TELECOMMUNICATIONS METHOD WITH PHASE-OFFSET POLAR CONSTELLATION FOR REDUCING PAPR, AND CORRESPONDING DEVICES

Abstract

A telecommunications method includes transmitting a multicarrier symbol constructed from points of a polar constellation that are modulated in blocks and controlling at least one phase rotation vector of one of the modulated blocks of points in order to reduce the peak-to-average power ratio of the transmitted multicarrier symbol.

Claims

1. A telecommunication method involving comprising: transmitting a multi-carrier symbol constructed from points of a polar constellation, said points being block modulated by at least two multi-carrier modulators; and controlling at least one phase-rotation vector of at least one of these blocks of modulated points to decrease a peak-to-average power ratio (PAPR) of the transmitted multi-carrier symbol.

2. The telecommunication method (1) as claimed in claim 1, comprising: mapping, via a mapper, input data to points of the polar constellation, comprising a set of M points having coordinates expressed in polar form a.sub.m×e.sup.jφm, m=0, . . . , M−1 and determined such that a.sub.m+1=a.sub.m+p, p>0, a real number, is an amplitude interval of the constellation, which is said to be polar, block modulating, via K multi-carrier modulators, the points of the constellation, these points being input into the K multi-carrier modulators, to generate K symbols, K≥2, 1.sup.st adding, via an adder, the K symbols, to obtain a multi-carrier symbol, and determination of a PAPR of the multi-carrier symbol, which is said to be the initial PAPR, phase rotating, via a phase shifter, of at least one of the K symbols by a phase-rotation angle θ, to generate K symbols, which are said to be phase-shifted, 2.sup.nd adding, via an adder, the K phase-shifted symbols, to obtain a new multi-carrier symbol, comparing the initial PAPR and of a PAPR of the new multi-carrier symbol, the lowest PAPR becoming the initial PAPR, transmitting the multi-carrier symbol of lowest PAPR.

3. The telecommunication method as claimed in claim 1, such that said points are block modulated via an inverse Fourier transform.

4. The telecommunication method as claimed in claim 2, such that the phase rotating, the 2.sup.nd adding, and the comparing are performed iteratively for a plurality of different phase-rotation-angle vectors.

5. The telecommunication method as claimed in claim 4, such that the iterations on the phase-rotation vectors are iterated for a plurality of symbols.

6. The telecommunication method as claimed in claim 1, the polar constellation comprising a set of M points having coordinates expressed in polar form a.sub.m×e.sup.jφm, m=1, . . . , M−1 and determined such that a.sub.m+1=a.sub.m+p, p>0, a real number, is an amplitude interval of the constellation, which is said to be polar, the method being such that two axes define quadrants and that the polar coordinates are determined per quadrant: $a_{m+1}=a_m+p,m=0,...,\frac{M}{4}-1.$

7. The telecommunication method as claimed in claim 6, such that M=16, p=1 and such that for each quadrant φ.sub.m=α×π/12 with α a natural number.

8. The telecommunication method as claimed in claim 6, such that for each quadrant ${\phi }_{m+1}={\phi }_m,m=0,...,\frac{M}{4}-1.$

9. The telecommunication method as claimed in claim 1, the polar constellation comprising a set of M points having coordinates expressed in polar form a.sub.m×e.sup.jφm, m=0, . . . , M−1 and determined such that a.sub.m+1=a.sub.m+p, p>0, a real number, is an amplitude interval of the constellation, which is said to be polar, the method being such that two axes define quadrants and that the polar coordinates are determined per set of two quadrants: $a_{m+1}=a_m+p,m=0,...,\frac{M}{2}-1.$

10. The telecommunication method as claimed in claim 8, such that for two quadrants taken together ${\phi }_{m+1}={\phi }_m,m=0,...,\frac{M}{2}-1.$

11. The telecommunication method as claimed in claim 1, the polar constellation comprising a set of M points having coordinates expressed in polar form a.sub.m×e.sup.jφm, m=0, . . . , M−1 and determined such that a.sub.m+1=a.sub.m+p, p>0, a real number, is an amplitude interval of the constellation, which is said to be polar, the method being such that the polar coordinates are further determined such that φ.sub.m+1=φ.sub.m+p′=φ.sub.m+p″″×π with p″″ a non-zero real number.

