A signal detection and time-frequency synchronization method based on symmetrical linear frequency modulation signal

Abstract

The present invention proposes a signal detection and time-frequency synchronization method based on a symmetrical linear frequency modulation signal, which includes the steps of sending a symmetrical linear frequency modulation signal at a transmitting end, calculating a correlation result at a receiving end, searching for a peak value, determining an amplitude threshold, determining a two-peak spacing threshold, estimating a carrier frequency deviation, estimating an arrival time, etc. The present invention can realize robust signal detection and accurate time and frequency synchronization when the receiving end has a large carrier frequency deviation, thereby improving the performance of the communication system. The present invention has low computational complexity, is simple to implement, is easy to implement in engineering, and can be applied to various mobile communication systems.

Description

Technical Field

[0001] The invention relates to a signal detection and time-frequency synchronization method based on symmetrical linear frequency modulation signals, and is particularly suitable for various mobile communication systems with large carrier frequency deviations at both transmitting and receiving ends. Background Art

[0002] Most of the data in modern communication systems are bursty, and there may be carrier frequency deviations at both ends of the transmitter and receiver due to clock deviation or relative motion. Therefore, it is necessary to first perform signal arrival detection and perform accurate time and frequency synchronization at the receiving end. The purpose of signal detection is to determine whether a signal has arrived, and then perform time and frequency synchronization after confirming that a signal has arrived. The purpose of time synchronization is to obtain the exact arrival time of the signal, and the purpose of frequency synchronization is to estimate the carrier frequency deviation of the received signal. Signal detection and time and frequency synchronization are the basis for subsequent processing at the receiving end, and their accuracy directly affects the performance of the communication system.

[0003] Signal detection and time synchronization usually require the help of a known pilot signal. Then, at the receiving end, the received pilot signal is correlated with the local pilot signal. Signal detection is achieved by judging whether the size of the correlation peak is higher than the threshold, and time synchronization is achieved by the position of the correlation peak. Since the correlation peak of a pseudo-random sequence signal (such as an m-sequence) is significantly reduced in a large frequency offset environment, the pilot signal usually selects a signal that is insensitive to frequency offset, such as a linear frequency modulation signal.

[0004] Figure 1 and Figure 2 The figure shows the correlation peaks of the m-sequence and the linear frequency modulation signal at the receiving end under different normalized carrier frequency offsets. The normalized carrier frequency offset is the product of the real frequency offset Δf and the symbol period T, which is also equivalent to the ratio of the real frequency offset Δf to the signal bandwidth.

[0005] The common simulation parameters of the m-sequence and the linear frequency modulation signal are: sampling rate 100kHz, bandwidth 25kHz, and signal points 2048. The frequency modulation slope of the linear frequency modulation signal is greater than 0. The actual arrival time of the signal is set to 0.

[0006] Depend on Figure 1 It can be seen that the correlation peak of the m-sequence will be significantly reduced or even completely disappear in a large frequency offset environment, which will make it impossible to perform signal detection and time synchronization. Figure 2 It can be seen that the linear frequency modulation signal can obtain a higher correlation peak even in a large frequency deviation environment, thereby successfully realizing signal detection; however, when the frequency deviation is large, the correlation peak of the linear frequency modulation signal will deviate from the actual arrival position of the signal, thereby causing a deviation in time synchronization.

[0007] To address this problem, multiple correlators can be used at the receiving end. The local signal input of each correlator is a copy of the pilot signal with a frequency offset applied. Then the correlator with the largest output peak is selected for signal detection and time synchronization, and the frequency offset value corresponding to the correlator can be used as the frequency offset estimate. In this way, signal detection and time-frequency synchronization can be achieved in a large frequency offset environment. The flowchart of this method is as follows: Figure 3 However, the synchronization accuracy of this method depends on the number of correlators, and the computational complexity is too high to obtain high accuracy.

