A method for symbol timing offset estimation and compensation in ambient backscatter communication

Abstract

The present application relates to symbol timing offset estimation and compensation method in ambient backscatter communication, the method comprises based on ambient backscatter communication network model, the influence of symbol timing offset is fused, the received signal model under symbol timing offset is built;Design backscatter transmitter transmission protocol, convert symbol timing offset estimation problem into change point detection problem, and adopt the estimator based on maximum likelihood cumulative sum to identify symbol mutation point to obtain the estimated value of symbol timing offset;According to the estimated value of symbol timing offset, the synchronization compensation of received signal is realized through time translation, the symbol decision is completed in combination with energy detector, the parameters required for detection threshold are estimated using synchronization pilot sequence, so that the detection threshold suitable for actual system is obtained.The present application can realize reliable estimation of symbol timing offset without relying on the cooperation of ambient radio frequency source, and theoretically depicts the statistical distribution law of residual symbol timing offset.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to a method for estimating and compensating symbol timing offset in environmental backscatter communication. Background Technology

[0002] Ambient Backscatter Communication (AmBC), by supporting low-power communication through passive dumb terminals, is one of the key technologies for realizing massive connectivity in the Ambient Internet of Things (AIoT). Unlike traditional IoT technologies, AmBC allows backscatter transmitters (BTs) to transmit information without the need for high-power components such as oscillators. Specifically, the BT achieves high spectral efficiency and ultra-low power communication by modulating its own information onto the incident ambient radio frequency (RF) signal. For reliable transmission in the AmBC system, accurate timing synchronization is crucial for the backscatter receiver (BR) to correctly recover BT symbols. However, due to the inherent startup delay during BR activation, symbol timing offset (STO) is unavoidable and significantly degrades symbol detection performance.

[0003] To address the aforementioned issues, existing technologies have proposed a low-power AmBC system called HitchHike, which achieves synchronization between the ambient RF source and the backscatter transmitter (BT) through energy edge detection. Subsequently, studies have proposed layered wake-up and synchronization protocols to further improve synchronization accuracy. However, both of these methods are based on energy detection mechanisms, requiring energy accumulation over a certain period, which limits synchronization accuracy. In contrast, another type of method employs a correlation-based synchronization mechanism, achieving synchronization between the ambient RF source and the BT, as well as between the BT and the backscatter receiver (BR). Some studies have further proposed symbol timing offset (STO) estimation methods based on expectation maximization, but these methods require the ambient RF source to transmit dedicated pilot signals. To alleviate the pilot dependency problem, some schemes achieve synchronization by correlation matching between the ambient RF source signal and the LTE base station synchronization signal. Building on this, template matching synchronization methods replace multiplication with addition through quantization operations, significantly reducing computational complexity. Subsequent studies have proposed discontinuous template matching schemes that further improve synchronization performance. However, all of the above methods assume that the ambient RF source signal is of the LTE standard. In practical applications, the ambient RF source signal of the AmBC system is often unknown to the backscattering device (BT / BR), and the lack of cooperation mechanisms between systems makes existing methods difficult to apply directly. To address this challenge, a timing synchronization method based on maximum likelihood (ML) has been proposed, but its performance is limited in low signal-to-noise ratio (SNR) scenarios, and it lacks theoretical analysis of estimation errors.

[0004] Therefore, it is necessary to study efficient STO estimation and compensation methods applicable to non-cooperative AmBC systems. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method for estimating and compensating symbol timing offset in environmental backscatter communication.

[0006] According to a first aspect of the present invention, a method for estimating and compensating symbol timing offset in environmental backscatter communication is provided, comprising the following steps: S1. Based on the environmental backscatter communication network model and considering the influence of symbol timing offset, establish an environmental backscatter received signal model under symbol timing offset. S2. Design a backscatter transmitter transmission protocol, realize backscatter receiver activation and coarse synchronization based on energy detection mechanism, and introduce observable synchronization error into the received synchronization signal through the transmission protocol, thereby transforming the symbol timing offset estimation problem into a change point detection problem. S3. Based on the received synchronization signal in step S2, construct a statistic based on the maximum likelihood cumulative sum to enhance the sensitivity to statistical changes in the received synchronization signal, thereby accurately identifying the location of symbol mutation points and obtaining an estimate of the symbol timing offset. S4. Using the symbol timing offset estimate obtained in step S3, perform time shift compensation on the received signal to reduce the impact of symbol timing offset on the received signal. S5. The energy detection mechanism is used to make symbol decisions on the compensated received signal, the symbol detection bit error rate after symbol timing offset compensation is analyzed, the parameters required for the detection threshold are estimated using the received synchronization signal, and the detection threshold applicable to the actual system is calculated accordingly. S6. Based on the estimated value of symbol timing offset obtained in S3, analyze the statistical distribution characteristics of the symbol timing offset estimation error.