12. The telecommunication method as claimed in claim 1, the polar constellation comprising a set of M points having coordinates expressed in polar form a.sub.m×e.sup.jφm, m=0, . . . , M−1 and determined such that a.sub.m+1=a.sub.m+p, p>0, a real number, is an amplitude interval of the constellation, which is said to be polar, the method being such that φ.sub.m=φ for m=0, . . . , M−1.

13. A telecommunication equipment which comprises: at least one processor; at least one non-transitory computer readable medium comprising instructions stored thereon which when executed by the processor configure the telecommunication equipment to: map input data to points of a constellation, the constellation comprising a set of M points having coordinates expressed in polar form a.sub.m×e.sup.jφm, m=0, . . . , M−1, which are said to be polar coordinates, with reference to a representation with two axes defining four quadrants, and determined such that a.sub.m+1=a.sub.m+p, p>0, a real number, is an amplitude interval of the constellation, block modulate with K multi-carrier modulators the points of the constellation and generating K symbols, K≥2, add the K symbols to obtain a multi-carrier symbol, compute a peak-to-average power ratio (PAPR) of the multi-carrier symbol, which is said to be an initial PAPR, shift a phase of at least one of the K symbols by a phase-rotation vector, to generate K symbols, which are said to be phase-shifted, add the K phase-shifted symbols to obtain a new multi-carrier symbol, compare the initial PAPR and a PAPR of the new multi-carrier symbol, the lowest PAPR becoming the initial PAPR, a transmitter for transmitting the multi-carrier symbol of lowest PAPR.

14. (canceled)

15. A non-transitory computer readable data medium comprising program instructions stored thereon which are suitable for implementing a telecommunication method when said program instructions are loaded and executed in a telecommunication equipment, the telecommunication method comprising: transmitting a multi-carrier symbol constructed from points of a polar constellation, said points being block modulated by at least two multi-carrier modulators; and controlling at least one phase-rotation vector of at least one of these blocks of modulated points to decrease a peak-to-average power ratio (PAPR) of the transmitted multi-carrier symbol.

16. (canceled)

Description

LIST OF THE FIGURES

[0072] Other features and advantages of the invention will become more clearly apparent on reading the following description of embodiments, which are given by way of simple illustrative and non-limiting examples, and the appended drawings, in which:

[0073] FIG. 1 is a diagram illustrating a transmission-end baseband processing chain according to the prior art,

[0074] FIG. 2 is a representation of a conventional 16 QAM constellation,

[0075] FIG. 3 is a conventional time-frequency representation of OFDM symbols,

[0076] FIG. 4 is a time-domain representation of an OFDM signal delivered by a conventional transmission-end baseband chain with an OFDM modulator by which only 10% of the carriers are used,

[0077] FIG. 5 is a representation, against a real axis X(I) and an imaginary axis Y(Q), of a first configuration of a polar constellation employable in a method according to the invention,

[0078] FIG. 6 is an illustration of one example of the phase variation applicable to the points of the modulation illustrated in FIG. 5,

[0079] FIG. 7 is a representation, against a real axis X(I) and an imaginary axis Y(Q), of a second configuration of a polar constellation employable in a method according to the invention,

[0080] FIG. 8 schematically shows the maximum phase variation applicable to the points of the modulation illustrated in FIG. 7,

[0081] FIG. 9 is a block diagram illustrating the implementation of a method according to the invention by a corresponding device,

[0082] FIG. 10 shows the curve of the CCDF values obtained without the reduction method according to the invention, and the curve of the CCDF values obtained with the reduction method according to the invention with a block of 120 carriers,

[0083] FIG. 11 shows the curve of the CCDF values obtained without the reduction method according to the invention, and the curve of the CCDF values obtained with the reduction method according to the invention with a block of 12 carriers,

[0084] FIG. 12 is a diagram of the simplified structure of an equipment according to the invention able to implement a telecommunication method according to the invention.

[0085] FIG. 13 is a diagram of the simplified structure of an equipment according to the invention able to implement a reception method according to the invention.

