Method and system for cooperative radio direction finding in transmission mode

The present invention relates to a method and a device for cooperative direction-finding in transmission for signals comprising a reference signal.

The invention applies particularly to the case of signals comprising a synchronization signal or reference signal, composed of a series of known symbols defined by the transmission standard used within the transmission system.

For example, GSM signals (Global System for Mobile communications), made up of several reference signals, exhibit this characteristic. In such a context, a reception system such as a base station can perform selective direction finding and associate a direction of arrival with a synchronization sequence. Selective direction finding techniques allow one emitter to be isolated from the others on the basis of knowledge of its reference signal. It is thus possible to achieve selective direction finding per transmitter, which makes it possible to reduce the risk of ambiguities.

Patent FR 2 764 074 describes a method making it possible to carry out goniometry in the case of a single user and for linear modulations or waveforms which can be approximated in linear modulations. In this patent, digital signals are emitted s_e(t) linearly modulated. The symbols ai, a₂, at₃, etc., associated with the signal are transmitted at period T_s to then be filtered by an FIR (Finitre Impulse Response) filter with response h (t).

Under these conditions, the relation between the transmitted signal s_e(t) and the symbols a_not is the following :

s_e (t) = £ h (t-nT_s) at_not at

(1) where h (t) is the shaping filter.

FIG. 1 schematically shows the principle of the process.

The example given in this patent mainly concerns the GSM standard where the transmitted signal is a phase modulation of the GMSK (Gaussian Minimum Shift Keying) type such as:

s_e(t) = exp {j £ O (t-nT_s) at_not} (2) n

where has_not corresponds to a symbol sent to T_s samples per symbol.

For the GMSK standard to be part of linear modulations, the authors of this patent make the following approximation:

Se (t) «X Co (t-nT_s) j^not bn with b_not = Π ^atk (³) not

The linearization is carried out, for example, by applying the method described in the document entitled “Exact and approximate construction of digital phase modulations by superposition of modulated puise (AMP)” by Pierre André Laurent, IEEE trans. on communications Vol 34 (1986) pp 150-160.

In the sequence of symbols {a_not}, there is a sequence of symbols {s_k} such that a_{p +}ki = {s_k} for 1 <k <K. The sequence of symbols {s_k} is defined by the transmission standard and is called a learning sequence. In particular, the GSM standard comprises 8 different sequences composed of K = 26 symbols.

The signal s_e(t) transit to n '^eme antenna of a reception system through a propagation channel C (t) of linear filter Fl R. Under these conditions, there is a linear filtering relation between the comb of symbol s (t) (such that s_e(t) = h (t) * s (t) where "*" denotes the product of convolution) and the sensor signals x_not(t), shown in Figure 2.

Knowing that C (t) = [Ci (t) .... Cn (î)]^t the relation between the symbols a_not transmitted and the signal x (t) received is expressed in the form:

x (t) = C (t) * Se (t) = (C * AW) * s (t) = £ G (t-nT_s) at_not + b₀(t) (4) n

where for t = nT_s, s (t) = a_not and for you_s, s (t) = O.

G (t) = C (t) * h (t) is a vector of dimension Nx1 and b (t) is the vector made up of the background noise of the N receivers.

The process disclosed in patent FR 2 764 074 is broken down into 3 stages:

1^,time step: Digitization of the received signal x (t) at the sampling period T_e. The input of the system being composed of the symbols {a_not}, T_e must be chosen so that T_s = PT_e where P is an integer. So by posing

Gp._notp = G ((p-nP) T_e) the relation (4) becomes:

x (pT_e) = X Gp.np a_not + b₀(pT_e) (5) n

In the description of the patent, the authors set P = 2. Choosing the sampling period T_e according to the symbol period T_s is a strong constraint. Generally, the material does not directly obtain T_s = PT_e (P integer). Sampling is carried out at T '_e and then to have a sampling at T_e, it is necessary to perform digital processing which resamples the signal at T_e. In the standard

GSM the transmitted signals verify the 1 / T relationship_s = 270kHz. To meet Shannon's conditions upon receipt, the system receives them at 1 / T_e = 500kHz and T_s / T_e = 500/270 is in fact an integer.

2^first step: Synchronization procedure: The objective is to determine the instant t₀= pT_e of appearance of the learning sequence {s_k} such that a_{p + k}-i = {s_k} for 1 <k <K:

x ((k + p) T_e) = £ G_k-_notps_not+ b₀((k + p) T_e) (6) n

For this we consider that the comb of symbol s (n T_e) is the input signal and we try to maximize in τ the following synchronization criterion:

Scream (T) = r ^ t) f_xsM

KP

With f_xs(r) = - £ x (kT_e+ T) s (kT_e) 'and ^^{(τ) =}κρΣ X (kT_e+ t) X (kT_e+ t)^H (7)

K: number of symbols in the learning sequence and s (n T_e) = s_kP for n = kP and s (n T_e) = 0 for n ^ kP and where x^H denotes the transpose and conjugate of x.

