KR19990065801A - Rapid acquisition means and method of PN signal - Google Patents

Abstract

The present invention relates to a means and a method for capturing a pseudo noise signal in a shortest possible time in a direct sequence spread spectrum system (hereinafter referred to as a DS / SS system) A phase estimator for estimating a phase of a pseudo noise signal (first PN signal) and outputting a phase estimate; a phase estimator for receiving a phase estimate from a second PN signal and a phase estimator received after a predetermined period of time; And a phase matching detector for searching for phase coincidence with the second PN signal while changing the phase and outputting the phase coincidence signal directly to the tracking means in the sequence spread spectrum system when the phases coincide with each other. The method includes: estimating a phase of a first PN signal received for a predetermined period of time; outputting an estimated phase estimate; estimating a phase of a third PN signal based on a second PN signal received after a predetermined period of time; And searching for phase coincidence with the second PN signal. Such an acquisition means and an acquisition method estimate the phase of the received PN signal as soon as possible and then search for the phase coincidence of the PN signal, thereby improving the performance of the entire DS / SS system by greatly reducing the waiting time required for data transmission and reception There is an advantage.

Description

Rapid acquisition means and method of PN signal

The present invention relates to an acquisition means for acquiring a pseudo noise signal (hereinafter referred to as PN signal) of a direct sequence spread spectrum system (hereinafter referred to as a DS / SS system) and a method thereof, To an acquisition means for estimating the phase of a received PN signal in a shortest possible time and then searching for the phase coincidence of the PN signal, and a method thereof.

The DS / SS communication scheme spreads the baseband signal to a PN signal of a frequency much higher than the symbol rate, and synchronizes the PN signal on the receiving side, then converts the received PN signal into a narrowband signal to be. This system is advantageous for security, strong in jamming, and suitable for multiple accesses, and is widely used as a commercial system of military and code division multiplexing (CDMA).

In order to receive the spread spectrum signal from the receiver at the receiver side, a synchronization process is required to make the phase of the received PN signal equal to the phase of the PN signal of the receiver. This synchronization process consists of two stages: acquisition and tracking. The acquisition is a step of performing phase synchronization within a period of one chip of the spread PN signal. In the tracking, it is determined whether the received PN signal and the PN signal of the receiver are correctly synchronized. Respectively. The system for tracking can be relatively simple to implement, but the system for capturing is very different in configuration and complexity from performance to performance, and is difficult to implement in accordance with the requirements for acquisition.

The conventional trapping technique is performed by sequentially detecting the phase of the PN signal of the receiver and detecting whether or not the PN signal is synchronized with the received PN signal. A serial search for searching one phase at a time, And a parallel search for searching for the phases of the two points.

While the serial and parallel search is performed while blindly changing the PN signal phase of the receiver in a certain direction, recently, an auxiliary signal having a special characteristic is used to more effectively change the PN signal phase of the receiver A method of searching for a phase has been proposed (see, for example, M. Salih and Sawasd Tantaratana, 'A Closed-Loop Coherent Acquisition Scheme for PN Sequences Using an Auxiliary Sequence', IEEE J. Selected Areas in Comm. pp. 1653-1659, Oct. 1996.). In addition, a fast acquisition means using this auxiliary signal for phase estimation has been proposed (Suwon Kang, Y.-H. Lee and Sawasd Tantaratana, 'Rapid Acquisition of PN Signal for DS / SS using on auxiliary signal' submitted to IEE proceedings .

However, since the above-described serial and parallel search is performed while blinking the phase of the PN signal of the receiver in a certain direction, the acquisition time becomes long. The method of searching for the phase using the auxiliary signal has a complexity of the acquisition means .

Accordingly, in order to solve such a problem, the present invention provides an acquisition means and a method for shortening the acquisition time and greatly increasing the complexity of the system by performing the phase matching search after estimating the phase of the received PN signal do.

1 is a block diagram showing the configuration of a synchronization system applied in accordance with the present invention;

FIG. 2 is a block diagram showing the configuration of the phase estimator in FIG. 1 acquisition means;

FIG. 3 is a block diagram showing the configuration of the sinusoidal phase estimator in FIG. 2. FIG.

Fig. 4 is a block diagram showing the configuration of the phase coincidence detector in Fig. 1 acquisition means; Fig.

