A Carrier Frequency Offset Estimation and Compensation Method for Zero-Pilot OCDM Underwater Acoustic Communication in the Fresnel Domain

Abstract

The present invention discloses a carrier frequency offset estimation and compensation method for Fresnel domain zero-pilot OCDM underwater acoustic communication, which relates to the field of underwater acoustic communication. Considering the current situation of energy limitation of underwater transmitting devices, the present invention uses the method of inserting zero suffixes to eliminate the interference between OCDM signal blocks. For the two cases where the underwater acoustic channel delay is known and unknown, by utilizing the characteristic that the energy of the zero-pilot in the Fresnel domain is zero, a CFO estimation metric is established, and different carrier frequency offset estimation and compensation methods are designed. The present invention is carried out on the basis that the OCDM signal has completed the detection and synchronization work and the preliminary compensation of Doppler shift at the receiving end. By finding the minimum value of the CFO estimation metric of the zero-pilot in the Fresnel domain of the OCDM system, the optimal CFO candidate value is determined, and the carrier frequency offset parameters of the received signal are estimated and compensated. The present invention effectively improves the feasibility and communication effect of OCDM signals in underwater communication and reduces the energy consumption of device information processing.

Description

Technical Field

[0001] The present invention relates to the field of underwater acoustic communication, and particularly to a carrier frequency offset estimation and compensation method for Fresnel domain zero-pilot OCDM underwater acoustic communication. Background Art

[0002] Orthogonal Chirp Division Multiplex (OCDM) is a newly proposed multi-carrier modulation technology in recent years. This technology uses orthogonal chirp signals to modulate payload information, which is mathematically represented as the Fresnel transform to achieve the mutual transformation between the time domain and the Fresnel domain. This transform is similar to the Fourier transform in Orthogonal Frequency Division Multiplex (OFDM). The OCDM modulation method exhibits good anti-interference performance against burst interference in both the time domain and the frequency domain, and is currently widely used in optical communication scenarios. However, the OCDM modulation method is sensitive to carrier frequency offset, and the transmitted signal in the underwater environment will also have a large frequency offset. The influence of this offset cannot be completely eliminated only by resampling operations. In addition, the underwater acoustic signal transmission environment is mostly an energy-limited scenario, and the zero suffix technology is more widely used. Currently, the common OCDM carrier frequency offset estimation algorithms for adding cyclic prefixes cannot be directly applied to OCDM signals with zero suffixes. At the same time, the use of existing OCDM carrier frequency offset estimation algorithms depends on the information of the channel delay length, which is often difficult to obtain in underwater acoustic communication. Therefore, considering the above situation and the known and unknown channel delays, designing a carrier frequency offset estimation and compensation method for the Fresnel domain zero-pilot OCDM system is an important idea to improve the performance of the OCDM underwater acoustic communication system.

[0003] The domestic application number 202010708335.4 with the title "A Low-Complexity Frequency-Selective Channel Estimation Method for Orthogonal Chip Multiplexing Modulation" provides a low-complexity channel estimation method for OCDM systems, which can be used to estimate channel parameters with multipath characteristics. The domestic application number 201710793527.8 with the title "A Mobile Underwater Acoustic Communication Method" provides an underwater acoustic communication method for the OCDM system transmitter to supplement the order scanning search iterative algorithm to reduce the computational complexity and reduce the influence of Doppler frequency shift. The domestic application number 201510919217.7 with the title "A Carrier Frequency Offset Estimation Method and System" provides a system for correcting the carrier frequency offset before the OFDM signal is transmitted. Although the above methods have explored the application advantages of the OCDM system in different scenarios to a certain extent, and the methods for the OFDM system to cope with carrier offset, they do not point out how to estimate the carrier frequency offset of the OCDM system using zero suffixes in the underwater acoustic communication environment, which limits the communication effect obtained by the zero-pilot OCDM system in the Fresnel domain in underwater acoustic communication.

[0004] Therefore, those skilled in the art are committed to developing a carrier frequency offset estimation and compensation method for zero-pilot OCDM underwater acoustic communication. The present invention is directed to an OCDM underwater acoustic communication system, and proposes a carrier frequency offset estimation and compensation method based on the zero-pilot OCDM underwater acoustic communication system in the Fresnel domain. Different from the traditional OCDM carrier frequency offset estimation and compensation method, the present invention comprehensively considers the current situation of limited energy in underwater acoustic communication and difficult-to-obtain channel information, and designs a carrier frequency offset estimation algorithm for OCDM signals using zero suffixes considering known and unknown channel delays. The energy of the zero-pilot in the Fresnel domain is used as a measure for carrier frequency offset estimation to find the best candidate value for carrier frequency offset as the final carrier frequency offset estimation value. It realizes the purpose of estimating the carrier frequency offset within the OCDM system using zero suffixes under the conditions of known and unknown underwater channel delays, and achieves a better underwater acoustic communication effect. Summary of the Invention

[0005] In view of the above-mentioned defects of the prior art, the technical problem to be solved by the present invention is to achieve the purpose of estimating the carrier frequency offset within the OCDM system using zero suffixes under the conditions of known and unknown underwater channel delays, and achieve a better underwater acoustic communication effect.

