A sub-sampling high-precision wireless ranging and synchronization method based on ZC sequence

Abstract

This invention discloses a sub-sampling high-precision wireless ranging and synchronization method based on ZC sequences, belonging to the field of wireless communication and signal processing technology. It addresses the problems of traditional software-defined radio devices being limited by the physical sampling grid of the ADC, and the systematic bias in parabolic interpolation caused by the asymmetry of correlation peaks in traditional pseudo-random sequences. This method generates a ZC (Zadoff-Chu) preamble sequence with a 0dB peak-to-average power ratio at the transmitter and transmits it at full power; at the receiver, the discrete peak index and amplitude are obtained through matched filtering; relying on the constant amplitude and zero autocorrelation characteristics of the ZC sequence, distortion-free sample points in the symmetrical neighborhood of the main peak are accurately extracted; unbiased quadratic least squares (QLS) is used for continuous domain extremum fitting to analyze the sub-sampling time offset, and finally outputs a high-resolution absolute time of flight that breaks through the physical grid. This invention greatly eliminates interpolation fitting errors, significantly improves the ranging signal-to-noise ratio, and achieves sub-nanosecond-level high-precision synchronization and centimeter-level high-precision ranging on computationally limited platforms.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication, cooperative positioning, and signal processing technology for distributed systems. In particular, it relates to a method that utilizes the ideal correlation characteristics of the ZC (Zadoff-Chu) sequence and the first-path locking algorithm (FAP) to optimize the stability of subsampling fitting under strong multipath interference and limited hardware sampling grids, thereby achieving sub-nanosecond-level high-precision synchronization and centimeter-level high-precision ranging. Background Technology

[0002] In short-range (e.g., 100-meter range) distributed wireless networks, UAV swarms, and cooperative detection systems, nodes require extremely high-precision time synchronization. Traditional timing methods based on software-defined radio (SDR) typically rely on extracting the extreme points of the cross-correlation peaks of the received signals.

[0003] However, existing technologies have the following bottlenecks:

[0004] 1. ADC physical sampling grid limitation: The analog-to-digital converter (ADC) sampling rate of typical SDR devices is limited (e.g., 200 MSPS), which results in the timing accuracy being strictly limited to discrete physical grids (e.g., 5 ns), making it impossible to meet the sub-nanosecond level synchronization requirements.

[0005] 2. Systematic bias in subsampling fitting: To overcome sampling grid limitations, quadratic least squares (QLS) or parabolic interpolation algorithms are often used to estimate peak values ​​in the continuous domain. However, the QLS algorithm has extremely high requirements for the local symmetry of the correlation peak. Traditional communication signals (such as pseudo-random PN codes and OFDM) exhibit severe sidelobe fluctuations and asymmetric distortions in their correlation peaks under limited bandwidth. This can lead to a serious centroid shift in the vertex of the parabola fitted by QLS, introducing uncontrollable systematic timing errors.

[0006] 3. Limitations of Peak-to-Average Power Ratio (PAPR) on Signal-to-Noise Ratio: Long-distance or high-precision synchronization requires extremely high transmit power to ensure signal-to-noise ratio. However, traditional high PAPR signals are prone to nonlinear clipping of the RF power amplifier (PA) when transmitted at full power, further destroying the ideal shape of the relevant peaks.

[0007] 4. Envelope distortion caused by multipath effects: In real metal trusses (such as power transmission towers) or indoor industrial scenarios, multipath reflected waves and direct waves severely overlap in the time domain. Traditional methods only search for global maxima, which is highly susceptible to interference from reflection paths with stronger energy, causing the envelope of the relevant peaks to lose symmetry and rendering subsampling fitting completely ineffective. Summary of the Invention