3^ith step: We use the signals x (t + t_k) and the combs of symbols s (n Τθ) associated with a source in order to isolate the latter and perform a direction finding on a single source at time t₀= p T_e. Using the received signal x (t + t_k) and a single comb of symbols s (n Τθ) we say that the process is single-user.

The method according to the prior art, if it proves to be efficient, nevertheless has certain limitations. It is applicable for waveforms which can be linearized or which can be approximated in such a form, and in single-user contexts.

The method according to the invention is based on a new approach which consists in particular in using the reference signal or sequence containing symbols specific to a standard used or to a given format for the signal, the received signal and the knowledge of the times of arrival. different reference sequences, to determine the coordinates of a source from the measurement of its incidence, an operation usually known by the expression goniometry.

In the description, the terms “issuers”, “users” or “useful” designate the same object.

The invention relates to a method of cooperative direction-finding in transmission in a direction-finding system for a radiocommunication system comprising one or more emission sources or transmitters, the transmitted signal comprising a reference sequence composed of a series of symbols {s_k}, the receiver comprising at least one network of several sensors coupled to a direction finder. It is characterized in that it comprises at least the following steps:

a) determine the reference signal (s) dj (t) associated with a transmitter m from the symbols and the modulation defined by the format of the signals,

b) define the arrival time t_k one or more sequences of references,

c) from the signal x (t) received on the sensors, the times of arrival t_k and from the reference signal (s) d, (t) resulting from step a), determining the incidence (s) of the signals for a given transmitter.

Step a) is repeated as many times as there are transmitters M_o in the system.

It may include a step of separating the emitters M_o by estimating the transfer matrix of the transmission channel H^u of the set of useful and by extracting from this matrix the transfer matrices H_m^u of the channel associated with a useful m in order to determine the observation vector x^m(t) corresponding.

Step c) is carried out for example using a bleach goniometry implemented on the observation vectors x^m(t) or by projection.

Step a) can be carried out over a duration δΓ> δί, where δί is the base duration of the reference signal.

We can determine a spatial filter W_m from the reference signal d_m(t) of a transmitter m in order to deduce the signal s_m (t) from the transmitter before applying a direction finding step.

The method applies in particular in radiocommunication systems for signals of the GSM or UMTS type.

The invention also relates to a direction-finding device comprising at least means suitable for implementing the steps of the aforementioned method.

The object of the invention has the following advantages in particular:

• the possibility of carrying out direction finding, in a broader context (single or multi-user, single or multi-path) than that offered by the methods of the prior art, • by choosing the working or observation interval, the possibility of improving the direction finding results, • by modifying, for example the lengthening, of the duration of the reference signals, the possibility of improving the direction finding results, • the possibility of locating mobiles in order to transmit in a directive manner in the direction of each mobile, based on the knowledge of the direction of arrival of the direction-finding mobiles, • the possibility of locating mobiles or base stations in a control context of the spectrum, • the decrease in the transmission power at constant range or the increase in the transmission range, at constant power and therefore the reduction in interference to other cells, • the process is applied for different waveforms, without specific treatment.

• by using bleaching or projection techniques which allow better rejection of interference, the possibility of improving goniometry results.

Other characteristics and advantages of the invention will appear in the description which follows, given by way of illustration and in no way limiting, given with reference to the appended drawings which represent:

• Figures 1 and 2, the principle of transmission and reception of a linear modulation according to the prior art, • Figure 3, a location system from a base station, • Figure 4, a block diagram of the principle of transmission-reception according to the invention, • Figure 5, the shape of a signal s_e(t) emitted by a source m comprising a reference signal d (t), • Figure 6, the result of the sync in a multi-user context, • Figure 7, a block diagram of the detection and multi direction finding process -users, • Figure 8 a diagram showing the lengthening of the duration of the reference signal, • Figures 9 and 10 two examples of implementation in the case of multi-users, • Figures 11, 12, 13 and 14 test results.

The following description, given by way of illustration and in no way limiting, relates to a direction-finding device having in particular the objective of direction-finding the sources on an airplane and / or on the ground.

FIG. 3 is a diagram of an example of a system for locating one or more mobiles Mi from a base station. The signals are propagated along direct paths (shown in solid lines in the figure) or indirect paths following the various reflections on obstacles (dotted lines).

The base station 1 comprises, for example, an array of antennas 2, behind which there is a system 3 for receiving signals from the antennas. A processor 4 suitable for executing in particular the steps of the method according to the invention detailed below is connected to the reception system.