[0008] In satellite communications, a dual Chirp signal is used, that is, a positive sweep linear frequency modulation signal and a negative sweep linear frequency modulation signal superimposed in the time domain, to achieve signal detection and time-frequency synchronization. The schematic diagram of the receiving end is shown in the figure below. Figure 4 As shown. However, under the condition of constant transmitter power, the transmission power of both the positive sweep signal and the negative sweep signal is lost by half, which makes this method have poor performance under low signal-to-noise ratio. In addition, this method requires two FFT operations, and there is still room for optimization of the calculation amount.

[0009] In addition, most existing methods only use amplitude threshold judgment for signal detection. If a pseudo peak higher than the threshold appears accidentally due to interference or noise, it will cause a false alarm and bring about an erroneous detection result. Summary of the invention

[0010] The technical problem to be solved by the present invention is to avoid the deficiencies in the above-mentioned background and provide a novel signal detection and synchronization method based on symmetrical linear frequency modulation signals, which can realize robust signal detection and precise time-frequency synchronization under large carrier frequency deviation conditions with lower computational complexity, thereby improving the performance of the communication system.

[0011] The technical solution adopted by the present invention is:

[0012] A signal detection and time-frequency synchronization method based on a symmetrical linear frequency modulation signal includes the following processes:

[0013] (1) The transmitting end sends a symmetrical linear frequency modulation signal, including a first linear frequency modulation signal and a second linear frequency modulation signal;

[0014] (2) The receiving end uses the first correlator and the second correlator to respectively calculate the cross-correlation between the first linear frequency modulation signal and the second linear frequency modulation signal and the received signal;

[0015] (3) Perform peak search on the cross-correlation output results of the first correlator and the second correlator, and record the amplitude of the peak value in the output of the first correlator as The peak position is recorded as The amplitude of the peak in the second correlator output is recorded as The peak position is recorded as

[0016] (4) Set the amplitude threshold A thr , determine whether and If yes, it is considered that a real signal has been detected and the process continues with step (5); otherwise, it is considered that no signal has arrived and the process returns to step (2);

[0017] (5) Setting the range of carrier frequency deviation Δf, and determining the distance between the two peaks based on the frequency modulation slope, duration and protection interval of the first linear frequency modulation signal and the second linear frequency modulation signal Whether the requirements are met, if yes, continue to step (6), otherwise, return to step (2);

[0018] (6) calculating a carrier frequency deviation Δf according to a frequency modulation slope, a duration, a guard interval, and a peak-to-peak distance of the first linear frequency modulation signal and the second linear frequency modulation signal;

[0019] (7) Calculate the actual arrival time τ of the signal based on the relationship between the carrier frequency deviation and the first signal correlation peak position and the actual arrival time of the signal.

[0020] Furthermore, the expression of the symmetrical linear frequency modulation signal in step (1) is as follows:

[0021]

[0022] Where x1(t) is the first linear frequency modulation signal, x2(t) is the second linear frequency modulation signal, T is the duration of the first linear frequency modulation signal and the second linear frequency modulation signal, and T g is the guard interval between the first linear frequency modulation signal and the second linear frequency modulation signal, T g ≥0;

[0023] The expression of the first linear frequency modulation signal x1(t) is as follows:

[0024]

[0025] in, is the starting frequency of the first linear frequency modulation signal, and K1 is the frequency modulation slope of the first linear frequency modulation signal;

[0026] The expression of the second linear frequency modulation signal x2(t) is as follows:

[0027]

[0028] in, is the starting frequency of the second linear frequency modulation signal, K2 is the frequency modulation slope of the second linear frequency modulation signal, and

[0029]

[0030] Furthermore, step (5) is specifically as follows:

[0031] According to the prior information, the range of the carrier frequency deviation Δf is set to [-Δf max ,Δf max ], where Δf max >0;

[0032] When K1>0, it is determined that if the distance between the two peaks exist If the two peaks are within the range, it is considered that both peaks are correlation peaks of the real signal, and step (6) is continued; otherwise, it is considered that at least one peak is caused by interference or noise, and the process returns to step (2);

[0033] When K1<0, determine if the distance between the two peaks exist If the two peaks are within the range, it is considered that both peaks are correlation peaks of the real signal, and step (6) is continued; otherwise, it is considered that at least one peak is caused by interference or noise, and the process returns to step (2).

