Telecommunication method with polar constellations and corresponding devices

Abstract

A telecommunication method which includes mapping, by a mapper, input data to points of a constellation, modulating, by a modulator, points of the constellation to generate modulated symbols, and transmitting a radio signal representative of the modulated symbols. The constellation includes a set of N points, the coordinates of which expressed in polar form α.sub.n X e.sup.jφn, n = 1,..., N, referred to as polar coordinates, are determined such that a.sub.n+1 = a.sub.n + p, p > 0, the real number being the pitch amplitude of the constellation.

Claims

1. A telecommunication method implemented by a telecommunication equipment and comprising: mapping, by a mapper input data to points of an N-order constellation comprising a set of N points, the coordinates of which expressed in polar form a.sub.n × e.sup.jφn, called polar coordinates, such that a.sub.n+1 = a.sub.n + p, with p being the amplitude pitch of the constellation, p > 0 being a real number; modulating, by a modulator ,points of the constellation in order to generate modulated symbols; transmitting a radio signal representing the modulated symbols; wherein a.sub.1 > 0, and the polar coordinates are determined per quadrant with a value taken from among {π/2, π, 2π} and such that per quadrant φ.sub.n+1 = φ.sub.n + p′, with p′ ≥ 0 being a real number and with n = 1, ..., M and M ∈{N/4, N/2, N}.

2. The telecommunication method as claimed in claim 1, such that the modulation is a multi-carrier modulation.

3. The telecommunication method as claimed in claim 1, such that a quadrant equals π/2 and that M = N/4.

4. The telecommunication method as claimed in claim 1, such that a quadrant equals π and that M = N/2.

5. The telecommunication method as claimed in claim 4, wherein the points are shifted by π between the two quadrants.

6. The telecommunication method as claimed in claim 1, such that p′ ≠ 0.

7. The telecommunication method as claimed in claim 1, such that p′ = 0 and φ.sub.1 = φ ∈ [0,2π[.

8. A reception method implemented by a telecommunication equipment and comprising: receiving a radio signal representing modulated symbols; demodulating, by a demodulator the modulated symbols in order to estimate points of a constellation; detnapping, by a detnapper ,points of the constellation in order to estimate data mapped to these constellation points; wherein the constellation comprises a set of N points, the coordinates of which expressed in polar form a.sub.n × e.sup.jφn, called polar coordinates, are such that a.sub.n+1 = a.sub.n + p, p > 0 being a real number which is the amplitude pitch of the constellation, a.sub.1 > 0, and such that they are determined per quadrant with a value taken from among {π/2, π, 2π} and such that per quadrant φ.sub.n+1 = φ.sub.n + p′, with p′ ≥ 0 being a real number and with n = 1, ..., M and M with a value taken from among {N/4, N/2, N}.

9. A telecommunication equipment which comprises: a mapper which maps input data to points of a constellation, the constellation comprising a set of N points, the coordinates of which expressed in polar form a.sub.n × e.sup.jφn, called polar coordinates, are such that a.sub.n+1 = a.sub.n + p, p > 0 being a real number which is the amplitude pitch of the constellation, a.sub.1 > 0, and such that they are determined per quadrant with a value taken from among {π/2, π, 2π} and such that per quadrant φ.sub.n+1 = φ.sub.n + p′, with p′ ≥ 0 being a real number and with n = 1, ..., M and M with a value taken from among {N/4, N/2, N}; a modulator which modulates points of the constellation and generating modulated symbols; and a transmitter which transmits a radio signal representing the modulated symbols.

10. A telecommunication equipment which comprises: a receiver which receives a radio signal representing modulated symbols; a demodulator which demodulates the modulated symbols and estimating points of a constellation, the constellation comprising a set of N points, the coordinates of which expressed in polar form a.sub.n × e.sup.jφn, called polar coordinates, are such that a.sub.n+1 = a.sub.n + p, p > 0 being a real number which is the amplitude pitch of the constellation, a.sub.1 > 0, and such that they are determined per quadrant with a value taken from among {π/2, π, 2π and such that per quadrant φ.sub.n+1 = φ.sub.n + p′, with p′ ≥ 0 being a real number and with n = 1, ..., M and M with a value taken from among {N/4, N/ 2,N}; a demapper which demaps the points of the constellation and estimating data mapped to these constellation points.