DESCRIPTION OF PARTICULAR EMBODIMENTS

[0086] The general principle behind the invention is to map input data to a polar constellation the M points of which are distributed on concentric circles, there being a constant interval p between the circles, and then to perform multi-carrier block modulation of the points of the constellation and controlled rotation of the phase of the blocks before addition to form a multi-carrier symbol. The modulation employs N.sub.IFFT subcarriers. The modulation is performed blockwise by K modulators of N.sub.IFFT subcarriers. Each output of a modulator or block may be phase shifted with a phase-rotation vector before the blocks are added together. The PAPR of the multi-carrier symbol resulting from a complex addition after phase rotation of a symbol resulting from a block is compared with the PAPR of a multi-carrier symbol obtained with a different phase rotation. The comparison may be repeated for various phase-rotation values. Only the symbol of lowest PAPR is selected and transmitted.

Polar Constellations According to the Invention

[0087] The interval p is a non-zero positive real number. The points of the constellation are therefore distributed over at least two distinct circles. The M points have coordinates expressed in polar form a.sub.m×e.sup.jφm, m=0, . . . , M−1, which are said to be polar coordinates, with reference to a representation with two axes defining four quadrants, with the constraint that a.sub.m+1=a.sub.m+p. a.sub.m is the amplitude of a point, and φ.sub.m is the phase of this point. M is the order of the modulation.

[0088] For example, a 16 QAM modulation has an order M=16.

[0089] The constellation has the particularity that there is at most one point on each circle per quadrant considered in respect of the expression in polar form of the constellation. When the constellation is determined for a quadrant of size 27π, namely the quadrant [0−2π[, then there is at most one point per circle. When the constellation is determined per quadrant of size π, namely for the quadrants

[00006]$[0,\pi [\mathrm{and}[\pi ,0[,\mathrm{or}[\frac{\pi }{2},3\frac{\pi }{2}[\mathrm{and}[3\frac{\pi }{2},0[,$

then there is at most one point per semicircle.

[0090] When the constellation is determined per quadrant of size π/2, namely for the quadrants

[00007]$[0,\pi /2[,[\pi /2,\pi [,[\pi ,3\frac{\pi }{2}[\mathrm{and}[3\frac{\pi }{2},0[,$

then there is at most one point per quarter circle.

[0091] The Cartesian coordinates (x, y) before normalization corresponding to the polar coordinates of the points of the constellation may be expressed in the form:

s.sub.m=a.sub.m.Math.cos (φ.sub.m);y.sub.m=a.sub.m.Math.sin (φ.sub.m) with φ.sub.mε[0,2π[

[0092] If the size of an interval is set so p=1 and the amplitude of the first point is considered to be equal to one, then:

a.sub.0=1 and a.sub.m+1=a.sub.m+1.

[0093] It is common to apply a normalization factor during mapping or at the end of mapping to the various symbols. The normalization factor “F” depends on the interval between the points of the constellation and on the modulation order M. Under these conditions, it is given by the expression:

[00008]$F\left(M\right)=\frac{1}{\sqrt{\frac{{.Math.}_{m=1}^M{a}_m^2}{M}}}$

[0094] The normalization operation is an operation well known to those skilled in the art, so it is not described further. FIG. 5 shows a first configuration of a polar constellation used according to the invention, which configuration is said to be a spiral configuration. This first configuration has the particularity that the points are distributed over a quadrant [0-2π[. The configuration shown corresponds to a constellation of order M=16. Each point has the coordinates: a.sub.m×e.sup.jφm, a.sub.m=(m+1)×p, m=0, . . . , 15 and a phase φ.sub.m with a determined interval between two successive points i.e. on two successive circles, for example a constant interval of π/4, φφ.sub.m+1=φ.sub.m+π/4. Hence, unlike configurations that have not been illustrated, the phase φ.sub.m does not remain constant but varies between the successive points. This first configuration is particularly advantageous with respect to phase variations because the reception-end demodulation may be performed based solely on detection of the amplitude of the received constellation points. Any phase variation during the transmission between the transmitter and the receiver does not affect the demodulation. The following table is one possible example of the way in which binary input data may be mapped to the points of a polar constellation according to the first configuration (illustrated in FIG. 5), employing Gray code. The modulation order is M=16, the amplitude interval of the points of this constellation is p=1 and the phase is a multiple of π/4.