FIG. 5 is a view showing the phase of a PN signal generated in the PN signal generator of FIG. 4; FIG.

Description of the main parts of the drawings

10: capturing means 11: switch

12: phase estimator 13: phase match detector

20: Tracking means

According to another aspect of the present invention, there is provided a direct sequence spread spectrum system comprising: a phase estimator for estimating a phase of a pseudo noise signal (first PN signal) received for a predetermined period of time and outputting a phase estimate; A second PN signal received after a lapse of time and a phase estimate from the phase estimator are received and the phase of the third PN signal is changed while the phase of the third PN signal is changed based on the phase estimate, To the tracking means in the sequence spread spectrum system, and estimates the phase of the PN signal in a shortest time, and then searches the phase coincidence of the PN signal.

According to another aspect of the present invention, there is provided a method of capturing a pseudo noise signal (PN signal) received by a receiver of a direct sequence spread spectrum system, the method comprising: detecting a phase of a first PN signal And outputting the estimated phase estimation value; and searching phase matching between the second PN signal and the second PN signal while changing the phase of the third PN signal based on the second PN signal received after a predetermined time and the estimated phase estimate, And to capture the pseudo noise signal as quickly as possible.

Preferred embodiments of the present invention will be described with reference to the accompanying drawings.

1 is a block diagram showing a configuration of a synchronization system applied in accordance with the present invention. The system of FIG. 1 largely consists of a capture means 10 and a tracking means 20. The capturing means 10 includes a switch 11 for outputting a PN signal r (t) to which the switching contact a is connected by contact b or c as time elapses. The output terminal of the switch 11 is connected to the contact b of the switch 11 and connected to the phase estimator 12 for estimating the phase of the received PN signal r (t) (T) and a phase of the received PN signal r (t) while changing the phase of the receiver PN signal based on the phase estimate received from the phase estimator 12, A phase matching detector 13 is connected which outputs a signal to the tracking means 20 and receives the phase update signal from the tracking means 20 and repeats the above-mentioned process. Thus, the capture means 10 is constructed. The tracking means 20 is connected to the output terminal of the phase coincidence detector 13 and receives the phase coincidence signal from the phase coincidence detector 13 to start tracking. If it is confirmed that the correct phase coincidence is not obtained, And outputs it to the search device 13.

The operation of the synchronous system having such a configuration will be described with reference to Figs. 2, 3, 4, and 5.

First, the switch contact a of the switch 11 in the capturing means 10 is connected to the contact b until time t = 0 and t = t ₁ . Thus, the time t = ₁ 0~t PN signal r (t) received on the DS / SS system for is input to the phase estimator 12. Assuming that no data is transmitted during the acquisition time of the received PN signal r (t), the received PN signal r (t) can be expressed as an equivalent signal of the baseband as shown in Equation 1 below.

Where P represents the power of the passband signal and? ₀ represents the unknown delay time. Then, n (t) represents noise and c (t) is a PN signal. This c (t) is expressed by the following equation (2).

Where c _k is one of the values of -1 and 1 as the kth signal value of the PN signal train with period N, and T _c is the chip duration. Is expressed by the following equation (3).

An m-sequence is used as the PN signal sequence c _k . Assuming that the chip units are synchronized, the unknown delay time? ₀ in Equation (1) is expressed by? T _c (? Is an integer). This? Is a phase value to be estimated by the phase estimator 12, and? _{1, which} is an estimate of?, Is input to the phase coincidence detector 13. Referring to FIG. 2, a process of the phase estimator 12 for obtaining the phase estimate? ₁ will be described.

2 is a block diagram showing the configuration of the phase estimator 12 in the acquisition means 10 of FIG. The phase estimator 12 includes a matched filter 21 for matching and sampling the received PN signal r (t), a switch 22 for receiving and outputting the output of the matched filter 21 in a closed state at time kT _c , And a sinusoidal phase estimator 23 that receives the output of the switch 22 and estimates the phase of the sinusoidal wave.

The PN signal r (t) received by the phase estimator 12 having the above- Is matched to the matched filter 21 matched to the filter 21 and sampled in units of _Tc time. When the influence of the channel is ignored, the output r _k of the matched filter 21 is given by Equation (4).

Here, η _k is a noise component, _k c is the period N of PN sequence. c _k can be expressed by the following equation (5).