[0034] Furthermore, the calculation method of the carrier frequency deviation Δf in step (6) is:

[0035]

[0036] Furthermore, the calculation method of the actual arrival time τ of the signal in step (7) is:

[0037]

[0038] The present invention constructs a symmetrical linear frequency modulation signal and cleverly utilizes its properties to perform signal detection and time-frequency synchronization in a large frequency deviation environment. It has the following advantages:

[0039] First, the present invention realizes reliable signal detection through two amplitude threshold judgments and one two-peak distance threshold judgment, thereby reducing the occurrence of false alarms.

[0040] Second, the present invention overcomes the problem of time synchronization error caused by linear frequency modulation signals in a large frequency deviation environment by deriving the analytical relationship between the carrier frequency deviation and the linear frequency modulation signal correlation peak offset and cleverly designing the transmission waveform, thereby achieving accurate estimation of the carrier frequency deviation and arrival time.

[0041] Third, the present invention only needs to use two correlators and does not need to perform FFT operations, so the calculation complexity is low, the processing delay is small, and it is easy to implement in engineering.

[0042] Fourth, the signal used in the present invention is symmetrical. In practical applications, it is only necessary to generate and store the first linear frequency modulation signal or the second linear frequency modulation signal, and then control the positive or reverse sequence reading to send a complete symmetrical linear frequency modulation signal. The storage complexity is low and system resources are saved. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a schematic diagram of correlation peaks at the receiving end of the m sequence under different normalized frequency offsets;

[0044] Figure 2 Schematic diagram of correlation peaks of linear frequency modulation signal receiving end under different normalized frequency offsets;

[0045] Figure 3 It is the flow chart of time-frequency synchronization by multiple correlation method;

[0046] Figure 4 It is a flow chart of time-frequency synchronization of dual Chirp signal receiving end;

[0047] Figure 5 It is a schematic diagram of the time domain waveform of a symmetrical linear frequency modulation signal;

[0048] Figure 6 It is a schematic diagram of the time-frequency domain of a symmetrical linear frequency modulation signal;

[0049] Figure 7 is a time-frequency domain schematic diagram of the first linear frequency modulation signal at both ends of the transmitter and receiver;

[0050] Figure 8 is a schematic diagram of the correlation peak time of the first linear frequency modulation signal;

[0051] Fig. 9 It is a processing flow chart of the receiving end of the method of the present invention;

[0052] Fig.10 This is a simulation diagram of the output results of the two correlators at the receiving end;

[0053] Fig.11 It is the simulation curve of frequency offset estimation error changing with signal-to-noise ratio;

[0054] Fig.12 is the simulation curve of arrival time estimation error changing with signal-to-noise ratio;

[0055] Fig.13 is the simulation curve of frequency offset estimation error changing with signal-to-noise ratio (after increasing the sampling rate);

[0056] Fig.14 is the simulation curve of arrival time estimation error changing with signal-to-noise ratio (after increasing the sampling rate);

[0057] Fig.15 This is a possible way of applying the present invention to an actual communication system. DETAILED DESCRIPTION

[0058] The method of the present invention is further described below in conjunction with specific implementation cases.

[0059] A signal detection and time-frequency synchronization method based on a symmetrical linear frequency modulation signal includes the following processes:

[0060] (1) The transmitter sends a symmetrical linear frequency modulation signal

[0061] The expression of the symmetrical linear frequency modulation signal is as follows:

[0062]

[0063] Wherein, x1(t) is called the first linear frequency modulation signal, and x2(t) is called the second linear frequency modulation signal. T is the duration of the first linear frequency modulation signal and the second linear frequency modulation signal. g is the guard interval between the first linear frequency modulation signal and the second linear frequency modulation signal, T g ≥ 0. The function of the guard interval is to prevent the multipath tailing of the first linear frequency modulation signal in a multipath channel from affecting the correlation detection of the second linear frequency modulation signal.