[0006] To achieve the above object, the present invention provides a carrier frequency offset estimation and compensation method for zero-pilot OCDM underwater acoustic communication, including the following steps:

[0007] Step 1: Generate an OCDM modulation signal with a length of M = 2L + N using a pilot symbol p(i) with a length of L in the Fresnel domain, a zero-pilot symbol 0 with a length of L, and a data symbol d(i) with a length of N Among them is the inverse Fresnel transform matrix, including M subcarriers, and allocating energy E;

[0008] Step 2: Perform serial-to-parallel conversion work, and add a preamble v with a length of L pre ,v post and a guard interval with a length of N g to generate a transmission sequence, and use the preamble to complete signal detection and preliminary compensation operations for the Doppler scaling factor;

[0009] Step 3: For the resampled signal, express the OCDM received signal under the influence of carrier frequency offset Among them is the carrier frequency offset normalized by the carrier frequency space, and D M+L (w o ) is the influence of the intra-block carrier frequency offset, H is the multipath channel parameter matrix, and w(i) is the additive white Gaussian noise;

[0010] Step 4: Select candidate values of the carrier frequency offset We give the received signal after compensating the carrier frequency offset Perform a time-domain superposition operation R OLA and a Fresnel domain shifting operation Φ M , and obtain the preprocessed signal under the condition of the candidate value of the carrier frequency offset Considering the maximum channel delay L h in both known and unknown cases to construct a carrier frequency offset estimation metric. L h When it is known, the zero pilot in the pre-compensated signal Among them, r null (L h ) is the zero pilot selection vector with L h known; when L h is unknown, the zero pilot in the pre-equalized signal Among them, r null (0) is the zero pilot selection vector with L h unknown, where is the inverse Fourier transform matrix, G is the equalization matrix, and Γ M is the Fresnel parameter matrix.

[0011] Step 5: Use the Fresnel domain zero pilots u null extracted in the two cases respectively, calculate the corresponding energy of the zero pilot, and use this as the estimation metric of the carrier frequency offset

[0012] Step 6: After calculating the estimation metrics of all candidate values of the carrier frequency offset , find the minimum value of the estimation metric and determine the corresponding is the optimal carrier frequency offset estimation value, and the calculation method of the optimal carrier frequency offset estimation value is

[0013] Step 7, according to the estimated optimal carrier frequency offset estimation value Compensate the OCDM received signal y(i) to obtain the compensated signal z(i);

[0014] Step 8, perform preprocessing operations on the signal z(i) compensated using the optimal carrier frequency offset estimation value to obtain the preprocessed signal where Φ M is the Fresnel transform matrix, and R OLA is the cyclic superposition operation; perform channel estimation operations to obtain the MMSE channel estimator and the ZF channel estimator Perform equalization operations on the preprocessed signal to estimate the data symbols in the OCDM system

[0015] Furthermore, Steps 4 to 6 are the steps of calculating the estimation metric of the carrier frequency offset candidate values. For different carrier frequency offset candidate values it is necessary to calculate their estimation metrics one by one, find the minimum metric, and select the corresponding optimal carrier frequency offset estimation value.

[0016] Furthermore, Steps 4 to 6 can use a two-step coarse and fine search algorithm to reduce the computational complexity. Use a coarse step size μ in the candidate range of [0,1) c to perform a coarse search to obtain a coarse carrier frequency offset estimation Secondly, in the candidate range of use a fine step size to perform a fine two-way search. According to the required accuracy, reduce the order of magnitude of the fine step size, and repeat the fine two-way search step until the optimal carrier frequency offset estimation value is obtained

[0017] Furthermore, Step 1, similar to the generation of OFDM signals using Fourier transform, the generation of OCDM signals uses a Discrete Fresnel Transform (DFnT) matrix, specifically expressed as where M is the number of subcarriers in the OCDM system. After adding pilots in the Fresnel domain, the data symbol composition of the OCDM system is where the number of zero pilots is 2L - 1, and the data symbol d(i) = [d(iN), d(iN + 1), …, d(iN + N - 1)] T, taken from a complex modulation alphabet, with a length of N; the pilot symbol p(i) of length L = [b, 0, …, 0] T , with a fixed power evenly distributed to the pilot symbols. The transmitted symbols are modulated using an M×M inverse DFnT matrix. The i-th transmission block is expressed as After each zero-pilot OCDM transmission block in the Fresnel domain, add a zero suffix of length L to eliminate inter-block interference. The number of transmission blocks is K, and the signal is transmitted using energy E, so that the symbols in the pilot and transmitted data experience the same signal-to-noise ratio. Then the energy is allocated to the transmitted data, and the energy that can be allocated to the pilot is Therefore

[0018] Further, in step 2, the preambles added at the beginning and end are used to detect the signal and perform a resampling operation to perform a preliminary compensation for the Doppler scaling factor in the underwater environment.

[0019] Further, in step 3, the OCDM received signal of the zero-pilot in the Fresnel domain is expressed as where the carrier frequency offset is w o ∈ (0, 1) is the carrier frequency offset normalized by the carrier frequency space, f o is the manifestation of the carrier frequency offset in Hz, and B is the transmission signal bandwidth. In addition, w(i) is additive white Gaussian noise with a variance of σ 2 , is the intra-block carrier frequency offset, H is the channel parameter matrix, a Toeplitz matrix of (M + L)×M, and the first column is expressed as h = [h(0), …, h(L h ), 0, …, 0] T , where l p and A p are the transmission delay and channel gain of the p-th path respectively. There are a total of P channels generated by multipath, and L h is the maximum channel delay. To eliminate inter-block interference, set L h + 1 ≤ L.

[0020] Further, step 4 includes the following steps:

[0021] Step 41: Compensate the received signal y(i) with the candidate value of the carrier frequency offset to obtain the signal Perform a time-domain superposition operation R OLA and a Fresnel domain shift operation Φ M, obtain the preprocessed signal under the condition of the carrier frequency offset candidate value

[0022] Step 42: When the maximum channel delay is known, use the carrier frequency offset candidate value Pre-compensate the OCDM preprocessed signal Extract the Fresnel domain zero pilot in the pre-compensated received signal Among them, the selection vector of the zero pilot The number of selected zero pilots is Among them

[0023] Step 43: When the maximum channel delay is unknown, set L h = 0, use the carrier frequency offset candidate value Perform pre-channel estimation on the preprocessed signal Pre-channel estimation R1 is the pilot selection matrix, and then pre-equalize the OCDM preprocessed signal Extract the Fresnel domain zero pilot in the pre-equalized received signal Among them, the zero pilot selection vector is Equalizer Channel frequency response is a diagonal matrix of size M×M, The first column is the pre-estimated channel parameter F M is the Fourier transform matrix.

