Primary synchronization signal rapid detection algorithm based on Fourier transform and convolution theorem

Abstract

The invention discloses a primary synchronization signal rapid detection algorithm based on Fourier transform and a convolution theorem. The algorithm comprises the following steps: S1, transmitting a primary synchronization signal; s2, establishing an NR system channel model; s3, PSS algorithm analysis and improvement; and S4, obtaining an algorithm simulation result. The 5 / 6G NR system main synchronization signal rapid detection algorithm based on Fourier transform and the convolution theorem has remarkable beneficial effects in the aspects of reducing the algorithm complexity, reducing the detection time delay, improving the frequency offset resistance, accelerating the establishment of a downlink synchronization communication link and the like, and is of great significance in improving the base station performance and the user experience.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a fast detection algorithm for a main synchronization signal based on Fourier transform and convolution theorem. Background Art

[0002] In the field of wireless communication technology, especially in 5G and future 6G NR systems, when a user equipment (UE) accesses the wireless network, it first needs to achieve downlink time and frequency synchronization. This synchronization process is completed by blindly detecting the primary synchronization signal (PSS), which is the first physical signal received by the UE. The success or failure of PSS detection is directly related to the establishment of a downlink synchronous communication link and is a key step for users to access the network.

[0003] Currently, NR systems generally adopt a downlink transmission scheme based on CP-OFDM technology. However, this scheme is very sensitive to carrier frequency deviation and timing error. Factors such as Doppler frequency shift, local oscillator frequency deviation at the transmitting and receiving ends, and multipath effects may destroy the orthogonality between subcarriers, thereby affecting the overall performance of the system. At the same time, the high sampling rate characteristics of the NR system put forward more stringent requirements on the carrier frequency deviation and timing error. The UE needs to quickly achieve downlink time and frequency synchronization with the base station in a short time, which places high demands on the reliability and efficiency of the PSS detection algorithm.

[0004] Although the existing PSS detection algorithms can achieve downlink time-frequency synchronization to a certain extent, they still have deficiencies in algorithm complexity and frequency deviation resistance. High-complexity algorithms will increase detection delays and affect user experience; while insufficient frequency deviation resistance may lead to detection failures in large frequency deviation environments, affecting network stability and reliability. With the rapid development of mobile communication technology, network latency and reliability have become increasingly important considerations. Especially in the new era, research on high-reliability, low-complexity and low-latency primary synchronization signal fast detection algorithms is of great significance. Such algorithms can improve detection speed and reduce latency while ensuring detection accuracy, thereby improving the overall performance of base stations and user experience. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention proposes a fast detection algorithm for a primary synchronization signal based on Fourier transform and convolution theorem, which is mainly used in 5G / 6G NR systems. The fast detection algorithm for a primary synchronization signal (PSS) based on Fourier transform and convolution theorem aims to improve the efficiency and accuracy of downlink time and frequency synchronization between a user equipment (UE) and a base station when accessing a network, especially in the presence of a carrier frequency offset. In the PSS coarse synchronization detection stage, the algorithm reduces the synchronization point range to the overlapping area when the received PSS frequency domain sequence and the local PSS frequency domain sequence are subjected to a translation operation of a convolution operation through a sliding Fourier transform, which greatly reduces the complexity of the algorithm and reduces the detection delay. In the PSS fine synchronization stage, the algorithm extracts fine synchronization points based on Fourier transform based on the coarse synchronization point and three local PSS sequences, and compensates for the frequency offset with the help of the negative exponential order formula carried by the Fourier transform formula, thereby improving the algorithm's ability to resist frequency offset.

[0006] The technical solution adopted by the present invention is: a fast detection algorithm for the main synchronization signal based on Fourier transform and convolution theorem, the algorithm comprising the following steps:

[0007] S1. Transmit primary synchronization signal: The NR system introduces the principles of beamforming and beam scanning to transmit an SSB synchronization block consisting of a primary synchronization signal (PSS), a secondary synchronization signal (SSS) and a physical broadcast channel (PBCH) to cover all users in the cell.

[0008] S2. Build the NR system channel model: The NR system adopts a downlink transmission solution based on CP-OFDM technology. After the primary synchronization signal (PSS) sent by the base station is transmitted through the channel, in addition to being affected by Gaussian white noise, it will also produce frequency deviation due to Doppler frequency shift, local oscillator frequency deviation at the transceiver end, etc. The PSS sequence received by the UE can be expressed as a function of the frequency deviation and additive Gaussian white noise.