TABLE-US-00001 TABLE 1 m Gray code X.sub.m before normalization  0 0000 1 .Math. e.sup.jπ/4  1 0001 2  2 0011 [00009]$3.Math.e^{-j\frac{\pi }{4}}$  3 0010 [00010]$4.Math.e^{-j\frac{\pi }{2}}$  4 0110 [00011]$5.Math.e^{-j\left(\frac{3\pi }{4}\right)}$  5 0111 6 .Math. e.sup.−jπ  6 0101 [00012]$7.Math.e^{-j\left(\frac{5\pi }{4}\right)}$  7 0100 [00013]$8.Math.e^{j\frac{\pi }{2}}$  8 1100 9 .Math. e.sup.jπ/4  9 1101 10 10 1111 [00014]$11.Math.e^{-j\frac{\pi }{4}}$ 11 1110 [00015]$12.Math.e^{-j\frac{\pi }{2}}$ 12 1010 [00016]$13.Math.e^{-j\left(\frac{3\pi }{4}\right)}$ 13 1011 14 .Math. e.sup.−jπ 14 1001 [00017]$15.Math.e^{-j\left(\frac{5\pi }{4}\right)}$ 15 1000 [00018]$16.Math.e^{j\frac{\pi }{2}}$

[0095] FIG. 6 illustrates me result or a frequency deviation between the transmitter and the receiver with the constellation defined above over a plurality of consecutive OFDM symbols. FIG. 6 illustrates one example of the phase variation applicable to the points of the modulation called the spiral modulation, which is illustrated in FIG. 5, that remains acceptable with respect to obtaining correct demodulation. This “spiral” structure makes it possible to withstand large variations in phase between the transmitter and the receiver of the system. This embodiment is particularly suitable for systems operating in the terahertz's, by which a lot of phase noise is generated due to poor oscillator performance.

[0096] FIG. 7 shows a second configuration of a polar constellation used according to the invention. This constellation is of order M=16. It has the particularity that the pattern of points is reproduced between the four quadrants, each quadrant representing [0, π/2[. Each point of a quadrant has the coordinates:

[00019]$a_m\times e^{j{\phi }_m},a_m=\left(m+1\right)\times p,m=0,...,\frac{M}{4}-1,M=16.$

Thus, for each quadrant, there is only one point per concentric circle and the phase φ.sub.m of the point m is chosen according to a determined criterion, for example with a constant interval of π/8 between two points or an interval of zero between the two points on the circles most distant in the same quadrant. This second mode is robust against additive white Gaussian noise because the minimum distance between the emitted points is large. According to the illustrated example of this second embodiment, the phase φ.sub.m is a multiple of π/12 and more particularly φ.sub.0=φ.sub.3=π/2, φ.sub.1=π/12 and φ.sub.2=5π/12. This second embodiment as illustrated is very advantageous because it is compatible with many existing OFDM demodulators capable of demodulating an OFDM/16 QAM modulation. Specifically, for each quadrant, the points are close to those of a conventional 16 QAM constellation as shown in FIG. 2.

[0097] FIG. 8 shows the maximum amount of phase variation applicable to the points of the modulation illustrated in FIG. 7, transmission-end, that remains compatible with obtaining correct demodulation reception-end. Within the limits of this maximum amount, i.e. as long as the phase variation remains within the limit +π/4 with respect to the phase of the transmitted point, the receiver is able to demodulate, without ambiguity, the received modulation points despite the phase variation between the transmitter and the receiver.

[0098] The block diagram of FIG. 9 illustrates implementation of one embodiment of a method according to the invention by a corresponding device.

[0099] A symbol binary encoder MAP converts (maps) an input binary data packet, for example a binary code word of data of a multimedia communication, into a complex point of a constellation using a conventional technique known to those skilled in the art. According to the invention, the constellation is a polar constellation.

[0100] The obtained points of the constellation are then input into K modulators MOD.sub.1, MOD.sub.2, MOD.sub.3 and block modulated−K=3 in the illustration. K is configurable. The constellation points are input into the K modulators in such a way that each point is modulated using a different subcarrier of the equivalent modulator of N.sub.IFFT subcarriers. Each of the K modulators performs a frequency-time conversion, conventionally via an inverse Fourier transform IFFT of N.sub.IFFT subcarriers, to generate a multi-carrier symbol of N time-domain samples, N=N.sub.IFFT.