FIG. 4 shows schematically the principle of transmission-reception implemented in the method according to the invention. The elements identical to those in FIG. 2 bear the same references. The signal emitted s_e(t) propagates by a transmission channel C (t) before being received on the network of sensors of the base station.

The signal emitted s_e(t), an example of form and structure of which is given in FIG. 5, comprises several reference signals d (t) which appear several times, at given instants fi, t₂...... The reference signal d (t) is composed for example of the series of symbols {s_k} for 1 <k <K, where K is the number of symbols in the sequence. The duration Ôt of the reference signal d (t) then depends on the number K, on ​​the symbol time T_s and the sampling period T_e.

Step a) of the process: construction of the reference signal d (t)

The method constructs the reference signal d (t) from the symbols of the training sequence {s_k}, time symbol T_s of the transmitted signal, of the sampling period T_e and of the emitted modulation (standard used for the signals and which may be the waveform h (t) in the case of linear modulations).

In the multi-user case, with M_o users or useful, step

a) is repeated as many times as there are users, in order to determine for each of them the reference signals di (t) ... dMo (t). This makes it possible to carry out multi-user direction finding using the presence of the M_o reference signals between times t_k and t_k+ ôt where ôt is the duration of the reference signals.

For example, for GSM signals, the reference d (t) is calculated using the aforementioned expression (2).

For signals of UMTS type, the method determines the reference sequence d (t) from the spectrum spreading sequences known to those skilled in the art and from expression (1) where h (t) is a filter of Roll-off nyquist 0.25.

This step a) is for example followed by a step of digitizing the received signal x (t) at the sampling period T_e. In this step it is not necessary to choose T_e such as T_s= PT_e where P is an integer.

Step b) or synchronization step

The next step consists in determining, in the received signal x (t), the instants t-ι, t₂ etc. of appearance of the reference signal d (t) such as according to the relation (4):

x (t + t_k) = XC (t) d (t-nTe) + b₀(t + t_k) for 0 <t <5t (8) n

because x (t) = C (t) * s_e(t) + b₀(t) and s_e(t + t_k) = d (t) for 0 <t <ôt. For this, the method considers that the reference signal d (t) is the input signal and seeks to maximize in τ the following synchronization criterion:

Scream (T) = f_xdw^HR ^ '¹(T) r ^ ir) with Ç_dk) = ^ X x (t + x) d (t) * and V) = | X x (M * (M^H (9) Ôt to νί t = O

Step c) determination of the directions of arrival or direction finding

We use the signals x (t + tk) and d (t) associated with a source m in order to isolate it and perform a direction finding on a single source at a given time t_k.

The implementation of step c) depends in particular on the context of use, for example in the context of single-user or multi-user. The description differentiates these two cases.

Application of the process in the single-user case

The method first of all searches for the times of synchronization at t_k= pT_e for example using the method described in the patent

FR 2 715 488. Knowing the different times of synchronization, the instants of appearance tk of the learning sequence, it performs the direction finding, for example according to a MUSIC type method known to those skilled in the art on the signal d ( t) modulated reconstructed from step a) and the observations x (t + t_k) over the time interval 0 <t <ôt. Such a method is for example described in the document entitled “A signal subspace approach to multiple emitters location and spectral estimation”, by ROSchmidt, PhD Thesis, Stanford University, CA, Nov 1981].

Application of the process in the multi-user case

In a more general context, we may want to search in the received signal x (t), several sources which are associated with reference signals di (t) different from each other. In GSM, for example, the idea is to search for sources associated with the 8 possible TSC sequences, 1 <i <8. Under these conditions, we will name t_k(i) the synchronization instants associated with i^eme synchronization signal dj (t).

Finding the M number_o useful or useful transmitters

The method will first find the number M_ouseful. To illustrate the process implemented, the description considers the case where there are 2 payloads or transmitters.

Figure 6 shows the presence of 2 reference signals d, (t) and dj (t) which are detected at the respective instants t_k(i) and t_k(j) and which correspond to 2 users or 2 transmitters.

If the deviation Δίί, = t_k(j) - t_k(i) is low enough, for example,

Atij <and ôt (typically œ = 0.1), we can apply a multi-user algorithm (for example by implementing a multi-user gonio technique described in this patent using the signals d, (t) and dj (t) in the model of equation (16) between times t_k(i) and t_k(j) + ôt, time period or signal slot where both users are present. According to expression (6), the signal x (t + t_k(i)) is written as follows:

x (t + tk (i)) = X Ci (t) di (t-nTe) + £ Cj / t + Atg) d / t + Aty-nTe) + b²(t) n = -L / 2 n = -L / 2 for 0 <t <6tij (10) where ôtjj corresponds to the signal slice used to multi-user the i^em® and the i^em® signals.