[0009] S3. Analysis and improvement of PSS algorithm: It includes three stages: PSS coarse synchronization point extraction, PSS fine synchronization point extraction and PSS final synchronization point extraction; in the coarse synchronization stage, the algorithm uses the properties of Fourier transform and convolution theorem to perform Fourier transform on the received PSS sequence and the local PSS sequence at the receiving end to determine the synchronization point position area and select the peak position as the coarse synchronization point; in the fine synchronization stage, the algorithm is based on the coarse synchronization point, through the fast Fourier transform synchronization algorithm of the new received signal and the local PSS sequence, to compensate for the frequency deviation and select the peak maximum value position as the fine synchronization point; finally, the coarse synchronization point and the fine synchronization point are calculated to obtain the final synchronization point of the PSS signal.

[0010] S4. The algorithm simulation results are as follows: Under the conditions of specific subcarrier spacing and number of transmission bandwidth physical resource blocks, the overall algorithm calculation amount is reduced by reducing the amount of multiplication operations and appropriately increasing the amount of addition operations, so that the algorithm can complete the main synchronization signal detection faster under the same channel conditions, reducing the algorithm detection delay.

[0011] In S1, SSB occupies 240 subcarriers in the frequency domain and 4 OFDM symbols in the time domain. Its period is variable and can be flexibly configured according to scenario requirements.

[0012] In S1, the start position, symbol length and physical layer cell identifier (PCI) of the OFDM symbol are obtained by decoding the PSS, so as to achieve downlink frequency synchronization and symbol-level time synchronization between the UE and the base station.

[0013] The PSS is a pseudo-random sequence of length 127 using a frequency domain BPSK M sequence, mapped on the 127 subcarriers in the middle of the SSB block. The function is shown in formula (1):

[0014]

[0015] The x(n) in the formula is defined by formula (2):

[0016]

[0017] The PSS sequence can take three different values, which are the physical layer identifier of the group with the physical layer cell identifier PCI. Corresponding.

[0018] Assuming s(n) is the PSS sequence sent by the base station, the PSS sequence r(n) received by the UE can be expressed as:

[0019]

[0020] In the formula, is the frequency deviation at position n (ε is the normalized frequency deviation, defined as Δf / f sc , Δf is the frequency deviation, f sc is the subcarrier spacing), is the additive white Gaussian noise introduced into the channel.

[0021] Based on the negative exponential order formula carried by the Fourier transform formula, the positive exponential order frequency deviation formula carried by the channel transmission is compensated and rewritten into the following expression:

[0022]

[0023] The essence of formula (6) is the time domain product signal Fourier transform; According to the frequency domain property of the convolution theorem, "time domain product is expressed as 1 / 2π times frequency domain convolution in the frequency domain", F k (n,m) is converted into formula (5):

[0024]

[0025] FFT[r(n+i)] and The upper and lower limits of the convolution are r(n+i) and The boundary of the overlapping part when performing the translation operation of the convolution operation in the frequency domain is lowered by the maximum of the left boundaries of the two frequency domain signals, and the upper limit is the minimum of the right boundaries of the two frequency domain signals.

[0026] The corresponding rough synchronization point extraction algorithm is shown in formula (6):

[0027]

[0028] Where, the upper and lower limits of F(n,m) are the received PSS frequency domain sequence FFT[r(n+i)] and the local PSS frequency domain sequence corresponding to the cell that the UE last accessed The boundary of the overlapping part when performing the translation operation of the convolution operation; determine the peak value of F(n,m), and determine the position of the peak value as the rough synchronization point of the PSS signal, as shown in formula (7):

[0029] (V' max ,L' max )=argmax(|F(n,m)|) (7)

[0030] Take the points from Off before the rough synchronization point of the received signal r(n) to Off+N after the rough synchronization point to form a new received signal r'(n):

[0031]

[0032] (n=L' max -Off,L' max -Off+1,...,L' max +Off+N) (8)

[0033] Where Off is the synchronization position offset value taken according to the frequency offset caused by the terminal's moving speed, and N is the number of local PSS sequence sampling points;

[0034] The new received signal r'(n) is used to perform a synchronization algorithm based on fast Fourier transform with the three local PSS sequences. The positive exponential frequency deviation of the received PSS signal is compensated by the negative exponential formula carried by the Fourier transform formula. The expression is shown in formula (9):

[0035]

[0036] Determine the peak value of the three-time Fourier transform operation, and the location of the maximum peak value is the PSS fine synchronization point, as shown in formula (10):

[0037] (V” max ,L” max )=argmax(max(|F' k (n',m)|)),(k=0,1,2) (10)

[0038] Where F' k (n,m) is the Fourier transform value of the new received signal r'(n) at position n' multiplied by the conjugate of the kth local PSS sequence; V" max is the maximum value of the 3rd Fourier transform peak, L” max For V max The corresponding position index is the precise synchronization point of the PSS signal.

