification in the phase rotation look-up table. In particular this second Application provides a method of effecting phase rotation of a digital signal by applying said digital signal as partial address signals for a look-up table in a memory together with rotation control signals forming additional address signals whereby the memory output represents the phase rotated signal, each input vector being modified so that points representing digitised input vector values plotted on a rectangular co-ordinate grid are transformed to lie on an alternative co-ordinate system, in particular a circular system, the rotated vector magnitudes being retransformed and requantised to a digital output. Difficulties have arisen when putting the above referred to phase rotator into practice in certain cases owing to size of the PROM required for the look-up table. The present invention thus seeks to reduce the size of the PROM required for the look-up table. According to one aspect of the present invention there is provided a method of effecting phase rotation in a range of up to 360° of a digital input signal, the method including the steps of providing a memory holding a "look-up" table incorporating combinations of signal input conditions, using the digitised input signal to form partial address signals for the memory, generating additional address signals for the memory in response to control signals, whereby phase rotation of the input signal is effected by accessing the memory in accordance with both the partial address signals and the additional address signals to produce an output phase rotated signal, characterised in that the range of rotations is divided into four 90° quadrants and the "look-up" table incorporates combinations of signal input conditions for only one 90° quadrant, the method further including the steps of dividing the digitised input signal into first and second parts wherein the first part contains magnitude and vector information of the input signal and forms the partial address signals used to access the memory and the second part contains information as to which quadrant the input signal is in, decoding said quadrant information to provide a quadrant transforming control signal and transforming or not said first part of said input signal in response to said quadrant transforming control signal to provide the partial address for the "look-up" table in the memory. According to another aspect of the present invention there is provided apparatus for effecting phase rotation in a range up to 360° of a digitised input signal, the apparatus including a digital data memory means loaded with data in the form of "look-up" tables incorporating combinations of signal input conditions, means for using the digital input signal to form partial address signals for the memory means, means for generating additional address signals for the memory means in response to control signals whereby phase rotation of the input signal is effected by accessing the memory means in accordance with both the partial address signals and the additional address signals to produce an output phase rotated signal, characterised in that the range of rotation up to 360° is divided into four 90° quadrants and the memory means is loaded with "look-up" data for only one 90° quadrant, the apparatus further including means for dividing the digitised input signal into first and second parts wherein the first part contains magnitude and vector information of the input signal and forms the partial address signals used to address the memory means and the second part contains information as to which quadrant the input signal is in, means for decoding said quadrant information to provide a quadrant transforming control signal, and means for transforming or not said first part of said input signal in response to said quadrant transforming control signal to provide the partial address for the "look-up" table in the memory means. Embodiments of the invention will now be described with reference to the accompanying drawings, in which Fig. 1 illustrates highly schematically a known phase rotator; Fig. 2 illustrates phase rotation and the four quadrants in which it can take place; Fig. 3 illustrates a block diagram of one embodiment of phase rotator according to the present invention; Fig. 4 illustrates a block diagram of another embodiment of phase rotator according to the present invention; Fig 5 illustrates in block form the functions of the PROM of Fig. 4, and Fig. 6 illustrates I/Q transformation. The phase rotator described in the aforementioned Applications for the digital Navstar receiver is used to close the carrier loop providing phase corrections to the digitised I and Q samples from the zero IF. One proposed configuration uses, say, 3 bits each of I and Q samples with 6 bits of phase rotation, giving 3 bits of I and Q as output. This leads to implementation as a 4K × 8 bit PROM look-up table as illustrated in Fig. 1. The input vector description of.I and Q is rotated by a rotation angle R (Fig. 2). All possible I and Q vector combinations are coded into 3 bits of I and 3 bits of Q. The rotation vector is a 6 bit quantisation of the complete rotation required (360°), giving a 5.265° quantisation (5.265° is assumed to be the minimum phase angle). For a given I and Q input vector and a given rotation angle, there is a unique output answer which is the rotated solution. The phase rotation input of Fig. 1 is a rotation word from a numerically controlled oscillator (NCO). A channel processor (not shown) calculates the rotation frequency to be applied to correct the Doppler loss in the received signal. This rotation frequency is fed to the NCO which derives the phase rotation angle R which is described by the rotation word and required to effect the necessary phase rotation of the signal vector. Whereas such an arrangement is not wholly impracticable for 3 bits of I and Q values, it is impracticable for 4 bits of I and Q values. In any event reduction in size of the PROM would be desirable even for 3 bits of I and Q values. The present invention is based on the realisation that there is symmetry of the rotation operation and that