[0008] To overcome the fitting bias caused by the asymmetry of signal correlation peaks in traditional methods under multipath interference, this invention proposes a sub-sampling high-precision method based on ZC sequences. The first-path-locking (FAP) algorithm is used to extract the direct path, and the constant-amplitude zero-autocorrelation (CAZAC) characteristic of the ZC sequence provides ideal symmetrical samples, completely eliminating fitting system errors and achieving sub-nanosecond clock synchronization and centimeter-level ranging far exceeding physical bandwidth limitations.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] Step S101: ZC timing preamble sequence generation and full-power transmission

[0011] The transmitting node generates a ZC constant envelope sequence in the digital baseband. Let the length of the ZC sequence be... The root index is ,and .when When taking odd numbers, the ZC sequence can be represented as:

[0012]

[0013] in, The length of the ZC sequence. For the root index, These are the discrete sampling point indices. Since this sequence satisfies the constant envelope condition:

[0014]

[0015] Its peak-to-average power ratio can be expressed as:

[0016]

[0017] The corresponding is:

[0018]

[0019] Taking advantage of the ZC sequence's peak-to-average power ratio of 0 dB, the RF front-end power amplifier is driven to its maximum linear output power and the signal is transmitted to obtain the limiting signal-to-noise ratio.

[0020] Step S102: Receiver-side matched filtering and first-path locking (FAP) coarse positioning

[0021] The receiving node performs correlation operations on the I / Q data stream using its local ZC root sequence. Let the discrete baseband signal obtained by the receiving end be... The local ZC reference sequence is The output of the matched filter is:

[0022]

[0023] in, For the first The relevant outputs at each candidate delay position This is the conjugate of the local ZC sequence. To avoid interference from multipath reflection peaks in the global maximum search, a first-path locking mechanism is introduced within the candidate search interval. The relevant amplitudes are scanned from left to right, and the first candidate peak exceeding the threshold is taken as the coarse localization result of the direct path:

[0024]

[0025] in, This is the detection threshold. This threshold can be adaptively set based on the noise floor in non-peak regions, for example:

[0026]

[0027] in, and These represent the mean and standard deviation of the correlation amplitude in the non-peak region, respectively. This is the threshold coefficient.

[0028] Step S103: Extract ideally symmetrical adjacent distortion-free samples

[0029] Let the index of the first diameter and main peak be... Then, extract the amplitude of the main peak and its left and right adjacent samples:

[0030]

[0031] Based on the constant amplitude and zero autocorrelation characteristic of the ZC sequence, it is ensured that the samples adjacent to the main peak in the direct envelope extracted by FAP satisfy the ideal symmetry condition. The neighborhood of the main peak in the ZC sequence has good local symmetry, which can approximately satisfy:

[0032]

[0033] By selecting samples from the neighborhood of the primary peak for subsequent fitting, the interference of subsequent multipath reflection components on the local morphology of related peaks can be reduced.

[0034] Step S104: Quadratic Least Squares (QLS) Continuous Domain Extremum Fitting

[0035] The three sample points in the neighborhood of the main peak are represented as follows:

[0036]

[0037] And a quadratic function is used for local fitting:

[0038]

[0039] Based on the three-point local quadratic fitting relationship, the subsampling peak offset It can be represented as:

[0040]

[0041] It can also be written equivalently as:

[0042]

[0043] in, Represents relative to the discrete main peak index The subsampling correction amount typically satisfies:

[0044]

[0045] This allows us to obtain the arrival time estimate for the continuous domain:

[0046]

[0047] in, This is the system sampling frequency.

[0048] Step S105: Output high-precision arrival time, bidirectional clock offset, and ranging results.