[0039] The expression of the PSS final synchronization point extraction algorithm is:

[0040] L final =L' max +L” max -Off-1 (11)

[0041] Where, L final It is the final synchronization point of the PSS signal.

[0042] The beneficial effects of the present invention are as follows: the 5 / 6G NR system master synchronization signal fast detection algorithm based on Fourier transform and convolution theorem proposed in the present invention shows significant beneficial effects in reducing algorithm complexity, reducing detection delay, improving anti-frequency deviation performance and accelerating the establishment of downlink synchronous communication links, which is of great significance for improving base station performance and user experience, and is specifically reflected in the following aspects:

[0043] (1) Significantly reduce algorithm complexity: The present invention uses Fourier transform and convolution theorem to extract the rough synchronization point of the PSS signal, and only needs to perform sliding Fourier transform on the received PSS signal and the local PSS sequence corresponding to the last access cell. This step effectively narrows the search range of the synchronization point to the overlapping area when the received PSS frequency domain sequence and the local PSS frequency domain sequence are convolved, thereby greatly reducing the complexity of the algorithm.

[0044] (2) Reducing algorithm detection delay: Due to the reduction of algorithm complexity and the method of optimizing the synchronization point search range through the convolution theorem, the present invention significantly reduces the processing time required for extracting synchronization points, thereby reducing the algorithm detection delay and accelerating the process of establishing the downlink synchronous communication link.

[0045] (3) Improving the algorithm's ability to resist frequency deviation: In the stage of fine synchronization point extraction, the present invention uses a Fourier transform-based method to compensate for the negative exponential sub-frequency deviation carried by the Fourier transform formula, thereby effectively improving the algorithm's ability to resist frequency deviation, allowing the algorithm to maintain good detection effects even in a large frequency deviation environment.

[0046] (4) Accelerating the establishment of a downlink synchronous communication link: The present invention can complete the detection of the main synchronization signal more quickly under the same channel conditions, thereby accelerating the downlink time and frequency synchronization process between the user terminal and the base station, and improving the overall performance of the base station and the user experience. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is the SSB block structure diagram of the present invention

[0048] Figure 2 Schematic diagram of the position of SSB in the half frame (Case B) in the present invention

[0049] Figure 3 This is the overall flow chart of the improved algorithm in the present invention

[0050] Figure 4 This is the PSS rough synchronization point extraction flow chart of the present invention

[0051] Figure 5 This is the PSS precise synchronization point extraction flow chart in the present invention

[0052] Figure 6 This is the PSS final synchronization point extraction flow chart in the present invention DETAILED DESCRIPTION

[0053] The specific implementation of the present invention is described in detail below with reference to the accompanying drawings:

[0054] like Figure 1-6 As shown, a fast detection algorithm for the main synchronization signal based on Fourier transform and convolution theorem, the algorithm comprises the following steps:

[0055] S1. Transmit primary synchronization signal: The NR system introduces the principles of beamforming and beam scanning to transmit an SSB synchronization block consisting of a primary synchronization signal (PSS), a secondary synchronization signal (SSS) and a physical broadcast channel (PBCH) to cover all users in the cell.

[0056] S2. Build the NR system channel model: The NR system adopts a downlink transmission solution based on CP-OFDM technology. After the primary synchronization signal (PSS) sent by the base station is transmitted through the channel, in addition to being affected by Gaussian white noise, it will also produce frequency deviation due to Doppler frequency shift, local oscillator frequency deviation at the transceiver end, etc. The PSS sequence received by the UE can be expressed as a function of the frequency deviation and additive Gaussian white noise.