[0101] For each time index n, n ε [0, N−1], complex addition by a 1.sup.st adder ADD.sub.[1] of the K outputs n of the K modulators gives a time-domain sample Ref.sub.ofdm .sub.[n] of a multi-carrier symbol Ref.sub.ofdm identical to the one obtained by the equivalent modulator of N.sub.IFFT subcarriers in the absence of phase rotation before addition.

[0102] The impact of a phase-rotation vector on one or more of the output symbols of the K modulators before complex addition of these symbols with one another is evaluated by the controller Ct_PAPR.

[0103] The controller Ct_PAPR receives, by way of input, each of the N outputs of the K modulators, and the N samples Ref.sub.ofdm[n] of the multi-carrier symbol Ref.sub.ofdm.

[0104] The controller Ct_PAPR determines the PAPR, which is said to be the initial PAPR, of the multi-carrier symbol Ref.sub.ofdm, which itself serves as initial value for the current reference multi-carrier symbol x.sub.ofdm_aux.

[0105] The controller Ct_PAPR determines at least one phase-rotation vector θ.sub.[1], θ.sub.[2], θ.sub.[3] and applies it to at least one of the symbols delivered by the K modulators. Thus, all the points of the constellation that are input into the K modulators undergo the phase rotations θ.sub.[1], θ.sub.[2], and θ.sub.[3] respectively. The various phase-rotation vectors θ.sub.[1], θ.sub.[2], and θ.sub.[3] may have different values or indeed some or all may be the same.

[0106] The controller Ct_PAPR compares the PAPR of the multi-carrier symbol x.sub.ofdm_i resulting from the complex addition by a 2.sup.nd adder ADD.sub.[2] of the samples n of the symbols after rotation of at least one of the symbols input into the adder, with the PAPR of the current reference x.sub.ofdm_aux. The output multi-carrier symbol x.sub.ofdm is that of the two input multi-carrier symbols that has the lowest PAPR. This multi-carrier symbol x.sub.ofdm of lower PAPR becomes the new current reference multi-carrier symbol x.sub.ofdm_aux.

[0107] The comparison may be repeated for various phase-rotation vectors using an iterative method of L iterations, L being configurable. At the end of the iterations, only the multi-carrier symbol of lowest PAPR is transmitted.

[0108] The phase rotation applied to a point of the constellation by means of the phase-rotation vector is bounded by the value θ.sub.max, which is configurable.

[0109] According to one mode of implementation, each modulator implements an inverse Fourier transform. The multi-carrier symbols obtained are said to be OFDM symbols.

[0110] The sample n of the time-domain signal delivered by a block IFFT (implementation of an inverse Fourier transform) is denoted: x.sub.b.sub.[k][n] with k the index of the IFFT block k ε [0: K−1], K the total number of IFFT blocks and n the time index n ε [0: N−1]. N=N.sub.IFFT the size of the inverse Fourier transform IFFT.

[0111] The reference OFDM symbol Ref.sub.ofdm is written for each time index “n”:

[00020]${\mathrm{Ref}}_{\mathrm{ofdm}\left[n\right]}=\underset{k=0}{\overset{K-1}{.Math.}}{x}_{b_{\left[k\right]\left[n\right]}}$

[0112] The method evaluates the PAPR of the reference OFDM symbol Ref.sub.ofdm, which is said to be the initial PAPR.

[0113] One particular iterative embodiment of the method may be carried out as follows: [0114] initialization: [0115] of the overall-rotation-angle vectors: θ.sub.G[k]=0, k ε [0: K−1] [0116] of a current reference OFDM symbol: x.sub.ofdm_aux=Ref.sub.ofdm [0117] PAPR=initial PAPR [0118] loop n.sup.∘1 of a number L of iterations of the method [0119] loop n.sup.∘2 of the number of blocks K: k ε [0: K−1] [0120] Initialization of the phase-rotation angle θ.sub.[k] with θ.sub.[k] ε [−θ.sub.max/2: θ.sub.max/2], θ.sub.max being the maximum range of phase variation in radians for a block “k”, [0121] loop n.sup.∘3 of a number P of phase rotations θ.sub.[k] to be tested with Δθ a phase increment, [0122] the complex rotation vector for block “k” is written: e.sup.(j2πθ.sup.[k].sup.), the variable “j” is the imaginary unit, [0123] for n ε [0: N−1], sample [n] of the new OFDM symbol x.sub.ofdm is thus obtained:

