METHOD FOR RECEIVING A SOQPSK-TG SIGNAL WITH PAM DECOMPOSITION

Abstract

The invention relates to a method for receiving a CPM signal with space-time encoding, preferably a SOQPSK-TG signal based on the IRIG-106 recommendation, emitted by two emission antennas A1, A2, wherein the received signal modulates a plurality of bits b.sub.i.sup.(j) j=0 or 1 and corresponds to the bits emitted on the antennas A1 and A2, respectively, said received signal comprising a temporal offset Δτ, said signal being received on one or a plurality of receiving antennas A3; —obtaining a digital signal y(k), which is sampled, and the offset version γ.sub.Δτ(k) thereof on an antenna, taking into account the temporal offset between the two antennas, each comprising the contributions of the signals originating from the two emission antennas, wherein said digital signals can be expressed according to the following decomposition: formula (I).

Claims

1. A method for receiving a CPM signal with space-time coding, said signal being an SOQPSK-TG signal based on the IRIG-106 recommendation transmitted from two transmitting antennas A1, A2 the received signal modulating a plurality of bits b.sub.i.sup.(j) j=0 or 1 and corresponding to the bits transmitted over the antenna A1 and A2 respectively, said received signal having a time offset Δτ taking into account the time offset between the signals transmitted from each antenna A1, A2, said signal being received over one or more receiver antennas A3; obtaining over one antenna a sampled digital signal y(k) and its offset version y.sub.Δτ(k) taking into account the time offset between the two transmitting antennas, each comprising the contributions of the signals output by the two transmitting antennas, said digital signals being able to be expressed according to the following decomposition $s_p\left(t\right)\approx \underset{i}{.Math.}{\rho }_{0,2i}^p{w}_0\left(t-2i{T}_b\right)-{\rho }_{1,2i+1}^p{w}_1\left(t-2i{T}_b-T_b\right)+\left(\underset{i}{.Math.}{\rho }_{02i+1}^p{w}_0\left(t-2i{T}_b-T_b\right)-{\rho }_{1,2i}^p{w}_1\left(t-2{\mathrm{iT}}_b\right)\right)$ where: T.sub.b is the duration of one bit;
p∈{0,1} ρ.sub.0,i.sup.0, ρ.sub.1,i.sup.0, are pseudo-symbols corresponding to the information bits b.sub.i.sup.(0) transmitted over the antenna A1, ρ.sub.0,i.sup.1, ρ.sub.1,i.sup.1 are pseudo-symbols corresponding to the information bits b.sub.i.sup.(1) transmitted over the antenna A2; w.sub.0(t) and w.sub.1(t) are shaping pulses, respectively a main pulse and a secondary pulse defining a Viterbi algorithm (Trellis 1, Trellis 2) having a fixed trellis with a number of states and metrics also a function of at least said main pulse; obtaining, by means of said Viterbi algorithm, LLRs on the transmitted information bits.

2. The receiving method as claimed in claim 1, wherein the digital signals obtained are expressed $y\left(k\right)\approx \underset{m=0}{\overset{1}{.Math.}}\underset{i=-\frac{N_t^m-1}{2}}{\overset{\frac{N_t^m-1}{2}}{.Math.}}{\rho }_{m,k-i}^0{\tilde{f}}_m^0\left(i\right)+\underset{m=0}{\overset{1}{.Math.}}\underset{i=-\frac{N_t^m-1}{2}}{\overset{\frac{N_t^m-1}{2}}{.Math.}}{\rho }_{m,k-i}^0{\tilde{f}}_m^{1,\Delta \tau }\left(i\right)+z\left(\mathrm{kT}+\Delta {\tau }_0\right)$ $y_{\Delta \tau }\left(k\right)\approx \underset{m=0}{\overset{1}{.Math.}}\underset{i=-\frac{N_t^m-1}{2}}{\overset{\frac{N_t^m-1}{2}}{.Math.}}{\rho }_{m,k-i}^0{\tilde{f}}_m^{0,\Delta \tau }\left(i\right)+\underset{m=0}{\overset{1}{.Math.}}\underset{i=-\frac{N_t^m-1}{2}}{\overset{\frac{N_t^m-1}{2}}{.Math.}}{\rho }_{m,k-i}^1{\tilde{f}}_m^1\left(i\right)+z\left(\mathrm{kT}+\Delta {\tau }_1\right)$ where Δτ=Δτ.sub.1−Δτ.sub.0 where Δτ.sub.0 is the delay of the direct path from the antenna A1 and Δτ.sub.1 is the delay of the direct path from the antenna A2, Δτ is the time offset; Δε is the integer the closest to the division of Δτ by T; ρ.sub.0,i.sup.0, ρ.sub.1,i.sup.0 are pseudo-symbols corresponding to the information bits transmitted over the antenna A1, ρ.sub.0,i.sup.0, ρ.sub.1,i.sup.0 are pseudo-symbols corresponding to the information bits transmitted over the antenna A2; δ(t) is the Dirac pulse centered on 0; N.sub.t.sup.m is the length of the filters {tilde over (f)}.sub.m.sup.0, {tilde over (f)}.sub.m.sup.0,Δτ, {tilde over (f)}.sub.m.sup.1, {tilde over (f)}.sub.m.sup.1,Δτ z is additive noise.

3. The receiving method as claimed in claim 2, wherein the values {tilde over (f)}.sub.m.sup.0, {tilde over (f)}.sub.m.sup.0,Δτ, {tilde over (f)}.sub.m.sup.1, {tilde over (f)}.sub.m.sup.1,Δτ are defined as follows
{tilde over (f)}.sub.m.sup.p(i)={tilde over (f)}.sub.m.sup.p(t=iT)
{tilde over (f)}.sub.m.sup.0,Δτ(i)={tilde over (f)}.sub.m.sup.0(t=iT+ΔεT)
{tilde over (f)}.sub.m.sup.1,Δτ(i)={tilde over (f)}.sub.m.sup.0(t=iT−ΔεT)
with
{tilde over (f)}.sub.m.sup.p(t)=∫f.sub.m.sup.k(θ)g(θ−t)dθ
and $f_m^0\left(t\right)=w_m\left(t\right)*\left(h_0\delta \left(t\right)+\underset{i=1}{\overset{N_0}{.Math.}}{h}_{2i}\delta \left(t-\left(\Delta {\tau }_{2i}-\Delta {\tau }_0\right)\right)\right),m\in \left\{0,1\right\}$ $f_m^1\left(t\right)=w_m\left(t\right)*\left(h_1\delta \left(t\right)+\underset{i=1}{\overset{N_1}{.Math.}}{h}_{2i+1}\delta \left(t-\left(\Delta {\tau }_{2i+1}-\Delta {\tau }_1\right)\right)\right),m\in \left\{0,1\right\}$ where N.sub.0, N.sub.1 are the number of multiple paths respectively coming from the antenna A1 and the antenna A2.

4. The method as claimed in claim 3, comprising prior to the step of obtaining the signals y(k) and its offset version y.sub.Δτ(k) a step (E51) of filtering the received signal by means of a Finite Impulse Response (FIR) low-pass filter of Equiripple type digitally constructed such that the normalized cut-off frequency is 0.45.

5. The method as claimed in claim 1, wherein in the absence of multiple paths, the digital signals obtained are grouped into groups of 4 samples and are expressed $y\left(4k\right)=h_0\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^0{\tilde{w}}_0\left(iT\right)+h_0{\rho }_{1,4k}^0{\tilde{w}}_1\left(0\right)+h_1\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k}^1{\tilde{w}}_0\left(\mathrm{iT}-\Delta \mathrm{.Math.}T\right)+h_1{\rho }_{1,4k}^1{\tilde{w}}_1\left(-\mathrm{\Delta .Math.}T\right)+\tilde{n}\left(4kT\right)y_{\Delta \tau }\left(4k\right)=h_0\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^0{\tilde{w}}_0\left(iT+\Delta \mathrm{.Math.}T\right)+h_0{\rho }_{1,4k}^0{\tilde{w}}_1\left(\Delta \mathrm{.Math.}T\right)+h_1\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-1}^1{\tilde{w}}_0\left(\mathrm{iT}\right)+h_1{\rho }_{1,4k}^1{\tilde{w}}_1\left(0\right)+\tilde{n}\left(4\mathrm{kT}+\Delta \mathrm{.Math.}T\right)$ where {tilde over (w)}.sub.0 and {tilde over (w)}.sub.1 are filtered versions of a main pulse w.sub.0 and a secondary pulse w.sub.1.