[0064] The expression of the first linear frequency modulation signal x1(t) is as follows:

[0065]

[0066] in, is the starting frequency of the first linear frequency modulation signal, and K1 is the frequency modulation slope of the first linear frequency modulation signal.

[0067] Since the instantaneous frequency of a signal (in Hz) is the derivative of the instantaneous phase with respect to time divided by 2π, the instantaneous frequency of the first linear frequency modulation signal can be expressed as

[0068]

[0069] It can be seen that it is a line segment on the time-frequency plane.

[0070] The expression of the second linear frequency modulation signal x2(t) is as follows:

[0071]

[0072] in, is the starting frequency of the second linear frequency modulation signal, K2 is the frequency modulation slope of the second linear frequency modulation signal, and

[0073]

[0074] According to the expression of the second linear frequency modulation signal, it can be known that the linear frequency modulation signal is about the straight line in the rectangular coordinate system with the first linear frequency modulation signal symmetry.

[0075] The time domain waveform diagram of the symmetrical linear frequency modulation signal s(t) is as follows Figure 5 As shown (assuming K1>0 and taking T g =T / 4, ).

[0076] The schematic diagram of the symmetrical linear frequency modulation signal in the time-frequency domain is as follows Figure 6 shown.

[0077] The sending end uses a frequency of f c The signal after up-converting s(t) by the carrier frequency can be expressed as Assume that due to the relative motion of the transmitter and receiver and the time variation of the channel, the carrier frequency in the received signal is f c becomes f c ′ , then the received passband signal can be expressed as

[0078]

[0079] Among them, τ is the time delay. If the sending time of the signal is considered to be 0, then τ is also the actual arrival time of the signal.

[0080] (2) Receiver-side cross-correlation calculation

[0081] The receiving end uses a frequency of f c,r The baseband signal r(t) obtained by down-converting y(t) with a carrier frequency can be expressed as

[0082]

[0083] where f c ′ -f c,r This is the carrier frequency deviation at the receiving end. The carrier frequency deviation is denoted as Δf, and the random phase 2πf c ′ τ is denoted by θ, then r(t) can be expressed as

[0084] r(t)=e j(2πΔft-θ) s(t-τ) (8)

[0085] Correlator 1 implements the following calculation process

[0086]

[0087] in, is the convolution operator, (·) * represents conjugation, and |·| represents modulus.

[0088] Correlator 2 implements the following calculation process

[0089]

[0090] (3) Peak search

[0091] The outputs of correlator 1 and correlator 2 are searched for amplitude peaks, and the peak amplitude in the output of correlator 1 is recorded as The peak position is recorded as The peak amplitude in the output of correlator 2 is recorded as The peak position is recorded as

[0092] (4) Amplitude threshold determination

[0093] Set the amplitude threshold A thr , judge if and It is considered that a real signal has been detected with a high probability, and step (5) is continued; otherwise, it is considered that no signal has arrived, and the detection process of steps (2) and (3) is continued.

[0094] (5) Two-peak distance threshold determination

[0095] The first linear frequency modulation signal in the received baseband signal can be written as

[0096]

[0097] where θ ′ =2πΔfτ-θ is a random phase. Its instantaneous frequency is

[0098]

[0099] Compared with formula (3), we can see that f 1,r (t) is the result of f1(t) being translated along the positive direction of the f-axis by Δf and then along the positive direction of the t-axis by τ on the time-frequency plane. 1,r (t) The schematic diagram in the time-frequency domain is shown in Figure 7 (assuming K1>0).

[0100] It can be seen that if x1(t) is used to 1,r (t) is correlated, the correlation peak will appear when the two line segments partially overlap, which is like Figure 8 shown.