[0057] S3. Analysis and improvement of PSS algorithm: It includes three stages: PSS coarse synchronization point extraction, PSS fine synchronization point extraction and PSS final synchronization point extraction; in the coarse synchronization stage, the algorithm uses the properties of Fourier transform and convolution theorem to perform Fourier transform on the received PSS sequence and the local PSS sequence at the receiving end to determine the synchronization point position area and select the peak position as the coarse synchronization point; in the fine synchronization stage, the algorithm is based on the coarse synchronization point, through the fast Fourier transform synchronization algorithm of the new received signal and the local PSS sequence, to compensate for the frequency deviation and select the peak maximum value position as the fine synchronization point; finally, the coarse synchronization point and the fine synchronization point are calculated to obtain the final synchronization point of the PSS signal.

[0058] S4. The algorithm simulation results are as follows: Under the conditions of specific subcarrier spacing and number of transmission bandwidth physical resource blocks, the overall algorithm calculation amount is reduced by reducing the amount of multiplication operations and appropriately increasing the amount of addition operations, so that the algorithm can complete the main synchronization signal detection faster under the same channel conditions, reducing the algorithm detection delay.

[0059] The following is a detailed description of the improvement of base station performance and user experience using a 5 / 6G NR system master synchronization signal fast detection algorithm based on Fourier transform and convolution theorem as a specific embodiment.

[0060] In this embodiment, the NR system introduces the principles of beamforming and beam scanning to transmit SSB synchronization blocks consisting of a primary synchronization signal (PSS), a secondary synchronization signal (SSS) and a physical broadcast channel (PBCH) to cover all users in the cell. SSB occupies 240 subcarriers in the frequency domain and 4 OFDM symbols in the time domain. Its period is variable and can be flexibly configured according to scenario requirements. By decoding the PSS, the start position, symbol length and physical layer cell identifier (PCI) of the OFDM symbol can be obtained to achieve downlink frequency synchronization and symbol-level time synchronization between the UE and the base station.

[0061] The NR system introduces the principles of beamforming and beam scanning, and transmits SSB (Synchronization Signal Block) to make the synchronization signal cover all users in the cell. The SSB block consists of the primary synchronization signal, the secondary synchronization signal (SSS) and the physical broadcast channel (PBCH), which occupies 240 consecutive subcarriers (20 RBs) in the frequency domain and 4 OFDM symbols in the time domain. Figure 1 shown.

[0062] PSS is a pseudo-random sequence of length 127 using frequency domain BPSK M sequence, mapped on the 127 subcarriers in the middle of the SSB block. The function is shown in formula (1):

[0063]

[0064] The x(n) in the formula is defined by formula (2):

[0065]

[0066] The PSS sequence can take three different values, which are the physical layer identifier of the group with the physical layer cell identifier PCI. Corresponding.

[0067] The period of the SSB block of the NR system is variable, which can be 5ms, 10ms, 20ms, 40ms, 80ms or 160ms, and can be flexibly configured in the physical layer frame structure according to the requirements of different scenarios. In each period, the multiple SSBs that constitute the SSBBurst are limited to a 5ms half-radio frame and are sent in a beam scanning manner. Depending on the SSB subcarrier spacing, the protocol specifies 5 candidate SSB block Case patterns, which define the time slot index of the SSB in the half frame and the OFDM symbol index value of the SSB in the time slot. Taking Case B as an example, SCS = 30kHz, and the first OFDM symbol index of the candidate SSB is {4,8,16,20}+28×n, such as Figure 2 shown.

[0068] By decoding the PSS, the start position, symbol length and PCI of the NR system OFDM symbol can be obtained. After decoding PSS, the SSB block timing and subcarrier spacing of the SSB block can be obtained with the help of the time-frequency structure of SSB. The detection of the primary synchronization signal PSS can achieve downlink frequency synchronization and symbol-level time synchronization between the UE and the base station. The signal can also be used as a reference for the internal frequency generation of the UE, which can largely eliminate the frequency fluctuation between the UE and the network.

[0069] S2. Build the NR system channel model: The NR system adopts a downlink transmission scheme based on CP-OFDM technology, which is sensitive to carrier frequency deviation. After the primary synchronization signal (PSS) sent by the base station is transmitted through the channel, in addition to being affected by Gaussian white noise, it will also produce frequency deviation due to Doppler frequency shift, local oscillator frequency deviation at the transceiver end, etc. The PSS sequence received by the UE can be expressed as a function of the frequency deviation and additive Gaussian white noise.