[0007] Based on the above scheme, in step S1, the environmental backscatter received signal model under symbol timing offset is as follows: (1) in, , This represents the number of samples corresponding to each symbol. , This indicates the number of symbols transmitted by the backscatter transmitter during the coherence time. This indicates that under ideal synchronization (i.e.) The received signal at the receiver is expressed as follows: (2) in, , Indicates environmental radio frequency signals, This represents the thermal noise signal at the receiver. Symbols representing backscattered signals from the environment; It follows a complex Gaussian distribution, and its distribution function is expressed as: (3) in, , .

[0008] Based on the above scheme, step S2, designing a backscatter transmitter transmission protocol, realizing backscatter receiver activation and coarse synchronization based on an energy detection mechanism, and introducing observable synchronization error into the received synchronization signal through the transmission protocol, thereby transforming the symbol timing offset estimation problem into a change-point detection problem, specifically includes: The backscatter transmitter transmission protocol includes a preamble transmission phase and a data transmission phase; During the preamble transmission phase, a sequence of all "1" bits is first sent as a wake-up symbol. The backscatter receiver, based on an energy detection mechanism, monitors the rising or falling edge of the average energy within a sliding window to determine the symbol's start position, thereby activating the receiver and coarsely synchronizing it. Subsequently, a sequence of bits consisting of "1" bits is sent. A synchronization sequence consisting of several symbols, the synchronization sequence starting with bit "0" and using an alternating "0-1" structure, wherein each synchronization symbol corresponds to a continuous signal from an ambient radio frequency source. One symbol; At the environmental backscatter receiver, a width of [missing information] is used. Signal sampling is performed using a non-overlapping window. The received synchronization signal corresponding to each sampling window is defined as follows: ,in, , ; The receive synchronization signal corresponding to bit "0" is located at an odd index position, and can be represented as follows: The receive synchronization information corresponding to bit "1" is located at an even index position, which can be represented as... ; Affected by symbol timing offset, it belongs to The received synchronization signal will contain a sign mutation point within any sampling window.

[0009] Based on the above scheme, under symbol timing offset, it belongs to the set. The receiving synchronization signal model can be represented as: (4) in, Given the location of the mutation point, and Represents the channel coefficients, corresponding to the intervals respectively. and Furthermore, these parameters are unknown to the environmental backscatter receiver. and They represent the first Environmental radio frequency signals and noise signals within each sampling window; To ensure that the STO always resides within a single synchronization symbol and to effectively distinguish between early and late sampling, the parameters... Need to meet This assumption; The distribution can be represented as: (5) in, , .

[0010] Based on the above scheme, step S3, which involves constructing a maximum likelihood cumulative sum statistic based on the received synchronization signal from step S2 to enhance the sensitivity to statistical changes in the received synchronization signal, thereby identifying the location of symbol abrupt change points and obtaining an estimate of the symbol timing offset, specifically includes: S301, Calculate the first The probability density function of the received synchronization signal for each sampling window is expressed as: (6) S302, Calculation The first observation Log-likelihood ratio at each sampling point , represented as (7) Using the maximum likelihood estimation method to and Estimate the value of , and in the estimation, Approximately the midpoint of the sampling window Place; S303. Construct the maximum likelihood cumulative sum statistic. , represented as (8) in, This indicates the floor function; S304, Symbol Timing Offset Estimator maximizes Determine the estimated value ,Right now (9) The above optimization problem can be solved by considering all candidate indexes. Perform a search to find the solution; Based on the estimation Symbol timing offset estimate It can be represented as (10) Based on the above scheme, in step S302, and The estimated values ​​are respectively and .

[0011] Based on the above scheme, step S4, which involves time-shifting the received signal under the symbol timing offset to eliminate the offset based on the symbol timing offset estimate obtained in step S3, specifically includes: By analyzing the received signal Perform the corresponding time shift to obtain the compensated signal. Its expression is (11) like The received signal will then shift forward. One sample; if The received signal will then shift backward. One sample.

[0012] Based on the above scheme, in S5, the step of using an energy detection mechanism to perform symbol decision on the compensated received signal and analyzing the bit error rate after symbol timing offset compensation specifically includes: The detection performance of the proposed compensation method is evaluated using an energy detector, and the decision criterion is as follows: (12) in, Indicates the first The estimated value of each symbol, , The detection threshold is expressed as follows: (13) In the formula, This represents the average power when the transmitted symbol is "0". This represents the average power when the transmitted symbol is "1"; Assuming the backscatter transmitter sends bits "0" and "1" with equal probability, that is... The bit error rate of the system can then be expressed as: (14) in, , , Gauss function.