[0101] Since the correlation between the first linear frequency modulation signal and the second linear frequency modulation signal is small, it can be considered that the peak position in the output of correlator 1 is

[0102]

[0103] Similarly, the peak position in the output of correlator 2 is

[0104]

[0105] Since K2=-K1, It can also be written as

[0106]

[0107] Therefore, the distance between the two peaks is Δt peak It can be expressed as

[0108]

[0109] According to the prior information, the range of Δf (in Hz) is set to [-Δf max ,Δf max ], where Δf max >0. Therefore, the range of the distance between the two peaks is (Here we assume that K1>0, the case where K1<0 is not described in detail).

[0110] Determine if the distance between the two peaks If the two peaks are within the above range, it is considered that both peaks are correlation peaks of the real signal, and step (6) is continued; otherwise, it is considered that at least one peak is caused by interference or noise, and the detection process of steps (2) to (4) is continued.

[0111] (6) Carrier frequency offset estimation

[0112] Using the relationship between the two peak distance and the carrier frequency deviation in equation (16), the estimated value of Δf can be obtained as

[0113]

[0114] (7) Arrival time estimation

[0115] Using the relationship between the correlation peak position of the first linear frequency modulation signal and the actual arrival time τ of the signal in equation (13), the estimated value of τ can be obtained as

[0116]

[0117] In summary, the receiving end processing flow chart of the method proposed by the present invention is shown in Fig. 9 middle.

[0118] The symmetrical linear frequency modulation signal parameters selected in this case are: K1=2.4414×10 6 , K2=-2.4414×106 , T = 2.048 × 10 -2 s, T g =5.12×10 -3 s. The amplitude detection threshold is set to A thr =1000, the maximum carrier frequency deviation is set to Δf max =2500Hz, the carrier frequency deviation range is set to [-2500, 2500], and the calculated range of the two peak distance is [0.023552, 0.027648].

[0119] First, the signal transmission delay is set to τ = 2 × 10 -3 s, the carrier frequency deviation at the receiving end is set to The corresponding normalized frequency deviation is 2e-2 (in order to facilitate the observation of the offset of the correlation peak relative to the arrival time of the signal, it is set larger here). The output of the two correlators at the receiving end is simulated in the absence of noise, and the sampling rate is set to 100kHz. The simulation results are shown in Fig.10 In order to observe the relationship between the correlation peak and the signal arrival time, the received signal is also drawn in the figure, and the amplitude of the correlator output is normalized.

[0120] From the figure, we can get According to the correlation peak amplitude before normalization, we can get

[0121] Since the correlation peak amplitude satisfies and Continue to the next steps.

[0122] The calculated interval between the two peaks is Since it is within the range [0.023552, 0.027648], continue to the subsequent steps.

[0123] From equations (17) and (18), we can get the estimation of carrier frequency offset: The estimated arrival time is It is basically consistent with the true value, and successfully achieves time and frequency synchronization under large carrier frequency deviation conditions.

[0124] The reason for the small error in the estimated value is the discretization error. Specifically, the correlation results of the discrete sampling signal are also discrete in the time domain, so it is impossible to accurately estimate the continuous carrier frequency offset and arrival time value through it. This problem also exists in other existing methods.

[0125] Next, the absolute value of the error of frequency offset estimation and arrival time estimation is simulated with the change curve of signal-to-noise ratio under Gaussian channel. At each signal-to-noise ratio, the simulation results of 10,000 times are averaged, and the frequency offset value of each simulation is randomly and uniformly sampled in the range of -1000 Hz to 1000 Hz. The signal transmission delay is set to τ = 2 × 10 -3 s. The simulation results are as follows Fig.11 , Fig.12 shown.

[0126] It can be seen that under the conditions of this implementation case, the method proposed in the present invention can achieve reliable time and frequency synchronization when the signal-to-noise ratio is higher than -18dB, and the frequency offset estimation error is about 6Hz, and the arrival time estimation error is about 1e-5s.

[0127] In order to illustrate that the error of this method under high signal-to-noise ratio comes from the discrete sampling of the signal, the sampling rate in the simulation is increased from 100kHz to 200kHz, and other simulation parameters remain unchanged. The simulation results are shown in Fig.13 , Fig.14 shown.