[0070] The NR system uses a downlink transmission solution based on CP-OFDM technology, which is very sensitive to carrier frequency deviation. In addition to adding Gaussian white noise, the main synchronization signal sent by the base station to the UE after transmission through the channel will be affected by Doppler frequency shift, local oscillator frequency deviation at the transceiver, etc., resulting in frequency deviation. Assuming s(n) is the PSS sequence sent by the base station, the PSS sequence r(n) received by the UE can be expressed as:

[0071]

[0072] In the formula, is the frequency deviation at position n (ε is the normalized frequency deviation, defined as Δf / f sc , Δf is the frequency deviation, f sc is the subcarrier spacing), is the additive white Gaussian noise introduced into the channel.

[0073] S3. Analysis and improvement of PSS algorithm: It includes three stages: PSS coarse synchronization point extraction, PSS fine synchronization point extraction, and PSS final synchronization point extraction. In the coarse synchronization stage, the algorithm uses the properties of Fourier transform and convolution theorem to perform Fourier transform on the received PSS sequence and the local PSS sequence at the receiving end to determine the synchronization point position area and select the peak position as the coarse synchronization point. In the fine synchronization stage, the algorithm is based on the coarse synchronization point and uses the fast Fourier transform synchronization algorithm of the new received signal and the local PSS sequence to compensate for the frequency deviation and select the peak maximum position as the fine synchronization point. Finally, the coarse synchronization point and the fine synchronization point are calculated to obtain the final synchronization point of the PSS signal. This algorithm reduces complexity, reduces detection delay, and improves anti-frequency deviation performance.

[0074] The existing PSS uses the M sequence, which has good correlation characteristics. The cross-correlation synchronization algorithm realizes PSS synchronization detection by performing cross-correlation operations on the received PSS signal and the three locally generated PSS sequences at the receiving end and searching for the cross-correlation peak. Its expression is:

[0075]

[0076] In the formula, R k (n) is the correlation value between the received signal r(n) at position n and the kth local PSS sequence, N is the number of local PSS sequence sampling points, and p k (i) is the kth local PSS sequence.

[0077] Compare the three cross-correlation peaks, and the location of the maximum peak is the PSS synchronization point:

[0078]

[0079] Where V max is the maximum value of the three cross-correlation peaks, L max V max The corresponding position index, The transmission bandwidth is configured as N RB The number of wireless subframe sampling points at the time.

[0080] The principle of the cross-correlation synchronization algorithm is simple, but the algorithm needs to perform cross-correlation operations with each local PSS sequence separately, which results in large algorithm calculations and long synchronization delay. The algorithm will accumulate frequency deviations during cross-correlation operations, which makes the algorithm's anti-frequency deviation performance worse. When the frequency deviation is small, it can meet the system synchronization requirements, but the performance drops sharply when the frequency deviation is large.

[0081] The segmented correlation synchronization algorithm divides the received PSS sequence and the local PSS sequence in the correlation window into M segments, performs cross-correlation operation on each segment, and accumulates the M correlation values ​​after taking the modulus. The expression is:

[0082]

[0083] Where L is the length of each data segment.

[0084] The segmented correlation synchronization algorithm shortens the length of the effective correlation window by segmenting, which reduces the cumulative impact of frequency deviation to a certain extent and improves the algorithm's ability to resist frequency deviation. However, too many segments will cause the peak correlation to decrease, seriously affecting the algorithm's anti-noise ability, and its computational complexity is also relatively high.

[0085] In order to reduce the algorithm complexity, reduce the delay and improve the algorithm's anti-frequency deviation performance, this paper proposes a fast detection algorithm for the main synchronization signal based on Fourier transform and convolution theorem. The algorithm first extracts the coarse synchronization point of the PSS signal based on Fourier transform and convolution theorem, then extracts the fine synchronization point based on Fourier transform based on the coarse synchronization point, and finally determines the final synchronization of the PSS based on the coarse and fine synchronization points. Figure 3 shown.

[0086] About the PSS coarse synchronization algorithm: In summary, the PSS signal sent by the base station will increase the positive exponential frequency deviation after being transmitted through the channel. The cross-correlation synchronization algorithm will accumulate the frequency deviation, making the algorithm's anti-frequency deviation performance worse. This requires us to find an algorithm that can resist the accumulation of positive exponential frequency deviation. It is well known that the Fourier transform equation contains negative exponential equations. We can consider using the negative exponential equations carried by the Fourier transform equation to compensate for the positive exponential frequency deviation equations carried by the channel transmission. Based on this, the cross-correlation algorithm can be rewritten as the following expression:

[0087]

[0088] It is not difficult to find that the essence of formula (14) is the time domain product signal Fourier transform. According to the frequency domain property of the convolution theorem, "time domain product is expressed as 1 / 2π times frequency domain convolution in the frequency domain", F k (n,m) is converted into formula (5):

[0089]

[0090] Since the essence of convolution operation is "flip, translate, and sum of products", FFT[r(n+i)] and The upper and lower limits of the convolution are r(n+i) and The boundary of the overlapping part when performing the translation operation of the convolution operation in the frequency domain is lowered by the maximum of the left boundaries of the two frequency domain signals, and the upper limit is the minimum of the right boundaries of the two frequency domain signals.

