A minimalist synchronization scheme based on double correlation operators

Abstract

The present invention proposes a minimalist synchronization scheme based on a dual-correlation operator. First, a demodulation operation is performed on the received pilot sequence to obtain a demodulated sequence. Then, a generalized correlation operation is performed on the demodulated sequence to obtain an autocorrelation operator and a cross-correlation operator. Then, frequency-phase decoupling estimation is performed on the autocorrelation operator to obtain a frequency offset estimate and a phase offset estimate. The obtained frequency offset estimate and phase offset estimate are then compensated to the cross-correlation operator and the received data sequence to obtain a corrected cross-correlation operator and a corrected received data sequence. Then, the corrected cross-correlation operator and the corrected received data sequence are separated into cross-correlation values and received data blocks. Then, block-correlation data compensation is performed on the cross-correlation values and the received data blocks to obtain secondary corrected received data blocks. Finally, the secondary corrected received data blocks are combined into a complete received data sequence. The present invention effectively solves the problems of dual limitations of pilot resources and storage resources in short burst communications, and provides an efficient and reliable minimalist synchronization scheme for short burst communications.

Description

Technical Field

[0001] The present invention relates to the technical field of short burst communications such as narrowband Internet of Things, radar, and cellular / satellite Internet of Things, and in particular to a minimalist synchronization scheme based on a dual correlation operator. Background Art

[0002] Currently, short burst communications are widely used in modern communication systems, such as narrowband IoT, radar, and cellular / satellite IoT. However, limited pilot and storage resources pose significant challenges to traditional synchronization schemes and their hardware implementation. Therefore, it is particularly important to design a minimalist synchronization scheme to support reliable short burst communications under resource-constrained conditions.

[0003] For short burst communications using low-cost oscillators, the corresponding transmitter and receiver are subject to large carrier frequency and phase offsets. As a result, traditional synchronization schemes, aided by a small number of pilot signals, severely impact phase offset estimation using frequency offset estimation, and data compensation consumes a large amount of storage space. In "Burst-mode synchronization for SOQPSK," Hosseini and Perrins proposed a pilot-assisted carrier synchronization scheme for short burst-shaped offset quadrature phase-shift keying transmission systems. Considering the preamble structure in the LoRa (Long Range) protocol, Tapparal, Afisiadis, Mayoraz et al. proposed a joint synchronization scheme for delay, carrier frequency offset, and phase offset in "An open-source LoRa physical layer prototype on GNU radio." For wideband linear frequency modulation radar systems, Yuan, He, Zhang et al. designed an effective joint frequency and phase offset estimation method using the frequency peak of envelope cross correlation as input in "Instantaneous velocity estimation based on envelope cross correlation and joint frequency-phase estimation for wideband LFM radar." Considering the orthogonal time-frequency modulation system of low-orbit satellites, Li, Zhang, Ju, et al., in their paper "Downlink carrier frequency offset estimation for OTFS-based LEO satellite communication system," used pilots to accurately estimate carrier frequency and phase offsets. Furthermore, to address the large Doppler frequency shift and phase offset issues in low-orbit satellite communication systems, Zhang Jiayi, Yu Zhongyang, Zhu Min, et al. designed a pilot-assisted carrier synchronization scheme in their paper "Design of a Carrier Synchronization Algorithm for SCMA Systems in Low-orbit Satellite Communications." However, these synchronization schemes all consider so-called frequency-phase coupled estimation, where the frequency offset estimator is executed before the phase offset estimator. Consequently, the performance of the phase offset estimator depends on the accuracy of the frequency offset estimator, representing the coupling effect of frequency offset on phase offset. To mitigate this coupling, frequency-phase coupled estimation often requires the use of a large pilot overhead, which is detrimental to short burst communications.In the paper "Carrier-phase and frequency-estimation bounds for transmissions with embedded reference symbols," Rice points out that in frequency-phase coupling estimation, as long as the initial sampling time is set at the middle of the preamble structure, the Cramer-Rao bounds for frequency offset estimation are decoupled from the Cramer-Rao bounds for phase offset estimation. However, since the receiver does not know the location of the initial sampling time, it cannot manually set this initial location. Furthermore, after frequency-phase coupling estimation, continuous data compensation is often used, compensating the received data for frequency and phase offsets moment by moment. This data compensation method can achieve good demodulation performance, but it has the disadvantage of requiring a large amount of storage space (proportional to the number of transmitted data symbols), which inevitably increases the difficulty of hardware implementation in burst communication systems. Summary of the Invention

[0004] In response to the problem that the existing technology has poor performance under the dual limitations of pilot resources and storage resources, the present invention proposes a minimalist synchronization scheme based on a dual correlation operator, which includes two parts: frequency-phase decoupling estimation and block-related data compensation: the first part includes an autocorrelation frequency offset estimation that is insensitive to fading and a maximum likelihood phase offset estimation with low complexity and resistance to large frequency offsets; the second part can significantly reduce the storage space occupancy and greatly reduce the maximum accumulated phase caused by the residual frequency offset in each data block.

