FR2670967A1 - A method and a device for recovering a carrier - Google Patents

Abstract

A method of recovering a carrier for modulations with several phase states, especially QPSK modulations, in which received symbols S, consisting of first codes X, Y are made to undergo a non-linear conversion in conversion means (20, 30, 50, 60) in order to supply an instantaneous phase-shift angle for a particular symbol, and the instantaneous phase-shift angles obtained are accumulated (70) for the various symbols preceding the particular symbol in order to supply an estimated phase angle Theta est, so as to calculate the codes X est, Y est constituting the particular symbol, decided on the basis of the first codes X, Y of the delayed particular symbol and of the said estimated phase angle in order to correct a phase offset in the carrier. A device for implementing the said method.

Description

A RECOVERY METHOD AND DEVICE
OF A CARRIER
The field of the invention is that of communication systems, more particularly satellite communication systems, using the transmission of digital data by pulse. Such communication systems also use multiple access techniques by time division of pulses. In multiple access systems by time division of pulses, the phase estimation on each successive pulse is a necessity because we use modulations with several phase states designated by the initials m-PSK (m Phase
Shift Keying), for example a modulation of the QPSK (Quadrature Phase shift Keying) type to optimize the spectral efficiency. The invention relates more particularly to a method of recovering a carrier for such modulations. The invention extends to a device for implementing such a method.

The article "Nonlinear Estimation of PSK Nodulated Carrier Phase With Application to Burst
Digital Transmission "by A. VITERBI published in the journal IEEE TRANSACTIONS ON INFORMATION THEORY, Vol IT29, N" 4, July 1983 describes a device and a method of carrier recovery for modulations with m phase states to overcome the drawbacks of the techniques carrier recovery based on a phase locked loop.

This known method is based on the use of a non-linear estimation technique of the carrier phase.

Referring to Figure 1A, the symbols
S decoded by the receiver, after quadratic demodulation, consist of first codes X, Y expressed in the form of Cartesian coordinates. The successive codes X, Y constitute the two binary trains originating from the filters (not shown) of the receiver.

The first codes X, Y are passed through non-linear transformation means to provide second codes X1, Y1 expressed in the form of Cartesian coordinates. In the case of a quadratic demodulation with four phase states, the first codes
X, Y expressed in Cartesian form are successively transformed into polar coordinates and again into Cartesian coordinates (20, 40) through a non-linear transformation (30), including the elevation to an integer of the first polar coordinate and multiplying by four the second polar coordinate before the transformation of polar coordinates to Cartesian coordinates, to provide second codes X1, Y1 expressed in the form of Cartesian coordinates. The second codes X1, Y1 are stored in memory means 50, for a predetermined number L of symbols S defining a phase estimation interval centered on a particular symbol, to supply third codes X1 avg,
Yl ~ avg respectively representative of an average of said second stored codes. In parallel with this storage, the symbols S are delayed in a delay means (90) from the particular symbol.

The third codes Xl ~ avg, Y1 avg are then converted into polar co-ordinates in a calculation means (60) to provide an instantaneous phase shift angle
Theta ~ inst. A correction means (80) finally calculates fourth codes X ~ is, Y ~ is constituting the particular symbol decided from said instantaneous phase shift angle and said first codes constituting the particular symbol for correcting a phase difference of the carrier.

 Consequently, the phase shift angle Theta ~ inst brings the constellation back to the correct position for the decision-making of a particular symbol.

 However, this known method only corrects substantially constant and small phase differences between the transmit carrier frequency and the receive carrier frequency. In the case where this phase difference changes over time, for example cumulatively, the VITERBI method does not allow tracking beyond the first quadrant [0, Pi / 2] of the trigonometric circle. In fact, the instantaneous phase shift angle corresponds to the instantaneous phase shift measured between a particular symbol and the previous symbol.

Consequently, this carrier recovery method is not suitable for correcting phase jumps greater than Pi / 2 and frequency differences between the transmission frequency and the reception frequency which are cumulative.