Where b²(t) is a noise made up of the background noise b₀(t) and jammers having no synchronization signal, sufficiently close to instants t_k(i) and t_k(j). This expression can also be expressed in the following form (11):

x (t + tk (i)) =

<img file="FR2829241B1_D0001.tif" />

Useful

Background noise + Jammers

Where H_m^u represents the propagation channel matrix for the useful m and r^mL (t) its reference vector.

For me₀= 2, the H_m^u and the r^mL (t) verify;

<td>'t /, (r- (L / 2) re) ·</td><td>and I²L (t) =</td><td>d₂ (t + AZ₁₂ - (LIl'jTe)</td>

<td>d_t(t + (L / 2) Te)</td><td></td><td>d-, (t + Afp + (L / 2) 77?)</td>

and

Η / = [CWJTe) ·· 0 · ι (ί + (Ι_ / 2) Τθ)]

H₂^u = [C₂(t- (L / 2) T_e+ At₁₂) .... VS₂(t + (LV2) T_e+ At₁₂)] (13)

Where L is the number of time offsets of the reference signal.

The optimum is for example to choose L equal to the temporal spreading of the channel of the transmitter spreading the most.

More generally, the number of useful M_o is equal to the number of times t_k(i) belonging to the time interval [t₀1₀+ Aty [, where Aty = a Ôt. The value of a is typically cc ~ 0.1 and ôt is the duration of the synchronization signals.

The multi-user direction finding and detection process is then illustrated in Figure 7.

In summary, the process in the case of a multi20 user context:

• Determine the different times of synchronization t_k(i) for all the signals i, • Determine the number of utilities or transmitters M_o, • Performs direction finding for each useful (transmitter) M_o by knowing the associated reference signal d, (t) and the synchronization instants t_k(i).

The direction finding step is carried out, for example, according to various methods, some of which are given below by way of indication and in no way limiting. Before implementing the direction finding, the method estimates the different propagation channels and separates the useful ones.

For this, the method considers the jammers correlated with the useful as useful. We are thus in a multi-user context with Mo useful transmitters and MM_o interfering transmitters.

After separation of the useful, the expression of the signal x^m(t) received on the network of sensors and coming from the user m, is equivalent to that of the single user and it is then possible to apply to this signal a single user direction finding algorithm.

Under these conditions, the signal received on the sensors is expressed as follows:

"O

X (t) = jr Hm^ur^mi_ (t) + b^M0(t) (14)

Where b^M0(t) = X Hm s^mL (t) + b (t)

The representative matrices of the transmission channel H_m^u and H_mHave the following expression (15):

<img file="FR2829241B1_D0002.tif" />

Where A_m= [a (u_m1)... at_mPm)] is the matrix of the direction vectors of the multipaths of the rn '^eme transmitter, Bm^uT= [pmibmi^U... pmpmb / npm^u] and Bm^T= [p_m'i / i_m'₇... pmPm'b_m'p_m'], u_mp is the incidence of p^ith route of the rn '^emeuser. The expression (14) of x (t) can be written as follows:

x (t) = H_u r^uL (t) + b^M0(t) (16) where H_u represents the matrix of the propagation channels of the M_o useful and r^uL (t) the associated multi-user reference vector.

d ^ t ~ (L / 2) 7th) with H_u = [H / ... H_Mo^u] and r^uL (t) =

E'lW d_}(t + (L / 2) Te) d_My(t- (L / 2yTeî _d_Mo(t + (L / 2) Te) _

The exponent u refers to the so-called useful transmitters and L corresponds to the number of time shifts of the reference signal. The optimum is to choose L equal to the time spread of the channel of the transmitter spreading the most.

The objective of the multi-user technique is to first separate the M_o useful signals to then apply a single-user type technique to each of the useful transmitters.

Separation of transmitters or useful

The separation of the emitters consists in estimating the transfer matrix H_u= [Hi^u ... HMo^u] then to extract from Hu the matrices H_m^u associated with each of the M_o useful transmitters. The method estimates H_u in the sense of least squares as in the single-user case. Thus from expression (16) the method estimates H_u by minimizing the difference between H_u r^uL (t) and x (t). By making this least square between times tmin and t_max we obtain :

h. = R „· (r„ T (17) with V - 1—2 x (t) r “_L(t)^H and R / = --— £ £^ulW r “_L(t)^H

Lnax ^ min Tiax Tun &lt;= '_min

By posing b^M0(t) = x (t) - H_u r^uL (t) we deduce that the covariance matrix of this noise + interfering vector is equal to:

^Rbb “= Lnax ^ min £ b^M° (t) b^M0(t)^H= R „- H„ R „-^h= R „- R„ (r „“ y R, “H with R_xx = -—1— £ x (t) * (t)^H ^ max ^ min i =^fmjn