[0005] In order to achieve the above object, the technical solution of the present invention is achieved as follows:

[0006] A minimalist synchronization scheme based on a dual-correlation operator includes the following steps:

[0007] S1: Get the received pilot sequence r p And receive the pilot sequence r p Perform a demodulation operation to obtain a demodulated sequence v;

[0008] S2: Perform a generalized correlation operation on the obtained demodulated sequence v to obtain the autocorrelation operator R(β 11 |v1) and the cross-correlation operator R(β|v);

[0009] S3: The obtained autocorrelation operator R(β 11 |v1) Perform frequency-phase decoupling estimation to obtain the frequency offset estimate and phase bias estimates

[0010] S4: The obtained frequency offset estimate and phase bias estimates Compensate to the cross-correlation operator R(β|v) and the received data sequence r dThe corrected cross-correlation operator R(β|v′) and the corrected received data sequence are obtained ;

[0011] S5: The obtained correction cross-correlation operator R(β|v′) and the correction received data sequence Separating into a plurality of corrected cross-correlation values and a plurality of corrected received data blocks;

[0012] S6: performing block correlation data compensation on the obtained multiple corrected mutual correlation values and the multiple corrected received data blocks to obtain multiple secondary corrected received data blocks;

[0013] S7: Combine the obtained multiple secondary correction received data blocks into a complete received data sequence r d ′.

[0014] The step S1 described in obtaining the received pilot sequence r p The method is:

[0015] S1.1: Consider a Ricean flat fading single-carrier communication system, the corresponding received signal r = {r(k), k∈κ p ∪κ d} and the received signal r(k) in the kth symbol period is expressed as:

[0016]

[0017] Where h is the channel gain, whose amplitude obeys the Rice distribution determined by the Rice factor, T s is the symbol period, f d and θ are the carrier frequency deviation and phase deviation respectively, s(k) is the energy-normalized modulation signal, n(k) is a complex Gaussian random variable, is the imaginary unit, There are m pilot blocks p1~p m The sampling index set of There are m-1 data blocks d1~d m-1 The sampling index set, and the i-th pilot block p i The sampling index of and the lth data block d l The sampling index of The specific forms are:

[0018]

[0019] in, Respectively represent the lengths of the lth, i-th, lth, and tth pilot blocks; Respectively represent the length of the lth and tth data blocks; according to the m pilot blocks p1~p m The sampling index set κ pGet the received pilot sequence r p .

[0020] According to the m pilot blocks p1~p m The sampling index set κ p Get the received pilot sequence r p The method is:

[0021] S1.2: At time k, traverse m pilot blocks p1~p m The sampling index set κ p , the corresponding received pilot sequence r p ={r p (k),k∈κ p}, and the received pilot signal r in the kth symbol period p (k) is expressed as:

[0022]

[0023] Where s p (k) is the modulated pilot signal in the kth symbol period.

[0024] The method of the demodulation operation described in step S1 is:

[0025] S1.3: Receive the pilot signal r p (k) and the modulated pilot signal s p The demodulated signal v(k) is obtained by multiplying the conjugate form of (k):

[0026] v(k)=r p (k)·s p (k) *

[0027] Where * is the conjugate operation;

[0028] S1.4: When time k traverses the pilot block sampling index set κ p When the demodulation signal v(k) forms the demodulation sequence

[0029]

[0030] The method of generalizing the related operations described in step S2 is:

[0031] S2.1: Demodulation sequence using the first pilot block p1 The conjugate form of the demodulated signal v(k) corresponding to the pilot block p1 is combined with its delayed signal v(k+β 11 ) is multiplied to obtain the autocorrelation operator R(β 11 |v1):

[0032]

[0033] Where, is the length of the pilot block p1, represents the autocorrelation delay length;