The object of the present invention is to overcome this drawback. To this end, the invention proposes a method for recovering a carrier for modulations with several phase states, in particular QPSK modulations, in which
- symbols S received, made up of first codes X, Y expressed in the form of Cartesian coordinates, are subjected to a nonlinear transformation to provide second codes X1, Y1 expressed in the form of Cartesian coordinates,
said second codes are memorized for a predetermined number L of symbols S defining a phase estimation interval centered on a particular symbol, in order to provide third codes Xl ~ avg, Y1 avg respectively representative of an average of said second memorized symbols,
- an instantaneous phase shift angle Theta ~ inst relative to said particular symbol is calculated from said third codes,
characterized method in that it further comprises the following steps:
- the instantaneous phase shift angles are successively cumulated to provide an estimated phase angle Theta ~ east and fourth codes X is calculated, Y ~ is constituting the particular symbol decided from the first codes constituting said symbol considered delayed and said angle of phase estimated to correct a phase difference of the carrier.

The invention extends to a device comprising:
- input means for receiving symbols S consisting of first codes X, Y expressed in the form of Cartesian coordinates,
non-linear transformation means for supplying second codes X1, Y1 expressed in the form of Cartesian coordinates in response to said first codes,
means for storing said second codes for a predetermined number L of symbols to provide third codes X1 avg, Yl ~ avg respectively representative of an average of said second codes,
- delay means for delaying said symbols from a particular symbol,
a calculation means for calculating instantaneous phase differences Thesta ~ inst from said third codes,
an accumulator means cumulating said instantaneous phase differences to provide an estimated phase angle Theta ~ is,
- And a correction means for providing fourth codes X ~ is, Y ~ is constituting the particular symbol decided from said estimated phase angle and said first codes constituting said particular delayed symbol.

Other characteristics and advantages of the invention will appear even better on reading the following description of an embodiment of the invention accompanied by the appended drawings in which:
FIG. 1A is a schematic representation of a known device for recovering a carrier according to the VITERBI method,
- Figure 1B is a schematic representation of a device for implementing the method according to the invention;
FIG. 2 is a table of correspondence between the number of symbols used for the step of calculating the mean Cartesian coordinates of non-linearity and the symbol rate.

 FIG. 1B shows a device for implementing the method for recovering a carrier, according to the invention, for quadratic modulation with four phase states (QPSK). In this figure, the elements identical to those of the device shown in FIG. 1A bear the same references. It will be understood subsequently that the method of recovering a carrier and its implementation device according to the invention can easily be extended to modulations with more than four phase states.

Referring to Figure 1B, the symbols
S decoded by the receiver, after quadratic demodulation, consist of first codes X, Y expressed in the form of Cartesian coordinates. The first successive codes X, Y constituting the two binary trains originating from the filters (not shown) of the receiver are applied to inputs 10A, 10B to pass into non-linear transformation means 20, 30, 40. These non-transformation means - linear convert first into 20 the first codes
X, Y expressed in Cartesian form in polar coordinates to provide the Rho and Theta data. The first Rho polar coordinate is then raised to an integer power k: O, 1, 2, 3 or 4 (depending on the noise level of the receiver but preferably equal to 0) while the second polar coordinate Theta is multiplied by four in 30 to provide the data Rho "k and 4 * Theta. The data 4 * Theta represents the phase of a symbol brought on the axis o- Pi.

 The RhoAk and 4 * Theta data are again converted into Cartesian form in 40 to provide the second codes X1, Yl.

The second codes X1, Y1 are stored respectively in parallel storage means 50A, 50B of the serial shift register type or the like, for a predetermined number L of symbols S defining a phase estimation interval centered on a particular symbol. Consequently, each symbol received on the inputs 10 shifts the second codes X1, Y1 in the storage means 50. For each particular symbol considered, the storage means supply third codes X1 avg, Ylmoy respectively representative of an average of said second codes These third codes are obtained from the following relationships:

L being equal to 2N + 1
In parallel with the storage of the second codes, the symbols S are delayed in a delay means 90 from the particular symbol. This delay means 90 is therefore designed to delay (L-1) / 2 symbols from the particular symbol and at each symbol instant delivers the particular symbol consisting of the codes Xtn- (L-1) / 2], Y [n- (L-1) / 2], n representing the index of the symbol S received at the same time on the inputs 10.