<img file="FR2829241B1_D0003.tif" />

(18)

As the matrices H_m^u are sub-blocks of the matrix Hu by checking HU = [H,^U ... HN1O^U] we extract them directly from H_u by selecting the correct columns. We therefore separated the useful signals and estimated the covariance matrix R_bb“Of the noise + jammer component. We notice that to estimate the matrices R_bb“And H_m^uwe use the matrix R / which is the covariance matrix of the vector r^uL (t). This matrix has, according to (16), the following structure:

R “=

<td>5l (°)</td><td></td><td></td><td></td>

<td>r, l (O</td><td> 5,(0)</td><td></td><td></td>

<td> (0)</td><td></td><td>Li₀M₀ (0)</td><td></td>

<td>/ λ,₀, (Ό</td><td>^PM „l (0)</td><td> (^)</td><td>&lt;W₀, V₀ (θ) _</td>

(19)

We see that the matrix involves intercorrelation terms (T) between the reference signals d, (t) and dj (tT) such as:

Ç (O =

Enax Ο, in r = J, nnax

Σ &lt;“t) di (tT) i

(20)

Under these conditions, the multi-user method exploits the correlation coefficients / (T) between the reference signals, which are not necessarily harmful. This remark makes it possible to check intuitively that the use of the coefficients / (T) is necessary to achieve the separation of reference signals dj (t) and dj (t) in the correlated case.

From the knowledge of the transfer matrix H_m^u of m '^emeuseful emitter we can constitute an observation vector x^m(t) by having rejected the other useful transmitters. The following transformation is carried out according to (14):

X^m(t) = X (t) - X Hm '“τ' _L(t) U x^m(t) = H / A (t) + b^M0(t) (21)

The expression of the signal x^m(t) is equivalent to that of the one-user case where M_o= 1 and the process applies to the signal x^m(t) a single-user direction finding algorithm, two examples of which are given below by way of illustration and in no way limiting.

Goniometry by bleaching

Knowing that the transfer matrix is ​​worth H_m^u = A_m B_m^u and assuming that r^uL (t) and b^M0(t) are decorrelated, the covariance matrix R_xx^m signal x^m(t) has the following structure from expressions (21) and (15):

R_xx^m = E [x^m(t) x^m(t)^H] = A_m R_sm^u Am^H + Rbb^u (22) with

Rsm^u= Bm^u E [r^mL (t) r^mL (t) ^H] B_m^uH

Where R_bb^u is the covariance matrix of signal b^M0(t) whose expression is that of formula (18). Matrix A_m consists of the direction vectors a (u_mp) from p '^eme route of the rn '^eme useful transmitter. Like Rbb^u is different from σ²Ι and that this matrix is ​​known, we apply the MUSIC method by whitening the observations x^m(t) by the matrix Rbb^u. According to (21) the matrix R_xx^m can be written as follows:

R_xx^æ = Hm^u Rrr^m Hm^{u H} + Rbb^u with Rrr^m = E [r^mL (t) r^mL (t)^H] (23)

Under these conditions the steps of the algorithm are as follows:

1^1st step: Calculation of Rxx = E [x (t) x (t)^H], Rxr “= E [x (t) r^uL (t)^H] and R / = E [r^uL (t) r^uL (t)^Hj

2^ith step: Calculation of the transfer matrix H „= R_xr“(R / ^¹

3^ith step: Extraction of the estimated matrices of the propagation channels for each of the emitters m H_m“For 1 &lt;m &lt;M₀ of the matrix H_u knowing that ... H_mo^u]

4^ith step: Calculation of the noise matrix Rbb “= Rxx - Rxr (r /)¹ R „“^hFor each transmitter or useful m of transfer matrix Hm^u . We initialize by m = 1:

5^th step: Calculation of Rxx^m= Hm^u R / Hm^uH+ Rbb “with R / = E [r^mu (t) r^mL (t)^H]

6^ith step: Rxx bleaching^m by Rbb “such as: R_xx^bm = W^1/2Rxx^m W^{1 / 2H}with Rbb “= W^1/2W^{1 / 2H}

7^th step: Applying MUSIC on Rxx^bm with guiding vectors a^b(u) = W '^1/2 a (u) to estimate the incidences ump for 1 &lt;p &lt;P_m multi_trajects of the m '^eme transmitter.

8^th step: m = m + 1

9'^eme step: if m &lt;M₀ back to 5^ith step.

At the output, the process has the effects u_ip(t_k(i)) associated with k '^eme instants of the p '^eme route of the i '^eme reference signal from this source. The implications u_ip(t) can either be azimuths 0_ip(t) for a 1D direction finding either be the pair of parameters (0_Îp(t), Δ,_ρ(ί)) for a 2D direction finding where Aj_P(t) is the elevation angle.