[0034] S2.2: Use the demodulation sequence of the first pilot block p1 and other m-1 pilot blocks p2~p m Demodulation sequence The pilot blocks p2~p m The conjugate form of the corresponding demodulated signal v(k) and its delayed signal v(k+β 1i ) are multiplied to obtain the cross-correlation operator R(β|v)={R(β 12 |v 12 ),…,R(β 1i |v 1i ),...,R(β 1m |v 1m )}, the i-th (i=2,3,...,m) cross-correlation value R(β 1i |v 1i )for:

[0035]

[0036] In the formula, the modulation sequence Demodulation sequence v 1i The demodulation sequence v1 of the pilot block p1 and the pilot block p i The demodulation sequence v i The union of is the cross-correlation delay length.

[0037] The method for frequency-phase decoupling estimation described in step S3 is:

[0038] S3.1: Using the autocorrelation operator R(β 11 |v1), and obtain the frequency offset estimate by taking the argument operation

[0039]

[0040] Where arg{·} is the argument operation;

[0041] S3.2: Using the autocorrelation operator By comparing the demodulated signal v(k) corresponding to the pilot block p1 with the autocorrelation operator The conjugate form of is summed and the phase angle is obtained to obtain the phase deviation estimate represents a special autocorrelation delay length and Phase bias estimate The calculation formula is:

[0042]

[0043] Where λ=1,2,... is the decoupling coefficient.

[0044] The method for obtaining the corrected cross-correlation operator R(β|v′) in step S4 is:

[0045] S4.1: The frequency offset estimate and phase bias estimates Compensate to the cross-correlation operator R(β|v) to obtain the corrected cross-correlation operator R(β|v′)={R(β 12 |v′ 12 ),...,R(β 1i |v′ 1i ),...,R(β 1m |v′ 1m )}, and the i-th corrected cross-correlation value R(β 1i |v′ 1i )for:

[0046]

[0047] In the formula, the modulation sequence The result after compensating the frequency offset and phase offset estimation value of v(k) is the demodulation sequence For v(k+β 1i )v(k) is the result after frequency offset and phase offset estimation are compensated, v′ 1i The demodulation sequence v1′ of the pilot block p1 and the pilot block p i The demodulation sequence v i ′’s union,

[0048] The corrected received data sequence obtained in step S4 The method is:

[0049] S4.2: The frequency offset estimate and phase bias estimates Compensate to the received data sequence r d The corrected received data sequence is obtained from in, And the corrected received data signal r′(k) in the kth symbol period is:

[0050]

[0051] Step S5 is to obtain the corrected cross-correlation operator R(β|v′) and the corrected received data sequence. The method of separating into multiple correction mutual correlation values and multiple correction received data blocks is:

[0052] S5.1: Sampling index sets by data block Separate the corrected cross-correlation operator R(β|v′) into m-1 corrected cross-correlation values R(β 12 |v′ 12 ),R(β 13 |v′ 13 ),...,R(β 1m |v′ 1m );

[0053] S5.2: Sampling index sets by data block The received data sequence will be corrected Split into m-1 correction receiving data blocks

[0054] The method for compensating the block-related data in step S6 is:

[0055] The m-1 corrected cross-correlation values R(β 12 |v′ 12 ),R(β 13 |v′ 13 ),...,R(β 1m |v′ 1m ) and m-1 corrected received data blocks Multiply them respectively to get m-1 secondary correction receiving data blocks And the lth secondary correction received data block The secondary correction received data signal in the kth symbol period Has the following form:

[0056]

[0057] Step S7 combines the obtained multiple secondary corrected received data blocks into a complete received data sequence r d 'The method is:

[0058] Sampling index collections by data block m-1 secondary correction received data blocks Synthesize a complete receive data sequence

[0059] The beneficial effects of the present invention are:

[0060] 1. Reducing pilot overhead: Compared with the frequency-phase coupled estimation of the traditional synchronization scheme, the frequency-phase decoupled estimation of the present invention can reduce the dependence of the phase offset estimation on the frequency offset estimation performance, thereby reducing the pilot overhead.

[0061] 2. Reduce storage space usage: Compared with the continuous moment data compensation of the traditional synchronization scheme, the block-related data compensation of the present invention can reduce the number of data compensation values, thereby reducing storage space usage.

[0062] 3. Guaranteeing system performance: With limited pilot overhead, the solution of the present invention can achieve error performance close to that of traditional synchronization solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0064] Figure 1 This is a flowchart of the implementation process of the minimalist synchronization solution based on the dual correlation operator proposed in the present invention.