[0013] Based on the above scheme, in S5, the step of estimating the parameters required for the detection threshold using the received synchronization signal and calculating the detection threshold applicable to the actual system accordingly specifically includes: The detection threshold in equation (13) needs to be known. and Using the compensated synchronization signal to and The estimation is performed, and its expressions are as follows: (15) (16) Based on this, by and Substituting into equation (13) yields the detection threshold in the actual system.

[0014] Based on the above scheme, step S6, analyzing the statistical distribution characteristics of the symbol timing offset estimation error based on the estimated value of the symbol timing offset obtained in S3, specifically includes: The residual symbol timing offset of the symbol timing offset estimator is defined as... (17) in, This represents the actual symbol timing offset value. Based on this, the asymptotic residual symbol timing offset is defined as... ,in Indicates asymptotic conditions The symbol timing offset estimate obtained below; Under asymptotic conditions, the residual symbol timing offset can be approximated as: (19) in, , To and Fisher information content of relevant variance parameters , Represents random variables The cumulative distribution function is expressed as: (18) in This represents the cumulative distribution function of the Gaussian distribution.

[0015] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects: This invention provides a method for STO estimation and compensation without relying on environmental RF source cooperation. First, for non-cooperative AmBC systems, a transmission protocol including a preamble transmission phase and a data transmission phase is designed at the BT (Bit Transmission Point), employing a synchronization sequence consisting of alternating 0 and 1 bits. Based on the statistical differences introduced by this structure, the STO estimation problem is modeled as a change-point detection problem, and a novel STO estimator based on maximum likelihood cumulative sum is proposed. The estimated STO is then used to compensate the received signal. Furthermore, to characterize the performance of the proposed method, the asymptotic distribution of residual symbol timing offset is derived. Simulation results show that the proposed STO estimation and compensation method can achieve effective symbol timing synchronization without environmental RF source cooperation. In addition, the derived analytical expression for RSTO is highly consistent with its empirical distribution, revealing key system parameters affecting RSTO. Compared with existing methods, the proposed method significantly improves the estimation accuracy of symbol timing offset, effectively alleviating the symbol detection performance degradation caused by symbol timing offset, and providing support for the application of environmental backscatter communication in the Internet of Things (IoT). Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of an environmental backscatter communication network system model with STO present according to an exemplary embodiment; Figure 2 This is a schematic diagram of the architecture of a backscatter transmitter transmission protocol according to an exemplary embodiment; Figure 3 This is a schematic diagram illustrating the presence of a receive synchronization signal in the next sampling window of an STO according to an exemplary embodiment (shown). (situation) Figure 4 This is a schematic diagram illustrating the presence of a receive synchronization signal in the next sampling window of an STO according to an exemplary embodiment (shown). (situation) Figure 5 This is a graph illustrating the relationship between MAE and SNR under CG and PSK radio frequency sources according to an exemplary embodiment. Figure 6 A comparison diagram of RSTO distribution between the method of the present invention and a prior art method according to an exemplary embodiment (showing the method of the present invention). Figure 7 A comparison diagram of RSTO distribution between the method of the present invention and a prior art method according to an exemplary embodiment (showing the prior art method); Figure 8 As illustrated in an exemplary embodiment and Comparison of BER performance under different conditions (shown) (situation) Figure 9 As illustrated in an exemplary embodiment and Comparison of BER performance under different conditions (shown) (The situation). Detailed Implementation

[0018] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0019] Figure 1 A model of an AmBC network system with Symbol Timing Offset (STO) is shown, the system comprising: An ambient radio frequency source used to provide the initial radio frequency signal; A backscatter transmitter used to modulate radio frequency signals received from an ambient radio frequency source; And a backscatter receiver used to receive signals reflected from a backscatter transmitter and demodulate them to recover the original data information.

[0020] Specifically, the ambient radio frequency (RF) source does not provide a dedicated pilot signal. Since the ambient RF signal is unknown to both the backscatter transmitter (BT) and the backscatter receiver (BR), it is modeled as a complex Gaussian (CG) random variable. The backscatter transmitter (BT) uses on-off keying (OOK) to modulate its own information onto the incident ambient RF signal and reflect it back. Each backscatter transmitter (BT) symbol corresponds to a consecutive element of the ambient RF source. A symbol. Let... , and Let represent the channel coefficients from the ambient radio frequency source to the backscatter receiver (BR), from the ambient radio frequency source to the backscatter transmitter (BT), and from the backscatter transmitter (BT) to the backscatter receiver (BR), respectively. It is assumed that all channels experience frequency flat block fading, meaning that the channel coefficients remain constant within each channel coherence time, but change independently between different coherence times.

