LFM-based amplitude and phase response measurement timing method

Abstract

The present application relates to a kind of LFMs based on amplitude-phase response measurement timing method, belong to telemetry, radar and test measurement technical field, in the measurement method of amplitude-phase response, it is usually based on the way of single tone or double tone scanning and time-consuming is longer, and single tone cannot measure system phase response;And based on the way of multi-carrier, due to power limit, leading to the signal-to-noise ratio of each sub-carrier reduces, measurement result is poor. Again due to the related advantages of LFM signal, such as bandwidth, energy concentration and pulse compression etc., it gradually obtains application in this kind of measurement calibration system. After using the timing estimation of the present application, not only the amplitude response can be accurately measured, but also the phase response can be accurately measured. The actual measurement results show that the phase measurement curve of each time is very close to even coincide, so the idea of average noise reduction can be further used to improve the measurement accuracy of phase response.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of telemetry, radar and signal test measurement, and particularly relates to a LFM-based amplitude and phase response measurement timing method. BACKGROUND

[0002] In the telemetry, radar system and signal source, spectrum analyzer and other test and measurement instruments, the amplitude and phase distortion of the system often leads to the deterioration of the signal quality. Therefore, a calibration system is often added in the system to compensate for the amplitude and phase distortion of the original system. Therefore, the measurement of the amplitude and phase response becomes a prerequisite.

[0003] In the amplitude and phase response measurement method, the single-tone or double-tone scanning method usually takes a long time, and the single-tone cannot measure the phase response of the system. The multi-carrier method leads to the reduction of the signal-to-noise ratio of each sub-carrier due to the limited power, and the measurement result is poor. The linear frequency modulation (LFM) signal is widely used due to its advantages such as large bandwidth, energy concentration and pulse compression, and is therefore very suitable for the research in the above-mentioned fields. When the LFM signal is used for amplitude and phase distortion measurement, the existing method is to compare the amplitude and phase after correlation, without accurate timing synchronization, and therefore only the amplitude response of the system can be measured, and the phase response of the system cannot be accurately measured.

[0004] Therefore, at present, a LFM-based amplitude and phase response measurement timing method needs to be designed to solve the above problems. SUMMARY

[0005] The application aims to provide a LFM-based amplitude and phase response measurement timing method to solve the technical problems existing in the prior art, such as: in the amplitude and phase response measurement method, the single-tone or double-tone scanning method usually takes a long time, and the single-tone cannot measure the phase response of the system; the multi-carrier method leads to the reduction of the signal-to-noise ratio of each sub-carrier due to the limited power, and the measurement result is poor; and the LFM-based method does not have accurate timing synchronization, and cannot measure the phase response.

[0006] To achieve the above-mentioned purpose, the technical scheme of the application is as follows:

[0007] A LFM-based amplitude and phase response measurement timing method, the specific steps are as follows:

[0008] In the measurement system, the sending end continuously sends the LFM signal, that is, the periodic extension of the baseband signal u(t) is as follows:

[0009]

[0010] The receiving end uses its periodicity to perform corresponding frequency offset estimation and compensation;

[0011] The received signal is a time delay of the transmitted signal. Let the time delay be Δt1, then the received signal is represented as:

[0012]

[0013] Consider the LFM transmission segment where i=0, and let the sampling interval be T. s ,and If the integer is true, then the sampled signal at the transmitting end is:

[0014]

[0015] n = 0, 1, ..., N-1

[0016] The receiving end also uses T s Sample U′(t); the sampling time at the receiving end has an offset of Δt2, that is:

[0017]

[0018] Δt=Δt2-Δt1

[0019] n=-∞,...,-1,0,1,...,+∞

[0020] Consider the LFM receive segment with i=0.

[0021]

[0022] n = 0, 1, ..., N-1

[0023] c. If there is no time deviation, i.e., Δt = 0, then:

[0024]

[0025] n = 0, 1, ..., N-1

[0026] The amplitude and phase response functions of the system are then obtained by the direct comparison method, i.e.:

[0027]

[0028] d. If there is a time deviation, i.e. Δt≠0, there are two cases:

[0029] 3)|Δt|≥T s If the deviation is such that there is a sample-level deviation, the sample-level time delay can be directly obtained through correlation calculations; the remaining time delay then becomes case a or case 2).

[0030] 4) |Δt|<T sThen, the corresponding fractional sample level deviation is ignored, and the ambiguity of the boundary values ​​is disregarded, i.e., U′(t) in and Given that the values ​​in the vicinity are ambiguous, we can obtain:

[0031]

[0032] n = 0, 1, ..., N-1

[0033] The timing in case 2) is specifically as follows

[0034] The expressions for u0(n) and u′0(n) are as follows:

[0035]

[0036]

[0037] Dividing the two equations, we get:

[0038]

[0039] n = 0, 1, ..., N-1

[0040] remember then:

[0041]

[0042] i = 0, 1, ..., L-1

[0043] Using the maximum likelihood criterion, we can obtain:

[0044]

[0045]

[0046] Due to the ambiguity of the boundary values, let i start from 1, that is...