6. The method as claimed in claim 5, wherein the metrics of the Viterbi algorithm are defined by $\lambda \left(S_{n-1}\left(i\right).fwdarw.S_n\left(j\right)\right)=\underset{m=-1}{\overset{2}{.Math.}}\left[{.Math.B_{m,n}^{\left(0\right)}.Math.}^2+{.Math.B_{m,n}^{\left(\Delta \tau \right)}.Math.}^2\right]$ $\mathrm{with}$ $B_{m,n}^{\left(0\right)}=y\left(4n+m\right)-h_0\left(\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4n+m-i}^0{\tilde{w}}_0\left(iT\right)+{\rho }_{1,4n+m}^0{\tilde{w}}_1\left(0\right)\right)-h_1\left(\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4n+m-i}^1{\tilde{w}}_0\left(\mathrm{iT}-\Delta \mathrm{.Math.}T\right)+{\rho }_{1,4n+m}^1{\tilde{w}}_1\left(-\Delta \mathrm{.Math.}T\right)\right)$ $B_{m,n}^{\left(\Delta \tau \right)}=y_{\Delta \tau }\left(4n+m\right)-h_0\left(\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4n+m-i}^0{\tilde{w}}_0\left(iT+\Delta \mathrm{.Math.}T\right)+{\rho }_{1,4n+m}^0{\tilde{w}}_1\left(\Delta \mathrm{.Math.}T\right)\right)-h_1\left(\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4n+m-i}^1{\tilde{w}}_0\left(iT\right)+{\rho }_{1,4n+m}^1{\tilde{w}}_1\left(0\right)\right)$ where {tilde over (w)}.sub.0 and {tilde over (w)}.sub.1 are filtered versions of a main pulse w.sub.0 and a secondary pulse w.sub.1.

7. The method as claimed in claim 1, wherein in the presence of multiple paths, the method comprises a step (E54′) of estimating the propagation channel in such a way as to obtain the estimates of {tilde over (f)}.sub.m.sup.0, {tilde over (f)}.sub.m.sup.0,Δτ, {tilde over (f)}.sub.m.sup.1, {tilde over (f)}.sub.m.sup.1,Δτ, the Viterbi algorithm using the estimated parameters of the channel, the metrics of the Viterbi algorithm being defined by $\lambda \left(S_{n-1}\left(i\right).fwdarw.S_n\left(j\right)\right)=\underset{m=-1}{\overset{2}{.Math.}}\left[{.Math.B_{m,n}^{\left(0\right)}.Math.}^2+{.Math.B_{m,n}^{\left(\Delta \tau \right)}.Math.}^2\right]$ $\mathrm{with}$ $B_{m,n}^{\left(0\right)}=y\left(4n+m\right)-\left(\underset{i=-\frac{\left(N_t-1\right)}{2}}{\overset{i=\frac{\left(N_t-1\right)}{2}}{.Math.}}{\rho }_{0,4n+m-i}^0{\tilde{f}}_{0,n_p}^0\left(i\right)+\underset{i=-\frac{\left(N_t-3\right)}{2}}{\overset{i=\frac{\left(N_t-3\right)}{2}}{.Math.}}{\rho }_{1,4n+m-i}^0{\tilde{f}}_{1,n_p}^0\left(i\right)+\underset{i=-\frac{\left(N_t-1\right)}{2}}{\overset{i=\frac{\left(N_t-1\right)}{2}}{.Math.}}{\rho }_{0,4n+m-i}^1{\tilde{f}}_{0,n_p}^{1,\Delta \tau }\left(i\right)+\underset{i=-\frac{\left(N_t-3\right)}{2}}{\overset{i=\frac{\left(N_t-3\right)}{2}}{.Math.}}{\rho }_{1,4n+m-i}^1{\tilde{f}}_{1,n_p}^{1,\Delta \tau }\left(i\right)\right)$ $B_{m,n}^{\left(\Delta \tau \right)}=y_{\Delta \tau }\left(4n+m\right)-\left(\underset{i=-\frac{\left(N_t-1\right)}{2}}{\overset{i=\frac{\left(N_t-1\right)}{2}}{.Math.}}{\rho }_{0,4n+m-i}^0{\tilde{f}}_{0,n_p}^{0,\Delta \tau }\left(i\right)+\underset{i=-\frac{\left(N_t-3\right)}{2}}{\overset{i=\frac{\left(N_t-3\right)}{2}}{.Math.}}{\rho }_{1,4n+m-i}^0{\tilde{f}}_{1,n_p}^{0,\Delta \tau }\left(i\right)+\underset{i=-\frac{\left(N_t-1\right)}{2}}{\overset{i=\frac{\left(N_t-1\right)}{2}}{.Math.}}{\rho }_{0,4n+m-i}^1{\tilde{f}}_{0,n_p}^1\left(i\right)+\underset{i=-\frac{\left(N_t-3\right)}{2}}{\overset{i=\frac{\left(N_t-3\right)}{2}}{.Math.}}{\rho }_{1,4n+m-i}^1{\tilde{f}}_{1,n_p}^1\left(i\right)\right)$

8. The method as claimed in claim 1, wherein in the presence of multiple paths, the method comprises a step of equalization, the Viterbi algorithm using the equalized signal, the metric for each node of the Viterbi being defined by $\lambda \left(n\right)=\{\begin{array}{cc}{\beta }_n\left(2x_n-\left(D-C\right)\zeta {\beta }_{n+3}-C\zeta {\beta }_{n+1}-D\zeta {\beta }_{n-3}\right)-A\chi {.Math.{\beta }_n.Math.}^2& \mathrm{if}n=4k\\ {\beta }_n\left(2x_n-\left(D-C\right)\zeta {\beta }_{n+1}-C{\mathrm{\zeta \beta }}_{n-1}-D{\mathrm{\zeta \beta }}_{n+3}\right)-A\chi {.Math.{\beta }_n.Math.}^2& \mathrm{if}n=4k+1\\ {\beta }_n\left(2x_n-\left(D-C\right)\zeta {\beta }_{n-1}-D{\mathrm{\zeta \beta }}_{n+1}-D{\mathrm{\zeta \beta }}_{n-3}\right)-A\chi {.Math.{\beta }_n.Math.}^2& \mathrm{if}n=4k+2\\ {\beta }_n\left(2x_n-D{\mathrm{\zeta \beta }}_{n-1}-C{\mathrm{\zeta \beta }}_{n+3}\right)-A\chi {.Math.{\beta }_n.Math.}^2& \mathrm{if}n=4k+3\end{array}\mathrm{with}\chi ={.Math.h_0.Math.}^2+{.Math.h_1.Math.}^2\zeta =\mathrm{Im}\left(h_0^{*}{h}_1\right)A=\frac{1}{2}\left({\tilde{w}}_0\left(0\right)+{\tilde{w}}_0\left(\Delta \mathrm{.Math.}T\right)\right)C=\frac{1}{2}\left({\tilde{w}}_0\left(-T\right)+{\tilde{w}}_0\left(-T+\Delta \mathrm{.Math.}T\right)\right)D=\frac{1}{2}\left({\tilde{w}}_0\left(T\right)+{\tilde{w}}_0\left(T+\Delta \mathrm{.Math.}T\right)\right)$ where {tilde over (w)}.sub.0 and {tilde over (w)}.sub.1 are filtered versions of a main pulse w.sub.0 and a secondary pulse w.sub.1.

9. The method as claimed in claim 1, wherein the pseudo-symbols ρ.sub.0,i.sup.0, ρ.sub.1,i.sup.0 corresponding to the information bits transmitted over the antennas A1, A2, are expressed ${\rho }_{0,i}^p=\{\begin{array}{cc}\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{even}\\ j\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{odd}\end{array}{\rho }_{1,i}^p=\{\begin{array}{cc}-j\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_{i-1}^{\left(p\right)}-1\right)\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{even}\\ -\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_{i-1}^{\left(p\right)}-1\right)\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{odd}\end{array}$

10. The method as claimed in claim 1, comprising a step of decoding the LLRs by means of a channel decoder or obtaining the heavy-weight bits of the LLRs.

11. A receiving device comprising a processing unit configured to implement a method as claimed in claim 1.

12. A computer program product comprising code instructions for executing a method as claimed in claim 1, when the latter is executed by a processor.