[0024] Furthermore, in step 5, for the pre-compensated or pre-equalized OCDM received signal, select the zero pilot energy as the measure of the carrier frequency offset candidate value.

[0025] Furthermore, in step 6, after calculating the estimation measures of all carrier frequency offset candidate values, find the minimum value of the estimation measures and determine it as the optimal carrier frequency offset estimation value.

[0026] Furthermore, step 8 includes the following steps:

[0027] Step 81: For the signal z(i) after compensating the carrier frequency offset, use the matrix R OLA Perform the time-domain superposition operation, and then use the Fresnel transform matrix Φ M , transform the signal to the Fresnel domain to obtain the preprocessed signal

[0028] Step 82: For the preprocessed OCDM signal Perform channel estimation to obtain the MMSE channel estimator where the channel variance matrix is expressed as ∑ h , R1 = [I L 0 L×(N+L) is the pilot selection matrix, and the ZF channel estimator

[0029] Step 83. Perform equalization operations on the preprocessed OCDM signal to estimate the data symbols in the OCDM system where the OCDM data symbol selection matrix R2 = [0 N×L I N 0 N×L , and the ZF equalizer is G ZF (i) = Λ -1 (i), and the MMSE equalizer is where where σ 2 is the noise variance

[0030] In a preferred embodiment of the present invention, the existing OCDM system does not make good use of the feature that the energy of the zero pilot in the Fresnel domain is zero to design an algorithm for effectively estimating and compensating the interference of the carrier frequency offset in the OCDM signal. The algorithm proposed by the present invention utilizes the characteristic that the energy of the zero pilot OCDM signal in the Fresnel domain is zero to design a zero pilot selection matrix and a carrier frequency offset estimation metric, and completes the estimation and compensation algorithm for the carrier frequency offset of the OCDM underwater acoustic communication system. After selecting a candidate value of the carrier frequency offset, the received OCDM signal is pre-compensated using the candidate value, and then a zero symbol selection matrix is designed to extract relevant information. A carrier frequency offset estimation metric is designed with zero energy as an index, and the minimum metric is selected, and the corresponding carrier frequency offset value is the optimal carrier frequency offset estimation value. The carrier frequency offset estimation for the Fresnel domain zero pilot OCDM underwater acoustic communication system is realized, the compensation for the phase rotation of the OCDM signal after resampling is completed, and the communication effect of the OCDM system in the underwater environment is effectively improved

[0031] Existing OCDM carrier frequency offset estimation technologies do not consider the current situation that it is difficult to obtain the underwater channel delay variation. The algorithms rely on channel delay information and are difficult to be effectively applied in the underwater environment. The designed algorithm of the present invention comprehensively considers two cases where the underwater channel delay is known and unknown, and designs different carrier frequency offset estimation algorithms according to prior knowledge, so as to improve the feasibility of the designed algorithm in the complex underwater environment. For the case where the channel delay is known, pre-compensation is performed using the candidate values of the carrier frequency offset, and a zero-carrier selection matrix associated with the channel delay is designed; for the case where the channel delay is unknown, channel estimation is performed using the candidate values of the carrier frequency offset and then pre-equalization is carried out, and a zero-carrier selection matrix independent of the channel delay is designed. The designed algorithm realizes the estimation and compensation of the carrier frequency offset in the OCDM underwater acoustic communication system under two cases where the channel delay is known and unknown, effectively improving the feasibility of the OCDM signal in underwater communication.

[0032] Existing OCDM underwater acoustic communication systems do not consider the current situation of limited energy in underwater communication and all adopt the method of adding a cyclic prefix to eliminate inter-block interference. The present invention considers the current situation of limited energy in the underwater acoustic communication scenario and designs a carrier frequency offset estimation method for the OCDM underwater acoustic communication system using a zero suffix. By using the time-domain cyclic superposition method, the received OCDM signal has a cyclic characteristic, and then the cyclic alternating property of the Fresnel transform can be utilized to perform operations such as estimation and compensation. An underwater acoustic communication system that transmits OCDM signals with lower energy is realized, and the additional preprocessing links such as time-domain cyclic superposition effectively reduce the computational complexity and lower the energy consumption of device information processing.

[0033] The present invention provides a carrier frequency offset estimation and compensation method for a Fresnel-domain zero-pilot OCDM underwater acoustic communication system, aiming at the current underwater acoustic communication operation scenario of the Fresnel-domain zero-pilot OCDM system and the robust communication requirements of low energy consumption and high rate underwater.

[0034] The carrier frequency offset estimation and compensation method for the Fresnel-domain zero-pilot OCDM underwater acoustic communication system provided by the present invention is designed. Considering the current situation of limited energy of the underwater transmitting device, the method of inserting a zero suffix is adopted to eliminate the inter-block interference of the OCDM signal. For the two cases where the underwater acoustic channel delay is known and unknown, different carrier frequency offset estimation and compensation methods are designed by using the characteristic that the energy of the Fresnel-domain zero pilot is zero. The present invention is considered to be carried out on the basis that the OCDM signal has completed the detection work and synchronization work at the receiving end, and the preliminary compensation of the Doppler shift is completed using the preamble and postamble, and then the carrier frequency offset parameters of the OCDM system are estimated and compensated by using the Fresnel-domain zero-pilot characteristic.