11. (canceled)

12. (canceled)

13. (canceled)

Description

LIST OF FIGURES

[0055] FIG. 1 is a diagram showing a transmission baseband processing chain according to the prior art;

[0056] FIG. 2 is a conventional time-frequency representation of OFDM symbols;

[0057] FIG. 3 is a representation along a real axis X(I) and along an imaginary axis Y(Q) of a QPSK constellation with data mapping to the points of the constellation according to Gray coding;

[0058] FIG. 4 is a representation along a real axis X(I) and along an imaginary axis Y(Q) of a 16QAM constellation with data mapping to the points of the constellation according to Gray coding;

[0059] FIG. 5 is a representation along a real axis X(I) and along an imaginary axis Y(Q) of a 64QAM constellation with data mapping to the points of the constellation according to Gray coding;

[0060] FIG. 6 is a representation along a real axis X(I) and along an imaginary axis Y(Q) of a first configuration of a constellation used in a method according to the invention;

[0061] FIG. 7 is a representation along a real axis X(I) and along an imaginary axis Y(Q) of a second configuration of a constellation used in a method according to the invention;

[0062] FIG. 8 schematically shows the maximum of the phase variation capable of impacting the points of the modulation, shown in FIG. 7;

[0063] FIG. 9 is a representation along a real axis X(I) and along an imaginary axis Y(Q) of a third configuration of a constellation used in a method according to the invention;

[0064] FIG. 10 is a representation along a real axis X(I) and along an imaginary axis Y(Q) of a fourth configuration of a constellation used in a method according to the invention;

[0065] FIG. 11 schematically shows the maximum of the phase variation capable of impacting the points of the modulation, shown in FIG. 10;

[0066] FIG. 12 is a representation along a real axis X(I) and along an imaginary axis Y(Q) of another configuration of a constellation used in a method according to the invention;

[0067] FIG. 13 is a diagram of the simplified structure of an equipment according to the invention capable of implementing a telecommunication method according to the invention;

[0068] FIG. 14 shows a schematic diagram of the simplified structure of an equipment according to the invention capable of implementing a reception method according to the invention.

DESCRIPTION OF AN EMBODIMENT OF THE INVENTION

[0069] The general principle of the invention is based on mapping data to a constellation, the N points of which are distributed over concentric circles with a constant pitch p between the circles. The pitch p is a positive, non-zero real number. The points of the constellation are therefore distributed over at least two separate circles. The N points have coordinates expressed in polar form a.sub.n × e.sup.jφn, n = 1, ... , N, called polar coordinates with reference to a two-axis representation defining four quadrants, with the constraint that a.sub.n+1 = a.sub.n + p.

[0070] The constellation has the particular feature that there is at most one point on each circle per quadrant considered for the expression of the constellation in polar form. When the constellation is determined on a quadrant of size 2π, that is the quadrant [0 - 2π[, then there is at most one point per circle. When the constellation is determined per quadrant of size π, that is for the quadrants

[00001]$\left[0,\pi \left[\text{and}\right)\right)\left[\pi ,0\left[\text{or}\left[\frac{\pi }{2},3\frac{\pi }{2}\left[\text{and}\left[3\frac{\pi }{2},0\left[,\right)\right)\right)\right)\right)\right)$

then there is at most one point per semi-circle. When the constellation is determined per quadrant of size π/2, that is for the quadrants [0, π/2 [, [π/2, π[,

[00002]$\left[\pi ,3\frac{\pi }{2}\right[$

then there is at most one point per quarter circle.

[0071] The Cartesian coordinates (x, y) before normalization corresponding to the polar coordinates of the points of the constellation are expressed as: x(i) = a(i) .square-solid. cos(φ); y(i) = a(i) .square-solid. sin(φ), with φ ∈ [0, 2π[.

[0072] By configuring a pitch p = 1 and considering the amplitude of the first point as equal to one, then: a(1) = 1 and a(i + 1) = a(i) + 1.

[0073] The normalization factor “F” is dependent on the pitch between the points of the constellation and the modulation order m. Under these conditions, it is provided by the expression:

[00003]$F\left(m\right)=\frac{1}{\sqrt{\frac{{\displaystyle .Math.{}_i^{M}a{\left(i\right)}^2}}{m}}}.$

[0074] The normalization operation is an operation that is well known to a person skilled in the art, therefore it is not described any further. Indeed, it is quite common to apply a normalization factor to the various symbols when mapping or on completion of mapping.

[0075] FIG. 6 shows a first configuration of a constellation used according to the invention. This configuration has the particular feature that its points are distributed over a quadrant that represents [0 - 2π[ and that the phase φ is the same for all its points. Each point has the following coordinates: a.sub.n × e.sup.jφ, a.sub.n = n × p, n = 1, ..., N. Therefore, the amplitude of a point simply needs to be found in order to determine this point. Thus, the receiver can demodulate the data which are mapped according to this configuration only by using the amplitude of the received data.