Description

OVERVIEW OF THE FIGURES

[0065] Other features, aims and advantages of the invention will become apparent from the following description, which is purely illustrative and non-limiting, and which must be read with reference to the appended drawings in which, besides the FIGS. 1 to 4 already discussed:

[0066] FIG. 5 illustrates a transmission-reception scheme according to the invention;

[0067] FIG. 6 illustrates a transmission scheme according to the invention

[0068] FIG. 7 illustrates a pulse for the PAM—OQPSK decomposition according to the invention;

[0069] FIG. 8 illustrates a pulse for the PAM-FQPSK-JR decomposition according to the invention;

[0070] FIG. 9 illustrates a recursive precoder according to the invention;

[0071] FIG. 10 illustrates a pulse for the PAM-MSK decomposition according to the invention;

[0072] FIG. 11 illustrates a pulse for the PAM-GMSK decomposition with a width BT=0.25 according to the invention;

[0073] FIG. 12 illustrates a pulse for the PAM-SOQPSK-MIL decomposition according to the invention;

[0074] FIG. 13 illustrates a pulse for the PAM-SOQPSK-TG decomposition according to the invention;

[0075] FIG. 14 illustrates a reception scheme according to the invention;

[0076] FIG. 15 illustrates a demodulation scheme according to a first embodiment of the invention;

[0077] FIG. 16 illustrates a filter reducing the inter-symbol interference used in the first embodiment of the invention;

[0078] FIG. 17 illustrates a trellis used in the first and second embodiments of the invention;

[0079] FIG. 18 illustrates a demodulation scheme according to a second embodiment;

[0080] FIG. 19 illustrates a channel estimator of known type;

[0081] FIG. 20 illustrates a channel estimator used in the second embodiment of the invention;

[0082] FIG. 21 illustrates the principle of the estimation of the channel;

[0083] FIG. 22 illustrates a demodulation scheme according to a third embodiment of the invention;

[0084] FIG. 23 illustrates a filter reducing the inter-symbol interference used in the third embodiment of the invention;

[0085] FIG. 24 illustrates a trellis used in the third embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

1) Description of the Transmission Method

[0086] In relation to FIG. 5, two transmitting antennas A1 and A2, which can be mobile at respective speeds {right arrow over (v)}.sub.1 and {right arrow over (v)}.sub.2 respectively send a signal s.sub.0(t) and s.sub.1(t) to several receiving antennas 3I, I varying from 1 to N, which can, also, be mobile at a speed {right arrow over (v)}.sub.3I.

[0087] The transmitting antennas A1 and A2 are fed by a transmitting device 20 described hereinafter.

[0088] The receiving antenna A3 then receives a signal which feeds a receiving device 10 itself described hereinafter.

[0089] FIG. 6 describes the transmitting device 20 feeding the transmitting antennas.

[0090] A series of bits b.sup.d=b.sub.k.sup.d, b.sub.k+1.sup.d, . . . can advantageously be encoded by an error correcting code (encoder 21 of LDPC or Turbo-Code type for example) in order to make the system robust to noise. A series of bits b= . . . b.sub.k, b.sub.k+1, . . . is obtained at the output of the encoder 21 or without channel encoding and is then encoded according to a binary rearrangement encoding such that two trains of bits b.sub.u.sup.(0)= . . . c.sub.k,c.sub.k+1, . . . and b.sub.u.sup.(1)= . . . d.sub.k, d.sub.k+1, . . . are obtained at the output of the encoder 22.

[0091] This binary rearrangement code is a combination of operations of binary permutation and binary inversion.

[0092] On each of the binary trains b.sub.u.sup.(0) and b.sub.u.sup.(1), preamble bits written P(0) and P(1) are added. Thus on the sequence b.sub.u.sup.(0) (respectively b)), the preamble P(0) (or P(1) respectively) of size L.sub.p is inserted between two data blocks of size L.sub.d.

[0093] The frames b.sup.(0) and b.sup.(1) composed of preamble bits and bits corresponding to the useful data are represented at the bottom of FIG. 6.

[0094] These frames thus obtained are modulated by a CPM-type modulation which can be written as a OQPSK modulation by means of two modulators 23, 24, respectively receiving the frames in order to obtain the two signals s.sub.0(t) and s.sub.1(t) which are transmitted on each of the antennas 1, 2.

[0095] A signal coming from a modulation of CPM type is written as follows:

[00009]$s\left(t\right)=\sqrt{\frac{E}{T}}\exp \left(j\mathrm{2\pi }\underset{i}{.Math.}{h}_i{\alpha }_{i}q\left(t-\mathrm{iT}\right)\right)$

with: [0096] α.sub.i is an information symbol coming from the alphabet {0, ±2, . . . , ±(M−1)} when M is odd and {±1, ±3, . . . , ±(M−1)} when M is even. [0097] E is the energy of the information symbol [0098] T is the duration of the information symbol [0099] h.sub.i is the modulation index [0100] q(t)=∫.sub.−∞.sup.tg(τ)d.sub.τ is defined as the phase pulse and g(t) is the frequency pulse.

[0101] The STC-SOQPSK case as described in the IRIG-106 recommendation is a special case of this model where [0102] the transmitting antennas 1 and 2 are mobile; [0103] there is only one receiving antenna (N=1); [0104] the error-correcting code is an LDPC code as described in the IRIG-106 recommendation [0105] the binary rearrangement code constructed on the basis of the sequence b= . . . b.sub.4k, b.sub.4k+1, b.sub.4k+2, b.sub.4k+3, . . . the sequences b.sub.u.sup.(0)= . . . b.sub.4k, b.sub.4k+1, b.sub.4k+2, b.sub.4k+3, . . . and b.sub.u.sup.(1)= . . . b.sub.4k+2 b.sub.4k+3, b.sub.4k, b.sub.4k+1, . . . where the operation x represents the binary inversion operation of the bit x [0106] the preambles P(0) and P(1) are as described in the IRIG-106 recommendation with L.sub.p=128 and L.sub.d=3200 [0107] M=3 [0108] The symbols α.sub.i are as described in the IRIG-106 recommendation. [0109] h.sub.i=½ [0110] q(t) and g(t) are as described in the IRIG-106 recommendation

2) CPM Signals that can be Written in the Form of OQPSK Modulation

[0111] A signal resulting from a CPM-type modulation that can be written as an OQPSK modulation makes it possible to write accurately or approximately the signal s(t) previously defined as:

[00010]$s_p\left(t\right)\approx \underset{i}{.Math.}{\rho }_{0,2i}^p{w}_0\left(t-2{\mathrm{iT}}_b\right)-{\rho }_{1,2i+1}^p{w}_1\left(t-2{\mathrm{iT}}_b-T_b\right)+\left(\underset{i}{.Math.}{\rho }_{0,2i+1}^p{w}_0\left(t-2{\mathrm{iT}}_b-T_b\right)-{\rho }_{1,2i}^p{w}_1\left(t-2{\mathrm{iT}}_b\right)\right)$

where: [0112] p∈{0,1} [0113] ρ.sub.i.sup.0 and ρ.sub.i.sup.1 are pseudo-symbols analytically expressed as follows:

[00011]${\rho }_{0,i}^p=\{\begin{array}{cc}\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{even}\\ j\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{odd}\end{array}{\rho }_{1,i}^p=\{\begin{array}{cc}-j\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_{i-1}^{\left(p\right)}-1\right)\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{even}\\ -\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{odd}\end{array}$ [0114] b.sub.i.sup.(0) and b.sub.i.sup.(1) are respectively the information bits feeding the SOQPSK modulator of path 1 and path 2. [0115] w.sub.0(t) and w.sub.1(t) are shaping pulses.

[0116] The obtainment of this analytical expression is described in detail in the document [A4]. [0117] [A4]: R. Othman, A. Skrzypczak, Y. Louët, “PAM Decomposition of Ternary CPM with Duobinary Encoding”, IEEE Transactions on Communications, vol. 65, no. 10, pp. 4274-4284, October 2017;

[0118] The decomposition above can be applied to certain modulations such as OQPSK modulation. In this scenario, the pulses w.sub.0 and w.sub.1 are shown in FIG. 7.

[0119] Similarly, FQPSK-JR modulation (Feher's patented Quadrature Phase Shift Keying), described in the IRIG 106, can also be expressed in this form with the pulses w.sub.0 and w.sub.1 shown in FIG. 8.

[0120] Finally, any CPM modulation of index h=½ containing a recursive precoder of the form described in FIG. 9 can be written in this form.

[0121] In particular, MSK (Minimum Shift Keying) modulation falls within this category. The associated pulses w.sub.0 and w.sub.1 are shown in FIG. 10.

[0122] In particular, GMSK (Gaussian Minimum Shift Keying) modulation can also be written in this form. For the special case of GMSK with BT=0.25, the associated pulses w.sub.0 and w.sub.1 are shown in FIG. 11.

[0123] In particular, SOQPSK-MIL modulation as described in the IRIG 106 also falls within this category. The associated pulses w.sub.0 and w.sub.1 are shown in FIG. 12.

[0124] Finally, SOQPSK-TG modulation as described in the IRIG 106 also falls within this category. The associated pulses w.sub.0 and w.sub.1 are shown in FIG. 13.