[0091] In summary, no matter which local PSS sequence the received PSS signal is synchronized with for Fourier transform-based synchronization, the result of the operation will be located within the area formed by the maximum value of the left boundary of the overlapping part when the received PSS frequency domain sequence and the local PSS frequency domain sequence are shifted during the convolution operation to the minimum value of the right boundary of the overlapping part. Based on this, the received PSS sequence can be used at the receiving end to perform Fourier transform on any local PSS sequence, thereby determining the location area of ​​the PSS synchronization point, and the position corresponding to the Fourier transform peak can be used as the coarse synchronization point of the PSS signal. Furthermore, the local PSS sequence corresponding to the cell that the UE last accessed can be selected as the local PSS sequence for the coarse synchronization point extraction algorithm, such as Figure 4 shown.

[0092] The corresponding rough synchronization point extraction algorithm is shown in formula (6):

[0093]

[0094] Where, the upper and lower limits of F(n,m) are the received PSS frequency domain sequence FFT[r(n+i)] and the local PSS frequency domain sequence corresponding to the cell that the UE last accessed The boundary of the overlapping part when performing the translation operation of the convolution operation.

[0095] Determine the peak value of F(n,m) and set the peak position as the rough synchronization point of the PSS signal, as shown in formula (7):

[0096] (V' max ,L' max )=argmax(|F(n,m)|) (7)

[0097] About the PSS fine synchronization algorithm: The PSS coarse synchronization point extraction algorithm reduces the PSS synchronization point position to the overlapping area when the received PSS frequency domain sequence and the local PSS frequency domain sequence are shifted by the convolution operation, and takes the peak position of F(n,m) as the coarse synchronization point of the PSS signal. However, the coarse synchronization point is not necessarily the true synchronization point, and can span several OFDM symbols in the convolution overlap area. The downlink time-frequency synchronization specified by the protocol needs to be accurate to the OFDM symbol level, so it is necessary to continue PSS fine synchronization based on the coarse synchronization point, such as Figure 5 shown.

[0098] Take the points from Off before the rough synchronization point of the received signal r(n) to Off+N after the rough synchronization point to form a new received signal r'(n):

[0099]

[0100] Where Off is the synchronization position offset value taken according to the frequency offset caused by the terminal's moving speed, and N is the number of local PSS sequence sampling points.

[0101] The new received signal r'(n) is used to perform a synchronization algorithm based on fast Fourier transform with the three local PSS sequences. The positive exponential frequency deviation of the received PSS signal is compensated by the negative exponential formula carried by the Fourier transform formula. The expression is shown in formula (9):

[0102]

[0103] Determine the peak value of the three-time Fourier transform operation, and the location of the maximum peak value is the PSS fine synchronization point, as shown in formula (10):

[0104] (V” max ,L” max )=argmax(max(|F' k (n',m)|)),(k=0,1,2) (10) where F' k (n,m) is the Fourier transform value of the new received signal r'(n) at position n' multiplied by the conjugate of the kth local PSS sequence. V" max is the maximum value of the 3rd Fourier transform peak, L” max For V max The corresponding position index is the precise synchronization point of the PSS signal.

[0105] About the extraction of the final synchronization point of PSS: The PSS fine synchronization point extracted by the fine synchronization point algorithm is a relative synchronization point based on the PSS coarse synchronization point. The coarse synchronization point of the PSS signal needs to be added to the fine synchronization point and subtracted from the value Off. The synchronization point obtained at this time is the final synchronization point of the PSS signal, such as Figure 6 As shown. The expression of PSS final synchronization point extraction algorithm is:

[0106] L final =L' max +L” max -Off-1 (11)

[0107] Where, L final It is the final synchronization point of the PSS signal.