[0047]

[0048] Thus, the estimated value of the time deviation Δt is obtained;

[0049] The optimal sampling position signal is recovered, and then the amplitude and phase response functions of the system are obtained.

[0050] Furthermore, in case 2), the estimated value of the time deviation Δt is as follows:

[0051] Estimate the range of possible values ​​for Δt, that is:

[0052] -π≤angle(Y)≤π

[0053] then:

[0054]

[0055] 2LT s ≈T and 2LT s <T, then:

[0056]

[0057] Because the sampling rate is higher than the signal bandwidth, i.e., BT s <1, therefore:

[0058]

[0059] Thus, a sampling period T can be estimated. s Time deviation within.

[0060] Furthermore, the time-domain representation of the LFM signal is as follows:

[0061]

[0062] Its baseband signal is represented as:

[0063]

[0064] Where T is the pulse width of the LFM signal; and B is the bandwidth of the LFM signal. It is the slope of the frequency change.

[0065] Furthermore, methods for recovering the optimal sampling position signal include cubic spline interpolation or Lagrange interpolation.

[0066] Furthermore, the methods for obtaining the amplitude and phase response functions of the system are the direct comparison method or the correlation windowing method.

[0067] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0068] After using the timing estimation method of this method, not only can the amplitude response be accurately measured, but also the phase response can be accurately measured. The measurement curves of each phase response are very close or even overlap. Therefore, the idea of ​​averaging and noise reduction can be further used to improve the measurement accuracy of the phase response. Attached Figure Description

[0069] Figure 1 This is a schematic diagram of amplitude and phase response measurement based on LFM in the implementation of this scheme.

[0070] Figure 2 This is a schematic diagram of the amplitude and phase distortion measurement method in the implementation of this scheme.

[0071] Figure 3This is a schematic diagram of the amplitude and phase response measurement results under the condition of not performing fractional time delay measurement and calibration in the implementation of this scheme.

[0072] Figure 4 This is a schematic diagram of the amplitude and phase response measurement results after timing estimation using this method in the implementation of this scheme. Detailed Implementation

[0073] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described embodiments are merely some embodiments of the invention, and not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0074] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention. It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

[0075] Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0076] like Figure 1 As shown, a timing method for amplitude and phase response measurement based on LFM is proposed. Among them,

[0077] The time-domain representation of the LFM signal is as follows:

[0078]

[0079] Its baseband signal is represented as:

[0080]

[0081] Where T is the pulse width of the LFM signal; and B is the bandwidth of the LFM signal. It is the slope of the frequency change.

[0082] In the measurement system, the transmitting end continuously sends LFM signals, that is, the periodic extension of the baseband signal u(t):

[0083]

[0084] The receiver can use this periodicity to perform corresponding frequency offset estimation and compensation.

[0085] Typically, the received signal is a time delay of the transmitted signal. Let the time delay be Δt1, then the received signal can be expressed as:

[0086]

[0087] Consider the LFM transmission segment where i=0, and let the sampling interval be T. s ,and If the integer is true, then the sampled signal at the transmitting end is:

[0088]

[0089] n = 0, 1, ..., N-1

[0090] The receiving end also uses T s Sample U′(t). Due to the asynchronous sampling at the transmitting and receiving ends, the sampling time at the receiving end will have an offset of Δt2, i.e.:

[0091]

[0092] Δt=Δt2-Δt1

[0093] n=-∞,...,-1,0,1,...,+∞

[0094] Consider the LFM receive segment with i=0.

[0095]

[0096] n = 0, 1, ..., N-1

[0097] e. Obviously, if there is no time deviation, i.e., Δt = 0, then:

[0098]

[0099] n = 0, 1, ..., N-1

[0100] At this point, the amplitude and phase response functions of the system can be obtained through methods such as direct comparison or correlation windowing, such as the direct comparison method:

[0101]

[0102] f. If there is a time deviation, i.e. Δt≠0, there are two cases:

[0103] 5)|Δt|≥T s If there is a sample-level deviation, then the sample-level delay can be directly obtained through correlation calculations; the remaining delay then becomes case a or case 2).

[0104] 6)|Δt|<T s Then, the corresponding fractional sample level deviation is ignored, and the ambiguity of the boundary values ​​is disregarded, i.e., U′(t) in and Given that the values ​​in the vicinity are ambiguous, we can obtain:

[0105]

[0106] n = 0, 1, ..., N-1

[0107] The timing issue in scenario 2) will be discussed below.