3) Description of the Receiving Method

[0125] There now follows a model of the expression of the signal at the input of the receiving device E2 of FIG. 1. This signal received over the antenna I, written r.sub.I(t), with I varying from 1 to N, is analytically expressed:

r.sub.I(t)=[h.sub.0,Is.sub.0(t−Δt.sub.0,I)+h.sub.1,Is.sub.1(t−Δt.sub.1,I)]e.sup.j2πΔf.sup.I.sup.t+z.sub.I(t)

with [0126] h.sub.0,I the complex gain associated with the direct-line propagation of the signal s.sub.0(t) from the transmitting antenna 1 to the receiving antenna I. [0127] h.sub.1,I the complex gain associated with the direct-line propagation of the signal s.sub.1(t) from the transmitting antenna 2 to the receiving antenna I. [0128] Δt.sub.0,I is the delay due to the propagation of the signal s.sub.0(t) between the transmitting antenna 1 and the receiving antenna I; [0129] Δτ.sub.1,I is the delay due to the propagation of the signal s.sub.1(t) between the transmitting antenna 2 and the receiving antenna I; [0130] Δf.sub.I the frequency offset seen from the receiving antenna I; [0131] z.sub.I(t) an additive noise on the antenna I.

[0132] The time offset seen on the antenna I will be written in the remainder of the text as Δτ.sub.I=Δt.sub.1,I−Δt.sub.0,I.

[0133] The reception device of this signal is described in FIG. 14.

[0134] On each reception channel I corresponding to the processing path of the signal received over the antenna I, I varying from 1 to N, the signal is first filtered (step E1) by a receiving filter. This filtered signal is then digitized (step E2).

[0135] A synchronization method (step E3) identical to that described in the document [A3] is used in order to synchronize the signal in time and in frequency (by estimating Δf.sub.I) and in order to estimate the delays Δt.sub.0,I and Δt.sub.1,I as well as the channel gains h.sub.0,I and h.sub.1,I.

[0136] The frequency offset is corrected (step E4) using the estimate of the frequency offset previously produced.

[0137] This gives N sequences of samples r.sub.0,1(n), . . . , r.sub.0,N(n) feeding the demodulator. In the same way, the different estimates of the delays Δt.sub.0,I and Δt.sub.1,I and of the channel gains h.sub.0,I and h.sub.1,I are involved as parameters of the demodulator.

[0138] At the demodulator output, an LLR sequence is obtained. This LLR sequence then feeds a decoder.

[0139] The present invention described here consists in the demodulation (step E5, E5′, E5″) of the signal by the demodulator using the advantageous expression of the signal STC-SOQPSK based on the IRIG-106 recommendation modeled as described above. Such an expression makes it possible to simplify the processing of the demodulator.

[0140] According to a first embodiment (see part 4) hereinafter), the demodulation (step E5) dispenses with multiple paths (and only takes into account the two main paths) such that the N sequences of samples r.sub.0,1(n), . . . , r.sub.0,N(n) feeding the demodulator have expressions that simplify. As will be seen in more detail, each sequence of samples is first filtered by a matched filter (step E51) then the signal is sampled (step E52) using the parameters Δt.sub.0,I and Δt.sub.1,I estimated at the times kT and also at the times kT+Δt.sub.I. This respectively gives the sequences of samples y.sub.I(k),y.sub.Δτ.sub.I(k) and y.sub.Δτ.sub.I(k) being the offset version of the time offset of the signal y.sub.I(k). These signals thus sampled then feed a Viterbi algorithm (Trellis 1) (step E53) having branch metrics specific to the expressions of the signals. This gives at the output of Trellis 1 a sequence of soft-output demodulated bits of LLR (Log Likelihood Ratio) type. This sequence of demodulated bits is then decoded (step E6).

[0141] According to a second embodiment (see part 5) hereinafter), the demodulation (step E5′) considers the multiple paths in addition to the direct paths. The expressions of the N sequences of samples r.sub.0,1(n), . . . , r.sub.0,N(n) feeding the demodulator are certainly more complex than those of the first embodiment, but the demodulator performs better. As for the first embodiment, each sequence of samples is firstly filtered by a matched filter (step E51′) then the signal is sampled (step E52′) using the parameters Δt.sub.0,I and Δt.sub.1,I estimated at the times kT and also at the times kT+Δt.sub.I. This respectively gives the sequences of samples y.sub.I(k) and y.sub.Δτ.sub.I(k). This second embodiment differs from the first in that it comprises a step of estimating the parameters of the propagation channels (step E54′) which are used by the Viterbi algorithm which uses the parameters of the channels to estimate the gains h.sub.0,1, h.sub.1,1, . . . , h.sub.0,N, h.sub.1,N and equalize the signals at the same time as the demodulation. Thus, the sampled signals and the parameters of the propagation channels feed a Viterbi algorithm (Trellis 1) (step E53′) having branch metrics specific to the expressions of the signals. This gives at the output of Trellis 1 a sequence of soft-output demodulated bits of LLR type. This sequence of demodulated bits is then decoded (step E6).

[0142] According to a third embodiment (see part 6)), the demodulation (step E5″) considers, as for the second embodiment, the multiple paths in addition to the direct paths. The different between this third embodiment and the second embodiment is that the signals are equalized before being input into the Viterbi algorithm (Trellis 2). Here again, each sequence of samples is first filtered by a matched filter (step E51″) then the signal is sampled (step E52″) using the parameters Δt.sub.0,I and Δt.sub.1,I estimated at the times kT and also at the times kT+Δt.sub.I. This respectively gives the sequences of samples y.sub.I(k) and y.sub.Δτ.sub.I(k). These sampled signals are then equalized (step E54″) by means of estimates of the channel gains h.sub.0,I and h.sub.1,I, and the equalized signals then feed a Viterbi algorithm (Trellis 2) (step E53″). This gives at the output of Trellis 2 a sequence of soft-output demodulated bits of LLR (Log Likelihood Ratio) type. This sequence of demodulated bits is then decoded (step E6).

[0143] There follows a description of the different embodiments presented.

4) First Embodiment, without Multiple Paths

[0144] This demodulation architecture is described in FIG. 15. This architecture has N inputs corresponding to the N sequences of samples r.sub.0,1(n), . . . , r.sub.0,N(n) feeding the demodulator. This architecture also requires the estimates of the delays Δt.sub.0,1, Δt.sub.1,1, . . . , Δt.sub.0,N, Δt.sub.1,N along with the estimates of the channel gains h.sub.0,1, h.sub.1,1, . . . , h.sub.0,N, h.sub.1,N. At the output of this demodulation architecture, a sequence of soft-output demodulated bits (LLR) is obtained.

[0145] The sequence of samples r.sub.0,I(n) with I varying from 1 to N is first filtered by a filter making it possible to optimize the signal-to-noise ratio at the demodulation input. This filter can be simply a matched filter.

[0146] Using the parameters Δt.sub.0,I and Δt.sub.1,I, the signal is sampled firstly at the times kT and secondly at the times kT+Δt.sub.I. This then respectively gives the sequences of samples y.sub.I(k) and y.sub.Δτ.sub.I(k).

[0147] The two sequences y.sub.1(k), y.sub.Δτ.sub.1(k), . . . , y.sub.N (k),y.sub.Δτ.sub.N(k) then feed a trellis 1. This method also requires the knowledge of certain parameters Δt.sub.0,1,Δt.sub.1,1, . . . , Δt.sub.0,N, Δt.sub.1,N as well as the parameters h.sub.0,1, h.sub.1,1, . . . , h.sub.0,N, h.sub.1,N.

[0148] By writing L the number of bits involved in the space-time coding, the trellis used then has 2.sup.L states and 2.sup.2L branches.

[0149] This trellis can then be used to estimate the most likely transmitted binary sequence. Moreover, a single trellis having a fixed number of states can be used to compute LLRs. This is referred to as a fixed trellis.

[0150] The computation of the LLRs on the information bits can then be done by way of a SOVA (Soft Output Viterbi Algorithm). The description of this algorithm is given in the document [A5]. [0151] [A5]: J. Hagenauer and P. Hoeher, “A Viterbi Algorithm with Soft-Decision Outputs and its Application”, Global Telecommunications Conference and Exhibition (IEEE GLOBECOM), pp. 1680-1686, vol. 3, November 1989.

[0152] The advantages of this architecture are several.

[0153] 1. The presence of the filter for reducing the inter-symbol interference present at the input of the demodulator makes it possible to greatly reduce the complexity of the equalization blocks and to simplify the trellis used for the Viterbi algorithm.

[0154] 2. The particular decomposition of the CPM signal in the form of a modulation of OQPSK type has the consequence of enabling the use a fixed trellis.

[0155] 3. The single and fixed trellis used in the Viterbi algorithm has the advantage of using an algorithm of SOVA type in order to compute the LLRs on the demodulated bits.

[0156] 4. The whole demodulation method is more robust at high values of the time offset Δt.sub.1,I−Δt.sub.0,N by comparison with the solution of the prior art.

[0157] 5. The trellis has the advantage of requiring fewer computational resources by comparison with the solution of the prior art.

[0158] 6. Even without a channel decoder for decoding the LLRs, the use of a hard decision (Most Significant Bit, (MSB)) on the LLRs leads to an improvement of the performance.