[0065] Figure 2 is the estimation performance of the autocorrelation frequency offset estimator in the present invention.

[0066] Figure 3 It is the frequency offset resistance capability of the maximum likelihood phase offset estimator under the decoupling coefficient λ=1 in the present invention.

[0067] Figure 4 The anti-frequency deviation capability of the maximum likelihood phase deviation estimator under the decoupling coefficient λ=2 in the present invention is

[0068] Figure 5 The performance comparison of block-related data compensation and continuous-time data compensation in the present invention is shown in FIG. DETAILED DESCRIPTION

[0069] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0070] like Figure 1 As shown in FIG, a minimalist synchronization scheme based on a double correlation operator includes the following steps:

[0071] S1: Get the received pilot sequence r p And receive the pilot sequence r p Perform a demodulation operation to obtain a demodulated sequence v.

[0072] Get the received pilot sequence r p The method is as follows: traverse the pilot block sampling index set at the sampling time of the received signal to obtain a received pilot sequence.

[0073] Step S1.1: For short burst communication systems such as narrowband IoT, radar, cellular / satellite IoT, etc., consider the Rice flat fading transmission channel, and the corresponding received signal r = {r(k), k∈κ p ∪κ d} and the received signal r(k) in the kth symbol period is expressed as:

[0074]

[0075] Where h is the channel gain, whose amplitude obeys the Rice distribution determined by the Rice factor, T s is the symbol period, f d and θ are the carrier frequency deviation and phase deviation respectively, s(k) is the energy-normalized modulation signal, n(k) is a complex Gaussian random variable, is the imaginary unit, There are m pilot blocks p1~p m The sampling index set of Data blocks d1~d m-1 The sampling index set, and the i-th pilot block p i The sampling index of and the lth data block d l The sampling index of The specific forms are:

[0076]

[0077]

[0078] Where, Respectively represent the lengths of the lth, i-th, lth, and tth pilot blocks; Represent the length of the lth and tth data blocks respectively.

[0079] Step S1.2: Consider time k and traverse the pilot block sampling index set κ p , the corresponding received pilot sequence r p ={r p (k),k∈κ p}, and the received pilot signal r in the kth symbol period p (k) is expressed as:

[0080]

[0081] Where sp (k) is the modulated pilot signal in the kth symbol period.

[0082] The method of the demodulation operation described in step S1 is:

[0083] Step S1.3: Receive the pilot signal r p (k) and the modulated pilot signal s p The demodulated signal v(k) is obtained by multiplying the conjugate form of (k):

[0084]

[0085] Where * is the conjugate operation, n′(k)=n(k)·s p (k) * is Gaussian noise, because s p (k) is a known modulated pilot signal.

[0086] Step S1.4: At time k, traverse the pilot block sampling index set κ p When the demodulation signal v(k) forms the demodulation sequence

[0087]

[0088] S2: Perform a generalized correlation operation on the obtained demodulated sequence v to obtain the autocorrelation operator R(β 11 |v1) and the cross-correlation operator R(β|v), where the autocorrelation operator is used to construct the frequency-phase decoupling estimation in the minimalist synchronization scheme, and the cross-correlation operator is used to construct the block-correlation data compensation in the minimalist synchronization scheme.

[0089] The method of generalizing the related operations described in step S2 is:

[0090] Step S2.1: Use the demodulation sequence of the first pilot block p1 The conjugate form of the demodulated signal v(k) corresponding to the pilot block p1 is combined with its delayed signal v(k+β 11 ) is multiplied to obtain the autocorrelation operator R(β 11 |v1):

[0091]

[0092] Where, is the length of the pilot block p1, represents the autocorrelation delay length, ψ=E{|h| 2} is the equivalent average energy of the received pilot signal, E represents the expected operation, h is the channel gain, ξ(β 11 ) is the noise term and can be expressed as:

[0093]

[0094] Where n′(k+β 11 ) is the delayed signal of Gaussian noise n′(k),

[0095] Step S2.2: Use the demodulation sequence of the first pilot block p1 and other m-1 pilot blocks p2~p m Demodulation sequence The pilot blocks p2~p m The conjugate form of the corresponding demodulated signal v(k) and its delayed signal v(k+β 1i ) are multiplied to obtain the cross-correlation operator R(β|v)={R(β 12 |v 12 ),...,R(β 1i |v 1i ),...,R(β 1m |v 1m )}, and the i-th (i=2,3,...,m) cross-correlation value R(β 1i |v 1i )for:

[0096]

[0097] In the formula, the modulation sequence Demodulation sequence v 1i The demodulation sequence v1 of the pilot block p1 and the pilot block p i The demodulation sequence v i The union of is the cross-correlation delay length, ξ(β 1i ) is the noise term, which can be expressed as:

[0098]

[0099] Where n′(k+β 1i ) is the delayed signal of Gaussian noise n′(k).