[0108] The expressions for u0(n) and u′0(n) are as follows:

[0109]

[0110]

[0111] Dividing the two equations, we get:

[0112]

[0113] n = 0, 1, ..., N-1

[0114] remember then:

[0115]

[0116] i = 0, 1, ..., L-1

[0117] Using the maximum likelihood criterion, we can obtain:

[0118]

[0119]

[0120] Due to the ambiguity of the boundary values, i can start from 1, that is...

[0121]

[0122] Therefore, an estimate of the time deviation Δt can be obtained.

[0123] If the value of Δt is not estimated, according to the Fourier principle, the time deviation in the time domain corresponds to the continuously increasing phase difference in the frequency domain. At this time, although the amplitude response of the system can be correctly estimated, the phase response will be inaccurately estimated.

[0124] After obtaining the timing error, the optimal sampling position signal can be recovered using interpolation methods such as cubic splines and Lagrange multiplication. Then, the amplitude and phase response functions of the system can be obtained using methods such as direct comparison or correlation windowing. The specific process is shown in Figure 2.

[0125] Furthermore, the range of values ​​for Δt that can be obtained by this method can be determined. Obviously:

[0126] -π≤angle(Y)≤π

[0127] then:

[0128]

[0129] Generally, 2LT s ≈T and 2LT s <T, then:

[0130]

[0131] Typically, the sampling rate is higher than the signal bandwidth, i.e., BT. s <1, therefore:

[0132]

[0133] This method can estimate a sampling period T. s Time deviation within.

[0134] Simulation analysis:

[0135] The following simulation comparison illustrates the case with and without fractional-level bias estimation compensation. The simulation data is actual data collected from the hardware in a real-world environment.

[0136] in, Figure 3 These are the amplitude and phase response measurement results without fractional time delay measurement and calibration, using the correlation windowing method. It can be seen that the amplitude response results are consistent across the three measurements, but the phase responses are all different, and the differences are very large. This is due to the presence of Δt, which leads to errors in frequency domain phase estimation. (Comparison) Figure 4 After using the timing estimation method of this method, not only can the amplitude response be accurately measured, but the phase response curve is also very close or even coincident. Therefore, the idea of ​​averaging and noise reduction can be further used to improve the measurement accuracy of the phase response.

[0137] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A timing method for amplitude and phase response measurement based on LFM, characterized in that, The specific steps are as follows: The time-domain representation of the LFM signal is as follows: ； Its baseband signal is represented as: ； Where T is the pulse width of the LFM signal; and B is the bandwidth of the LFM signal. It is the slope of the frequency change; In the measurement system, the transmitting end continuously sends LFM signals, that is, it sends baseband signals. The periodic extension is as follows: ； The receiver uses its periodicity to perform corresponding frequency offset estimation and compensation; The received signal is a time delay of the transmitted signal; let the time delay be... The received signal is then represented as: ； consider The LFM transmission segment, with a sampling interval of . T s ,and If the integer is true, then the sampled signal at the transmitting end is: ； The receiving end also uses right Sampling is performed; the sampling time at the receiving end has a... The offset, that is: ； consider i LFM receive segment with =0, ； If there is no time deviation, that is ,but: ; The amplitude and phase response functions of the system are then obtained by the direct comparison method, i.e.: ； If there is a time discrepancy, that is There are two scenarios at this point: 1) Then there is a sample-level deviation, which can be directly calculated using correlation calculations; the remaining delay then becomes case a or case 2). 2) This corresponds to the fractional sample point level deviation. In this case, the ambiguity of the boundary values ​​is ignored. exist and Given that the values ​​in the vicinity are ambiguous, we can obtain: ； The timing in case 2) is as follows: and The expression is as follows: ； Dividing the two equations, we get: ； remember ,then: ； Using the maximum likelihood criterion, we can obtain: ； Due to the ambiguity of the boundary values, let i Starting from 1, that is Thus, the time deviation is obtained. The estimated value; The optimal sampling position signal is recovered, and then the amplitude and phase response functions of the system are obtained.

2. The amplitude and phase response measurement timing method based on LFM according to claim 1, characterized in that, In case 2), time deviation The estimated values ​​are as follows: Estimate what can be obtained. The range of values ​​for is: ； then: ； and ,but: ； Because the sampling rate is higher than the signal bandwidth, i.e. ,then: ； Thus, a sampling period can be estimated. Time deviation within.

3. The amplitude and phase response measurement timing method based on LFM according to claim 1, characterized in that, The methods for recovering the signal at the optimal sampling position are cubic spline interpolation or Lagrange interpolation.

4. The amplitude and phase response measurement timing method based on LFM according to claim 1, characterized in that, The methods for obtaining the amplitude and phase response functions of a system are the direct comparison method or the correlation windowing method.

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