[0159] This demodulation architecture makes use of the fact that the received signal can be written via a very precise approximation of the signals.

[0160] In the special case of STC-SOQPSK based on the IRIG-106 recommendation, supposing that the frequency offset has been perfectly corrected, the received signal can be written as follows:

[00012]$r_0\left(n\right)\approx h_0\underset{\underset{s_0\left({\mathrm{nT}}^{\prime }\right)}{︸}}{\left[\underset{i}{.Math.}{\rho }_{0,i}^0{w}_0\left({\mathrm{nT}}^{\prime }-\mathrm{iT}\right)+\underset{i}{.Math.}{\rho }_{1,i}^0{w}_1\left({\mathrm{nT}}^{\prime }-\mathrm{iT}\right)\right]}+h_1\underset{\underset{s_0\left({\mathrm{nT}}^{\prime }-\mathrm{\Delta \tau }\right)}{︸}}{\left[\underset{i}{.Math.}{\rho }_{0,i}^1{w}_0\left({\mathrm{nT}}^{\prime }-\mathrm{iT}-\mathrm{\Delta \tau }\right)+\underset{i}{.Math.}{\rho }_{1,i}^1{w}_1\left({\mathrm{nT}}^{\prime }-\mathrm{iT}-\mathrm{\Delta \tau }\right)\right]}+z\left({\mathrm{nT}}^{\prime }\right)$

where: [0161] T′ is the sampling duration of the analog-to-digital converter (consequently T′<<T) [0162] w.sub.0 is the main pulse of the decomposition of the CPM signal in the form of OQPSK modulation, shown in FIG. 13 [0163] w.sub.1 is the secondary pulse of the decomposition of the CPM signal in the form of OQPSK modulation, shown in FIG. 13 [0164] h.sub.0, h.sub.1 and Δτ are respectively the channel gain resulting from the propagation between the transmitting antenna 1 and the receiving antenna, the channel gain resulting from the propagation between the transmitting antenna 2 and the receiving antenna and the time offset defined as Δτ=Δt.sub.1−Δt.sub.0. [0165] z is additive noise [0166] ρ.sub.0,i.sup.0, ρ.sub.0,i.sup.1, ρ.sub.1,i.sup.0 and ρ.sub.1,i.sup.1 are pseudo-symbols analytically expressed as, respectively:

[00013]${\rho }_{0,i}^p=\{\begin{array}{cc}\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{even}\\ j\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{odd}\end{array}{\rho }_{1,i}^p=\{\begin{array}{cc}-j\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_{i-1}^{\left(p\right)}-1\right)\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{even}\\ -\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{odd}\end{array}$ [0167] b.sub.i.sup.(0) and b.sub.i.sup.(1) are respectively the information bits feeding the SOQPSK modulator of the path 1 and the path 2 (see FIG. 6).

[0168] It is recalled that b.sub.i.sup.(0) and b.sub.i.sup.(1) are connected to one another by way of the binary rearrangement code defined in the IRIG-106 recommendation. The binary rearrangement code constructs on the basis of the sequence b= . . . b.sub.4k, b.sub.4k+1, b.sub.4k+2, b.sub.4k+3, . . . the sequences:

b.sub.u.sup.(0)= . . . b.sub.4k.sup.(0),b.sub.4k+1.sup.(0),b.sub.4k+2.sup.(0),b.sub.4k+3′.sup.(0), . . . = . . . b.sub.4k,b.sub.4k+1,b.sub.4k+2,b.sub.4k+3, . . .

b.sub.u.sup.(1)= . . . b.sub.4k.sup.(1),b.sub.4k+1.sup.(1),b.sub.4k+2.sup.(1),b.sub.4k+3′.sup.(1), . . . = . . . b.sub.4k+2,b.sub.4k+3,b.sub.4k,b.sub.4k+1, . . .

where the operation x represents the binary inversion operation of the bit x. This consequently gives L=4.

[0169] The samples r.sub.0(n) are then filtered by a filter making it possible to reduce the inter-symbol interference. Specifically, as w.sub.0 and w.sub.1 are pulses having a time base larger than T, inter-symbol interference is present in the received signal.

[0170] This filter must have the following features: [0171] It must not color the noise component present in the received signal [0172] It must have a bandwidth wider than that of the useful signal. [0173] It must reduce the inter-symbol interference.

[0174] A matched filter can be sufficient. However, it has the drawback of coloring the noise.

[0175] Different filters satisfying the above conditions are possible. The reference [A6] has several filters that can be used in this scenario. [0176] [A6] Geoghegan, Mark, “Optimal Linear Detection of SOQPSK,” in International Telemetering Conference Proceedings, October 2002

[0177] The filter g shown in FIG. 16 has been determined such as to satisfy the conditions above.

[0178] The filter chosen is a FIR (Finite Impulse Response) low-pass filter of Equiripple type digitally constructed such that the normalized cut-off frequency is 0.45.

[0179] Thus, at the output of this filter and after the operations of sampling at the symbol rate, we have:

[00014]$y\left(4k\right)=h_0\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^0{\tilde{w}}_0\left(\mathrm{iT}\right)+h_1\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^1{\tilde{w}}_0\left(\mathrm{iT}-\mathrm{\Delta .Math.}T\right)+\tilde{n}\left(4\mathrm{kT}\right)$$y_{\mathrm{\Delta \tau }}\left(4k\right)=h_0\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^0{\tilde{w}}_0\left(\mathrm{iT}+\mathrm{\Delta .Math.}T\right)+h_1\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^1{\tilde{w}}_0\left(\mathrm{iT}\right)+\tilde{n}\left(4\mathrm{kT}+\mathrm{\Delta .Math.}T\right)$

where {tilde over (w)}.sub.0 is the result of the convolution product between the pulse w.sub.0 and the filter g, ñ is the result of the convolution product between the noise z and the filter g and Δε is the closest integer of the division of Δτ by T.

[0180] Thus, at the output of this filter and after the sampling operations, we have:

[00015]$y\left(4k\right)=h_0\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^0{\tilde{w}}_0\left(\mathrm{iT}\right)+h_0{\rho }_{1,4k}^0{\tilde{w}}_1\left(0\right)+h_1\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^1{\tilde{w}}_0\left(\mathrm{iT}-\mathrm{\Delta .Math.}T\right)+h_1{\rho }_{1,4k}^1{\tilde{w}}_1\left(-\mathrm{\Delta .Math.}T\right)+\tilde{n}\left(4\mathrm{kT}\right)$$y_{\mathrm{\Delta \tau }}\left(4k\right)=h_0\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^0{\tilde{w}}_0\left(\mathrm{iT}+\mathrm{\Delta .Math.}T\right)+h_0{\rho }_{1,4k}^0{\tilde{w}}_1\left(\mathrm{\Delta .Math.}T\right)+h_1\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4k-i}^1{\tilde{w}}_0\left(\mathrm{iT}\right)+h_1{\rho }_{1,4k}^1{\tilde{w}}_1\left(0\right)+\tilde{n}\left(4\mathrm{kT}+\mathrm{\Delta .Math.}T\right)$

[0181] These two sample sequences then feed a trellis which has the aim of finding a binary sequence making it possible to maximize or minimize a given cost function.

[0182] In this scenario, this trellis seeks to minimize the mean quadratic error between the received signal and the signal reconstructed by approximation.

[0183] In other words, a Viterbi algorithm is used seeking to find the best sequence of bits Ŝ making it possible to solve the following problem:

[00016]$\underset{\_}{\hat{S}}=\underset{S}{\mathrm{argmin}}\Lambda \left(\underset{\_}{S}\right)$$\mathrm{with}:\Lambda \left(\underset{\_}{S}\right)=\underset{n=0}{\overset{\left(N-1\right)/4}{.Math.}}\left(\underset{m=-1}{\overset{2}{.Math.}}\left[{.Math.B_{m,n}^{\left(0\right)}.Math.}^2+{.Math.B_{m,n}^{\left(\Delta \tau \right)}.Math.}^2\right]\right)$$\mathrm{Writing}:B_{m,n}^0=y\left(4n+m\right)-h_0\left(\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4n+m-i}^0{\tilde{w}}_0\left(\mathrm{iT}\right)+{\rho }_{1,4n+m}^0{\tilde{w}}_1\left(0\right)\right)-h_1\left(\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4n+m-i}^1{\tilde{w}}_0\left(\mathrm{iT}-\mathrm{\Delta .Math.}T\right)+{\rho }_{1,4n+m}^1{\tilde{w}}_1\left(-\mathrm{\Delta .Math.}T\right)\right)$$B_{m,n}^{\left(\mathrm{\Delta \tau }\right)}=y_{\mathrm{\Delta \tau }}\left(4n+m\right)-h_0\left(\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4n+m-i}^0{\tilde{w}}_0\left(\mathrm{iT}+\mathrm{\Delta .Math.}T\right)+{\rho }_{1,4n+m}^0{\tilde{w}}_1\left(\mathrm{\Delta .Math.}T\right)\right)-h_1\left(\underset{i=-1}{\overset{1}{.Math.}}{\rho }_{0,4n+m-i}^1{\tilde{w}}_0\left(\mathrm{iT}\right)+{\rho }_{1,4n+m}^1{\tilde{w}}_1\left(0\right)\right)$

[0184] The information bits are therefore retrieved using a Viterbi algorithm associated with the trellis illustrated in FIG. 17.