[0021] Since the actual arrival time of the first data symbol is unknown to the backscatter receiver (BR), the initial sampling time may be earlier or later than the actual symbol arrival time, resulting in a symbol timing offset (STO), denoted as . Specifically, when "Time" indicates advance sampling, while This indicates delayed sampling. Due to the existence of STO, the samples collected by the current symbol may contain data from neighboring symbols. The nth sample received at BR at this time. The symbolic signal can be represented as a time-shifted form of an ideal synchronization signal, and its expression is: (1) in, , This represents the number of samples corresponding to each symbol. , Indicates the number of BT symbols. This indicates that under ideal synchronization conditions (i.e.) The received signal of BR is expressed as follows: (2) in, , Indicates environmental radio frequency signals, This represents the thermal noise signal at BR. This represents the symbol sent by BT. Furthermore, It follows a CG distribution, and its probability distribution is: (3) in, , .

[0022] when When the value is large, the signal received by the current symbol will contain a large number of samples from neighboring symbols. This will cause the statistical characteristics of the received signal to deviate from the true symbol distribution given by equation (3) in the presence of STO, making it difficult for the backscatter receiver (BR) to correctly recover the symbols transmitted by the backscatter transmitter (BT). Therefore, accurate STO estimation and compensation become a critical issue.

[0023] An embodiment of the symbol timing offset estimation and compensation method in environmental backscatter communication of the present invention.

[0024] In this embodiment, the method disclosed in this invention includes the following steps: S1. Based on the environmental backscatter communication network model and considering the influence of symbol timing offset, establish an environmental backscatter received signal model under symbol timing offset. S2. Design a backscatter transmitter transmission protocol, realize backscatter receiver activation and coarse synchronization based on energy detection mechanism, and introduce observable synchronization error into the received synchronization signal through the transmission protocol, thereby transforming the symbol timing offset estimation problem into a change point detection problem. S3. Based on the received synchronization signal in step S2, construct a statistic based on the maximum likelihood cumulative sum to enhance the sensitivity to statistical changes in the received synchronization signal, thereby accurately identifying the location of symbol mutation points and obtaining an estimate of the symbol timing offset. S4. Using the symbol timing offset estimate obtained in step S3, perform time shift compensation on the received signal to reduce the impact of symbol timing offset on the received signal. S5. The energy detection mechanism is used to make symbol decisions on the compensated received signal, the symbol detection bit error rate after symbol timing offset compensation is analyzed, the parameters required for the detection threshold are estimated using the received synchronization signal, and the detection threshold applicable to the actual system is calculated accordingly. S6. Based on the estimated value of symbol timing offset obtained in S3, analyze the statistical distribution characteristics of the symbol timing offset estimation error.

[0025] This application first designs a transmission protocol at the Bit Transmission Point (BT) of a non-cooperative AmBC system, including a preamble transmission phase and a data transmission phase, and employs a synchronization sequence consisting of alternating "0" and "1" bits. Based on the statistical differences introduced by this structure, the STO estimation problem is modeled as a change-point detection problem, and a novel STO estimator based on maximum likelihood cumulative sum (ML-CUSUM) is proposed, which is then used to compensate the received signal. Furthermore, to characterize the performance of the proposed method, the asymptotic distribution of the residual symbol timing offset (RSTO) is derived. Simulation results show that the proposed STO estimation and compensation method can achieve effective symbol timing synchronization without the need for environmental RF source cooperation. In addition, the derived analytical expression for RSTO is highly consistent with its empirical distribution, and key system parameters affecting RSTO are revealed.

[0026] The symbol timing offset estimation and compensation method in environmental backscatter communication of this embodiment will be further explained below.

[0027] S1. Based on the environmental backscatter communication network model and considering the influence of symbol timing offset, establish an environmental backscatter received signal model under symbol timing offset. S2. Design a backscatter transmitter transmission protocol, realize backscatter receiver activation and coarse synchronization based on energy detection mechanism, and introduce observable synchronization error into the received synchronization signal through the transmission protocol, thereby transforming the symbol timing offset estimation problem into a change point detection problem. like Figure 2As shown, the proposed backscatter transmitter (BT) transmission protocol consists of two phases: a preamble phase and a data transmission phase. In the preamble phase, the BT first sends a sequence of all "1" bits as a wake-up symbol. The BR, based on an energy detection mechanism, monitors the rising or falling edge of the average energy within a sliding window to achieve BR wake-up and coarse synchronization. Since the energy decision is based on energy accumulation within a finite window, a certain synchronization error is inevitably introduced; this error is known as STO. Subsequently, the BT transmits data of length... The synchronization sequence, which begins with bit "0" and uses an alternating "0-1" structure, wherein, This represents the number of "0-1" bit pairs, with each synchronization symbol corresponding to a consecutive bit from the ambient radio frequency source. 1 symbol. At BR, the sampling uses a width of 1. The non-overlapping window is used. The received synchronization signal corresponding to each sampling window is defined as follows: ,in, , Based on this, the receive synchronization signal corresponding to bit "0" is located at an odd index position, and can be represented as follows: The receive synchronization information corresponding to bit "1" is located at an even index position, which can be represented as... .