Here, A _i is a discrete Fourier transform coefficient of c _k given by Equation (6).

Using the characteristic of the autocorrelation function of the PN signal, it is known that A _i in Equation (6) can be expressed by the following Equation (7).

Here, φ _i (hereinafter also referred to as the reference phase) indicate the phase of the A _i, these values are given different unique value based on the type of the PN signal. Since c _k is a real signal, the relationship A _N-1 = A _i ^* holds. Thus, c _k can be expressed simply as the following equation (8).

Therefore, r _k sampled and output from the matched filter 21 is expressed by the following equation (9).

Thus, the output r _k of the matched filter 21 in Equation 9 passes through the switch 22 at time kT _c and is input to the sinusoidal phase estimator 23. The sinusoidal phase estimator 23 estimates ξ from the input r _k . In Equation 9, the cosine signal sequence having the period N / i is delayed by 2πξi / N compared to the reference phase φ _i . Therefore, we can estimate ξ by knowing the phase delay of this cosine signal sequence with respect to the reference phase. Therefore, the sinusoidal phase estimator 23 will be described with reference to FIG. 3 showing a process for estimating?.

3 is a block diagram showing the configuration of the sinusoidal phase estimator 23 of FIG. The sinusoidal phase estimator (23) of a number of sine-wave signal sequence constituting a c _k, by using a delay for the reference phase period of the cosine signal N columns calculate the phase estimate ξ _1.

The sinusoidal phase estimator 23 of FIG. 3 corresponds to the two multipliers 31 and 32 and the multipliers 31 and 32 for multiplying the input r _k by a constant function to output the outputs of the multipliers 31 and 32 And a summer 33, 34 for summing up to a certain signal sequence. Here, the multipliers 31 and 32 and the adders 33 and 34 are referred to as a first calculator 30. A phase delay estimator 35 for estimating and outputting a phase delay estimate γ by using the outputs of the summer 33 and 34 is connected to the output terminals of the adders 33 and 34. The phase delay estimator 35 is connected to the adder 33, A third multiplier 36 for multiplying the output phase delay estimate of the phase delay estimator 35 by a constant is connected. A quantizer 37 for quantizing the output of the third multiplier 36 and outputting the result is connected to the output terminal of the third multiplier 36. The third multiplier 36 and the quantizer 37 are referred to as a second calculator 28.

The sinusoidal phase estimator 23 constructed as described above first obtains the inphase component I ₁ and the quadrature component Q ₁ of the input r _k through the first calculator 30, Accumulates values multiplied over the PN signal train of L periods to attenuate the influence. Thus, the input r _k is input to the multipliers 31 and 32, respectively. The first multiplier 31 multiplies the input r _k by a function of cos (2πk / N + φ ₁ ) and outputs it to the first adder 33. The second multiplier 32 multiplies r _k by sin (2πk / N +? ₁ ) function and outputs it to the second summer 34. [ Each of the adders 33 and 34 adds the output values received from the multipliers 31 and 32 to k = 0 to LN-1 and outputs the result to the phase delay estimator 35. At this time, the first and summing the in-phase component I ₁ of r _k is the value that is output from the 33 inputs, the second summer 34 is r _k quadrature component Q ₁ in which the values are input to be output from the . I ₁ and Q ₁ thus obtained are given by the following equations (10) and (11).

Where v _I and v _Q denote the components of the noise.

Obtained I ₁ and Q ₁ are inputted to a phase delay estimator 35, a phase delay estimator 35 is to estimate the phase delay estimate γ of the sine wave by the following equation (12).

In this case, the phase delay estimate γ of the sinusoidal wave obtained has an error with the true value 2πξ / N due to the noise components υ _I and ν _Q , and the phase delay estimate γ of the obtained sinusoidal wave is multiplied by a third multiplier 36). The third multiplier 36 multiplies the received [gamma] by a constant N / (2 [pi]). Thus,? Is converted into the value of the [0, N] region in the [0, 2?] Region and input to the quantizer 37. The quantizer 37 quantizes the value input from the third multiplier 36 to the closest integer. The quantized output value is obtained by the following equation 13 as? ₁ .

Here, the Q function indicates quantization with the closest integer. From the periodicity of the PN signal sequence, ξ ₁ and ξ ₁ + mN (m is an arbitrary integer) are in phase.