[0076] The configuration that is shown corresponds to a constellation of the order m = 16. The following table is an example of Gray coding used with this configuration.

TABLE-US-00001 i Gray coding 1 0000 2 0001 3 0011 4 0010 5 0110 6 0111 7 0101 8 0100 9 1100 10 1101 11 1111 12 1110 13 1010 14 1011 15 1001 16 1000

[0077] This first configuration advantageously allows the common phase variation to be estimated of an OFDM symbol between the transmitted signal and the received signal by computing the average phase error on an OFDM symbol. This allows pilots called continuous pilots to be dispensed with. This first configuration is very efficient with respect to phase variations but to the detriment of robustness against additive white Gaussian noise, since the minimum distance between the transmitted points is short.

[0078] FIG. 7 shows a second configuration of a constellation used according to the invention. This constellation is of the order m = 16. It has the particular feature that the pattern of the points is reproduced between the four quadrants, with each quadrant representing [0, π/2 [. Each point of a quadrant has the following coordinates: a.sub.n × e.sup.jφn, a.sub.n = n × p, n = 1, ... , N/4, N = 16. Thus, for each quadrant, there is only one point per concentric circle and the phase φ.sub.n of the point n is selected according to a determined criterion, for example, with a constant pitch of π/8 between two points or a zero pitch between the two points on the remotest circles in the same quadrant. This second embodiment is less efficient with respect to phase variations than the first embodiment but is more robust against additive white Gaussian noise, since the minimum distance between the transmitted points is longer.

[0079] According to the illustrated example of this second embodiment, the phase φ.sub.n is a multiple of π/12 and more particularly φ.sub.1 = φ.sub.4 = π/2, φ.sub.2 = π/12 and φ.sub.3 = 5π/12. This second embodiment as illustrated is highly advantageous since it is compatible with many existing OFDM demodulators capable of demodulating an OFDM/16QAM modulation. Indeed, for each quadrant, the points are close to those of a conventional 16QAM constellation, as shown in FIG. 4.

[0080] FIG. 8 shows the maximum phase variation that can affect the points of the modulation, shown in FIG. 7, during the transmission that remains compatible with a correct reception demodulation. Within the limit of this maximum, i.e., as long as the phase variation remains within the limit of +π/4 with respect to the phase of the transmitted point, the receiver can demodulate the received points of the modulation despite the phase variation between the transmitter and the receiver, and without ambiguity.

[0081] FIG. 9 shows a third configuration of a constellation used according to the invention. This constellation is of the order m = 16. It has the particular feature that the pattern of the points is reproduced between the two quadrants, with each quadrant representing [0 - π[. Each point of a quadrant has the following coordinates:

[00004]$a_n\times e^{j{\phi }_n},a_n=n\times p,n=1,\mathrm{...},N/2,N=16.$

Thus, for each quadrant, there is only one point per concentric circle and the phase φ.sub.n of the point n is selected according to a determined criterion, for example, with a constant pitch of π/4 and modulo 2π between two successive points in order to remain in the same quadrant.

[0082] The points can be considered to be described with an amplitude pitch of “1” and with a periodicity of 8, resulting in two constellation points for the same amplitude. The Cartesian coordinates can be expressed as:

[00005]$x\left(i\right)=a\left(i\right)\cdot \cos \left({\phi }_i\right);y\left(i\right)=a\left(i\right)\cdot \sin \left({\phi }_i\right)$

[00006]$\text{with}a\left(1\right)=1\text{and}a\left(i+1\right)=a\left(i\right)+1\left(\text{period}\text{of}8\right),a\left(9\right)=a\left(1\right)=1$

and φ.sub.i = φ.sub.1 + [i/9] × π - iπ/4 with, for example, φ.sub.1 = π/4 being the starting point of the constellation.

[0083] This constellation is very robust against phase variations of ±π/2 but exhibits reduced performance capabilities with respect to additive white Gaussian noise compared to a modulation shown in FIG. 7.

[0084] FIG. 10 shows a fourth configuration of a constellation used according to the invention, called spiral constellation. As for the first configuration shown in FIG. 6, this fourth configuration has the particular feature that the points are distributed over a quadrant that represents [0 - 2π[. The configuration shown corresponds to a constellation of the order m = 16. Each point has the following coordinates: a.sub.n × e.sup.jφn, a.sub.n = n × p, n = 1, ... , 16 and a phase φ.sub.n with a determined pitch between two successive points, i.e., on two successive circles, for example, a constant pitch of π/4, φ.sub.n+1 = φ.sub.n + π/4. Therefore, unlike the first configuration, the phase φ.sub.n is not constant but varies between the successive points. As for the first configuration, this fourth configuration is particularly advantageous with respect to phase variations since the reception demodulation can take place only upon detection of amplitude of the received constellation points. Any phase variation when transmitting between the transmitter and the receiver does not affect the demodulation. This fourth configuration is more advantageous than the first configuration in terms of the minimum distance between all points and is therefore more robust against additive white Gaussian noise since the minimum distance between the transmitted points is greater than for the first configuration.