this can be taken advantage of to reduce the size of the look-up table. In particular the look-up table size may be reduced by examining the rotation operation and eliminating the duplication of quadrant information in the table by suitable combinations logic, this reduces the phase look-up to a single quadrant. Thus the look-up of one quadrant is performed by the PROM and this is then transferred for the other quadrants by external logic. The quadrant which the input vector is in is determined by looking at the sign bits of the I and Q components after removing them from the I and Q sub-quadrant information. For 3 bits of I and Q values there are 2 bits of I and Q magnitude and 1 bit of sign. Referring to Fig. 2 the quadrants are labelled 1, 2, 3 and 4. The sign bits are decoded into input quadrant information which is used to determine if the remaining I and Q inputs should be swapped in order to reference the angle to 0° before application to the PROM, as indicated below. If quadrant = 1 (i.e. I and Q+ve) then do nothing If quadrant = 2 (i.e. I-ve, Q+ve) then swap I,Q If quadrant = 3 (i.e. I-ve, Q-ve) then do nothing If quadrant = 4 (i.e. I+ve, Q-ve) then swap I,Q The block circuit diagram of Fig. 3 is of a first embodiment of phase rotator according to the present invention and for 3 bits of I and Q values. The circuit includes an I/Q swapper 10, a sign (quadrant) decoder 11, a look-up PROM 12, a module 5, adder 13, an output quadrant decoder (I/Q sign swap) 14, and another I/Q swapper 15. The phase rotation input (rotation word) R is of 6 bits which is split into 4 bits of sub-quadrant angle information R s that is applied to the look-up PROM 12 and 2 bits of (rotation) quadrant information R q that is applied to the module 5 adder 13. The I and Q inputs of 3 bits are split into 2 bits of magnitude which are applied to the I,Q swapper 10 and 1 bit of sign which are applied to the sign decoder 11 which determines which quadrant 1, 2, 3 or 4 the input values are in (input quadrant information) and whether or not I and Q need to be swapped in accordance therewith. If swapping is necessary this is attended to by the I,Q swapper 10. The input quadrant information as determined by the sign decoder 11 is applied as 2 bits to the module 5 adder 13 together with the 2 bits of quadrant information from the rotation input. The result of quadrant addition in the module 5 adder 13 is P which equals 1, 2, 3 or 4 and is applied as 3 bits to the quadrant decoder 14 which is required to determine if a further I Q sign swap is necessary following phase rotation by the PROM. This is necessary if the result of the addition of the two vectors together goes into the next quadrant. The look-up PROM is loaded with look-up tables whereby the input I,Q and R s are used to address locations in the PROM and the PROM gives outputs sign I, I′ and Q′. I′ and Q′ representing the phase rotated channel signals. If sign swap of I′ and Q′ is necessary this is attended to by IQ swapper 15. The quadrant decoder 14 has outputs concerning the signs of I′ and Q′ which are combined with the outputs of the IQ swapper 15 to give 3 bit values of I′ and Q′. The quadrant addition results in a sign change in I′ and Q′ corresponding to the quadrant and/or a swap of I′ and Q′ given by the following. where  = (P-1)π/₂ where the basic algorithm used for phase rotation is I′ = I cos  - Q sin  Q′ = Q cos  + I sin  By reducing the phase look-up to a single quadrant in the example described above the PROM size is reduced from 4096 × 8 bit to 256 × 5 bit. Fig. 4 illustrates an alternative embodiment of phase rotator of the present invention and which is illustrated for 4 bit I and Q values. The circuit includes an I/Q swapper 20, a sign decoder 21, a 2 bit adder 22, a look-up PROM 23, a quadrant decoder 24 and a further I,Q swapper 25. The 4 bit I and Q inputs are divided into 3 bit magnitude and 1 bit sign. As before the signs are decoded in decoder 21 into input quadrant information which is used to determine if the remaining I and Q inputs should be swapped in swapper 20 in order to reference the angle to O°. The input quadrant information is applied to the 2 bit adder 22 together with the 2 bits of rotation quadrant information from the rotation input R. The I-Q vector is rotated by the subquadrant angle, comprising the remaining 4 bits from the rotation input R (6 bit rotation angle) in the PROM 23 which gives 3 bits each of I′ and Q′ output and a carry bit which is applied to the 2 bit adder 22. The function of the PROM 23 is indicated schematically in Fig.5. In the "transform" block the phase of each input vector is maintained but its magnitude is scaled to lie on a circle whose radius equals the maximum amplitude of I or Q. This is illustrated in Fig. 6. The I/Q points, those indicated by a small circle, are transformed in the points indicated by a dot on the quarter circle curves. Thus the I and Q inputs are mapped onto a circular pattern. The transformed inputs are then rotated (phase rotation) in the "rotate" block in accordance with the formula I′ = I cos R - Q sin R Q′ = Q cos R + I sin R where R is the subquadrant angle. The output coordinates I′,Q′ are then scaled, for example by a factor of 1.05, and quantised. If the result is greater than 90° then the "carry flag" is set (CO input of adder 22) and the output = result - 90°. The sum of the input, rotation and carry quadrants as obtained by adder 22 is then decoded in decoder 24 into I′ and Q′ signs and put back on the outputs. If the quadrant sum gives quadrant 2 or 4 (Fig. 2) then the I′ and Q′ magnitudes are swapped in swapper 25. Both the input and output quadrant decoder sections 21 and 24 can be implemented using a few gates. The required size of the PROM 23 is of the order 1K × 7 bit rather than 16K by 7 bits, in order to satisfy access times, however, the look-up table may be comprised by two 512 × 8 bit PROMS. By taking advantage of the symmetry of the rotation operation the size of the look-up table may thus be substantially reduced to approximately 4% of the previously required size. Whilst extra logic functions are required these are only simple logic functions.