The total amount of time in the above-mentioned phase estimation is input to a phase matching the browser 13 of the LNT _c, and the quantizer 37, phase estimate ξ ₁ is t = determined in LNT _c (t ₁₎ 1 capture means (10) do. At this time, the switch contact a of the switch 11 of Fig. 1 is connected to the contact c. Thus, the phase coincidence detector 13 retrieves the phase coincidence between the received PN signal r (t) and the receiver PN signal based on the phase estimate? ₁ . Referring to FIG. 4, a description will now be given of a process of searching for the phase coincidence of the phase coincidence detector 13 with respect to the above.

4 is a block diagram showing the configuration of the phase coincidence detector 13; The phase coincidence detector 13 of FIG. 4 receives and initializes? ₁ from the phase estimator 12 and generates and outputs a PN signal while varying the phase according to the phase update signal output from the determinators 47 and 48 And a PN signal generator (41, 42). Multipliers 43 and 44 are connected to the output terminals of the PN signal generators 41 and 42 for receiving and multiplying the received PN signal r (t) and the PN signals received from the PN signal generators 41 and 42, respectively . Integrators 45 and 46 for receiving and integrating the outputs of the multipliers 43 and 44 are connected to the output terminals of the multipliers 43 and 44, respectively. The multipliers 43 and 44 and the integrators 45 and 46 are called a correlator 40 that correlates the received PN signal r (t) with the output PN signals of the PN signal generators 41 and 42. When the output of each of the integrators 45 and 46 coincides with the output of each of the integrators 45 and 46 and agrees with the predetermined threshold value, the phase matching signal is output to the tracking means 20 of FIG. 1, And the determinators 47 and 48 for generating phase update signals are connected to the PN signal generators 41 and 42, respectively.

The phase estimator 12 receives the phase estimate ξ ₁ from the PN signal generators 41 and 42 of the phase coincidence detector 13. Then, the PN signal generators 41 and 42 initialize the phases with ξ ₁ T _c , and then generate PN signals and output the PN signals to the multipliers 43 and 44, respectively. At this time, the phases of the PN signals output from the PN signal generators 41 and 42 have opposite polarities as shown in Fig. In FIG. 5, A represents the phase of the PN signal generated by the first PN signal generator 41, and B represents the phase of the PN signal generated by the second PN signal generator 42. The multipliers 43 and 44 multiply the received PN signal r (t) by the input PN signal and outputs the multiplied signals to the integrators 45 and 46. The integrators 45 and 46 integrate the received values, , 48). Each of the determinators 47 and 48 compares the value received from each integrator 45 and 46 with a predetermined threshold value to determine the phase of the output PN signal of the PN signal generator 41 or 42 And judges whether or not they match. At this time, the correlation time and the threshold value for correlating the received PN signal r (t) received from the correlator 40 with the output PN signal of the PN signal generators 41 and 42 are determined by the erroneous detection probability (false detection probability) and true detection probability (true detection probability). When the output values of the respective integrators 45 and 46 are smaller than the threshold value, the determining devices 47 and 48 determine that the phases do not coincide with each other and output a phase update signal to the PN signal generators 41 and 42. Then, the PN signal generators 41 and 42 update the PN signals in units of? T _c and -T _c phases and output the multiplied signals to the multipliers 43 and 44, and the multipliers 43 and 44, the integrators 45 and 46, The determinators 47 and 48 operate in the same manner as described above. The phase update period of the PN signal is set to r (t) and the PN signal generators 41 and 42 for a specific PN signal, and " 0 " The time required to determine whether or not the phase is matched by the determining devices 47 and 48 and the time required to change the phase of the PN signal in the PN signal generators 41 and 42, same. The above operation is continuously repeated while the judging devices 47 and 48 output the phase update signals to the PN signal generators 41 and 42 and the PN signal phase that is phase-renewed by the PN signal generators 41 and 42 each (ξ ₁ + λ) and T _c (ξ ₁ -λ) reaches T _c, signal PN phase of the PN signal generator, two (41, 42) after being reinitialized to ₁ ξ T _c is continued repeatedly performed. Where? Is a value of (N-1) / 2. When the above operation is continuously repeated and the output values of the respective integrators 45 and 46 are larger than the threshold value, the determining devices 47 and 48 output the phase matching signal to the tracking means 20 of FIG. The tracking means 20 starts tracking when a phase matching signal is input from the determinators 47 and 48. Thus, when the tracking means 20 confirms that the correct phase matches, the PN signal synchronization of the PN signal generators 41 and 42 is terminated. If, however, it is determined that it was not a correct phase match, the tracking means 20 outputs a phase update signal to the phase match detector 13. Then, the phase coincidence detector 13 repeats the phase coincidence search process described above with reference to FIG. 4 until the tracking means 20 confirms that it is a correct phase coincidence. In this manner, the acquisition means 10 matches the phase of the received PN signal r (t) with the phase of the output PN signal of the PN signal generators 41, 42 within a shortest possible time.