Goniometry by projection

As in the single-user case, the method uses, for example, a method by projection. Indeed knowing that H_æ^u = A_m B_m^u , the expression of x^m(t) is the following from (21):

x^m(t) = A_m B_m^u r^mL (t) + b^M0(t) (24) where the matrix A_m = [a (u_mi) ... a (u_mPm)] consists of the direction vectors a (u_mp) rn multipaths^{, eme} useful transmitter. Knowing from (15) that H_m'= A_m-B_m-, expression of interfering signals b^M0(t) of expression (14) becomes

M b^M0(t) = X AmBm'S^m'L (t) + b (t) = A_b^MOs_b(t) + h (t) (25) where A_b^MO= [AMo + i ··· Am] is the matrix of the direction vectors of all the interfering sources and sb (t) = [{BMo + iS^{MO + 1}L (t)}^T... {BM s^ML (t)}^T]^T is the vector of interfering signals.

The process is found in a multi-user case and the steps of the projection direction finding algorithm are as follows:

1^1st step: Calculation of R_xx = E [x (t) x (t)^H], R / = E [x (t) r^uL (t)^H] and R / = E [r^uL (t)

<img file="FR2829241B1_D0004.tif" />

2^ith step: Calculation of the transfer matrix of the propagation channel H „=

<img file="FR2829241B1_D0005.tif" />

3'^eme step; Extraction of the estimated matrices for the different propagation channels corresponding to users or useful m

H_m^ufor 1 &lt;m &lt;M0 of the matrix Hu knowing that HU = [H,^U ... HMO^U]

4^th step: Calculation of the noise matrix Rbb “= Rxx - Rxr“ (r /)¹ Rxr^K

5'^eme step: Applying MUSIC on R_bb“And deduction from A_b^M0

6^th step: Calculation of nb = I - Ab^M0 (Ab^M0HAb^M0)'¹ Ab^M0H

For each transmitter m of transfer matrix H_m^u . We initialize by m = 1:

7'^th step: Calculation of Rxx^m= Hm^u R / H_m^uH with R / = E [r^mL (t) r^mL (t)^H]

8^,^eme step: Calculation of the Ftxx matrix^urT1= nb (R /) n_b

9^,^eme step: Applying MUSIC on Rxx^um with direction vectors apro (u) = n_ba (u) to estimate the incidences u_mp for 1 &lt;p &lt;P_m multi_trajet of the rn '^eme transmitter.

10^th step: m = m + 1

11^Ieme step: if m &lt;M₀ back to 7^ith step.

At the end of this step the process is in possession of the effects

Ui_P(tk (i)) associated with k '^em® instants of p '^em® path of the i '^eme reference signal from this source. The implications u_ip(t) can either be azimuths 8_ip(t) for a 1D direction finding either be the pair of parameters (6i_P(t), A_ip(t)) for a 2D direction finding where A,_p(t) is the elevation angle.

Improved direction finding results

The steps which have been described above can be improved. Generally, the direction finding performance is inversely proportional to the time duration removed from the reference signal. Thus for a temporal duration of the learning signal 5t 'equal to αδί, the precision of the direction finding is 4a more precise.

The method then comprises a step in which the duration of the reference signal is increased. As shown in Figure 8, the method consists in deducing from the observed signal x (t) a reference signal s_m(t) of longer duration 5t 'such that δί'&gt; δί.

This value δί 'is determined for example as a function of the standard used.

For example, in the GSM standard, the 8 TSC signals have a duration 5t = 96, us and the duration of a user burst is ôt '= 577ps: At best we can therefore have a ratio a = ôt' / ôt = 6 and thus have more precise goniometries 4â = 2.5.

To obtain this result, the method implements the following steps:

Determine the reference sequence

Carry out step a) considering a time duration ôt '&gt; 5t in order to obtain one or more reference signals d_m(t) for one or more useful m.

Determine a spatial filter

From the reference signal d_m(t) of duration 5t determined in step a), from the signal x (t) received by the sensors, the method determines a spatial filter Wm such that d_m(t) = W_mx (t)

Determine the signal s_m(t)

To determine the signal s_m(t) of duration Ôt ', first of all a spatial filtering is carried out from the learning sequence d_m(t) to obtain an estimate s _m(t) of signal s_m(t) of duration δί '. Knowing that s_m(t) is not exactly equal to s_m(t) we can consider transforming it into a signal s _m(t) closer to s_m(t).

Depending on the characteristics of the signal received, the method achieves the following improvements:

(a) Demodulation of s_m(t) for digital signals: Knowing that in most cases the characteristics of the digital signals intercepted are known, for example for GSM, UMTS, an alternative consists in demodulating the signal s_m(t) to then remodulate the detected symbols and obtain the signal s _m(t).