[0049] By combining the discrete peak index, subsampling offset, and system sampling period, the high-resolution arrival time is calculated:

[0050]

[0051] in, This refers to the discrete main peak index of the matched filter output. This is the subsampling correction amount obtained by the QLS algorithm. Let be the system sampling frequency. When using the first-path locking mechanism, we have:

[0052]

[0053] In a bidirectional time-passing architecture, let the time when node A sends its request be denoted as . The request received by node B is at the time of The response sent by node B is at the following time. The response received by node A is at time . .in, and High-precision correction is obtained through ZC matched filtering and QLS subsampling fitting. The inter-node unidirectional propagation delay is estimated as follows:

[0054]

[0055] The clock skew between nodes is estimated as follows:

[0056]

[0057] If node A is used as the time base, then node B can be synchronized based on the aforementioned clock skew estimate:

[0058]

[0059] Furthermore, the distance between nodes is estimated as follows:

[0060]

[0061] in, This represents the speed of electromagnetic wave propagation.

[0062] Compared with the prior art, the beneficial effects of the present invention are:

[0063] 1. Greatly eliminates fitting errors caused by multipath: By combining the FAP algorithm with the symmetry characteristics of the ZC sequence, the system can extract pure direct path samples from complex reflection environments for fitting, avoiding the centroid shift of the parabola and bringing the accuracy close to the theoretical Cramer-Rao lower bound (CRLB).

[0064] 2. Make full use of radio frequency energy: By utilizing the extremely low peak-to-average power ratio of 0dB of the ZC sequence, there is no need to reserve power amplifier backoff margin. Under the same SDR hardware, the transmission energy can be several dB higher than that of OFDM signal, which greatly improves the ranging sensitivity of the receiver.

[0065] 3. Extremely low algorithm complexity and easy engineering deployment: It is not only suitable for clock synchronization, but can also be directly applied to high-precision distributed ranging, UAV collaborative positioning and structural micro-change monitoring, and is easy to deploy in real time on embedded platforms such as FPGA. Attached Figure Description

[0066] Figure 1 A flowchart of a subsampling time measurement method based on the ideal correlation characteristics of ZC sequences is provided for an embodiment of the present invention.

[0067] Figure 2 This is a comparison diagram of the anti-asymmetric distortion principle of traditional PN sequences and ZC sequences in QLS subsampling fitting in this invention. Detailed Implementation

[0068] Taking a 100-meter-level distributed drone collaborative platform as an example, SDR bandwidth ADC sampling rate (discrete grid) ).

[0069] 1. Generation of ZC timing leader sequence

[0070] Node A first generates a ZC timing preamble sequence in the digital baseband. Let the length of the ZC sequence be... The root index is And satisfy:

[0071]

[0072] when When taking odd numbers, the ZC sequence can be represented as:

[0073]

[0074] in, For the first Complex values ​​of the ZC sequence at discrete sampling points, For sequence length, This is the root index. As an optional implementation, in this embodiment, we take:

[0075]

[0076] because and The ZC sequences are coprime, therefore they exhibit good constant-amplitude zero autocorrelation characteristics. In the time domain, the sequence satisfies:

[0077]

[0078] Therefore, its peak-to-average ratio is:

[0079]

[0080] This corresponds to 0 dB. Utilizing this constant envelope characteristic, the transmitter can drive the RF front-end to near its maximum linear output power without causing significant power amplifier clipping distortion, thereby improving the signal-to-noise ratio at the receiver.

[0081] 2. ZC Preamble Signal Transmission and Reception

[0082] Node A transmits the generated ZC sequence via antenna after digital-to-analog conversion, up-conversion, and RF amplification. Node B receives the wireless signal and processes it through RF down-conversion, analog-to-digital conversion, and digital baseband processing to obtain a discrete complex baseband received signal. .

[0083] In a real wireless environment, the received signal can be represented as:

[0084]

[0085] in, Indicates the number of propagation paths. Indicates the first Complex channel coefficients of each path, Indicates the first The discrete delay corresponding to each path, This represents received noise. Typically, the direct path corresponds to the earliest arriving path, while subsequent reflection paths may have higher amplitudes. Therefore, if only a global maximum peak search is used, it is easy to misjudge stronger reflection paths as timing peaks.