x.sub.ofdm.sub.[n]=x.sub.ofdm)aux.sub.[n]+x.sub.b.sub.[k][n](e.sup.(j2πθ.sup.[k].sup.)−1) [0124] computation of the PAPR value of the new OFDM symbol x.sub.ofdm [0125] if this PAPR value is better than the previous one, storage in memory of the rotation angle, denoted θ.sub.opt[k]=θ.sub.[k], storage in memory of the new PAPR [0126] if the new value of the overall rotation angle θ.sub.G[k]+θ.sub.opt[k] exceeds the determined maximum threshold: θ.sub.G[k]+θ.sub.opt[k]≥θ.sub.max then exit loop n.sup.∘3 [0127] update of the overall rotation angle: θ.sub.G[k]=θ.sub.G[k]+θ.sub.opt[k] [0128] θ.sub.[k]=θ.sub.[k]+Δθ

[00021]$x_{{\mathrm{ofdm}}_{{\mathrm{aux}}_{\left[n\right]}}}=x_{{\mathrm{ofdm}}_{\left[n\right]}}$ [0129] for n ε [0: N−1] [0130] end of loop n.sup.∘3 [0131] if the angle of rotation θ.sub.opt[k] is different from “0”, then sample [n], for n ε [0: N−1], of the new OFDM symbol is updated with this angle θ.sub.opt[k] for the block k in question:

x.sub.ofdm.sub.[n]=x.sub.ofdm.sub.[n]+x.sub.b.sub.[k][n](e.sup.(j2πθ.sup.opt[k].sup.)−1)

Update of the: x.sub.b.sub.[k][n]

x.sub.b.sub.[k][n]=x.sub.b.sub.[k][n]e.sup.(j2πθ.sup.opt[k].sup.) [0132] end of loop n.sup.∘2 [0133] end loop n.sup.∘1 [0134] transmission of the new multi-carrier symbol: x.sub.ofdm.sub.[n] n ε [0: N−1].

[0135] According to one embodiment that is not very complex, the number of iterations L=1, only a few blocks of the set of K blocks are considered in loop n.sup.∘2 and a single rotation angle ±θ is used in loop n.sup.∘3 to test the improvement in PAPR.

[0136] According to one embodiment, the method scrambles the constellation points with a scrambler. This scrambling is carried out in the frequency domain, after the mapping by the mapper MAP and before the modulation by the K modulators. This scrambling makes it possible to reduce PAPR which is, as a result of the construction of a polar constellation, greater than that obtained with a QAM constellation. For example, the scrambler may be a succession of shift registers initialized to 1 implementing the sequence p(n) obeying the following relationship p(n)=X.sup.11+X.sup.2+1, with X the registers. The scrambling function applied to data d.sub.(n) input into the register input is:

d.sub.(n)=d.sub.(n)*Pseudo.sub.(n)

Pseudo.sub.(n)=2*p.sub.(n)−1

[0137] If scrambling is used transmission-end, the same but inverse scrambling function must be used reception-end.

[0138] Performance in terms of PAPR reduction is assessed by measuring the CCDF (Complementary

[0139] Cumulative Distribution Function). There are two formulas for this measurement:

[00022]$\begin{array}{cc}\mathrm{PAPR}=\frac{{\max }_{0\le t\le N.T}\left[{.Math.x_{\left(t\right)}.Math.}^2\right]}{E\left[{.Math.x_{\left(t\right)}.Math.}^2\right]}& \left(1\right)\end{array}$$\begin{array}{cc}{\mathrm{PAPR}}_{\left(t\right)}=\frac{\left[{.Math.x_{\left(t\right)}.Math.}^2\right]}{E\left[{.Math.x_{\left(t\right)}.Math.}^2\right]}& \left(2\right)\end{array}$

[0140] The second (2) is used to illustrate the performance in terms of PAPR reduction obtained according to the invention.

[0141] Performance was assessed with a transmission-end device employing a 2048-point FFT with 1200 payload carriers, the other carriers being null. Reception-end, a 1504-bit duo-binary turbo-code decoder and 8 iterations were used for decoding.