(b) Case of constant modulus signals: Knowing that these signals have a constant modulus equal to 1, I s_m(t) l = 1, the process builds a reference signal s _m(t) as follows: s _m(t) = exp (j angle (s _m(t))) where angle (z) denotes the argument of the complex z. According to expression (2), this principle can be applied in GSM because the symbols are modulated in a phase modulation which is (a GMSK.

(c) Case of any signals: Under these conditions the reference sequence that can be used can only be s _m(t) such that s _m(t) = s _m(t).

Determination of the spatial filter of the signal s_m(t)

In the presence of M_o useful signals the signal x (t) received on the N sensors of the network is written as follows (26):

x (t) = £ H_m^u r^mL (t) + b^M0(t) = H^u r^uL (t) + b^M0(t) for L &lt;t &lt;

ti + ôt

<td colspan="2"></td><td>Α (ί)</td><td></td><td>~ d_m(t- (L / 2) Te) '</td>

<td>15 WHERE</td><td>I^uL (t) =</td><td></td><td>and r^mL (t) =</td><td></td>

<td></td><td></td><td>MO Γ l (î)</td><td></td><td>d_m(t + (L! 2) Te) _</td>

The signal d_m(t) is the learning signal of rn '^eme transmitter for h &lt;t &lt;ti + St. The reference vector r^uL (t) is therefore composed of the reference signals d_m(tk) Mo useful signals. Assuming the rn^th transmitter transmits a signal s_m(t) as in figure 8 we deduce, for all times t:

x (t) = Hu s^uu (t) + b^M0(t) (27)

<td colspan="2"></td><td>s'l (î)</td><td></td><td>\ s_m(t- (LI2) Te)</td>

<td>OR</td><td>S^UL (t) =</td><td></td><td>ets^mL (t) =</td><td></td>

<td></td><td></td><td></td><td></td><td>_s_m(t + (LI2) Te) _</td>

From the relation (26) the method determines the spatiotemporal filter W making it possible to estimate r^uL (t) from x (t). According to (27) this same filter makes it possible to estimate the signal s^uL (t) from x (t). In the absence of noise and jammers W checks: s^uL (t) = W x (t). Under these conditions we estimate W from equation (26) by minimizing the difference between W x (t) and r^uL (t) for t-, &lt;t &lt;t-i + ôt:

w = R / (28)

LJ 1 ί | + &lt;5ί LJ with R_rx^l,= ^ - £ r^uL (t) x (t)^H and £ x (t) ï (t)

We then deduce an estimate s^uL (t) of the reference vector s^uL (t) for t / &lt;t &lt;fl '+ ôt' verifying:

s^uL (t) = wx (t) pourt-ι '&lt;t &lt;fl' + ôt '29)

<td></td><td></td><td>'Îl (î)'</td><td></td><td>\ (i- (L / 2) r_e)’</td>

<td>or</td><td>S^UL (t) =</td><td></td><td>and s^mL (t) =</td><td></td>

<td></td><td></td><td>-Λ / 0 ... sl (î)</td><td></td><td>_s_m(t + (L / 2) Te \</td>

The signal s_m(t) is the estimated reference sequence of rn '^emetransmitter over a period of time. As indicated at the beginning of this paragraph, this estimate s_m(t) can be refined by transforming it into a signal s _m(t).

Transformation of a multi-source case into a multi-user

Figure 9 shows the time range in which the multi-user algorithm is applicable. This corresponds to a duration δί_Ί2less than the duration δί of the sequences delimited by the instants t₁₂ and tl2 + 5ti₂.

To be able to apply the multi-user algorithm without reducing the duration of the reference signals, it is therefore necessary to estimate the sequences â ^ t) and s₂(t) of Figure 10.

First of all, we will estimate in single-user the signals s_m(t) for 1 &lt;m &lt;M₀ from observations x (t) and the reference signal d_m(t) such that r^uL (t) = r^mL (t). Signals s_m(t) are therefore estimated independently. As previously stated, the M_o estimates can be refined by transforming them into signals s _m(t).

Examples of implementation of the method according to the invention

FIG. 11 represents results obtained with two plane arrays of N = 5 sensors, comprising a circular array of radius R = 21.1cm and a V ”array. The azimuth Θ is the incidence of a source in the network plane and the elevation angle Δ is the incidence with respect to the perpendicular to the network plane. For the simulations in (θ, Δ), the direction finding is carried out according to the parameters (u, v) which are the components of the wave vector of the source in the network plane. These components can be expressed in the form:

u = cos (A) cos (0) and v = cos (A) sin (0) (30)

Both networks are suitable for the 900MHz-1GHz frequency range of GSM. In the simulations the central frequency is equal to f_yeart = 900Mhz and thus the wavelength is equal to λ = ο / f_yeart = 33.33cm.