[0086] 3. Receiver-side matched filtering and first-path locking

[0087] Node B uses the locally stored ZC root sequence to perform matched filtering on the received signal. The output of the matched filter is:

[0088]

[0089] in, For the first The relevant outputs at each candidate delay position It is the conjugate of the local ZC sequence.

[0090] To reduce the impact of multipath reflection peaks on timing results, this embodiment does not directly search for the global maximum correlation peak, but instead searches within the candidate search interval. The first-path locking mechanism is employed internally. Specifically, in the relevant amplitude sequence... The process scans from left to right, and the first candidate peak exceeding the detection threshold is designated as the first diameter peak. The first diameter peak index is defined as follows:

[0091]

[0092] in, This is the detection threshold. As an optional method, The settings can be adaptively adjusted based on the noise floor in non-peak regions:

[0093]

[0094] in, and Let represent the mean and standard deviation of the correlation amplitude in the non-peak region, respectively. This is the threshold coefficient. In practical applications, It can be set according to the requirements of received signal-to-noise ratio, false alarm probability, and missed detection probability.

[0095] 4. Extraction of samples from the neighborhood of the main peak

[0096] In obtaining the first apex index Then, extract the amplitudes of its left and right adjacent samples:

[0097]

[0098] Because ZC sequences possess constant amplitude and zero autocorrelation, the neighborhood of the main lobe of their correlation peak exhibits good local symmetry. After the direct path is extracted by the first-path locking mechanism, the samples adjacent to the main peak can approximately satisfy:

[0099]

[0100] Therefore, adopt , , By performing local quadratic fitting on three samples, the interpolation bias caused by the asymmetry of correlation peaks in traditional pseudo-random sequences can be reduced.

[0101] 5. QLS Subsampling Continuous Domain Fitting

[0102] The three sample points in the neighborhood of the main peak are represented as follows:

[0103]

[0104] Local fitting is performed using a quadratic function:

[0105]

[0106] Based on the three-point quadratic fitting relationship, the subsampling peak offset It can be represented as:

[0107]

[0108] in, Represents the index relative to the discrete first path peak. The subsampling correction amount typically satisfies:

[0109]

[0110] This allows us to obtain the arrival time estimate for the continuous domain:

[0111]

[0112] Compared to directly using discrete peak index The above processing method can further estimate the true peak position within the sampling period, thereby breaking through the limitation of the ADC physical sampling grid.

[0113] 6. Two-way time transfer and clock skew estimation

[0114] To further achieve time synchronization between nodes, node A and node B employ a bidirectional time transfer mechanism. Let the time when node A sends the request signal be denoted as _____. The time when node B receives the request signal is The time when node B sends the response signal is The time when node A receives the response signal is .

[0115] in, and Both can be corrected with high precision using ZC matched filtering and QLS subsampling fitting. Specifically, after node B receives the request signal from node A, it obtains the arrival time of the requested direction using the above method; after node A receives the response signal from node B, it also obtains the arrival time of the response direction using the above method.

[0116] Under the condition that the propagation link is approximately symmetrical, the one-way propagation delay between node A and node B is estimated as follows:

[0117]

[0118] The clock skew of node B relative to node A is estimated as follows:

[0119]

[0120] If the time of node A is used as the reference, then node B can perform synchronization correction based on the estimated clock deviation:

[0121]

[0122] in, For the local clock reading of node B, This is the corrected time for node B. In this way, node B's local time can be aligned to node A's time base.

[0123] 7. Distance Estimation

[0124] In obtaining the one-way propagation delay estimate Then, the distance between node A and node B can be expressed as:

[0125]

[0126] in, Let be the speed of electromagnetic wave propagation. In an airborne environment, it can be approximated as:

[0127]

[0128] For example, when the bidirectional time transfer solution yields a unidirectional propagation delay of:

[0129]

[0130] The distance between nodes is then estimated as follows:

[0131]

[0132] Therefore, this embodiment can output both the distance estimation result between nodes and the clock deviation estimation result between nodes, thereby simultaneously achieving wireless ranging and time synchronization.