[0100] S3: The obtained autocorrelation operator R(β 11 |v1) Perform frequency-phase decoupling estimation to obtain the frequency offset estimate and phase bias estimates

[0101] The method for frequency-phase decoupling estimation described in step S3 is:

[0102] Step S3.1: Using the autocorrelation operator R(β 11|v1), and obtain the frequency offset estimate by taking the argument operation

[0103]

[0104] Where arg{·} is the argument operation;

[0105] Step S3.2: Using the autocorrelation operator By comparing the demodulated signal v(k) corresponding to the pilot block p1 with the autocorrelation operator The conjugate form of is summed and the phase angle is obtained to obtain the phase deviation estimate represents a special autocorrelation delay length and

[0106]

[0107] where λ = 1, 2, ... is the decoupling coefficient and ξ is the noise term, and has the following form:

[0108]

[0109] S4: The obtained frequency offset estimate and phase bias estimates Compensate to the cross-correlation operator R(β|v) and the received data sequence r d The corrected cross-correlation operator R(β|v′) and the corrected received data sequence are obtained The purpose of the compensation operation is to reduce the accumulated phase caused by frequency offset and phase offset in the cross-correlation operator and the received data sequence, thereby facilitating subsequent block-related data compensation.

[0110] The specific method is:

[0111] Step S4.1: Set the frequency offset estimate and phase bias estimates Compensate to the cross-correlation operator R(β|v) to obtain the corrected cross-correlation operator R(β|v′)={R(β 12 |v′ 12 ),...,R(β 1i |v′ 1i ),...,R(β 1m |v′ 1m )}, and the i-th (i=2,3,...,m) corrected cross-correlation value R(β 1i |v′ 1i )for:

[0112]

[0113] In the formula, the modulation sequence The result after compensating the frequency offset and phase offset estimation value of v(k) is the demodulation sequence For v(k+β 1i )v(k) is the result after frequency offset and phase offset estimation are compensated, v′ 1i The demodulation sequence v1′ of the pilot block p1 and the pilot block p i The demodulation sequence v i ′, To estimate the residual frequency offset after compensation, ξ(β 1i ) is the noise term.

[0114] Step S4.2: Set the frequency offset estimate and phase bias estimates Compensate to the received data sequence r d The corrected received data sequence is obtained from in, And the corrected received data signal r′(k) in the kth symbol period has the following form:

[0115]

[0116] Where, is the residual phase deviation, It is still a Gaussian noise.

[0117] S5: The obtained correction cross-correlation operator R(β|v′) and the correction received data sequence Separated into multiple corrected cross-correlation values and multiple corrected received data blocks.

[0118] The specific method is:

[0119] Step S5.1: Sampling index sets according to data blocks Separate the corrected cross-correlation operator R(β|v′) into m-1 corrected cross-correlation values

[0120] Step S5.2: Sampling index sets according to data blocks The received data sequence will be corrected Split into m-1 correction receiving data blocks

[0121] S6: performing block correlation data compensation on the obtained multiple corrected mutual correlation values and the corrected received data blocks to obtain multiple secondary corrected received data blocks.

[0122] The method for compensating the block-related data in step S6 is:

[0123] The m-1 corrected cross-correlation values R(β 12 |v′ 12)~R(β 1m |v′ 1m ) and m-1 corrected received data blocks Multiply them respectively to get m-1 secondary correction receiving data blocks And the lth secondary correction received data block The secondary correction received data signal in the kth symbol period Has the following form:

[0124]

[0125] Where, is the new data sampling time index, is a superimposed noise term, which will have a great impact on the proposed block-related data compensation. There are two ways to reduce this impact: the first way is to keep the pilot block length small. The second method is to consider the smaller number of pilot blocks m and increase the length of each pilot block.

[0126] S7: Combine the obtained multiple secondary correction received data blocks into a complete received data sequence r d ′.