[0085] The constellation of FIG. 9 can be defined as two half-order spiral constellations on two quadrants [0, 2π[ offset by π with respect to each other.

[0086] The following table is a possible example of mapping binary data to the points of a constellation according to the fourth configuration shown in FIG. 10, in accordance with Gray coding. The modulation order is m = 16, the amplitude pitch of the points of this constellation is p = 1, the phase is a multiple of π/4.

TABLE-US-00002 i Gray coding Z(i) before normalization 1 0000 1.e.sup.jπ/4 2 0001 2 3 0011 [00007]$3.e^{-j\frac{\pi }{4}}$ 4 0010 [00008]$4.e^{-j\frac{\pi }{2}}$ 5 0110 [00009]$5.e^{-j\left(\frac{3\pi }{4}\right)}$ 6 0111 6.e.sup.-jπ 7 0101 [00010]$7.e^{-j\left(\frac{5\pi }{4}\right)}$ 8 0100 [00011]$8.e^{j\frac{\pi }{2}}$ 9 1100 9.e.sup.jπ/4 10 1101 10 11 1111 [00012]$11.e^{-j\frac{\pi }{4}}$ 12 1110 [00013]$12.e^{-j\frac{\pi }{2}}$ 13 1010 [00014]$13.e^{-j\left(\frac{3\pi }{4}\right)}$ 14 1011 14.e.sup.-jπ 15 1001 [00015]$15.e^{-j\left(\frac{5\pi }{4}\right)}$ 16 1000 [00016]$16.e^{j\left(\frac{\pi }{2}\right)}$

[0087] FIG. 11 shows the result of a frequency deviation between the transmitter and the receiver with the constellation defined above over several consecutive OFDM symbols. FIG. 11 shows the maximum phase variation that can affect the points of the “spiral” modulation, shown in FIG. 10, which remains acceptable for a correct demodulation. This “spiral” structure allows high phase variations to be withstood between the transmitter and the receiver of the system. This embodiment is particularly suitable for systems operating in THz bands, for which there is very high phase noise due to low-performance oscillators. In order to respond to an increase in throughput (for example, twice as much throughput), a new embodiment of a constellation according to the first configuration can be determined by reproducing the points of FIG. 6 on the third quadrant, as shown in FIG. 12. The order of the embodiment shown is m = 32. By reproducing the points of FIG. 6 on the three other quadrants an order of m = 64 is easily obtained.

[0088] In order to respond to an increase in throughput, the pitch p can be divided, for example, by two, by four, etc.

[0089] The simplified structure of an embodiment of an equipment according to the invention capable of implementing a telecommunication method according to the invention is shown in FIG. 13. This equipment DEV_E can be a base station as well as a mobile terminal.

[0090] The equipment DEV_E comprises a microprocessor .Math.P, the operation of which is controlled by executing a program Pg, the instructions of which enable a telecommunication method according to the invention to be implemented. The equipment DEV_E further comprises a mapper MAP, an OFDM-type modulator MOD, a transmitter EM, a memory Mem comprising a buffer memory. The OFDM-type modulator MOD is conventionally produced by implementing an inverse Fourier transform IFFT.

[0091] On initialization, the code instructions of the program Pg are loaded, for example, into the buffer memory Mem before being executed by the processor .Math.P. The microprocessor .Math.P controls the various components: mapper MAP, modulator MOD, transmitter EM.

[0092] The configuration of the equipment comprises at least the order of the modulation, the pitch of the constellation, as well as the value of a.sub.1. The order of the modulation determines the number of points N. Thus, by executing the instructions, the microprocessor .Math.P: [0093] determines the polar coordinates of the points of the constellation: a.sub.n × e.sup.jφn, n = 1, ... , N, such that a.sub.n+1 = a.sub.n + p, p > 0; [0094] controls the various components so that: [0095] the mapper MAP maps the input data DATA to the points of the constellation; [0096] the modulator MOD modulates the data which are mapped on the various carriers in order to generate OFDM symbols; [0097] the transmitter EM transmits a radio signal representing the OFDM symbols. The simplified structure of an embodiment of an equipment according to the invention capable of implementing a reception method according to the invention is shown in FIG. 14. This equipment DEV_R can be a base station as well as a mobile terminal.