As described above, since the acquisition means and the acquisition method according to the present invention match the phase of the received PN signal with the phase of the receiver PN signal in a shortest possible time, the waiting time required for data transmission and reception is greatly reduced, . ≪ / RTI >

Claims (26)

In a means for acquiring a direct sequence spread spectrum system, A phase estimator for estimating a phase of a pseudo noise signal (first PN signal) received for a predetermined time and outputting a phase estimate; And Receiving a second PN signal received after the lapse of the predetermined time and a phase estimate from the phase estimator and changing a phase of the third PN signal based on the phase estimate and searching for phase coincidence with the second PN signal, And a phase coincidence detector for outputting a phase coincidence signal to the tracking means in the direct sequence spread spectrum system to estimate the phase of the PN signal received in a shortest time, and to search for the phase coincidence of the PN signal. 2. The apparatus of claim 1, wherein the acquisition unit further comprises a switch for allowing the first PN signal to be input to the phase estimator for the predetermined time, and for inputting the second PN signal to the phase coincidence detector after the predetermined time elapses Wherein the means for capturing comprises: 2. The method of claim 1, wherein the phase estimator estimates a phase of the first PN signal using an m-sequence (ck) at the time of phase estimation of the first PN signal expressed as a linear combination of a sinusoidal signal sequence as follows . Here, N denotes a period of c _k , and φ _i is a reference phase having a value of [0, 2π] region. 2. The apparatus of claim 1, wherein the phase estimator A matched filter for matched filtering, sampling and outputting the first PN signal; And And a sinusoidal phase estimator for estimating a sinusoidal phase at the output of the matched filter and outputting the estimated phase estimate to the phase coincidence detector. [5] The apparatus of claim 4, wherein the phase estimator further comprises a switch positioned between the matched filter and the sinusoidal phase estimator and closed after a predetermined period of time to output the output of the matched filter to the sinusoidal phase estimator. Capturing means. 5. The acquisition means of claim 4, wherein the phase estimator estimates the phase estimate using a delay relative to a reference phase of a cosine signal sequence of period N. The method of claim 4, 5 or 6, wherein the sinusoidal phase estimator A first calculator to obtain and output an in-phase component (I ₁ ) and a quadrature-phase component (Q ₁ ) given by the following equation with respect to the output (r _k ) of the matched filter; A phase delay estimator for obtaining a phase delay estimate? Of a sinusoidal wave given by the following equation from the output of the first calculator and outputting the result; And A second calculator for receiving a γ from the phase delay estimator outputs the phase estimate (ξ ₁₎ obtained as shown in the formula below by quantized to an integer closest to the value after the conversion as the phase of the PN signal with the phase matching the browser, And the detection means. Here, L is an arbitrary integer,? ₁ is a reference phase value of a sinusoidal signal sequence having a period N, and the Q function represents quantization with the closest integer. 8. The apparatus of claim 7, wherein the first calculator Two multipliers for multiplying the output of the matched filter by cos (2? K / N +? ₁ ) and sin (2? K / N +? ₁ ), respectively; And And two adders located at respective output terminals of the multiplier and accumulating output values of the multiplier and outputting the accumulated values to the phase delay estimator. 8. The acquisition means of claim 7, wherein, in order to reduce an error of the phase estimator due to noise, the I ₁ and Q ₁ given by the following mathematical expression are obtained from the received PN signal sequence of L periods. Where P represents the power of the passband signal,? Represents the phase value, and? _I and? _Q represent the components of the noise. 8. The apparatus of claim 7, wherein the second operator A third multiplier receiving the? Output from the phase delay estimator and multiplying the output? By N / (2?) And outputting the result; And And a quantizer for quantizing the output value of the third multiplier to the closest integer and outputting the quantized value to the phase estimator. 