[0127] The specific method is:

[0128] Sampling index collections by data block m-1 secondary correction received data blocks Synthesize a complete receive data sequence

[0129] From the above steps, it can be found that the proposed block (cross) correlation data compensation only requires the compensation value of m-1 data blocks, while the continuous time data compensation of the traditional synchronization scheme requires Compensation value (i.e. ), so the proposed block (mutual) correlation data compensation occupies less (compensation value) storage space. In addition, combined with the definition of each data block sampling index set, it can be found that the proposed block (mutual) correlation data compensation can significantly reduce the storage space of each data block. The maximum cumulative phase (j = 1, 2, ..., m-1) is due to the fact that the range of the new data sampling time index k' has been changed from the original Reduce to

[0130] In order to further illustrate the beneficial effects of the present invention, a comparative explanation is given through simulation experiments in this embodiment, as follows:

[0131] Simulation condition 1: Quadrature phase shift keying modulation, symbol period T s =50μs, length of the first pilot block Signal-to-noise ratio SNR = 0:5:25dB, Rice factor K = 0, 5, 10dB.

[0132] Simulation condition 2: QPSK (Quadrature phase shift keying) modulation, symbol period T s =50μs, the residual frequency offset Δf (after performing frequency-phase decoupling estimation or frequency-phase coupling estimation) d =200Hz, Ricean factor K=10dB, number of pilot blocks m=3 (then number of data blocks m-1=2), data symbol length is 150, and pilot symbol lengths are 3, 6, and 9, respectively. It should be noted that when the pilot length is 3, it is necessary to use 1 pilot symbol in the first pilot block, and set the lengths of the second and third pilot blocks to 1. Similarly, when the pilot lengths are 6 and 9, it is necessary to use 2 and 3 pilot symbols in the first pilot block, and set the lengths of the second and third pilot blocks to 2 and 3, respectively.

[0133] Simulation 1:

[0134] Considering simulation condition 1, the following two cases are discussed: For the maximum likelihood phase deviation estimator under frequency-phase decoupling estimation, when the decoupling coefficient λ=1, it can be used in |f d The phase deviation in the range of [-π,π) can be captured within |≤1800Hz; when the decoupling coefficient λ>1, taking the decoupling coefficient λ=2 as an example, it can be captured within |f d The phase deviation in the range of [-10π / 11, 10π / 11) is estimated within ≤3600Hz.

[0135] Figure 2 The mean square error (MSE) performance of the autocorrelation frequency offset estimator is given. Here we assume that the frequency offset f d =1600Hz (within the frequency offset resistance range of the maximum likelihood phase offset estimator corresponding to the frequency-phase decoupling estimation when the decoupling coefficient λ=1).

[0136] from Figure 2 The simulation results show that for Rice factor K = 0dB and Rice factor K = 10dB, the autocorrelation frequency offset estimator can achieve good mean square error (MSE) performance. When the signal-to-noise ratio (SNR) is ≥ 25dB, the mean square error (MSE) of the autocorrelation frequency offset estimator will be less than 1×10 -4 From the statistical average point of view, the residual frequency deviation This value is the residual frequency deviation Δf in simulation condition 2 d =200Hz source.

[0137] Simulation 2:

[0138] Considering simulation condition 1, Figure 3 、 Figure 4 The MSE performance of the maximum likelihood phase deviation estimator under frequency-phase decoupled estimation and frequency-phase coupled estimation is shown. Here, the signal-to-noise ratio (SNR) is considered to be 20dB.

[0139] from Figure 3 、 Figure 4 The simulation results show that as long as the frequency deviation value is within the agreed range, Regardless of the decoupling coefficient λ and the Ricean factor K, the maximum likelihood phase deviation estimator under frequency-phase decoupling estimation can achieve better performance than the maximum likelihood phase deviation estimator under frequency-phase coupling estimation. This is because a specific delay length is selected in the autocorrelation operator. This not only reduces the number of complex multiplication operations for phase offset estimation, but also reduces the impact of large frequency offsets on phase offset estimation. Furthermore, since an increase in the Ricean factor K causes the imaginary part of the channel gain h to approach 0, the corresponding maximum likelihood phase offset estimator performance improves. Therefore, the phase offset estimation performance with a Ricean factor K = 10dB is better than that with a Ricean factor K = 5dB.