Claims: A method of effecting phase rotation in a range of up to 360° of a digital input signal, the method including the steps of providing a memory (12) holding a "look-up" table incorporating combinations of signal input conditions, using the digitised input signal to form partial address signals for the memory, generating additional address signals (R) for the memory in response to control signals, whereby phase rotation of the input signal is effected by accessing the memory (12) in accordance with both the partial address signals and the additional address signals to produce an output phase rotated signal, characterised in that the range of rotations is divided into four 90° quadrants and the "look-up" table incorporates combinations of signal input conditions for only one 90° quadrant, the method further including the steps of dividing the digitised input signal into first and second parts wherein the first part contains magnitude and vector information of the input signal and forms the partial address signals used to access the memory and the second part contains information (SIGN) as to which quadrant the input signal is in, decoding (11) said quadrant information to provide a quadrant transforming control signal (SWAP) and transforming (10) or not said first part of said input signal in response to said quadrant transforming control signal to provide the partial address for the "look-up" table in the memory. A method as claimed in claim 1, characterised in that the input signal comprises inphase and quadrature components (I,Q) and the input signal quadrant is determined by consideration of the signs of the input components. A method as claimed in claim 2, characterised in that if the input signal is in the first and third quadrant relative to 0° the input signal is unaffected and if the input signal is in the second or fourth quadrants the inphase and quadrature components (I,Q) are swapped. A method as claimed in claim 3 characterised in that the output from the look-up table in the memory (12) is applied to an inphase and quadrature component swapper (15) which is operated if the phase rotation effected by the look-up table served to locate the phase rotated signal in the next quadrant. Apparatus for effecting phase rotation in a range up to 360° of a digitised input signal, the apparatus including a digital data memory means (12) loaded with data in the form of "look-up" tables incorporating combinations of signal input conditions, means for using the digital input signal to form partial address signals for the memory means, means for generating additional address signals (R) for the memory means in response to control signals whereby phase rotation of the input signal is effected by accessing the memory means in accordance with both the partial address signals and the additional address signals to produce an output phase rotated signal, characterised in that the range of rotation up to 360° is divided into four 90° quadrants and the memory means (12) is loaded with "look-up" data for only one 90° quadrant, the apparatus further including means for dividing the digitised input signal into first and second parts wherein the first part contains magnitude and vector information of the input signal and forms the partial address signals used to address the memory means (12) and the second part contains information as to which quadrant the input signal is in, means (11) for decoding said quadrant information to provide a quadrant transforming control signal (SWAP), and means (10) for transforming or not said first part of said input signal in response to said quadrant transforming control signal to provide the partial address for the "look-up" table in the memory means. Apparatus as claimed in claim 5, characterised in that the input signal comprises inphase and quadrature components (I,Q) and the decoding means (11) determines the input signal quadrant by consideration of the signs of the input components. Apparatus as claimed in claim 6 characterised in that if the input signal is in the second or fourth quadrant relative to 0° the transforming means (10) swaps the inphase and quadrature components before application to the memory means (12). Apparatus as claimed in claim 7 characterised by further transforming means (15) wherein if the phase rotation effected by the look-up table in the memory means (12) serves to locate the phase rotated signal in the next quadrant the inphase and quadrature components of the phase rotated signal are swapped.

Inventors: FEARNHEAD GRAHAM ROY, FURNACE MARK LESLIEN CYRUS, GALE SIMON JOHN, FEARNHEAD, GRAHAM ROY, FURNACE, MARK LESLIEN CYRUS, GALE, SIMON JOHN
Applicants: NORTHERN TELECOM LTD, NORTHERN TELECOM LIMITED
Application year: 1986
Main classification: G06F1
IPC codes: G06F1, G01S1