[0133] 8. Implementation Results Description

[0134] After adopting the above implementation method, the system no longer relies solely on the discrete sampling grid of the ADC for arrival time determination. Instead, it utilizes the local symmetry of the ZC sequence correlation peaks and the QLS subsampling fitting method to perform continuous domain correction on the position of the correlation main peak. For In a software-defined radio system, the original sampling grid is 5 ns, but by using QLS subsampling fitting, a time offset estimate of less than one sampling period can be obtained, thereby improving the timing resolution.

[0135] Meanwhile, since this embodiment employs a first-path locking mechanism rather than a global maximum peak search mechanism, the system can still prioritize locking the earliest arriving direct path peak value even in the presence of subsequent strong reflection paths, thus reducing the impact of multipath reflections on the timing results. Furthermore, the 0 dB peak-to-average power ratio (PAPR) characteristic of the ZC sequence allows the transmitter to more fully utilize the linear output capability of the RF power amplifier, improving the peak signal-to-noise ratio of the matched filter at the receiver, thereby enhancing the stability of ranging and synchronization results.

[0136] In summary, this embodiment enables high-precision arrival time estimation, inter-node propagation delay estimation, clock skew estimation, and wireless distance estimation on a software radio platform with limited sampling rates through joint processing of ZC sequence, first-path locking, QLS subsampling fitting, and bidirectional time transfer.

Claims

1. A sub-sampling high-precision wireless ranging and synchronization method based on ZC sequences, characterized in that, Includes the following steps: Step S101: ZC timing preamble sequence generation and full-power transmission The transmitting node generates a ZC constant envelope sequence in the digital baseband. Let the length of the ZC sequence be... The root index is ,and .when When taking odd numbers, the ZC sequence can be represented as: in, The length of the ZC sequence. For the root index, These are the discrete sampling point indices. Since this sequence satisfies the constant envelope condition: Its peak-to-average power ratio can be expressed as: The corresponding is: Taking advantage of the ZC sequence's peak-to-average power ratio of 0 dB, the RF front-end power amplifier is driven to its maximum linear output power and the signal is transmitted to obtain the limiting signal-to-noise ratio. Step S102: Receiver-side matched filtering and first-path locking (FAP) coarse positioning The receiving node performs correlation operations on the I / Q data stream using its local ZC root sequence. Let the discrete baseband signal obtained by the receiving end be... The local ZC reference sequence is The output of the matched filter is: in, For the first The relevant outputs at each candidate delay position This is the conjugate of the local ZC sequence. To avoid interference from multipath reflection peaks in the global maximum search, a first-path locking mechanism is introduced within the candidate search interval. The relevant amplitudes are scanned from left to right, and the first candidate peak exceeding the threshold is taken as the coarse localization result of the direct path: in, This is the detection threshold. This threshold can be adaptively set based on the noise floor in non-peak regions, for example: in, and These represent the mean and standard deviation of the correlation amplitude in the non-peak region, respectively. This is the threshold coefficient. Step S103: Extract ideally symmetrical adjacent distortion-free samples Let the index of the first diameter and main peak be... Then, extract the amplitude of the main peak and its left and right adjacent samples: Based on the constant amplitude and zero autocorrelation characteristic of the ZC sequence, it is ensured that the samples adjacent to the main peak in the direct envelope extracted by FAP satisfy the ideal symmetry condition. The neighborhood of the main peak in the ZC sequence has good local symmetry, which can approximately satisfy: By selecting samples from the neighborhood of the primary peak for subsequent fitting, the interference of subsequent multipath reflection components on the local morphology of related peaks can be reduced. Step S104: Quadratic Least Squares (QLS) Continuous Domain Extremum Fitting The three sample points in the neighborhood of the main peak are represented as follows: And a quadratic function is used for local fitting: Based on the three-point local quadratic fitting relationship, the subsampling peak offset It can be represented as: It can also be written equivalently as: in, Represents relative to the discrete main peak index The subsampling correction amount typically satisfies: This allows us to obtain the arrival time estimate for the continuous domain: in, This is the system sampling frequency. Step S105: Output high-precision arrival time, bidirectional clock offset, and ranging results. By combining the discrete peak index, subsampling offset, and system sampling period, the high-resolution arrival time is calculated: in, This refers to the discrete main peak index of the matched filter output. This is the subsampling correction amount obtained by the QLS algorithm. Let be the system sampling frequency. When using the first-path locking mechanism, we have: In a bidirectional time-passing architecture, let the time when node A sends its request be denoted as . The request received by node B is at the time of The response sent by node B is at the following time. The response received by node A is at time . .in, and High-precision correction is obtained through ZC matched filtering and QLS subsampling fitting. The inter-node unidirectional propagation delay is estimated as follows: The clock skew between nodes is estimated as follows: If node A is used as the time base, then node B can be synchronized based on the aforementioned clock skew estimate: Furthermore, the distance between nodes is estimated as follows: in, This represents the speed of electromagnetic wave propagation.