[0140] Simulation 3:

[0141] Considering simulation condition 2, hardware-implemented storage resources are quite valuable for short-burst communication applications (such as narrowband IoT). Therefore, it is necessary to evaluate the storage space usage of these two types of data compensation. Based on the above conditions, the storage space usage of continuous-time data compensation can be considered as the length of the transmitted data, i.e., 150; while the storage space usage of the proposed block-dependent data compensation is only related to the number of data blocks used, i.e., 2. Clearly, during the data compensation process, the latter type of compensation consumes very little storage space for the compensation value.

[0142] Figure 5 The bit error rate (BER) performance of these two data compensations is given.

[0143] from Figure 5Simulation results show that when residual frequency offset exists, a QPSK system without frequency offset compensation cannot function properly. However, with both block-correlated data compensation and continuous-time data compensation, the corresponding system performance improves to varying degrees, and the larger the pilot block length, the more significant the improvement. Overall, the performance of the proposed data compensation is similar to that of continuous-time data compensation. However, in high signal-to-noise ratio (SNR) regions (e.g., SNR > 21dB) and when a small number of pilots (e.g., fewer than 6) is used, the proposed data compensation performs worse than continuous-time data compensation by more than 1 dB. This is because the noise variance of the latter is smaller at high SNRs.

[0144] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A minimalist synchronization scheme based on a dual-correlation operator, characterized in that: The following steps are involved: S1: Get the received pilot sequence r p And receive the pilot sequence r p Perform a demodulation operation to obtain a demodulated sequence v; S2: Perform a generalized correlation operation on the obtained demodulated sequence v to obtain the autocorrelation operator R(β 11 |v1) and the cross-correlation operator R(β|v); S3: The obtained autocorrelation operator R(β 11 |v1) Perform frequency-phase decoupling estimation to obtain the frequency offset estimate and phase bias estimates S4: The obtained frequency offset estimate and phase bias estimates Compensate to the cross-correlation operator R(β|v) and the received data sequence r d The corrected cross-correlation operator R(β|v′) and the corrected received data sequence are obtained S5: The obtained correction cross-correlation operator R(β|v′) and the correction received data sequence Separating into a plurality of corrected cross-correlation values and a plurality of corrected received data blocks; S6: performing block correlation data compensation on the obtained multiple corrected mutual correlation values and the multiple corrected received data blocks to obtain multiple secondary corrected received data blocks; S7: Combine the obtained multiple secondary correction received data blocks into a complete received data sequence r d ′.

2. The minimalist synchronization scheme based on dual correlation operators according to claim 1, characterized in that: Step S1 of obtaining the received pilot sequence r p The method is: S1.1: Consider a Ricean flat fading single-carrier communication system, the corresponding received signal r = {r(k), k∈κ p ∪κ d } and the received signal r(k) in the kth symbol period is expressed as: Where h is the channel gain, whose amplitude obeys the Rice distribution determined by the Rice factor, T s is the symbol period, f d and θ are the carrier frequency deviation and phase deviation respectively, s(k) is the energy-normalized modulation signal, n(k) is a complex Gaussian random variable, is the imaginary unit, There are m pilot blocks p1~p m The sampling index set of There are m-1 data blocks d1~d m-1 The sampling index set, and the i-th pilot block p i The sampling index of and the lth data block d l The sampling index of The specific forms are: in, Respectively represent the lengths of the lth, i-th, lth, and tth pilot blocks; Respectively represent the length of the lth and tth data blocks; according to the m pilot blocks p1~p m The sampling index set κ p Get the received pilot sequence r p .

3. The minimalist synchronization scheme based on dual correlation operators according to claim 2, characterized in that: According to the m pilot blocks p1~p m The sampling index set κ p Get the received pilot sequence r p The method is: S1.2: At time k, traverse m pilot blocks p1~p m The sampling index set κ p , the corresponding received pilot sequence r p ={r p (k),k∈κ p }, and the received pilot signal r in the kth symbol period p (k) is expressed as: Where s p (k) is the modulated pilot signal in the kth symbol period.