[0185] The trellis under consideration describes the transitions from a state S.sub.n=[b.sub.4n b.sub.4n+1 b.sub.4n+2 b.sub.4n+3] to a state S.sub.n+1=[b.sub.4n+4 b.sub.4n+5 b.sub.4n+6 b.sub.4n+7]. The transitions are weighted via the following branch metric:

[00017]$\lambda \left(S_{n-1}\left(i\right)->S_n\left(j\right)\right)=\underset{m=-1}{\overset{2}{.Math.}}\left[{.Math.B_{m,n}^{\left(0\right)}.Math.}^2+{.Math.B_{m,n}^{\left(\Delta r\right)}.Math.}^2\right]$

[0186] The trellis therefore includes 16 states, describing the 16 possible states of the variable S.sub.n. The number of branches to be computed is then 256.

[0187] The use of the trellis associated with this architecture therefore makes it possible, using the branch metrics defined above, to use an algorithm of SOVA type in order to compute the LLRs on the information bits.

[0188] Soft outputs in the form of LLRs and/or hard outputs are thus obtained by performing the following operations.

[0189] First the cumulative metrics Γ.sub.n(S.sub.n(j)) of the nodes S.sub.n(j) are computed at the epoch n:

Γ.sub.n(S.sub.n(j))=min.sub.i[γ.sub.n(S.sub.n−1(i),S.sub.n(j))],(i,j)∈{1, . . . ,16}.sup.2

with

γ.sub.n(S.sub.n−1(i),S.sub.n(j))=Γ.sub.n−1(S.sub.n−1(i))+λ(S.sub.n−1(i).fwdarw.S.sub.n(j))

[0190] The likelihood difference is computed:

R.sub.n(S.sub.n−1(i),S.sub.n(j))=Γ.sub.n(S.sub.n(j))−γ.sub.n(S.sub.n−1(i),S.sub.n(j)),(i,j)∈({1, . . . ,16}).sup.2

[0191] The maximum of the joint probability logarithm is then computed:

P(S.sub.n−1(i),S.sub.n(j),r.sup.f)=β.sub.n(S.sub.n(i))+R.sub.n(S.sub.n−1(i),S.sub.n(j))

with

β.sub.n−1(S.sub.n−1(j))=min.sub.i[R.sub.n(S.sub.n−1(i),S.sub.n(j))+β.sub.n(S.sub.n(i))]

[0192] The soft outputs (or LLRs) of the symbol Ŝ.sub.n, estimated from the symbol S.sub.n, are:

LLR(Ŝ.sub.n)=P(Ŝ.sub.n=S.sub.n(j)\r.sup.f)

with

P(Ŝ.sub.n=S.sub.n(j)\r.sup.f)=min.sub.i[P(S.sub.n−1(i),S.sub.n(j),r.sup.f]

[0193] The conversion of the symbol LLRs Ŝ.sub.n to the bit LLRs ({circumflex over (b)}.sub.4n, {circumflex over (b)}.sub.4n+1, {circumflex over (b)}.sub.4n+2, {circumflex over (b)}.sub.4n+3) is done as follows:

LLR({circumflex over (b)}.sub.4n)=min(LLR(Ŝ.sub.n=[0,{tilde over (b)}.sub.4n+1,{tilde over (b)}.sub.4n+2,{tilde over (b)}.sub.4n+3]))−min(LLR(Ŝ.sub.n=[1,{tilde over (b)}.sub.4n+1,{tilde over (b)}.sub.4n+2,{tilde over (b)}.sub.4n+3]))

LLR({circumflex over (b)}.sub.4n+1)=min(LLR(Ŝ.sub.n=[{tilde over (b)}.sub.4n,0,{tilde over (b)}.sub.4n+2,{tilde over (b)}.sub.4n+3]))−min(LLR(Ŝ.sub.n=[{tilde over (b)}.sub.4n,1,{tilde over (b)}.sub.4n+2,{tilde over (b)}.sub.4n+3]))

LLR({circumflex over (b)}.sub.4n+2)=min(LLR(Ŝ.sub.n=[{tilde over (b)}.sub.4n,{tilde over (b)}.sub.4n+1,0,{tilde over (b)}.sub.4n+3]))−min(LLR(Ŝ.sub.n=[{tilde over (b)}.sub.4n,{tilde over (b)}.sub.4n+1,1,{tilde over (b)}.sub.4n+3]))

LLR({circumflex over (b)}.sub.4n+3)=min(LLR(Ŝ.sub.n=[{tilde over (b)}.sub.4n,{tilde over (b)}.sub.4n+1,{tilde over (b)}.sub.4n+3,0]))−min(LLR(Ŝ.sub.n=[{tilde over (b)}.sub.4n,{tilde over (b)}.sub.4n+1,{tilde over (b)}.sub.4n+2,1]))

[0194] The hard outputs are thus obtained by:

{circumflex over (b)}.sub.4n=sign(LLR({circumflex over (b)}.sub.4n))

{circumflex over (b)}.sub.4n+1=sign(LLR({circumflex over (b)}.sub.4n+1))

{circumflex over (b)}.sub.4n+2=sign(LLR({circumflex over (b)}.sub.4n+2))

{circumflex over (b)}.sub.4n+3=sign(LLR({circumflex over (b)}.sub.4n+3))

[0195] With sign(x) a function that returns 1 if 1, if x≥0, −1 if x<0. The estimated binary sequence of data is therefore

{circumflex over (b)}.sub.n.sup.d=½({circumflex over (b)}.sub.n+1)

[0196] The bit LLRs are then supplied to the error correcting decoder (of LDPC type for example) in order to further correct the errors generated by the presence of noise. The decoder can operate with the two outputs (hard or soft outputs). However, it is more advantageous to use the bit LLRs since these information items are made more use of by the decoder to improve the overall performance of the system.

5) Second Embodiment: Taking into Account of the Multiple Paths and Channel Estimation as a Replacement for the Channel Gain Estimates of the First Embodiment

[0197] The architecture proposed here makes it possible to solve a more general problem. Specifically, this concerns the case where the signal received over the antenna I written r.sub.I(t) is composed of two main paths and a number of multiple paths. The multiple paths are the result of reflections of the transmitted signal either on the ground or in the atmosphere.

[0198] The received signal r(t) is expressed in this case as follows:

[00018]$r_I\left(t\right)=\left[\underset{i=0}{\overset{N_{0,I}}{.Math.}}{h}_{2i,I}{s}_0\left(t-{\mathrm{\Delta \tau }}_{2i,I}\right)+\underset{j=0}{\overset{N_{1,I}}{.Math.}}{h}_{2j+1}{s}_1\left(t-{\mathrm{\Delta \tau }}_{2j+1,I}\right)\right]e^{{\left(j2\mathrm{\pi \Delta }f\right)}_{I}t}+z_I\left(t\right)$

with [0199] N.sub.0,I, N.sub.1,I the number of paths associated respectively with the signals s.sub.0(t),s.sub.1(t) considering the receiving antenna I. [0200] {h.sub.2i,I}.sub.i∈{0,N.sub.0.sub.} the gains associated with the propagation channels of the direct-line path associated with the signal s.sub.0(t) over the receiving antenna I. The gain of the channel associated with the main path is h.sub.0,I [0201] {h.sub.2j+1,I}.sub.j∈{0,N.sub.1.sub.} the gains associated with the propagation channels of the direct-line path associated with the signal s.sub.1(t) over the receiving antenna I. The gain of the channel associated with the main path is h.sub.1,I [0202] {Δτ.sub.2i,I}.sub.j∈{0,N.sub.0.sub.}, {Δτ.sub.2j+1,I}.sub.j∈{0,N.sub.1.sub.} the delays associated with these paths on the receiving antenna I; [0203] Δf.sub.I the frequency offset; [0204] z.sub.I(t) additive noise.