[0035] The carrier frequency offset estimation and compensation algorithm provided by the present invention is a search algorithm, which performs a one-dimensional search on the candidate values of the carrier frequency offset. To simplify the algorithm, it is necessary to first determine the search step size and search range and then perform a coarse search. After the first search is completed, the accuracy needs to be increased, and a two-way fine search is performed. Then, the order of magnitude of the search step size is reduced to improve the estimated carrier frequency offset accuracy until the specified accuracy is reached.

[0036] The present invention considers the processing of a zero-pilot OCDM underwater acoustic communication system with a zero suffix for carrier frequency offset. The zero suffix is used to eliminate inter-block interference. When using cyclic prefix transmission, after canceling preprocessing operations such as time-domain superposition, it can be processed in the same way; the present invention is mainly applied to underwater acoustic communication scenarios where the carrier frequency offset interference is obvious. When there is a large carrier frequency offset interference in a terrestrial OCDM system, it can be processed in the same way.

[0037] Specifically, the carrier frequency offset estimation and compensation method for the zero-pilot OCDM underwater acoustic communication system is executed as follows. The following steps 4 to 6 are the steps for calculating the estimation metric of the carrier frequency offset candidate values. After repeating multiple times, the best carrier frequency offset estimation value is selected. Specifically, when implementing, the one-dimensional search method can be used to select the best carrier frequency offset estimation value. Specifically, first, a coarse search is performed in the candidate range of [0, 1) with a coarse step size μ c to obtain a coarse carrier frequency offset estimation. Secondly, in the candidate range, a fine two-way search is performed with a fine step size According to the required accuracy, the order of magnitude of the fine step size is reduced, and the fine two-way search step is repeated until the best carrier frequency offset estimation value is obtained.

[0038] (1) Step 1: Generate an OCDM modulation signal using the Fresnel domain pilot symbol p(i), zero-pilot symbol 0, and data symbol d(i) and allocate energy E.

[0039] Similar to the generation of OFDM signals using Fourier transform, the generation of OCDM signals uses a Discrete Fresnel Transform (DFnT) matrix, specifically expressed as

[0040]

[0041] where M is the number of subcarriers in the OCDM system. After adding pilots in the Fresnel domain in the OCDM system, the data symbol composition is where the number of zero pilots is 2L - 1, and the data symbol d(i) = [d(iN), d(iN + 1), …, d(iN + N - 1)] T, taken from a complex modulation alphabet, with length N; the pilot symbol p(i) of length L = [b, 0, …, 0] T , with fixed power The average is evenly distributed to the pilot symbols. The transmitted symbols are modulated using an M×M inverse DFT matrix. The i-th transmission block is expressed as After each zero-pilot OCDM transmission block in the Fresnel domain, a zero suffix of length L is added to eliminate inter-block interference. The number of transmission blocks is K, and the signal is transmitted using energy E, such that the symbols in both the pilot and transmitted data experience the same signal-to-noise ratio. The energy is allocated to the transmitted data, and the energy that can be allocated to the pilot is Therefore

[0042] (2) Step 2: Perform serial-to-parallel conversion and add preambles v pre , v post , to generate the transmitted sequence s[n], and use the preambles to complete the signal detection and preliminary compensation operation of the Doppler scaling factor.

[0043] Perform a serial-to-parallel conversion operation on the above signal, and add a preamble v of length L at both the beginning and the end pre , v post , and add a guard interval of length N g to generate the transmitted signal, whose n-th input is denoted as s[n], specifically The preambles added at the beginning and end are used to detect the signal and perform resampling operations to perform preliminary compensation of the Doppler scaling factor in the underwater environment.

[0044] (3) Step 3: Represent the OCDM received signal y(i) under the influence of carrier frequency offset for the resampled signal.

[0045] After resampling, there is a residual Doppler factor influence, i.e., the influence of carrier frequency offset, in the OCDM signal. Under the influence of carrier frequency offset, the OCDM received signal of zero pilot in the Fresnel domain is expressed as

[0046]

[0047] where w o ∈(0, 1) is the carrier frequency offset normalized by the carrier frequency space, where f o is the manifestation of the carrier frequency offset in Hz, and B is the transmitted signal bandwidth. In addition, H is the channel parameter matrix, a (M + L)×M Toeplitz matrix, and the first column is expressed as h = [h(0), …, h(L h ), 0, …, 0]T , where l p and A p are the transmission delay and channel gain of the p-th path respectively. There are P channels generated by multipath, and L h is the maximum channel delay, and w(i) is the Additive White Gaussian Noise (AWGN), which follows a zero-mean distribution with variance σ 2 . To eliminate inter-block interference, set L h +1 ≤ L.

[0048] (4) Step 4: Select candidate values for carrier frequency offset Perform time-domain superposition operation and shift it to the Fresnel domain, considering the maximum channel delay L h to represent the zero pilots in the processed signal for both known and unknown cases

[0049] Considering the OCDM underwater acoustic communication system, to improve its environmental adaptability, considering the maximum channel delay L h which is not always available, construct an estimation metric for carrier frequency offset in two cases. Select candidate values for carrier frequency offset w o ∈(0,1) Perform pre-compensation or pre-equalization operation on the received signal as follows.

[0050] (41) Step 41: Compensate the received signal with the candidate value of carrier frequency offset Perform time-domain superposition operation and Fresnel domain shift operation to obtain the pre-processed signal under the condition of the candidate value of carrier frequency offset

[0051] Select candidate values for carrier frequency offset from w o ∈(0,1) We give the expression of the received signal after compensating the carrier frequency offset

[0052]

[0053] Use the time-domain superposition matrix R OLA =[I M [I M :,1:L , [I M :,1:L is the first L columns of I M , and then, using the Fresnel matrix Φ M , transfer the signal to the Fresnel domain, and the pre-processed signal under the condition of the candidate value of carrier frequency offset

[0054] ​​(42) Step 42: When the maximum channel delay is known, use the carrier frequency offset candidate value Pre-compensate the OCDM preprocessed signal Extract the Fresnel domain zero pilots from the pre-compensated received signal

[0055] When the maximum channel delay is known, use Pre-compensate the OCDM received signal, and then use the zero pilot selection vector to select the zero pilots in the pre-compensated signal, specifically expressed as

[0056]

[0057] Among them, the selection vector of the zero pilots The number of selected zero pilots is Among them ⊙ is the element-by-element multiplication symbol.