4. The minimalist synchronization scheme based on dual correlation operators according to claim 3, characterized in that: The method of the demodulation operation described in step S1 is: S1.3: Receive the pilot signal r p (k) and the modulated pilot signal s p The demodulated signal v(k) is obtained by multiplying the conjugate form of (k): v(k)=r p (k)·s p (k) * Where * is the conjugate operation; S1.4: When time k traverses the pilot block sampling index set κ p When the demodulation signal v(k) forms the demodulation sequence 5. The minimalist synchronization solution based on dual correlation operators according to claim 4, characterized in that: The method of generalizing the related operations described in step S2 is: S2.1: Demodulation sequence using the first pilot block p1 The conjugate form of the demodulated signal v(k) corresponding to the pilot block p1 is combined with its delayed signal v(k+β 11 ) is multiplied to obtain the autocorrelation operator R(β 11 |v1): Where, is the length of the pilot block p1, represents the autocorrelation delay length; S2.2: Demodulation sequence using the first pilot block p1 and other m-1 pilot blocks p2~p m Demodulation sequence The pilot blocks p2~p m The conjugate form of the corresponding demodulated signal v(k) and its delayed signal v(k+β 1i ) are multiplied to obtain the cross-correlation operator R(β|v)={R(β 12 |v 12 ),...,R(β 1i |v 1i ),...,R(β 1m |v 1m )}, the i-th (i=2,3,...,m) cross-correlation value R(β 1i |v 1i )for: In the formula, the modulation sequence Demodulation sequence v i ={v(β 1i ),v(1+β 1i ),..., v 1i The demodulation sequence v1 of the pilot block p1 and the pilot block p i The demodulation sequence v i The union of is the cross-correlation delay length.

6. The minimalist synchronization scheme based on dual correlation operators according to claim 5, characterized in that: The method for frequency-phase decoupling estimation described in step S3 is: S3.1: Using the autocorrelation operator R(β 11 |v1), and obtain the frequency offset estimate by taking the argument operation Where arg{·} is the argument operation; S3.2: Using the autocorrelation operator By comparing the demodulated signal v(k) corresponding to the pilot block p1 with the autocorrelation operator The conjugate form of is summed and the phase angle is obtained to obtain the phase deviation estimate represents a special autocorrelation delay length and Phase bias estimate The calculation formula is: Where λ=1,2,... is the decoupling coefficient.

7. The minimalist synchronization solution based on dual correlation operators according to claim 6, characterized in that: The method for obtaining the corrected cross-correlation operator R(β|v′) in step S4 is: S4.1: The frequency offset estimate and phase bias estimates Compensate to the cross-correlation operator R(β|v) to obtain the corrected cross-correlation operator R(β|v′)={R(β 12 |v′ 12 ),...,R(β 1i |v′ 1i ),...,R(β 1m |v′ 1m )}, and the i-th corrected cross-correlation value R(β 1i |v′ 1i )for: In the formula, the modulation sequence The result after compensating the frequency offset and phase offset estimation value of v(k) is the demodulation sequence For v(k+β 1i )v(k) is the result after frequency offset and phase offset estimation are compensated, v′ 1i The demodulation sequence v1′ of the pilot block p1 and the pilot block p i The demodulation sequence v i ′; The corrected received data sequence obtained in step S4 The method is: S4.2: The frequency offset estimate and phase bias estimates Compensate to the received data sequence r d The corrected received data sequence is obtained from in, And the corrected received data signal r′(k) in the kth symbol period is:

8. The minimalist synchronization scheme based on dual correlation operators according to claim 7, characterized in that: Step S5 is to obtain the corrected cross-correlation operator R(β|v′) and the corrected received data sequence. The method of separating into multiple correction mutual correlation values and multiple correction received data blocks is: S5.1: Sampling index sets by data block Separate the corrected cross-correlation operator R(β|v′) into m-1 corrected cross-correlation values R(β 12 |v′ 12 ),R(β 13 |v′ 13 ),...,R(β 1m |v′ 1m ); S5.2: Sampling index sets by data block The received data sequence will be corrected Split into m-1 correction receiving data blocks 9. The minimalist synchronization scheme based on dual correlation operators according to claim 8, characterized in that: The method for compensating the block-related data in step S6 is: The m-1 corrected cross-correlation values R(β 12 |v′ 12 ),R(β 13 |v1′3),...,R(β 1m |v1′ m ) and m-1 corrected received data blocks Multiply them respectively to get m-1 secondary correction receiving data blocks And the lth secondary correction received data block The secondary correction received data signal in the kth symbol period Has the following form:

10. The minimalist synchronization solution based on dual correlation operators according to claim 9, characterized in that: Step S7 combines the obtained multiple secondary corrected received data blocks into a complete received data sequence r d 'The method is: Sampling index sets according to data blocks, m-1 secondary correction received data blocks Synthesize a complete receive data sequence

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