[0098] The equipment DEV_R comprises a microprocessor .Math.P, the operation of which is controlled by executing a program Pg, the instructions of which enable a reception method according to the invention to be implemented. The equipment DEV_R further comprises a demapper DEMAP, an OFDM-type demodulator DEMOD, a receiver RE, a memory Mem comprising a buffer memory. On initialization, the code instructions of the program Pg are loaded, for example, into the buffer memory Mem before being executed by the processor .Math.P. The microprocessor .Math.P controls the various components: demapper DEMAP, demodulator DEOD, receiver RE.

[0099] The demodulator DEMOD carries out the inverse operation of the modulator MOD. The demapper DEMAP carries out the inverse operation of the mapper MAP. Conventionally, the demodulator is produced by means of a Fourier transform FFT.

[0100] The configuration of the equipment comprises at least the order of the modulation, the pitch of the constellation, as well as the value of a.sub.1. The order of the modulation determines the number of points N. Thus, by executing the instructions, the microprocessor .Math.P: [0101] determines the polar coordinates of the points of the constellation: a.sub.n × e.sup.jφn, n = 1, ... , N, such that a.sub.n+1 = a.sub.n + p, p > 0; [0102] controls the various components so that: [0103] the receiver RE receives the radio signal representing OFDM symbols; [0104] the demodulator DEMOD demodulates the OFDM symbols in order to estimate the points of the constellation mapped on the various carriers; [0105] the demapper MAP demaps the points of the constellation in order to estimate the data DATA.

[0106] The equipment DEV_R that receives the radio signal which is transmitted according to an embodiment of a method according to the invention can demodulate the received points of the constellation by estimating the amplitude of the received point (x.sub.r(i),y.sub.r(i)):

[00017]$x_r\left(i\right)=a_r\left(i\right)cos\left({\phi }_r\left(i\right)\right)+b_x\left(i\right)$

[00018]$y_r\left(i\right)=a_r\left(i\right)sin\left({\phi }_r\left(i\right)\right)+b_y\left(i\right)$

b.sub.x and b.sub.y is the additive white Gaussian noise projected on the X and Y channels.

[0107] Knowing the constellation, and given that there is no more than one point per circle on a quadrant, the equipment DEV_R can therefore determine the received point on the basis of the amplitude, with uncertainty with respect to its position if several quadrants were considered on transmission in order to define the constellation.

[0108] After estimating the amplitude of the received point, the equipment DEV_R can estimate the phase error by comparing the estimated points projected on the X(I) and Y(Q) axes with the transmitted points. The phase error is essentially derived from the additive white Gaussian noise:

[00019]$\Delta \phi \left(i\right)=\phi \left(i\right)-\left({\phi }_r\left(i\right)\right)+b\left(i\right).$

[0109] By summing the various phase error estimates made on each OFDM carrier, i.e., for each point of the constellation that modulated a carrier, the equipment DEV_R can experience an improvement in the estimation of the phase error and thus reduce the influence of the white noise:

[00020]${\Delta }_{\phi }=M{\displaystyle .Math.{}_{i=1}^M}{\Delta }_{\phi \left(i\right)},$

with M being the number of OFDM carriers used to estimate the phase variations.

[0110] Once the estimation of the common phase error is complete, the equipment DEV_R can correct all the constellation points modulating an OFDM symbol. This correction can be carried out both in the frequency domain, i.e., after the IFFT demodulation, and in the time domain, i.e., before the IFFT demodulation. By making the correction in the time domain this allows the inter-carrier interference that is derived from the phase rotation to be reduced.

[0111] Determining the phase error allows the demodulation error to be reduced.

[0112] Accordingly, the invention also applies to one or more computer programs, in particular a computer program on or in a storage medium, suitable for implementing the invention. This program can use any programming language, and can be in the form of source code, object code, or of intermediate code between source code and object code, such as in a partially compiled form, or in any other form suitable for implementing a method according to the invention.

[0113] The information medium can be any entity or device capable of storing the program. For example, the medium can comprise a storage means, such as a ROM, for example, a CD-ROM or a microelectronic circuit ROM, or even a magnetic recording means, for example, a USB key or a hard disk.

[0114] Furthermore, the information medium can be a transmissible medium such as an electrical or optical signal, which can be routed via an electrical or optical cable, by radio or by other means. The program according to the invention particularly can be downloaded over an Internet-type network.

[0115] Alternatively, the information medium can be an integrated circuit in which the program is incorporated, with the circuit being adapted for executing or for being used in the execution of the method in question.