[0058] (43) Step 43: When the maximum channel delay is unknown, use the carrier frequency offset candidate value Perform pre-channel estimation on the preprocessed signal Pre-channel estimation Then pre-equalize the OCDM preprocessed signal Extract the Fresnel domain zero pilots from the pre-equalized received signal

[0059] When the maximum channel delay is unknown, set L h = 0. Because of the lack of channel-related information, a zero-forcing (ZF) channel estimator is adopted Among them, the pilot selection matrix R1 = [I L 0 L×(N+L) , and on this basis, pre-equalize the OCDM preprocessed signal Then use the zero pilot selection vector to select the zero pilots in the pre-equalized signal, specifically expressed as

[0060]

[0061] Among them, the zero pilot selection vector is Parameter matrix is a parameter matrix of size M×M, where the Fourier transform matrix is a unitary matrix; the equalizer Channel frequency response is a diagonal matrix of size M×M, The first column is the pre-estimated channel parameter

[0062] (5) Step 5: Utilize the Fresnel domain zero pilots u extracted respectively in the two casesnull , calculate the energy corresponding to the zero pilot, and use this as an estimation metric for the carrier frequency offset

[0063] For the maximum channel delay L h When known, obtain the pre-compensation signal or when L h When unknown, obtain the pre-equalization signal, calculate the energy corresponding to the zero pilot, and use this as an estimation metric for the carrier frequency offset, specifically

[0064]

[0065] If the receiving end compensates the correct carrier frequency offset parameter, then there will be no energy leakage of adjacent symbols on the zero pilot, that is

[0066] (6) Step 6: Find the minimum value of the estimation metric and determine the corresponding best carrier frequency offset estimation value

[0067] After calculating the estimation metrics of all candidate carrier frequency offset values , find the minimum value of the estimation metric and determine the corresponding As the best carrier frequency offset estimation value, the calculation method of the best carrier frequency offset estimation value is as follows

[0068]

[0069] (7) Step 7: Compensate the OCDM received signal y(i) according to the estimated best carrier frequency offset estimation value to obtain the compensated signal z(i).

[0070] Use the best carrier frequency offset estimation value to compensate the received OCDM signal y(i) with carrier frequency offset interference. If the carrier frequency offset is perfectly compensated, the compensated signal is expressed as follows

[0071]

[0072] Among them,

[0073] (8) Step 8: Perform preprocessing operations on the signal z(i) compensated using the best carrier frequency offset estimation value to obtain the preprocessed signal Perform channel estimation operations to obtain the channel estimator and Perform equalization operations to estimate the data symbols in the OCDM system

[0074] (81) Step 81: Perform time-domain superposition operations on the signal after compensating the carrier frequency offset and obtain the preprocessed signal

[0075] Use the matrix R for the signal z(i) after compensating for the carrier frequency offset. OLA Perform a time-domain superposition operation using the Fresnel transform matrix Φ. M Convert to the Fresnel domain, and the preprocessed signal expression is

[0076]

[0077] (82) Step 82: For the preprocessed OCDM signal Perform channel estimation to obtain a channel estimator.

[0078] For the preprocessed OCDM signal Use the Minimum Mean-Square Error (MMSE) channel estimator, which is specifically expressed as follows

[0079]

[0080] where the channel variance matrix is expressed as The pilot selection matrix R1 = [I L 0 L×(N+L) , and σ 2 is the noise variance. In an underwater communication environment, sometimes it is difficult to obtain the channel variance. In this case, the ZF channel estimator is used.

[0081] (83) Step 83: For the preprocessed OCDM signal Perform equalization operation to estimate the data symbols in the OCDM system

[0082] For the preprocessed OCDM signal Use the discrete Fourier matrix F M Convert it to the frequency domain, perform frequency-domain equalization, and use the OCDM data symbol selection matrix R2 = [0 N×L I N N 0×L to select the estimated OCDM symbols, which is expressed as

[0083]

[0084] Its equalization matrix G(i) is a diagonal matrix, and its (l, l) diagonal element is [H(i)] l,l , and the corresponding ZF equalizer is G ZF (i) = Λ -1 (i), where the channel frequency response is a diagonal matrix of size M×M, and the first column of H is the estimated channel parameter The MMSE equalizer is Wherein is the power of the data symbol in the transmitted signal. In addition, the noise after the superposition operation is colored noise, and its variance is

[0085] Compared with the prior art, the present invention has the following obvious substantial features and remarkable advantages:

[0086] 1. The present invention realizes the carrier frequency offset estimation for the zero-pilot OCDM underwater acoustic communication system in the Fresnel domain, constructs a carrier frequency offset estimation metric by using the energy of the zero-pilot in the Fresnel domain, realizes the compensation of the influence of the carrier frequency offset in the OCDM received signal, and effectively improves the communication performance of the underwater acoustic communication system of the OCDM system.

[0087] 2. The present invention improves the adaptability of the OCDM underwater acoustic communication system to the underwater environment, realizes the design of the zero-pilot selection vector in two cases where the maximum channel delay is known and unknown, extracts the zero-pilot in the Fresnel domain from the preprocessed received signal and the pre-equalized received signal, and further realizes the estimation and compensation of the carrier frequency offset in the received signal, effectively improving the feasibility of the OCDM signal in underwater communication.