The third codes Xlmoy, Y1 avg are then converted into polar co-ordinates in the first calculation means 60 which provides an instantaneous phase shift angle Theta inst for each particular symbol, from the following relation:
Theta ~ inst = 1/4 Arctang (Ylmoy / X1 avg)
Consequently Theta ~ inst corresponds to the difference between the phase angle of the particular symbol and the phase angle of the previous symbol.

 The successive phase shift angles Theta ~ inst are accumulated in an accumulator means 70 to provide an estimated phase angle Theta ~ is representing the overall phase of the recovered carrier.

Consequently the phase shift angles are added, modulo 2.Pi, in the accumulator means 70. A correction means (80) finally calculates fourth codes X ~ is, Y ~ is constituting the particular symbol decided from said angle estimated phase and said first codes X [n- (L-1) / 2], Y [n- (L-1) / 2] constituting the particular symbol delayed to correct the phase difference of the carrier from the following relationships ::
Xest = X [n- (L-1) / 2] .cos (Theta est) - n- (L- 1) / 2] .sin (Thetaest)
Y ~ is = X (n- (Ll) / 2] .sin (Theta ~ is) + Y [n- (L l) / 2] .cos (Thetaest)
Thus, the carrier recovery device according to the invention is capable of compensating for frequency differences between the transmission carrier frequency and the reception carrier frequency which accumulate, the compensable difference being more or less important depending on the characteristics that we give to carrier recovery. In the case presented above, the only variable characteristic is the number
L of symbols defining the length of the means of the second codes X1, Y1.

 Frequency tracking simulations have been performed for values of L ranging from 3 to 33, the results of which appear in the table in FIG. 3. In this table, Delta designates a frequency difference between the transmit carrier frequency and the carrier frequency. reception and Fd designates the symbol rate. Thus, for values of L close to 3, it is noted that the compensable frequency difference is large and the carrier recovery device is very sensitive to noise while for values of L close to 33 the compensable frequency difference is lower and the carrier recovery device resists noise better. For a symbol rate of 2.4 kHz to 16 kHz, however, we prefer a value of L close to and preferably equal to 17 to obtain a good compromise between the noise accepted and the compensated frequency difference.

 Of course, the invention is not limited to the embodiment described above and one can advantageously provide other variants without departing from the scope of the invention.

Claims (3)

 1.) A carrier recovery method for modulations with several phase states, in particular QPSK modulations, in which  - symbols S received, made up of first codes X, Y expressed in the form of Cartesian coordinates, are subjected to a nonlinear transformation to provide second codes X1, Y1 expressed in the form of Cartesian coordinates,  said second codes are memorized for a predetermined number L of symbols S defining a phase estimation interval centered on a particular symbol, to provide third codes X1 avg, Y1 avg respectively representative of an average of said second stored codes,  - an instantaneous phase shift angle Theta ~ inst relative to said particular symbol is calculated from said third codes,  c a r a c t e r i s e method in that it further comprises the following steps:  - the instantaneous phase shift angles are successively cumulated to provide an estimated phase angle Theta ~ east and fourth codes are calculated X ~ is, Y ~ is constituting the particular symbol decided from the first codes constituting said particular delayed symbol and said estimated phase angle to correct a phase difference of the carrier.  2.) A method of recovering carriers according to claim 1 in which the number L of symbols is preferably equal to 17.  3.) A device for implementing the method according to claim 1 comprising:  - input means (10) for receiving symbols S consisting of first codes X, Y expressed in the form of Cartesian coordinates,  - non-linear transformation means (20, 30, 40) for supplying second codes X1, Y1 expressed in the form of Cartesian coordinates in response to said first codes,  means for memorizing (50) said second codes for a predetermined number L of symbols to provide third codes X1 avg, Yl ~ avg respectively representative of an average of said second codes,  - delay means (90) for delaying said symbols from a particular symbol,  a calculation means (60) for calculating instantaneous phase differences Theta ~ inst from said third codes,  - an accumulator means (70) cumulating said phase differences to provide an estimated phase angle Theta ~ is,  - And a correction means (80) for providing fourth codes X ~ is, Y ~ is constituting the particular symbol decided from said estimated phase angle and said first codes constituting said particular delayed symbol.