[0142] FIG. 10 shows the curve of the CCDF values obtained without the reduction method according to the invention, and the curve of the CCDF values obtained with the reduction method according to the invention. To obtain the latter curve, the reduction method according to the invention was implemented with a block of 120 carriers, therefore 10 blocks resulting from the 10 IFFTs, a single iteration L=1 and a single rotation-angle value ±0.

[0143] FIG. 11 shows the curve of the CCDF values obtained without the reduction method according to the invention, and the curve of the CCDF values obtained with the reduction method according to the invention. To obtain the latter curve, the reduction method according to the invention was implemented with a block of 12 carriers, with reference to the block of 4G-LTE (Resource Block). Comparison of the curves of each of FIG. 10 and FIG. 11 illustrates the improvement in respect of reduction of PAPR obtained with the invention. Comparison of the curves according to the invention of FIG. 10 and FIG. 11 illustrates the fact that the increase in the number of blocks allows the reduction in PAPR to be increased.

[0144] The simplified structure of one embodiment of an equipment according to the invention able to implement a telecommunication method according to the invention is illustrated in FIG. 12. This equipment DEV_E may irrespectively be a base station or a mobile terminal. The equipment DEV_E comprises a microprocessor μP, operation of which is controlled via execution of a program Pg the instructions of which allow a telecommunication method according to the invention to be implemented. The equipment DEV_E further comprises a mapper MAP, an OFDM modulator MOD, a PAPR limiter Ct-PAPR, a transmitter EM, and a memory Mem comprising a buffer memory. The OFDM modulator MOD conventionally employs a plurality of inverse Fourier transforms IFFT, as illustrated in the diagram in FIG. 9.

[0145] On initialization, the code instructions of the program Pg are for example loaded into the buffer memory Mem before being executed by the processor μP. The microprocessor μP controls the various components: mapper MAP, K modulators MOD.sub.1, MOD.sub.2, MOD.sub.3, PAPR limiter Ct-PAPR, and transmitter EM.

[0146] Configuration of the equipment involves configuring at least the order of the modulation, the interval p of the constellation, the value of a.sub.0, the number of iterations L, the maximum rotation angle θ.sub.max, and the number K of (IFFT) blocks. The order of the modulation determines the number of points M.

[0147] Thus, by executing the instructions, the microprocessor μP: [0148] determines the polar coordinates of the points of the constellation: a.sub.m×e.sup.jφm, m=0, . . . , M−1, such that a.sub.m+1=a.sub.0+p, p>0, [0149] controls the various components so that, for an input data packet DATA: [0150] the mapper MAP maps the data DATA to points of the constellation, [0151] the K modulators MOD.sub.1, MOD.sub.2, MOD.sub.3 modulate the data mapped to the various carriers, to generate K symbols, [0152] a complex adder adds the K symbols to obtain the OFDM symbol with which the reference Ref is initialized, [0153] the PAPR limiter Ct-PAPR determines the rotation angles θ.sub.G[k] to be applied to the symbols output from the K modulators (K blocks of index k) to obtain the OFDM symbol to be transmitted, which has the lowest PAPR, via comparison with the Ref, which is updated, on each new determined rotation angle, with the obtained OFDM symbol of lower PAPR, [0154] the transmitter EM transmits a radio signal representing the OFDM symbol of lowest PAPR.

[0155] The simplified structure of one embodiment of an equipment according to the invention able to implement a reception method according to the invention is illustrated in FIG. 13. This equipment DEV_R may irrespectively be a base station or a mobile terminal.

[0156] The equipment DEV_R comprises a microprocessor μP, the operation of which is controlled via execution of a program Pg the instructions of which allows a reception method according to the invention to be implemented. The equipment DEV_R further comprises a demapper DEMAP, an OFDM demodulator DEMOD, a receiver RE, and a memory Mem comprising a buffer memory. On initialization, the code instructions of the program Pg are for example loaded into the buffer memory Mem before being executed by the processor μP. The microprocessor μP controls the various components: demapper DEMAP, demodulator DEMOD, and receiver RE.