[0088] 3. The present invention considers the actual situation of energy limitation in the underwater environment, realizes an underwater acoustic communication system that transmits OCDM signals with lower energy. Different from the traditional method using cyclic prefix, the present invention uses the zero-suffix method to eliminate inter-block interference. In addition, the present invention adds preprocessing links such as time-domain cyclic superposition, reasonably utilizes the characteristics of the Fresnel transform, effectively reduces the algorithm complexity at the receiving end, and reduces the energy consumption of device information processing.

[0089] The following will further illustrate the concept, specific structure and technical effects of the present invention with reference to the accompanying drawings to fully understand the purpose, features and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 is the execution flowchart of a preferred embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0091] The following introduces multiple preferred embodiments of the present invention with reference to the accompanying drawings of the specification to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms of embodiments, and the protection scope of the present invention is not limited to the embodiments mentioned in the text.

[0092] Figure 1This is the specific implementation process of a carrier frequency offset estimation and compensation method for a Fresnel-domain zero-pilot OCDM underwater acoustic communication system provided by the present invention. The present invention aims at the communication problems in the underwater acoustic communication operation scenario of the current Fresnel-domain zero-pilot OCDM system. Therefore, in actual use, specific parameters should be set according to the underwater acoustic communication machine and the transmission sea area.

[0093] The present invention designs a carrier frequency offset estimation and compensation method for a Fresnel-domain zero-pilot OCDM underwater acoustic communication system. In the subsequent description, considering the current situation of limited energy of underwater transmitting devices, the method of inserting zero suffixes is adopted to eliminate the interference between OCDM signal blocks. For the two cases where the underwater acoustic channel delay is known and unknown, different carrier frequency offset estimation and compensation methods are designed by using the characteristic that the energy of the zero-pilot in the Fresnel domain is zero. The present invention is carried out on the basis that the OCDM signal has completed the detection and synchronization work at the receiving end, and the preliminary compensation of the Doppler shift is completed by using the preamble and postamble, and then the carrier frequency offset parameters of the OCDM system are estimated and compensated by using the Fresnel-domain zero-pilot characteristics.

[0094] The carrier frequency offset estimation and compensation algorithm provided by the present invention is a search algorithm, which performs a one-dimensional search on the candidate values of the carrier frequency offset. To simplify the algorithm, it is necessary to first determine the search step size and search range and then perform a rough search. After the first search is completed, the accuracy needs to be increased and a two-way fine search is performed until the specified accuracy is reached. The estimation of the carrier frequency offset by the present invention makes full use of the characteristic that the energy of the zero-pilot in the Fresnel domain of the OCDM signal is zero, and in the face of the current situation of limited underwater energy, realizes the estimation of the carrier frequency offset parameters when using the OCDM signal to insert zero pilots.

[0095] As Figure 1 shown, the specific implementation steps of the present invention are as follows:

[0096] Step 1: Similar to the generation of OFDM signals using Fourier transform, the generation of OCDM signals uses the DFnT matrix, specifically expressed as where M is the number of subcarriers of the OCDM system. After adding pilots in the Fresnel domain, the data symbol composition of the OCDM system is where the number of zero pilots is 2L - 1, and the data symbol d(i) = [d(iN), d(iN + 1), …, d(iN + N - 1)] T , taken from the complex modulation alphabet, with a length of N; the pilot symbol p(i) of length L = [b, 0, …, 0] T , with a fixed power evenly distributed to the pilot symbols. The transmission symbol is modulated by the M×M inverse DFnT matrix. The i-th transmission block is expressed as Add a zero suffix of length L after each Fresnel domain zero-pilot OCDM transmission block to eliminate inter-block interference. The number of transmission blocks is K, and the signal is transmitted using energy E, so that the symbols in the pilot and the transmitted data experience the same signal-to-noise ratio. Allocate the energy to the transmitted data, and the energy that can be allocated to the pilot is Therefore

[0097] Step 2: Perform a serial-to-parallel conversion operation on the above signal, and add a preamble and a postamble v of length L at the beginning and the end respectively pre ,v post , and add a guard interval of length N g to generate the transmitted signal, where the nth input is represented by s[n], specifically The preamble and postamble added at the beginning and the end are used to detect the signal and perform resampling operations to perform preliminary compensation for the Doppler scaling factor in the underwater environment.

[0098] Step 3: After resampling, there is still the influence of the residual Doppler factor, that is, the carrier frequency offset, on the OCDM signal. Under the influence of the carrier frequency offset, the OCDM received signal in the Fresnel domain is expressed as where w o ∈(0,1) is the carrier frequency offset normalized by the carrier frequency space, where f o is the manifestation of the carrier frequency offset in Hz, and B is the transmitted signal bandwidth. In addition, To eliminate inter-block interference, set L h +1≤L.

[0099] Step 4: Select candidate values of the carrier frequency offset from w o ∈(0,1) We give the expression of the received signal after compensating the carrier frequency offset Use the time-domain superposition matrix R OLA =[I M [I M :,1:L on this signal, [I M :,1:L is the first L columns of I M , and then, use the Fresnel matrix Φ M to transfer the signal to the Fresnel domain. The preprocessed signal under the condition of the candidate value of the carrier frequency offset When the maximum channel delay is known, use to pre-compensate the OCDM received signal, and then use the zero-pilot selection vector to select the zero-pilot in the pre-compensated signal, specifically expressed as Among them, the selection vector of the zero-pilot​​ When the maximum channel delay is unknown, set L h = 0. Since the channel-related information is missing, a zero-forcing channel estimator is adopted where the selection matrix R1 = [I L 0 L×(N+L) . Based on this, pre-equalize the OCDM preprocessed signal Then use the zero-pilot selection vector to select the zero pilots in the pre-equalized signal, which is specifically expressed as where the zero-pilot selection vector is Parameter matrix is a parameter matrix of size M×M, where the Fourier transform matrix is a unitary matrix; the equalizer Channel frequency response is a diagonal matrix of size M×M, The first column is the pre-estimated channel parameter