[0028] In the presence of an STO, it belongs to The received synchronization signal will contain a sign abrupt change point within any sampling window, such as... Figure 3 As shown. Specifically, as Figure 3 As shown, when pre-sampling occurs (i.e. When ), the sign mutation point is located at ;like Figure 4 As shown, when hysteresis sampling occurs (i.e. When ), the sign mutation point is located at Therefore, the STO estimation problem can be equivalently modeled as the problem of detecting symbol abrupt changes within a sampling window. Based on this, for a given... , The Middle The received synchronization signal of each index can be represented as (4) in, and Represents the channel coefficients, corresponding to the intervals respectively. and And it is an unknown parameter for BR. and They represent the first Environmental radio frequency signals and noise signals within each sampling window.

[0029] Note 1: To ensure that the STO always resides within a single synchronization symbol and to effectively distinguish between early sampling and delayed sampling, the parameters... Need to meet This assumption.

[0030] According to equation (3). The distribution can be expressed as (5) in, , .

[0031] S3. Based on the received synchronization signal in step S2, construct a statistic based on the maximum likelihood cumulative sum to enhance the sensitivity to statistical changes in the received synchronization signal, thereby accurately identifying the location of symbol mutation points and obtaining an estimate of the symbol timing offset. Specifically, S301, calculate the first The probability density function of the received synchronization signal for each sampling window; The probability density function (PDF) is expressed as: (6) S302, Calculation The first observation Log-likelihood ratio at each sampling point ; Given Includes The synchronization signal observed independently, the first The log-likelihood ratio at each sampling point can be expressed as: (7) In the above formula, and The value of is unknown. Therefore, the machine learning (ML) method is used to estimate it, and Approximately the midpoint of the sampling window Based on this, and The estimated values ​​are respectively and .

[0032] S303. Construct the maximum likelihood cumulative sum statistic. ; Based on the above estimation results, we further construct the cumulative and log-likelihood statistics. (8) in, This indicates the floor function.

[0033] S304, Symbol Timing Offset Estimator maximizes Determine the estimated value ,Right now The proposed STO estimator maximizes Determine the estimated value ,Right now (9) The above optimization problem can be solved by considering all candidate indexes. A search is performed to find the solution. Based on the estimated... STO estimate It can be represented as (10) Note 2: Unlike existing technologies that use log-likelihood statistics, the estimator proposed in this invention uses ML-CUSUM statistics to accumulate the log-likelihood difference, thereby enhancing the sensitivity to subtle statistical changes under low SNR conditions.

[0034] Note 3: The above derivation assumes that the ambient radio frequency signal follows a CG distribution. When the ambient radio frequency source uses phase shift keying (PSK) modulation, the received synchronization signal follows a Gaussian mixture model, which means that the calculation of the relevant expressions requires known channel state information. However, since equations (7) and (9) only depend on second-order statistics, the received signal can be modeled using a moment-matched complex Gaussian approximation. Therefore, the proposed method is still applicable to PSK-modulated ambient radio frequency sources in practical situations.

[0035] S4. Using the symbol timing offset estimate obtained in step S3, perform time shift compensation on the received signal to reduce the impact of symbol timing offset on the received signal. Specifically, to mitigate the adverse effects of STO on symbol detection performance, the received signal can be compensated based on the estimated STO. Specifically, the compensated signal is obtained by performing a corresponding time shift on the received signal, and its expression is: (11) like The signal then shifts forward. One sample; like The signal will then shift backward. One sample.

[0036] S5. The energy detection mechanism is used to make symbol decisions on the compensated received signal, the symbol detection bit error rate after symbol timing offset compensation is analyzed, the parameters required for the detection threshold are estimated using the received synchronization signal, and the detection threshold applicable to the actual system is calculated accordingly. Specifically, the detection performance of the proposed compensation method is evaluated using an energy detector, and the decision criterion is as follows: (12) in, Indicates the first The estimated value of each symbol, , The detection threshold is expressed as follows: (13) Assuming that BT transmits bits "0" and "1" with equal probability, that is... Then the system's bit error rate (BER) can be expressed as: (14) in, , , Gauss function.

[0037] The detection threshold in equation (13) needs to be known. and However, in practical systems, these parameters are usually unknown and generally require estimation using additional pilot symbols. To avoid additional pilot overhead, this application directly utilizes the compensated synchronization signal. and The estimation is performed, and its expressions are as follows: (15) (16) Based on this, by and Substituting into equation (13) yields the detection threshold in the actual system.