2. The method according to claim 1, characterized in that, The length of the ZC constant envelope timing leader sequence in step S101 is The root index is And satisfy ;when When the number is odd, the ZC constant envelope timing leader sequence is represented as: in, The length of the ZC sequence. For the root index, This represents the sequence number of the discrete sampling point.

3. The method according to claim 1, characterized in that, The ZC constant envelope timing leader sequence satisfies: Its peak-to-average power ratio satisfies: The corresponding peak-to-average ratio is: This allows for increased transmit power within the linear operating range of the RF front-end, thereby enhancing the correlation detection signal-to-noise ratio at the receiver.

4. The method according to claim 1, characterized in that, The output of the matched filter in step S102 is: in, For the discrete baseband signal at the receiving end, The conjugate of the local ZC reference sequence, For the first The relevant outputs at each candidate delay position.

5. The method according to claim 1, characterized in that, The first-path locking mechanism includes: within the candidate search interval The relevant amplitude is scanned from left to right, and the first one exceeding the detection threshold is identified. The candidate peaks are used as coarse localization indexes for the direct path, denoted as: in, Candidate search interval A set of local candidate peaks within the region.

6. The method according to claim 5, characterized in that, The detection threshold Based on the adaptive setting of noise floor in non-peak regions, the following conditions are met: in, and These represent the mean and standard deviation of the correlation amplitude in the non-peak region, respectively. This is the threshold coefficient.

7. The method according to claim 1, characterized in that, The amplitudes of the main peak and its left and right adjacent samples extracted in step S103 are as follows: Furthermore, the local symmetry of the neighborhood of the main peak in the ZC sequence correlation is utilized to reduce the influence of multipath reflection on the fitting results.

8. The method according to claim 1, characterized in that, In step S104, the sub-sampling peak offset Calculated by the following formula: The continuous domain arrival time estimate is obtained from the following formula: in, The system sampling frequency, Represents relative to the discrete main peak index Subsampling correction amount.

9. The method according to claim 1, characterized in that, In a bidirectional time-transfer architecture, let the time when node A requests to send the request be denoted as . Node B requests to receive the message at the specified time. Node B's response was sent at the following time. Node A's response reception time is Then the estimated one-way propagation delay between nodes is: The clock skew between nodes is estimated as follows: in, and High-precision correction is obtained by ZC matched filtering and quadratic least squares subsampling fitting.

10. The method according to claim 9, characterized in that, When node A is used as the time base, node B performs synchronization correction according to the following formula: The distance between nodes is estimated based on the following formula: in, The local time before correction at node B. The corrected synchronization time for node B. This represents the speed of electromagnetic wave propagation.

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