[0128] It can be seen that after doubling the sampling rate, the frequency offset estimation error under high signal-to-noise ratio is reduced from 6Hz to 3Hz, and the arrival time estimation error is reduced from 1e-5s to 5e-6s. And because the number of signal samples is doubled, a signal-to-noise ratio gain of about 3dB is obtained.

[0129] The above simulation results verify the effectiveness and robustness of the method proposed in the present invention.

[0130] Finally, a possible way of applying the present invention to a practical communication system is shown in Fig.15 middle.

[0131] like Fig.15 As shown, the present invention can be flexibly applied to various communication systems, and the transmitting end only needs to send a symmetrical linear frequency modulation signal, and the receiving end uses the method of the present invention to perform signal detection and time-frequency synchronization. The implementation process of the above specific system can be modified according to actual application needs.

Claims

1. A signal detection and time-frequency synchronization method based on a symmetrical linear frequency modulation signal, characterized in that: The process includes: (1) The transmitting end sends a symmetrical linear frequency modulation signal, including a first linear frequency modulation signal and a second linear frequency modulation signal; (2) The receiving end uses the first correlator and the second correlator to respectively calculate the cross-correlation between the first linear frequency modulation signal and the second linear frequency modulation signal and the received signal; (3) Perform peak search on the cross-correlation output results of the first correlator and the second correlator, and record the amplitude of the peak value in the output of the first correlator as The peak position is recorded as The amplitude of the peak in the second correlator output is recorded as The peak position is recorded as (4) Set the amplitude threshold A thr , determine whether and If yes, it is considered that a real signal has been detected and the process continues with step (5); otherwise, it is considered that no signal has arrived and the process returns to step (2); (5) Setting the range of carrier frequency deviation Δf, and determining the distance between the two peaks based on the frequency modulation slope, duration and protection interval of the first linear frequency modulation signal and the second linear frequency modulation signal Whether the requirements are met, if yes, continue to step (6), otherwise, return to step (2); (6) calculating a carrier frequency deviation Δf according to a frequency modulation slope, a duration, a guard interval, and a peak-to-peak distance of the first linear frequency modulation signal and the second linear frequency modulation signal; (7) calculating the actual arrival time τ of the signal based on the relationship between the carrier frequency deviation and the position of the correlation peak of the first signal and the actual arrival time of the signal; Wherein, step (5) is specifically as follows: According to the prior information, the range of the carrier frequency deviation Δf is set to [-Δf max ,Δf max ], where Δf max >0; When K1>0, it is determined that if the distance between the two peaks exist If the two peaks are within the range, it is considered that both peaks are correlation peaks of the real signal, and step (6) is continued; otherwise, it is considered that at least one peak is caused by interference or noise, and the process returns to step (2); wherein T is the duration of the first linear frequency modulation signal and the second linear frequency modulation signal, T g is the guard interval between the first linear frequency modulation signal and the second linear frequency modulation signal, T g ≥0, K1 is the frequency modulation slope of the first linear frequency modulation signal; When K1<0, determine if the distance between the two peaks exist If the two peaks are within the range, it is considered that both peaks are correlation peaks of the real signal, and step (6) is continued; otherwise, it is considered that at least one peak is caused by interference or noise, and the process returns to step (2); The calculation method of the carrier frequency deviation Δf in step (6) is: The calculation method of the actual arrival time τ of the signal in step (7) is:

2. The signal detection and time-frequency synchronization method based on symmetrical linear frequency modulation signal according to claim 1, characterized in that: The expression of the symmetrical linear frequency modulation signal in step (1) is as follows: Wherein, x1(t) is the first linear frequency modulation signal, and x2(t) is the second linear frequency modulation signal; The expression of the first linear frequency modulation signal x1(t) is as follows: in, is the starting frequency of the first linear frequency modulation signal; The expression of the second linear frequency modulation signal x2(t) is as follows: in, is the starting frequency of the second linear frequency modulation signal, K2 is the frequency modulation slope of the second linear frequency modulation signal, and

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