[0038] S6. Based on the estimated value of symbol timing offset obtained in S3, analyze the statistical distribution characteristics of the symbol timing offset estimation error.

[0039] In practical systems, synchronization estimation errors are unavoidable. Therefore, the residual symbol timing offset (RSTO) of the proposed estimator is defined as follows: (17) in, This represents the actual STO value.

[0040] Although increasing the synchronization sequence length can improve estimation accuracy and reduce RSTO, the sequence length is determined by... and The RSTO is jointly determined by these two parameters, as well as other system parameters, but their impact on RSTO remains unclear. Therefore, it is necessary to model the statistical distribution of RSTO to reveal the mechanism by which each parameter influences it, and to further theoretically validate the effectiveness of the proposed estimator. However, directly obtaining... The closed-form expression for the distribution is very difficult. Therefore, the asymptotic RSTO is defined as follows: ,in Indicates asymptotic conditions The STO estimate obtained below. Further, let... and define To and Fisher information content of the relevant variance parameters. Let The limiting distribution is described below using Lemma 1.

[0041] Lemma 1: Under asymptotic conditions Below, random variables The distribution can be approximated by having a cumulative distribution function (CDF). The distribution of is expressed in equation (18), where Let represent the CDF of a Gaussian distribution. This CDF satisfies the symmetry property. Therefore, .

[0042] (18) In AmBC systems, the backscattered signal undergoes multiplicative fading, and its power is typically much smaller than that of the direct link signal. Therefore, Typically smaller, thus satisfying asymptotic conditions.

[0043] Based on Lemma 1, we can further obtain The distribution of is summarized in Theorem 1.

[0044] Theorem 1: Asymptotic RSTO The probability mass function (PMF) can be approximated as: (19) Proof: For The synchronization signal for the next observation is defined. ,in According to Lemma 1, in Fixed and satisfying asymptotic conditions When, random variable Converging with respect to a random variable according to its distribution Its CDF is As shown in equation (18). Since both the true STO and its estimated value correspond to discrete sampling indices, therefore Let it be a random variable with integer values. Therefore, The probability mass corresponding interval By introducing a continuity correction, we can obtain... (A.1) Thus, Theorem 1 is proved.

[0045] Note 4: As can be seen from equation (19), the distribution of the asymptotic RSTO is entirely determined by the composite scaling factor. What it depicts. This indicates The performance is also affected by the number of "0-1" synchronization bit pairs. ,and Fisher information related to variance parameters And the difference in received signal power between bit "0" and bit "1". The combined effects. When When it increases, PMF will gradually focus on This reduces RSTO by being located nearby.

[0046] The effectiveness of the proposed estimator is verified through simulation results. For ease of comparison and analysis, this invention uses the same parameter settings as existing technologies, specifically as follows: channel coefficients. , and All obey Distribution, noise power set to 1, SNR defined as The number of samples for each synchronization symbol is set to STO set to or Mean Absolute Error (MAE) is defined as follows: Error in sub-independent trials The average value.

[0047] First, the STO estimation accuracy under CG and PSK RF source conditions is evaluated. Quadrature Phase Shift Keying (QPSK) is used in the simulation. Figure 5 Different The MAE as a function of SNR is plotted and compared with existing methods. Under CG environment RF source conditions, the proposed estimator achieves a smaller MAE across all SNR ranges, with a particularly significant advantage in the low SNR region. For example, when the SNR is 5 dB and At that time, the MAE of the proposed method was 0.9347, while the MAE of the prior art method was 2.992. Furthermore, with the increase in SNR and... As the value increases, the MAE gradually decreases, indicating a larger... A higher SNR helps improve the accuracy of STO estimation. Under QPSK environment RF source conditions, the proposed estimator can also work effectively and obtain a smaller MAE, thus verifying the conclusion in Note 3.

[0048] Subsequently, the RSTO distribution of the proposed estimator was evaluated, and the accuracy of the theoretical analysis results was verified. Figures 6-7 The RSTO distribution of the proposed method was compared with that of existing methods. The SNR was set to 10 dB in the simulation. ,and In the interval or Random selection from within. For example... Figure 6 As shown, the theoretical distribution of RSTO is close to the empirical distribution obtained from simulation, thus verifying the theoretical result of equation (19). Since Theorem 1 is based on asymptotic conditions... It was established below, while in the simulation Since these are finite values, a certain degree of deviation is reasonable. For example... Figure 7 As shown, the RSTO distribution of the existing method is more dispersed than that of the proposed method, indicating that the proposed method has higher STO estimation accuracy.