2. The apparatus of claim 1, wherein the phase match detector Two PN signal generators for generating and outputting a third PN signal while independently varying the phase of the third PN signal when receiving the phase update signal from the determining unit and the tracking unit; Two correlators for multiplying a third PN signal by a second PN signal received from each PN signal generator, integrating the second PN signal, and outputting the result; And And two determiners for comparing the correlation value output from each correlator with a preset threshold value and outputting a phase coincidence signal to the tracking means if they match and outputting a phase update signal to the PN signal generator if they do not match, . 12. The method of claim 11, wherein the phase update period of each PN signal output from each PN signal generator is a time period for correlating a received second PN signal with a third PN signal that is an output of the PN signal generator, And the time taken to change the phase of the third PN signal in the PN signal generator. 12. The acquisition means of claim 11, wherein a phase of a third PN signal generated by each PN signal generator is opposite in polarity. 12. The method of claim 11, wherein each of the PN signal generator is a phase of the first 3PN signal in response to receiving input for ξ ₁ from the phase estimator receiving the start phase of the first 3PN signal in ξ ₁ T _c input to the phase update signal the θT -θT _c and _c units of the phase (θ is a phase update amount, has a value of one of values of 0.5 and 1, T _c is the chip duration being) by increasing or decreasing seeker to generate the first signal 3PN And the detection means. 15. The method of claim 14, wherein each of the phases of the 3PN signal generated from PN generator respectively (ξ ₁ + λ) and T _c (ξ ₁ -λ) T _c (where λ = (N-1) / 2 being ), The third PN signal phase is again initialized to ξ ₁ T _c and then a third PN signal is generated. A method for capturing a pseudo noise signal (PN signal) received by a means of acquisition in a direct sequence spread spectrum system, Estimating a phase of the first PN signal received for a predetermined period of time and outputting an estimated phase estimate; And And searching phase matching between the second PN signal and the second PN signal while changing the phase of the third PN signal based on the second PN signal received after the lapse of the predetermined time and the estimated phase estimate, How to capture. The method of claim 16, wherein the phase of the first PN signal is estimated by using an m-sequence (c _k ) at the time of phase estimation of the first PN signal expressed as a linear combination of a sinusoidal signal sequence as expressed by the following equation To capture. Here, N denotes a period of c _k , and φ _i is a reference phase having a value of [0, 2π] region. 17. The method of claim 16, wherein the first PN signal for phase estimation is matched filtered and sampled. 17. The acquisition method according to claim 16, wherein the phase estimate is estimated using a delay with respect to a reference phase of a cosine signal sequence having a period of N when phase estimation of the first PN signal is performed. The method of claim 16, wherein the in-phase component (I ₁ ) and the quadrature-phase component (Q ₁ ) given as in the following equation are obtained from the sampled value (r _k ) To capture. Here, L is an arbitrary integer, and? ₁ is a reference phase value of a sine wave signal train having a period N. 21. The acquisition method according to claim 20, wherein, in order to reduce an error in phase estimation, the I ₁ and Q ₁ given by the following equation are obtained from the received PN signal sequence of L periods. Where P represents the power of the passband signal,? Represents the phase value, and? _I and? _Q represent the components of the noise. 22. The acquisition method according to any one of claims 19 to 21, wherein the phase delay estimation value (gamma) is determined from the in-phase component (I ₁ ) and the quadrature-phase component (Q ₁ ) 23. The method of claim 22, wherein the phase estimate < RTI ID = 0.0 &_gt;# ₁ < / RTI &_gt; Here, the Q function represents quantization with the closest integer. 17. The method of claim 16, wherein each third phase is a second third PN signal that is independently varied. Of claim 16 to claim 24, wherein said phase estimate (ξ ₁₎ Based on the respective to a phase of the second signal starting from the 3PN ξ T _{c 1} and _c θT -θT _c (θ is the phase of the phase update unit The value of one of the values 0.5 and 1, and T _c is the chip duration). 26. The method of claim 25, wherein each of the phases of each of said signal 3PN (ξ ₁ + λ) and T _c (ξ ₁ -λ) T _c (where λ = (N-1) / 2 Im) is reached, after the re-initialized to ₁ ξ T _c acquisition method characterized in that the second signal generating 3PN.