[0157] According to one embodiment, the demodulator DEMOD implements a two-step demodulation to combat against a relative weakness of a polar constellation with respect to additive white Gaussian noise. In a first step, the demodulator DEMOD assesses the common phase error for a received OFDM symbol and corrects the OFDM symbol accordingly. In a second step, the demodulator DEMOD demodulates the constellation points in a conventional way by means of an LLR computation (LLR being the acronym of Log-Likelihood Ratio), as with a QAM constellation.

[0158] Conventionally, the demodulator employs a Fourier transform FFT. The demapper DEMAP performs the inverse operation of the mapper MAP.

[0159] Configuration of the equipment comprises at least configuring the order of the modulation, the interval of the constellation, and the value of a.sub.0. The order of the modulation determines the number of points M.

[0160] Thus, by executing the instructions, the microprocessor μP: [0161] determines the polar coordinates of the points of the constellation: a.sub.m×e.sup.jφm, m=0, . . . , M−1, such that a.sub.m+1=a.sub.m+p, p>0, [0162] controls the various components so that: [0163] the receiver RE receives the radio signal representative of the OFDM symbols, [0164] the demodulator DEMOD demodulates the successive OFDM symbols to estimate the points of the constellation mapped to the various carriers, [0165] the demapper DEMAP demaps the points of the constellation to estimate the data DATA.

[0166] The equipment DEV_R, which receives the radio signal transmitted according to one embodiment of a method according to the invention, may demodulate the received constellation points by estimating the amplitude of the received point (x.sub.r.sub.i, y.sub.r.sub.i):

x.sub.r.sub.i=a.sub.r.sub.m cos (φ.sub.r.sub.i)+b.sub.x.sub.i

y.sub.r.sub.i=a.sub.r.sub.i sin (φ.sub.r.sub.i)+b.sub.y.sub.i

[0167] b.sub.x and b.sub.y being the additive white Gaussian noise projected onto the channels X and Y.

[0168] Since the constellation is known, and given that there is at most one point per circle in a quadrant, the equipment DEV_R is therefore able, based on amplitude, to determine the received point even if there is an uncertainty in its position, provided that a plurality of quadrants were employed transmission-end to define the constellation.

[0169] After having estimated the amplitude of the received point, the equipment DEV_R may estimate phase error by comparing the estimated points projected onto the axes X(I) and Y(Q) with the transmitted points. The common phase error results mainly from variations in the oscillators and/or in Doppler shift:

Δφ.sub.i=φ.sub.i−(φ.sub.r.sub.i)+b.sub.i

[0170] By summing the various phase-error estimates made for each OFDM carrier i.e. for each point of the constellation that modulated a carrier, the equipment DEV_R is able to improve the phase-error estimate and thus to decrease the influence of white noise on the estimation of the emitted point:

Δ.sub.φ=LΣ.sub.i=1.sup.LΔ.sub.φi

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

[0171] Once the common phase error has been estimated, the equipment DEV_R may correct all of the constellation points modulating an OFDM symbol. This correction may be made 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, it is possible to decrease the interference between carriers that results from the phase rotation.

[0172] Determination of phase error allows demodulation error to be decreased.

[0173] Reception-end correction power is directly related to the structure of the polar constellations—for example, for the polar constellation limited to one quadrant, the maximum phase rotation is ±π/4 and for the spiral constellation the limit is ±π. Limiting phase rotation to reduce PAPR also makes it possible to continue to assess phase variations caused by Doppler shift or by the phase noise of the oscillators.

[0174] As a result, the invention also applies to one or more computer programs, in particular a computer program on or in a data medium, suitable for implementing the invention. This program may use any programming language and take the form of source code, object code or of code intermediate between source code and object code, such as code in a partially compiled form, or in any other form desirable for implementing a method according to the invention.

[0175] The data medium may be any entity or device capable of storing the program. For example, the medium may comprise a storage means, such as a ROM, for example a CD-ROM or a microelectronic circuit ROM, or else a magnetic recording means, for example a USB key or a hard disk.

[0176] Moreover, the data medium may be a transmissible medium such as an electrical or optical signal, which may be routed via an electrical or optical cable, by radio or by other means. The program according to the invention may in particular be downloaded from a network such as the Internet.

[0177] As an alternative, the data medium may be an integrated circuit into which the program is incorporated, the circuit being configured to execute or to be used in the execution of the method in question.