[0108] In summary, the main synchronization signal rapid detection algorithm based on Fourier transform and convolution theorem proposed in this embodiment is based on the Fourier transform formula and the frequency domain properties of the convolution theorem in the PSS coarse synchronization stage. This allows the algorithm to only use the received PSS sequence at the receiving end to perform Fourier transform on the local PSS sequence corresponding to the cell that the UE most recently accessed, and reduce the position of the PSS synchronization point to the overlapping area when the received PSS frequency domain sequence and the local PSS frequency domain sequence perform the translation operation of the convolution operation, which greatly reduces the complexity of the algorithm and reduces the algorithm detection delay. In the PSS fine synchronization stage, the frequency deviation of the positive exponential formula corresponding to the frequency deviation of the new received signal PSS sequence composed of the coarse synchronization point is compensated by using the negative exponential formula carried by the Fourier transform formula, which reduces the frequency deviation accumulation of the algorithm and can improve the algorithm's anti-frequency deviation performance.

[0109] Regarding the algorithm simulation results: From the previous analysis of the PSS algorithm, it can be seen that the PSS synchronization algorithm consists of multiplication and addition operations. The amount of calculation of the cross-correlation synchronization algorithm, the segmented correlation synchronization algorithm, and the improved algorithm based on Fourier transform and convolution theorem proposed in this paper are shown in Table 2:

[0110] Table 2 Algorithm complexity analysis table

[0111]

[0112] When the subcarrier spacing μ = 30KHz and the number of transmission bandwidth physical resource blocks N RB =100, the number of sampling points in the wireless subframe is T NRB The number of sampling points N of the local PSS sequence is 122880 points, and the number of sampling points N of the local PSS sequence is 4096 points. When the terminal moving speed is 0-600km / h, the synchronization position offset value Off is more suitable to be 100. The calculation amount of the three synchronization algorithms is shown in Table 3:

[0113] Table 3 Algorithm complexity value analysis table

[0114]

[0115] From Table 3, we can see that compared with the cross-correlation synchronization algorithm, the multiplication operation of the improved algorithm proposed in this article is reduced by 28.855%, and the addition operation is increased by 21.993%; compared with the segmented correlation synchronization algorithm, the multiplication operation of the improved algorithm is also reduced by 28.855%, while the addition operation is increased by 22.08%. Through analysis, it can be seen that the improved main synchronization signal detection algorithm based on Fourier transform and convolution theorem proposed in this article can reduce the algorithm operation to a certain extent, reduce the algorithm detection delay, and complete the main synchronization signal detection faster under the same channel conditions.

Claims

1. A fast detection algorithm for a master synchronization signal based on Fourier transform and convolution theorem, characterized in that: The algorithm comprises the following steps: S1. Transmitting the primary synchronization signal: The NR system introduces the principles of beamforming and beam scanning to transmit the SSB synchronization block consisting of the primary synchronization signal (PSS), secondary synchronization signal (SSS) and physical broadcast channel (PBCH) to cover all users in the cell; S2. Build the NR system channel model: The NR system adopts a downlink transmission scheme based on CP-OFDM technology. After the primary synchronization signal (PSS) sent by the base station is transmitted through the channel, in addition to being affected by Gaussian white noise, it will also produce frequency deviation due to Doppler frequency shift, local oscillator frequency deviation at the transceiver end, etc. The PSS sequence received by the UE can be expressed as a function of the frequency deviation and additive Gaussian white noise. S3, PSS algorithm analysis and improvement: including three stages: PSS coarse synchronization point extraction, PSS fine synchronization point extraction and PSS final synchronization point extraction; in the coarse synchronization stage, the algorithm uses the properties of Fourier transform and convolution theorem to perform Fourier transform on the received PSS sequence and the local PSS sequence at the receiving end to determine the synchronization point position area and select the peak position as the coarse synchronization point; in the fine synchronization stage, the algorithm is based on the coarse synchronization point, through the fast Fourier transform synchronization algorithm of the new received signal and the local PSS sequence, to compensate for the frequency deviation and select the peak maximum value position as the fine synchronization point; finally, the coarse synchronization point and the fine synchronization point are calculated to obtain the final synchronization point of the PSS signal; S4. The algorithm simulation results are as follows: Under the conditions of specific subcarrier spacing and number of transmission bandwidth physical resource blocks, the overall algorithm calculation amount is reduced by reducing the amount of multiplication operations and appropriately increasing the amount of addition operations, so that the algorithm can complete the main synchronization signal detection faster under the same channel conditions, reducing the algorithm detection delay.