[0100] Step 5: For the pre-compensation signal obtained when the maximum channel delay L h is known or the pre-equalized signal obtained when L h is unknown, calculate the energy corresponding to its zero pilots, and use this as the estimation metric of the carrier frequency offset, specifically as If the receiving end compensates the correct carrier frequency offset parameter, then there will be no energy leakage of adjacent symbols on the zero pilots, that is

[0101] Step 6: After calculating the estimation metrics of all carrier frequency offset candidate values , find the minimum value of the estimation metric and determine the corresponding as the best carrier frequency offset estimation value. The calculation method of the best carrier frequency offset estimation value is

[0102] Step 7: Use the best carrier frequency offset estimation value to compensate the received OCDM signal with carrier frequency offset interference. If the carrier frequency offset is perfectly compensated, the compensated signal is expressed as

[0103] Step 8: Perform a time-domain superposition operation on the signal after compensating the carrier frequency offset using the matrix R OLA and use the Fresnel transform matrix Φ M to convert it to the Fresnel domain, and the expression of the preprocessed signal is Use the MMSE channel estimator for this signal Pilot selection matrix R1 = [I L 0 L×(N+L) , ZF channel estimator, For the preprocessed OCDM signal Use the discrete Fourier matrix F M Convert it to the frequency domain, perform frequency domain equalization, and use the OCDM data symbol selection matrix R2 = [0 N×L I N 0 N×L to select the estimated OCDM symbols. Its equalization matrix G(i) is a diagonal matrix, and its (l, l) diagonal element is [G(i)] l,l , and the corresponding ZF equalizer is G ZF (i) = Λ -1 (i), where the channel frequency response is a diagonal matrix of size M×M, and the first column of H is the estimated channel parameter The MMSE equalizer is where is the power of the data symbol in the transmitted signal. In addition, the noise after the superposition operation is colored noise, and its variance is

[0104] As Figure 1 shown, in the actual use process, steps 3 to 5 are the steps of calculating the estimation metric of the carrier frequency offset candidate values. After multiple loops, the best carrier frequency offset estimation value needs to be selected. Specifically, when implementing, the one-dimensional search method can be used to select the best carrier frequency offset estimation value. Specifically, first, a coarse search is performed with a coarse step size in the candidate range to obtain a coarse carrier frequency offset estimation; secondly, a fine two-way search is performed with a fine step size in the refined candidate range. According to the required accuracy, the fine two-way search step is repeated until the best carrier frequency offset estimation value is obtained.

[0105] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations according to the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should be within the protection scope determined by the claims.

Claims

1. A carrier frequency offset estimation and compensation method for zero-pilot OCDM underwater acoustic communication in the Fresnel domain, characterized in that, including the following steps: Step 1: Generate an OCDM modulation signal with a length of M = 2L + N using a pilot symbol p(i) with a Fresnel domain length of L, a zero pilot symbol 0 with a length of L, and a data symbol d(i) with a length of N where is an inverse Fresnel transform matrix, containing M subcarriers, and allocating energy E; Step 2: Perform serial-to-parallel conversion work, and add preambles v with length L pre , v post and guard intervals with length N g to generate a transmission sequence, and use the preambles to complete signal detection and preliminary compensation operations for the Doppler scaling factor; Step 3: For the resampled signal, express the OCDM received signal under the influence of carrier frequency offset where w o ∈(0, 1) is the carrier frequency offset normalized by the carrier frequency space, D M+L (w o ) is the influence of the in-block carrier frequency offset, H is the multipath channel parameter matrix, and w(i) is the additive white Gaussian noise; Step 4: Select candidate values of carrier frequency offset Give the received signal after compensating for the carrier frequency offset Perform the time-domain superposition operation R OLA and the Fresnel domain shift operation Φ M , and obtain the preprocessed signal under the condition of candidate values of carrier frequency offset The maximum channel delay L h Construct carrier frequency offset estimation metrics for the known and unknown cases respectively; L h When it is known, the zero pilot in the pre-compensated signal where r null (L h ) is the zero pilot selection vector with L h known; L h When it is unknown, the zero pilot in the pre-equalized signal where r null (0) is the zero pilot selection vector with L h unknown, where is the inverse Fourier transform matrix, G is the equalization matrix, and Γ M is the Fresnel parameter matrix; Step 5: Using the Fresnel domain zero pilots u extracted separately in the two cases null , calculate the energy corresponding to its zero pilot as the estimation metric of the carrier frequency offset Step 6, after calculating all carrier frequency offset candidate values of the estimation metric, find the minimum value of the estimation metric and determine the corresponding as the optimal carrier frequency offset estimation value. The calculation method of the optimal carrier frequency offset estimation value is Step 7, according to the estimated optimal carrier frequency offset estimation value Compensate the OCDM received signal y(i) to obtain the compensated signal z(i); Step 8: Perform preprocessing operations on the signal z(i) after compensating with the optimal carrier frequency offset estimate to obtain a preprocessed signal where Φ M is the Fresnel transform matrix, and R OLA is the cyclic superposition operation; perform channel estimation operations to obtain the MMSE channel estimator and the ZF channel estimator Perform equalization operations on the preprocessed signal to estimate the data symbols in the OCDM system 2. The carrier frequency offset estimation and compensation method for the Fresnel domain zero-pilot OCDM underwater acoustic communication according to claim 1, characterized in that, The steps 4 to 6 are the steps of calculating the estimation metric of the carrier frequency offset candidate values. For different carrier frequency offset candidate values calculate the estimation metric one by one, find the minimum metric, and select the corresponding best carrier frequency offset estimation value.