[0205] It is moreover recalled that:

[00019]$s_0\left(t\right)=\underset{i}{.Math.}{\rho }_{0,i}^0{w}_0\left(t-\mathrm{iT}\right)+\underset{i}{.Math.}{\rho }_{1,i}^0{w}_1\left(t-\mathrm{iT}\right)$$s_1\left(t\right)=\underset{i}{.Math.}{\rho }_{0,i}^1{w}_0\left(t-\mathrm{iT}\right)+\underset{i}{.Math.}{\rho }_{1,i}^1{w}_1\left(t-\mathrm{iT}\right)$

[0206] This architecture, described in FIG. 18, then has the advantage of being able to estimate the different parameters of the propagation channels and inject these estimates at the time of demodulation.

[0207] A notable difference with respect to the architecture of the first embodiment lies in the fact that it is not necessary to feed the demodulator with the estimates of the channel gains h.sub.0,1, h.sub.1,1, . . . , h.sub.0,N, h.sub.1,N insofar as this step is done in the demodulator.

[0208] This architecture has N inputs corresponding to the N sequences of samples r.sub.0,1(n), . . . , r.sub.0,N(n) feeding the demodulator. This architecture also requires the estimates of the delays Δt.sub.0,1, Δt.sub.1,1, . . . , Δt.sub.0,N, Δt.sub.1,N. At the output of this demodulation architecture, this gives a sequence of soft-output demodulated bits (LLR).

[0209] The sequence of samples r.sub.0,I(n) with I varying from 1 to N is first filtered by a filter used to optimize the signal-to-noise ratio at the demodulation input. This filter can be simply a matched filter.

[0210] Using the parameters Δt.sub.0,I and Δt.sub.1,I, the signal r.sub.0,I(n) is sampled firstly at the times kT and secondly at the times kT+Δt.sub.I. This respectively gives the sequences of samples y.sub.I(k) and y.sub.Δτ.sub.I(k).

[0211] The sequences y.sub.1(k), y.sub.Δτ.sub.1(k), . . . , y.sub.N(k),y.sub.Δτ.sub.N(k) then feed a channel estimating method.

[0212] The aim of this method is to provide K channel estimates to the trellis 1.

[0213] By writing L the number of bits involved in the space-time coding, the trellis used then has 2.sup.mL states and 2.sup.2mL branches where m is a variable parameter dependent on the impulse response of the propagation channel.

[0214] The sequences y.sub.1(k), y.sub.Δτ.sub.I(k), . . . , y.sub.N(k),y.sub.Δτ.sub.N(k), coupled to the K channel estimates resulting from the channel estimating method, feed the trellis 1. This method also requires the knowledge of the parameters Δt.sub.0,1, Δt.sub.1,1, . . . , Δt.sub.0,N, Δt.sub.1,N.

[0215] The use of this trellis then makes it possible to estimate the most probable binary sequence transmitted. Moreover, the use of a single trellis having a fixed number of states makes it possible to compute LLRs.

[0216] The computation of the LLRs on the information bits can then be done by way of a SOVA (Soft Output Viterbi Algorithm). The description of this algorithm is given in the document [A3].

[0217] The advantages of this architecture are several.

[0218] 1. The presence of the filter for reducing the inter-symbol interference present at the input of the demodulator makes it possible to greatly reduce the complexity of the equalization blocks and to simplify the trellis used for the Viterbi algorithm.

[0219] 2. The particular decomposition of the CPM signal in the form of a modulation of OQPSK type has the consequence of enabling the use of a fixed trellis.

[0220] 3. The channel estimator makes it possible to estimate multi-path channels.

[0221] 4. The channel estimates provided to the demodulation trellis then make it possible to equalize the received signal.

[0222] 5. The single and fixed trellis used in the Viterbi algorithm has the advantage of using an algorithm of SOVA type in order to compute the LLRs on the demodulated bits.

[0223] 6. The whole of the demodulation method is more robust to the effects of the multi-path channels by comparison with the solution of the prior art.

[0224] 7. Even without a channel decoder for decoding the LLRs, the use of a hard decision by extraction of the “Most Significant Bit” (MSB) on the LLRs leads to an improvement in performance.

[0225] In the special case of STC-SOQPSK based on the IRIG-106 recommendation, supposing that the frequency offset has been perfectly corrected, the received signal can be written as follows after the steps of filtering by g and sampling:

[00020]$y\left(k\right)\approx \underset{m=0}{\overset{1}{.Math.}}\underset{i=-\frac{N_t^m-1}{2}}{\overset{\frac{N_t^m-1}{2}}{.Math.}}{\rho }_{m,k-i}^0{\tilde{f}}_m^0\left(i\right)+\underset{m=0}{\overset{1}{.Math.}}\underset{i=-\frac{N_t^m-1}{2}}{\overset{\frac{N_t^m-1}{2}}{.Math.}}{\rho }_{m,k-i}^1{\tilde{f}}_m^{1,\mathrm{\Delta \tau }}\left(i\right)+z\left(\mathrm{kT}+{\mathrm{\Delta \tau }}_0\right)$$y_{\mathrm{\Delta \tau }}\left(k\right)\approx \underset{m=0}{\overset{1}{.Math.}}\underset{i=-\frac{N_t^m-1}{2}}{\overset{\frac{N_t^m-1}{2}}{.Math.}}{\rho }_{m,k-i}^0{\tilde{f}}_m^{0,\mathrm{\Delta \tau }}\left(i\right)+\underset{m=0}{\overset{1}{.Math.}}\underset{i=-\frac{N_t^m-1}{2}}{\overset{\frac{N_t^m-1}{2}}{.Math.}}{\rho }_{m,k-i}^1{\tilde{f}}_m^1\left(i\right)+z\left(\mathrm{kT}+{\mathrm{\Delta \tau }}_1\right)$

where: [0226] Δτ=Δτ.sub.1−Δτ.sub.0 où Δτ.sub.0 is the delay of the direct path from the antenna 1 and Δτ.sub.1 is the delay of the direct path from the antenna 2. Δτ is the time offset. [0227] Δε is the closest integer to the division of Δτ by T. [0228] The values {tilde over (f)}.sub.m.sup.p(i) and {tilde over (f)}.sub.m.sup.p,Δτ(i) are defined as follows:

{tilde over (f)}.sub.m.sup.p(i)={tilde over (f)}.sub.m.sup.p(t=iT)

{tilde over (f)}.sub.m.sup.0,Δτ(i)={tilde over (f)}.sub.m.sup.0(t=iT+ΔεT)

{tilde over (f)}.sub.m.sup.1,Δτ(i)={tilde over (f)}.sub.m.sup.0(t=iT−ΔεT)

with

{tilde over (f)}.sub.m.sup.p(t)=∫f.sub.m.sup.k(θ)g(θ−t)dθ

and

[00021]$f_m^0\left(t\right)=w_m\left(t\right)*\left(h_0\delta \left(t\right)+\underset{i=1}{\overset{N_0}{.Math.}}{h}_{2i}\delta \left(t-\left({\mathrm{\Delta \tau }}_{2i}-{\mathrm{\Delta \tau }}_0\right)\right)\right),m\in \left\{0,1\right\}$$f_m^1\left(t\right)=w_m\left(t\right)*\left(h_1\delta \left(t\right)+\underset{i=1}{\overset{N_1}{.Math.}}{h}_{2i+1}\delta \left(t-\left({\mathrm{\Delta \tau }}_{2i+1}-{\mathrm{\Delta \tau }}_1\right)\right)\right),m\in \left\{0,1\right\}$ [0229] δ(t) is the Dirac pulse centered on 0. [0230] N.sub.t.sup.m is the length of the filters {tilde over (f)}.sub.m.sup.0, {tilde over (f)}.sub.m.sup.0,Δτ, {tilde over (f)}.sub.m.sup.1, {tilde over (f)}.sub.m.sup.1,Δτ, [0231] z is an additive noise [0232] ρ.sub.0,i.sup.0, ρ.sub.0,i.sup.1, ρ.sub.1,i.sup.0, ρ.sub.1,i.sup.1 are pseudo-symbols the analytical expression of which is respectively:

[00022]${\rho }_{0,i}^p=\{\begin{array}{cc}\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{even}\\ j\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{odd}\end{array}{\rho }_{1,i}^p=\{\begin{array}{cc}-j\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_{i-1}^{\left(p\right)}-1\right)\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{even}\\ -\left(2b_{i-2}^{\left(p\right)}-1\right)\left(2b_{i-1}^{\left(p\right)}-1\right)\left(2b_i^{\left(p\right)}-1\right)& \mathrm{if}i\mathrm{is}\mathrm{odd}\end{array}$ [0233] b.sub.i.sup.(0) and b.sub.i.sup.(1) are respectively the information bits feeding the SOQPSK modulator of the path 1 and the path 2, each channel corresponding to the antennas A1, A2.