2. The fast detection algorithm for the master synchronization signal based on Fourier transform and convolution theorem according to claim 1, characterized in that: In S1, SSB occupies 240 subcarriers in the frequency domain and 4 OFDM symbols in the time domain. Its period is variable and can be flexibly configured according to scenario requirements.

3. The fast detection algorithm for the master synchronization signal based on Fourier transform and convolution theorem according to claim 1, characterized in that: In S1, the start position, symbol length and physical layer cell identifier (PCI) of the OFDM symbol are obtained by decoding the PSS, so as to achieve downlink frequency synchronization and symbol-level time synchronization between the UE and the base station.

4. The fast detection algorithm for the master synchronization signal based on Fourier transform and convolution theorem according to claim 1, characterized in that: The PSS is a pseudo-random sequence of length 127 using a frequency domain BPSKM sequence, mapped on the 127 subcarriers in the middle of the SSB block. The function is shown in formula (1): The x(n) in the formula is defined by formula (2): The PSS sequence can take three different values, which are the physical layer identifier of the group with the physical layer cell identifier PCI. Corresponding.

5. The fast detection algorithm for the primary synchronization signal based on Fourier transform and convolution theorem according to claim 1 or 3, characterized in that: Assuming s(n) is the PSS sequence sent by the base station, the PSS sequence r(n) received by the UE can be expressed as: In the formula, is the frequency deviation at position n (ε is the normalized frequency deviation, defined as Δf / f sc , Δf is the frequency deviation, f sc is the subcarrier spacing), is the additive white Gaussian noise introduced into the channel.

6. The fast detection algorithm for the master synchronization signal based on Fourier transform and convolution theorem according to claim 1, characterized in that: Based on the negative exponential order formula carried by the Fourier transform formula, the positive exponential order frequency deviation formula carried by the channel transmission is compensated and rewritten into the following expression: The essence of formula (14) is the time domain product signal Fourier transform; According to the frequency domain property of the convolution theorem, "time domain product is expressed as 1 / 2π times frequency domain convolution in the frequency domain", F k (n,m) is converted into formula (5): FFT[r(n+i)] and The upper and lower limits of the convolution are r(n+i) and The boundary of the overlapping part when performing the translation operation of the convolution operation in the frequency domain is lowered by the maximum of the left boundaries of the two frequency domain signals, and the upper limit is the minimum of the right boundaries of the two frequency domain signals.

7. The fast detection algorithm for the master synchronization signal based on Fourier transform and convolution theorem according to claim 1, characterized in that: The corresponding rough synchronization point extraction algorithm is shown in formula (6): Where, the upper and lower limits of F(n,m) are the received PSS frequency domain sequence FFT[r(n+i)] and the local PSS frequency domain sequence corresponding to the cell that the UE last accessed The boundary of the overlapping part when performing the translation operation of the convolution operation; Determine the peak value of F(n,m) and set the peak position as the rough synchronization point of the PSS signal, as shown in formula (7): (V m ' ax ,L' max )=argmax(|F(n,m)|)(7) 8. The fast detection algorithm for the master synchronization signal based on Fourier transform and convolution theorem according to claim 1, characterized in that: Take the points from Off before the rough synchronization point of the received signal r(n) to Off+N after the rough synchronization point to form a new received signal r'(n): (n=L' max -Off,L' max -Off+1,...,L' max +Off+N) (8) Where Off is the synchronization position offset value taken according to the frequency offset caused by the terminal's moving speed, and N is the number of local PSS sequence sampling points; The new received signal r'(n) is used to perform a synchronization algorithm based on fast Fourier transform with the three local PSS sequences. The positive exponential frequency deviation of the received PSS signal is compensated by the negative exponential formula carried by the Fourier transform formula. The expression is shown in formula (9): Determine the peak value of the three-time Fourier transform operation, and the location of the maximum peak value is the PSS fine synchronization point, as shown in formula (10): (V” max ,L” max )=argmax(max(|F’ k (n',m)|)),(k=0,1,2) (10) Where F' k (n,m) is the Fourier transform value of the new received signal r'(n) at position n' multiplied by the conjugate of the kth local PSS sequence; V m ” ax is the maximum value of the 3rd Fourier transform peak, L” max For V max The corresponding position index is the precise synchronization point of the PSS signal.

9. The fast detection algorithm for the master synchronization signal based on Fourier transform and convolution theorem according to claim 1, characterized in that: The expression of the PSS final synchronization point extraction algorithm is: L final The max +L” max -Off-1 (11) Where, L final It is the final synchronization point of the PSS signal.

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