[0049] at last, Figures 8-9 The BER performance was compared under different conditions, among which Figure 8 It shows and Figure 9 It shows The comparison scenarios include: no STO compensation, STO compensation, using the method of this invention and the estimated detection threshold, using the method of this invention and the ideal detection threshold, and ideal synchronization. The results show that STO significantly degrades symbol detection performance, while compensation using the proposed estimator effectively mitigates this performance loss. Furthermore, the proposed compensation method significantly outperforms existing methods in detection performance. Moreover, the BER obtained using the estimated threshold is very close to the ideal threshold result, verifying the accuracy of the proposed practical threshold estimation method.

[0050] This invention investigates the STO estimation problem in non-cooperative AmBC systems. A synchronization sequence and transmission protocol are designed at the BT (Brain Transmission) stage, and a novel STO estimation and compensation method is proposed at the BR (Brain Transmission) stage. Furthermore, the statistical distribution of RSTO is analyzed under asymptotic conditions, and its closed-form approximation expression is derived, further revealing the influence mechanism of system parameters on RSTO. Simulation results show a high degree of consistency between the theoretical analysis and simulation results, and the proposed estimator achieves high synchronization accuracy while significantly improving BER (Brain Performance) performance in the presence of STO.

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[17] Y.-C. Yao, “Approximating the distribution of the maximumlikelihood estimate of the change-point in a sequence of independent random variables,” The Annals of Statistics, vol. 15, no. 3, pp. 1321-1328, 1987. In summary, this invention addresses the STO estimation problem in non-cooperative AmBC systems. A synchronization sequence and transmission protocol are designed at the BT (Brain Transmission) stage, and a novel STO estimation and compensation method is proposed at the BR (Brain Transmission) stage. Furthermore, the statistical distribution of RSTO is analyzed under asymptotic conditions, and its closed-form approximation expression is derived, further revealing the influence mechanism of system parameters on RSTO. Simulation results show a high degree of consistency between the theoretical analysis and simulation results, and the proposed estimator achieves high synchronization accuracy while significantly improving BER (Brain Performance) performance in the presence of STO.

[0052] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. The above descriptions are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for estimating and compensating symbol timing offset in environmental backscatter communication, characterized in that, Includes the following steps: S1. Based on the environmental backscatter communication network model and considering the influence of symbol timing offset, establish an environmental backscatter received signal model under symbol timing offset. S2. Design a backscatter transmitter transmission protocol, realize backscatter receiver activation and coarse synchronization based on energy detection mechanism, and introduce observable synchronization error into the received synchronization signal through the transmission protocol, thereby transforming the symbol timing offset estimation problem into a change point detection problem. S3. Based on the received synchronization signal in step S2, construct a statistic based on the maximum likelihood cumulative sum to enhance the sensitivity to statistical changes in the received synchronization signal, thereby accurately identifying the location of symbol mutation points and obtaining an estimate of the symbol timing offset. S4. Using the symbol timing offset estimate obtained in step S3, perform time shift compensation on the received signal to reduce the impact of symbol timing offset on the received signal. S5. The energy detection mechanism is used to make symbol decisions on the compensated received signal, the symbol detection bit error rate after symbol timing offset compensation is analyzed, the parameters required for the detection threshold are estimated using the received synchronization signal, and the detection threshold applicable to the actual system is calculated accordingly. S6. Based on the estimated value of symbol timing offset obtained in S3, analyze the statistical distribution characteristics of the symbol timing offset estimation error.

2. The symbol timing offset estimation and compensation method in environmental backscatter communication according to claim 1, characterized in that, In step S1, the environmental backscatter received signal model under symbol timing offset is as follows: (1) in, , This represents the number of samples corresponding to each symbol. , This indicates the number of symbols transmitted by the backscatter transmitter during the coherence time. This indicates that under ideal synchronization (i.e.) The received signal at the receiver is expressed as follows: (2) in, , Indicates environmental radio frequency signals, This represents the thermal noise signal at the receiver. Symbols representing backscattered signals from the environment; It follows a complex Gaussian distribution, and its distribution function is expressed as: (3) in, , .

3. The symbol timing offset estimation and compensation method in environmental backscatter communication according to claim 1, characterized in that, S2, designing a backscatter transmitter transmission protocol, realizing backscatter receiver activation and coarse synchronization based on an energy detection mechanism, and introducing observable synchronization error into the received synchronization signal through the transmission protocol, thereby transforming the symbol timing offset estimation problem into a change-point detection problem, specifically includes: The backscatter transmitter transmission protocol includes a preamble transmission phase and a data transmission phase; During the preamble transmission phase, a sequence of all "1" bits is first sent as a wake-up symbol. The backscatter receiver, based on an energy detection mechanism, monitors the rising or falling edge of the average energy within a sliding window to determine the symbol's start position, thereby activating the receiver and coarsely synchronizing it. Subsequently, a sequence of bits consisting of "1" bits is sent. A synchronization sequence consisting of several symbols, the synchronization sequence starting with bit "0" and using an alternating "0-1" structure, wherein each synchronization symbol corresponds to a continuous signal from an ambient radio frequency source. One symbol; At the environmental backscatter receiver, a width of [missing information] is used. Signal sampling is performed using a non-overlapping window. The received synchronization signal corresponding to each sampling window is defined as follows: ,in, , ; The receive synchronization signal corresponding to bit "0" is located at an odd index position, and can be represented as The receive synchronization information corresponding to bit "1" is located at an even index position, and can be represented as... ; Affected by symbol timing offset, it belongs to The received synchronization signal will contain a sign mutation point within any sampling window.