3. The carrier frequency offset estimation and compensation method for Fresnel domain zero-pilot OCDM underwater acoustic communication according to claim 1, characterized in that, Steps 4 to 6 can use a two-step search algorithm with coarse and fine steps to reduce the computational complexity. In the candidate range of [0, 1), a coarse step size μ c is used for coarse search to obtain a coarse carrier frequency offset estimate Secondly, in the candidate range, a fine step size is used for fine two-way search. According to the required accuracy, the order of magnitude of the fine step size is reduced, and the fine two-way search step is repeated until the optimal carrier frequency offset estimate value is obtained 4. The carrier frequency offset estimation and compensation method for the Fresnel domain zero-pilot OCDM underwater acoustic communication according to claim 1, characterized in that In step 1, similar to the generation of OFDM signals using Fourier transform, the generation of OCDM signals uses a discrete Fresnel transform matrix, specifically expressed as where M is the number of subcarriers in the OCDM system; after adding pilots in the Fresnel domain, the data symbols are composed of where the number of zero pilots is 2L - 1, and the data symbol d(i) = [d(iN), d(iN + 1), …, d(iN + N - 1)] T , taken from the complex modulation alphabet, with a length of N; the pilot symbol p(i) with a length of L = [b, 0, …, 0] T , with a fixed power evenly distributed to the pilot symbols; the transmission symbols are modulated by an M×M inverse DFnT matrix; the i-th transmission block is expressed as An L-length zero suffix is added after each zero-pilot OCDM transmission block in the Fresnel domain to eliminate inter-block interference; The number of transport blocks is K. The signal is transmitted using energy E, and the symbols in the pilot and the transmitted data experience the same signal-to-noise ratio. The energy is allocated to the transmitted data, and the energy that can be allocated to the pilot is Therefore 5. The carrier frequency offset estimation and compensation method for Fresnel domain zero-pilot OCDM underwater acoustic communication according to claim 1, characterized in that, In step 2, the preambles added at the beginning and the end are used to detect signals and perform resampling operations to preliminarily compensate the Doppler scaling factor in the underwater environment.

6. The carrier frequency offset estimation and compensation method for the Fresnel domain zero-pilot OCDM underwater acoustic communication according to claim 1, characterized in that In step 3, the OCDM received signal of the Fresnel domain zero pilot is expressed as where the carrier frequency offset is w o ∈(0, 1) is the carrier frequency offset normalized by the carrier frequency space, f o is the manifestation of the carrier frequency offset in Hz, B is the transmission signal bandwidth; w(i) is the additive white Gaussian noise with variance σ 2 ; is the intra-block carrier frequency offset, H is the channel parameter matrix, a Toeplitz matrix of (M + L)×M, the first column is expressed as h = [h(0), …, h(L h ), 0, …, 0] T , where l p and A p are respectively the transmission delay and the channel gain of the p-th path. There are P channels generated by multipath, and L h is the maximum channel delay. To eliminate the inter-block interference, it is set that L h +1 ≤ L.

7. The carrier frequency offset estimation and compensation method for Fresnel domain zero-pilot OCDM underwater acoustic communication according to claim 1, characterized in that Step 4 includes the following steps: Step 41, use the carrier frequency offset candidate value to compensate the received signal y(i) to obtain the signal Perform the time-domain superposition operation R OLA and the Fresnel domain translation operation Φ M to obtain the preprocessed signal under the condition of the carrier frequency offset candidate value Step 42: When the maximum channel delay is known, use the carrier frequency offset candidate value Pre-compensate the OCDM preprocessed signal Extract the Fresnel domain zero pilot in the received signal after pre-compensation where the selection vector of the zero pilot The number of selected zero pilots is where Step 43: When the maximum channel delay is unknown, set L h = 0, and use the carrier frequency offset candidate value to perform pre-channel estimation on the preprocessed signal R1 is the pilot selection matrix, and then pre-equalize the OCDM preprocessed signal Extract the zero pilots in the Fresnel domain from the pre-equalized received signal where the zero pilot selection vector is The equalizer The channel frequency response is a diagonal matrix of size M×M, The first column is the pre-estimated channel parameter F M is the Fourier transform matrix, and Γ M is the diagonalization parameter matrix.​ 8. The carrier frequency offset estimation and compensation method for Fresnel domain zero-pilot OCDM underwater acoustic communication according to claim 1, characterized in that, In step 5, for the OCDM received signal that has been pre-compensated or pre-equalized, the zero pilot energy is selected as a measure of the carrier frequency offset candidate value.

9. The carrier frequency offset estimation and compensation method for the Fresnel domain zero-pilot OCDM underwater acoustic communication according to claim 1, characterized in that In step 6, after calculating the estimated measures of all carrier frequency offset candidate values, find the minimum value of the estimated measures and determine it as the optimal carrier frequency offset estimate value.

10. The carrier frequency offset estimation and compensation method for Fresnel domain zero-pilot OCDM underwater acoustic communication according to claim 1, characterized in that, Step 8 includes the following steps: Step 81: For the signal z(i) after compensating for the carrier frequency offset, use the matrix R OLA to perform a time-domain superposition operation, and then use the Fresnel transform matrix Φ M to transform the signal to the Fresnel domain and obtain a preprocessed signal Step 82, perform channel estimation on the preprocessed OCDM signal to obtain the MMSE channel estimator where ∑ h is the channel variance matrix, R1 = [I L 0 L×(N+L) is the pilot selection matrix, and the ZF channel estimator Step 83, perform equalization on the preprocessed OCDM signal to estimate the data symbols in the OCDM system where the OCDM data symbol selection matrix R2 = [0 N×L I N 0 N×L , the ZF equalizer is G ZF (i) = Λ -1 (i), and the MMSE equalizer is where σ 2 is the noise variance.

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