The goniometry performance will then be estimated either with respect to the parameter Θ or with respect to the parameters (u, v) depending on whether a 1D or 2D direction finding is carried out. These performances are calculated in terms of MSE (Mean Quadratic Error) of parameter 0_m or (u_m, v_m) for the rn '^eme source. For this we carry out several goniometries of the source of incidence 0_m or (u_m, v_m) to estimate at the k^ith iteration incidence ê_m(k) or (û_m(k), v_m(k)). At each iteration, the same signal configuration is kept while having randomly drawn the noise and the symbols from the incident signals. Consequently for a source of incidence 0_m or (u_m, v_m), the 1D and 2D EQM calculations are as follows:

1D direction finding in θ: αθ ”_μ = © £ (ê_m(k) - e_m )²

I 1

2D direction finding in (u, v): ar ™_qm = J ^ £ K (k) - uj² + (v Jk) - v J²

Where nb denotes the number of iterations to calculate the EQMs:

The EQM of the m '^eme source is set by for 1D direction finding and by for 2D direction finding.

To finish it is necessary to establish a spatial distance between a useful of incidence 0_m or (Um, v_m) and incidence jammers 0_m or (u_m, v_m) for

2 &lt;m &lt;M. This distance depends on the direction vectors of the sources, the expression of which is given for example in the document entitled “A signal subspace approach to multiple emitters location and spectral estimation” and authored by RO Schmidt PhD Thesis, Stanford University, CA, Nov 1981. Noting by a_m the guiding vector of the m '^eme source, this distance is defined by the projection of the directing vector ai of the utility on the space defined by those of the jammers a₂... at_M such as :

The scalar Ci /₂-ma then the following expression:

01/2 - ^ = ^ - ^ —--—- with n_s(2, ..., M) = A₂_my₂_m^h A2.m) ¹A2-m^H

Where A₂-m = [a₂... at_M ] and a_m^H at_m= N for 1 &lt;m &lt;M. Under these conditions the parameter ci /₂-m called the spatial correlation coefficient varies between 0 and 1. When Cv2-m = 0 the useful is orthogonal to the jammers plane and is therefore spatially decorrelated to the jammers. However when Ci /₂-m = 1 the useful is in the jammers plane and becomes spatially coherent to the jammers. These spatial correlation configurations between the utility and the jammers will have an important influence on the direction finding performance (figure 12).

Examples of simulations with GSM signals

In the simulations of this paragraph the signals s_m(t) are the GMSK modulations of the GSM. As the signal emitted is at constant modulus, we transform the signal s_m(t) in s_m(t) by method (b). As previously, 8t = 56 is chosen to be in the configuration of the TSC signals at fe = 600 kHz. The duration of the new reference signal will be extended s_m(t) at 8t '= 200 so that it corresponds to the approximate duration of a GSM burst. The signal is simulated on the circular network at f_yeart = 900MHz. The goniometries are carried out in 1D and the incidence of the 1^first source is 0₁= 45 degrees.

In FIG. 13 in the presence of a single source, the performance of the reference algorithms is compared with the signals di (t) and si (t) of respective duration 8t = 56 and 8t '= 200. We draw in solid lines the Cramer Rao bounds associated with these integration times. The goniometry precision ΔΘ is given¹Εομ of the source as a function of its signal to noise ratio [S / BL.

It can be seen that the method with the known signal di (t) follows the Cramer Rao bound while the reference method with the signal si (t) follows this bound beyond OdB. Thus beyond OdB the method with si (t) is / 200/56 = 1.88 times more precise than the method with di (t). Below OdB, the method with the reference sequence if (t) is more precise with a gain less than 1.88.

FIG. 14 shows schematically the results obtained by simulation of the case of a source of sequence di (t) scrambled by a source without a synchronization signal. The spatial correlation coefficient between the two sources is equal to ci / 2 = 0.9. The reference direction finding algorithms are therefore one-user using the di (t) or si (t) method. The curves represent the precision ΔΘ¹ΕΟμ of the goniometry of the Î^time source as a function of the signal to noise ratio [S / N] of the two sources.

We note that the reference methods using d ^ t) or â i (t) have the same behavior when mono-source: The method with di (t) follows its bound of Cramer Rao and that with the extended sequence if (t) follows this terminal beyond signal-to-noise ratio OdB. As from a theoretical point of view the Cramer Rao bound with si (t) is 1.88 times more precise than that with di (t), this last simulation clearly shows that the method with the sequence of duration 5t 'is more precise than the one with the sequence of duration Ôt.

The method described above applies in particular in a transmission system comprising a receiver made up of N sensors connected to a device suitable for determining the directions of arrival of the various signals, such as a goniometer. The receiver comprises a processor equipped with software making it possible to implement the steps of the method, for all its application variants.