[0234] It is recalled that b.sub.i.sup.(0) and b.sub.i.sup.(1) are linked between them by way of the binary rearrangement code defined in the IRIG-106 recommendation. The binary rearrangement code constructs on the basis of the sequence b=b.sub.4k, b.sub.4k+1, b.sub.4k+2, b.sub.4k+3, . . . the sequences:

b.sub.u.sup.(0)= . . . b.sub.4k.sup.(0),b.sub.4k+1.sup.(0),b.sub.4k+2.sup.(0),b.sub.4k+3′.sup.(0), . . . = . . . b.sub.4k,b.sub.4k+1,b.sub.4k+2,b.sub.4k+3, . . .

b.sub.u.sup.(1)= . . . b.sub.4k.sup.(1),b.sub.4k+1.sup.(1),b.sub.4k+2.sup.(1),b.sub.4k+3′.sup.(1), . . . = . . . b.sub.4k+2,b.sub.4k+3,b.sub.4k,b.sub.4k+1, . . .

where the operation x represents the operation of binary inversion of the bit x.

[0235] The filtering operations make it possible to reduce the inter-symbol interference and the sampling operations are the same as those described in the architecture 1.

[0236] The channel estimation operation that takes as input the signal thus sampled can thus be produced by way of the method used in the literature (for this see the document [A3]) However, in the presence of multi-path channels, this reference method is no longer appropriate.

[0237] In the literature, the channel estimation methods have architectures as described in FIG. 19. As an input to this estimator, a sequence is injected of the form

[00023]$y\left(k\right)=\underset{i}{.Math.}{\rho }_{0,k-i}^0{f}_0^0\left(i\right)$

and this estimator provides us with an estimate of {circumflex over (f)}.sub.0.sup.0.

[0238] An example of such a method as well as many derivative techniques is described in [A7]. [0239] [A7] B. Farhang-Boroujeny, Adaptive Filters, Wiley, 1998.

[0240] However this structure has limits due to the fact that the received signal is a sum of modulations, the previous estimators are not appropriate as they only make it possible to estimate a single parameter at a time, whereas our formulation of the problem involves the estimation of 8 parameters at once.

[0241] In this context, the following channel estimation method is proposed.

This channel estimation method is described in FIG. 20. One injects into the method the samples y(k) and y.sub.Δτ(k) and retrieves at the output the 8 filters {tilde over (f)}.sub.m.sup.0, {tilde over (f)}.sub.m.sup.0,Δτ, {tilde over (f)}.sub.m.sup.1, {tilde over (f)}.sub.m.sup.1,Δτ, (m∈{−1,1}) with i varying by

[00024]$-\frac{N_t^m-1}{2}\mathrm{to}\frac{N_t^m-1}{2}.$

The following special relationship exists:

N.sub.t.sup.1=N.sub.t.sup.0−2=N.sub.t−2

[0242] The channel estimation method is done recursively and is described in FIG. 21. If the iteration is written k, the estimate of the filters with iteration k is then called {tilde over (f)}.sub.m.sup.0, {tilde over (f)}.sub.m.sup.0,Δτ, {tilde over (f)}.sub.m.sup.1, {tilde over (f)}.sub.m.sup.1,Δτ.

[0243] An initialization of these 8 filters is first carried out. This step involves the initialization of the vectors {circumflex over (f)}.sub.0,0.sup.0, {circumflex over (f)}.sub.0,0.sup.1, {circumflex over (f)}.sub.0,0.sup.0,Δτ, {circumflex over (f)}.sub.0,0.sup.1,Δτ (respectively {circumflex over (f)}.sub.1,0.sup.0, {circumflex over (f)}.sub.1,0.sup.1, {circumflex over (f)}.sub.1,0.sup.0,Δτ, {circumflex over (f)}.sub.1,0.sup.1,Δτ) of size N.sub.t (or N.sub.t−2) with the eight filters estimated by the pilot sequence of the previous frame (i.e. {circumflex over (f)}.sub.0,k.sub.f.sup.0, . . . , {circumflex over (f)}.sub.1,k.sub.f.sup.1 of the previous frame). For the first frame, the filters are initialized in this way (a frame is a binary sequence composed of a pilot sequence of length L.sub.p followed by a sequence of useful data of size L.sub.d:

[0244] This gives:

[00025]$\{\begin{array}{cc}{\hat{f}}_{0,0}^0\left(i\right)=w_0\left({\mathrm{iT}}_b\right),& \mathrm{for}i=-\frac{N_t-1}{2},\mathrm{.Math.},\frac{N_t-1}{2}\\ {\hat{f}}_{1,0}^0\left(i\right)=w_1\left({\mathrm{iT}}_b\right),& \mathrm{for}i=-\frac{N_t-3}{2},\mathrm{.Math.},\frac{N_t-3}{2}\\ {\hat{f}}_{0,0}^{1,\mathrm{\Delta \tau }}=w_0\left(\left(i-\mathrm{\Delta \tau }\right)T_b\right),& \mathrm{for}i=-\frac{N_t-1}{2},\mathrm{.Math.},\frac{N_t-1}{2}\\ {\hat{f}}_{1,0}^{1,\mathrm{\Delta \tau }}=w_1\left(\left(i-\mathrm{\Delta \tau }\right)T_b\right),& \mathrm{for}i=-\frac{N_t-3}{2},\mathrm{.Math.},\frac{N_t-3}{2}\\ {\hat{f}}_{0,0}^{0,\mathrm{\Delta \tau }}\left(i\right)=w_0\left(\left(i+\mathrm{\Delta \tau }\right)T_b\right),& \mathrm{for}i=-\frac{N_t-1}{2},\mathrm{.Math.},\frac{N_t-1}{2}\\ {\hat{f}}_{1,0}^{0,\mathrm{\Delta \tau }}\left(i\right)=w_1\left(\left(i+\mathrm{\Delta \tau }\right)T_b\right),& \mathrm{for}i=-\frac{N_t-3}{2},\mathrm{.Math.},\frac{N_t-3}{2}\\ {\hat{f}}_{0,0}^1\left(i\right)=w_0\left({\mathrm{iT}}_b\right),& \mathrm{for}i=-\frac{N_t-1}{2},\mathrm{.Math.},\frac{N_t-1}{2}\\ {\hat{f}}_{1,0}^1\left(i\right)=w_1\left({\mathrm{iT}}_b\right),& \mathrm{for}i=-\frac{N_t-3}{2},\mathrm{.Math.},\frac{N_t-3}{2}\end{array}\hspace{1em}$

[0245] Based on the preamble bits P(0) and P(1) as well as the signals y(k) and y.sub.Δτ(k), two error functions are then computed, defined as follows:

[00026]$e_k=y\left(k\right)-\left({.Math.}_{i=-\frac{\left(N_t-1\right)}{2}}^{i=\frac{\left(N_t-1\right)}{2}}{\rho }_{0,k-i}^0{\hat{f}}_{0,k}^0\left(i\right)+{.Math.}_{i=-\frac{\left(N_t-3\right)}{2}}^{i=\frac{\left(N_t-3\right)}{2}}{\rho }_{1,k-i}^0{\hat{f}}_{1,k}^0\left(i\right)+{.Math.}_{i=-\frac{\left(N_t-1\right)}{2}}^{i=\frac{\left(N_t-1\right)}{2}}{\rho }_{0,k-i}^1{\hat{f}}_{0,k}^{1,\mathrm{\Delta \tau }}\left(i\right)+{.Math.}_{i=-\frac{\left(N_t-3\right)}{2}}^{i=\frac{\left(N_t-3\right)}{2}}{\rho }_{1,k-i}^1{\hat{f}}_{1,k}^{1,\mathrm{\Delta \tau }}\left(i\right)\right)$$e_k^{\mathrm{\Delta \tau }}=y_{\mathrm{\Delta \tau }}\left(k\right)-\left(\underset{i=-\frac{\left(N_t-1\right)}{2}}{\overset{i=\frac{\left(N_t-1\right)}{2}}{.Math.}}{\rho }_{0,k-i}^0{\hat{f}}_{0,k}^{0,\mathrm{\Delta \tau }}\left(i\right)+\underset{i=-\frac{\left(N_t-3\right)}{2}}{\overset{i=\frac{\left(N_t-3\right)}{2}}{.Math.}}{\rho }_{1,k-i}^0{\hat{f}}_{1,k}^{0,\mathrm{\Delta \tau }}\left(i\right)+\underset{i=-\frac{\left(N_t-1\right)}{2}}{\overset{i=\frac{\left(N_t-1\right)}{2}}{.Math.}}{\rho }_{0,k-i}^1{\hat{f}}_{0,k}^1\left(i\right)+\underset{i=-\frac{\left(N_t-3\right)}{2}}{\overset{i=\frac{\left(N_t-3\right)}{2}}{.Math.}}{\rho }_{1,k-i}^1{\hat{f}}_{1,k}^1\left(i\right)\right)$$\mathrm{for}k=\frac{N_t-1}{2},\mathrm{.Math.},k_f\mathrm{with}{k}_f=L_p-1-\frac{N_t-1}{2}.$