4. The symbol timing offset estimation and compensation method in environmental backscatter communication according to claim 3, characterized in that, Belongs to the set under symbolic timing offset The receiving synchronization signal model can be represented as: (4) in, Given the location of the mutation point, and Represents the channel coefficients, corresponding to the intervals respectively. and Furthermore, these are unknown parameters for the environmental backscatter receiver. and They represent the first Environmental radio frequency signals and noise signals within each sampling window; To ensure that the STO always resides within a single synchronization symbol and to effectively distinguish between early and late sampling, the parameters... Need to meet This assumption; The distribution can be represented as: (5) in, , .

5. The symbol timing offset estimation and compensation method in environmental backscatter communication according to claim 1, characterized in that, The step S3, which involves constructing a maximum likelihood cumulative sum statistic based on the received synchronization signal from step S2 to enhance sensitivity to statistical changes in the received synchronization signal, thereby identifying the location of symbol abrupt change points and obtaining an estimate of the symbol timing offset, specifically includes: S301, Calculate the first The probability density function of the received synchronization signal for each sampling window is expressed as: (6) S302, Calculation The first observation The log-likelihood ratio at each sampling point , represented as (7) Using the maximum likelihood estimation method to and Estimate the value of , and in the estimation, Approximately the midpoint of the sampling window Place; S303. Construct the maximum likelihood cumulative sum statistic. , represented as (8) in, This indicates a floor operation; S304, the sign timing offset estimator, maximizes... Determine the estimated value ,Right now (9) The above optimization problem can be solved by considering all candidate indexes. Perform a search to find the solution; Based on the estimation Symbol timing offset estimate It can be represented as (10)。 6. The symbol timing offset estimation and compensation method in environmental backscatter communication according to claim 5, characterized in that, In step S302 and The estimated values ​​are respectively and .

7. The symbol timing offset estimation and compensation method in environmental backscatter communication according to claim 1, characterized in that, Step S4, the step of time-shifting the received signal under symbol timing offset to eliminate the offset based on the symbol timing offset estimate obtained in step S3, specifically includes: By analyzing the received signal Perform the corresponding time shift to obtain the compensated signal. Its expression is (11) like The received signal will then shift forward. One sample; like The received signal will then shift backward. One sample.

8. The symbol timing offset estimation and compensation method in environmental backscatter communication according to claim 1, characterized in that, In S5, the step of using an energy detection mechanism to perform symbol decision on the compensated received signal and analyzing the bit error rate after symbol timing offset compensation specifically includes: The detection performance of the proposed compensation method is evaluated using an energy detector, and the decision criterion is as follows: (12) in, Indicates the first The estimated value of each symbol, , The detection threshold is expressed as follows: (13) In the formula, This represents the average power when the transmitted symbol is "0". This represents the average power when the transmitted symbol is "1"; Assuming the backscatter transmitter sends bits "0" and "1" with equal probability, that is... The bit error rate of the system can then be expressed as: (14) in, , , Gauss function.

9. The symbol timing offset estimation and compensation method in environmental backscatter communication according to claim 8, characterized in that, In S5, the step of estimating the parameters required for the detection threshold using the received synchronization signal and calculating the detection threshold applicable to the actual system accordingly specifically includes: The detection threshold in equation (13) needs to be known. and Using the compensated synchronization signal to and The estimation is performed, and its expressions are as follows: (15) (16) Based on this, by and Substituting into equation (13) yields the detection threshold in the actual system.

10. The symbol timing offset estimation and compensation method in environmental backscatter communication according to claim 1, characterized in that, Step S6, analyzing the statistical distribution characteristics of the symbol timing offset estimation error based on the estimated value of the symbol timing offset obtained in S3, specifically includes: The residual symbol timing offset of the symbol timing offset estimator is defined as... (17) in, This represents the actual symbol timing offset value. Based on this, the asymptotic residual symbol timing offset is defined as... ,in Indicates asymptotic conditions The symbol timing offset estimate obtained below; Under asymptotic conditions, the residual symbol timing offset can be approximated as: (19) in, , To and Fisher information content of relevant variance parameters , Represents random variables The cumulative distribution function is expressed as: (18) in This represents the cumulative distribution function of the Gaussian distribution.

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