An OFDM cyclic cross-correlation function-based communication and positioning integrated waveform optimization method

Abstract

The application belongs to the technical field of underwater acoustic communication, and particularly relates to a communication and positioning integrated waveform optimization method based on an OFDM cyclic cross-correlation function. The application aims to solve the problem that the prior art cannot simultaneously consider the accuracy of communication and positioning. The process is as follows: obtaining an OFDM signal; transforming the obtained signal to obtain an inverse Fourier transform matrix; obtaining a time domain signal under an oversampling factor of a sonar transmission based on the matrix; constructing a cyclic cross-correlation function expectation model considering decoding errors; calculating high-order statistical moments under an M-element symmetric channel model; calculating the expectation of the square of the cyclic cross-correlation function; constructing a time delay estimation performance evaluation index expectation main lobe integral side lobe ratio; constructing an optimization target based on the time delay estimation performance evaluation index expectation main lobe integral side lobe ratio; solving the optimization target based on a particle swarm optimization algorithm to obtain an optimal pilot subcarrier set.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic communication technology, specifically relating to a waveform optimization method for integrated communication and positioning based on OFDM cyclic cross-correlation function. Background Technology

[0002] Integrated underwater acoustic communication and positioning technology is a core supporting technology for intelligent marine equipment and the marine Internet of Things (IoT), and is of great significance for military and civilian applications such as collaborative operations of autonomous underwater vehicles (AUVs), underwater target detection and identification, and long-term marine environmental monitoring. However, in traditional underwater systems, communication and positioning functions are implemented independently, resulting in low spectrum resource utilization and high hardware power consumption, making it difficult to meet the integration requirements of space- and power-constrained platforms (such as micro AUV clusters). Integrating sensing and communication (ISAC) functions through shared spectrum resources and hardware platforms has become a key technological path to overcome the bottleneck of intelligent underwater equipment. Underwater acoustic information technology is considered one of the key technologies for marine scientific research, underwater resource exploitation, and marine sensing networks. Underwater operational equipment often needs to be equipped with multiple sonar devices to support complex operational requirements, such as communication sonar and positioning sonar, which also brings additional acoustic compatibility management issues. Therefore, it is urgent to explore integrated communication, positioning, and sonar technology to complete multi-dimensional operational tasks with high spectral efficiency. When a communication-centric sonar adopts a waveform centered on communication, such as OFDM, it is necessary to study the correlation function characteristics based on random communication signals, evaluate the correlation function loss under different bit error rates, and provide important evaluation indicators for the communication-centric sonar to guide the design of the sonar system.

[0003] In underwater acoustic ISAC systems, waveform design is a fundamental factor determining system performance. OFDM, as the most widely adopted waveform standard for underwater acoustic communication, inherently possesses multi-carrier parallel transmission capabilities, providing the infrastructure for sharing time-frequency resources between communication and positioning functions. Unlike traditional positioning systems, it must utilize random communication data rather than the deterministic signals of traditional dedicated positioning to perform sensing tasks. Existing research has shown that positioning performance indicators derived from random data strongly depend on the statistical characteristics of the data constellation; however, these studies primarily focus on terrestrial wireless channels and fail to fully consider the unique propagation characteristics of underwater acoustic channels. For example, underwater acoustic OFDM systems employ a comb-like pilot structure to counteract the rapid time-varying characteristics of the channel, rather than the block-like pilots studied for terrestrial ISAC systems. This means that each received OFDM symbol contains random data and deterministic pilot subcarriers, rather than appending a pilot preamble to the OFDM symbol. In acoustic positioning systems, the reference signal must be reconstructed based on the decoded communication symbols, rather than being perfectly known as in terrestrial bistatic ISAC systems. Therefore, waveform design should mitigate decoding error effects to improve the robustness of sensing in integrated underwater acoustic communication and positioning systems. Summary of the Invention

[0004] The purpose of this invention is to address the problem that existing technologies cannot simultaneously ensure the accuracy of communication and positioning, and to propose a waveform optimization method for integrated communication and positioning based on OFDM cyclic cross-correlation function.

[0005] The specific process of a waveform optimization method for integrated communication and positioning based on OFDM cyclic cross-correlation function is as follows:

[0006] Step 1: Acquire the OFDM signal. The OFDM signal uses a comb pilot structure. Perform an inverse Fourier transform on the acquired OFDM signal to obtain the inverse Fourier transform matrix. Based on the inverse Fourier transform matrix Obtain the oversampling factor of sonar emission. OFDM time-domain signal ;

[0007] Step 2: Oversampling factor based on sonar emission OFDM time-domain signal Construct an expectation model of the periodic cross-correlation function that takes into account decoding errors;

[0008] Step 3: Based on the expected model of the periodic cross-correlation function considering decoding error constructed in Step 2, calculate the higher-order statistical moments under the M-ary symmetric channel model;

[0009] Step 4: Based on the higher-order statistical moments under the M-ary symmetric channel model in Step 3, calculate the expectation of the square of the periodic cross-correlation function;

[0010] Step 5: Based on the expectation of the square of the periodic cross-correlation function, construct the expected main lobe integral side lobe ratio as a performance evaluation index for time delay estimation;

[0011] An optimization objective is constructed based on the expected main lobe integral side lobe ratio, a performance evaluation metric for time delay estimation.

[0012] Step 6: Solve the optimization objective using the particle swarm optimization algorithm to obtain the optimal set of pilot subcarriers. .

[0013] The beneficial effects of this invention are as follows:

[0014] This invention addresses the rapidly time-varying characteristics of underwater acoustic channels and the need for decoding and reconstructing positioning reference signals. It derives the closed-form expectation of the periodic cross-correlation function (P-CCF) of comb-type pilot OFDM signals and quantitatively analyzes the impact of random data payload, deterministic pilots, and decoding errors on positioning performance. This invention defines the main lobe-integral sidelobe expectation ratio (E-MISR) as a positioning performance indicator. The receiver reconstructs the reference signal using decoded symbols and performs correlation processing. A particle swarm optimization algorithm is used to optimize pilot configuration and improve the robustness of multipath delay estimation. This method achieves joint optimization of communication and positioning performance while remaining compatible with existing underwater acoustic OFDM communication systems and comb-type pilot channel estimation algorithms, providing a highly reliable integrated waveform solution for applications such as autonomous underwater vehicle (AUV) swarms and underwater IoT.

[0015] This scheme proposes a joint optimization method for underwater acoustic OFDM communication and positioning. First, a comb-shaped pilot OFDM signal model is established, considering the expected characteristics of the periodic cross-correlation function (P-CCF) of decoding errors. An M-ary symmetric channel model is used to quantify the impact of constellation mismatch. An expected main lobe integral sidelobe ratio (E-MISR) index is constructed, comprehensively considering pilot power, number of pilots, decoding bit error rate (SER), and constellation statistical characteristics to accurately characterize the trade-off between randomness and determinism. Based on this, a pilot power optimization problem is established with E-MISR as the objective and total power as the constraint. The particle swarm optimization (PSO) algorithm is used to solve for the optimal power allocation vector. The system supports dynamic adjustment of pilot power based on real-time decoding bit error rate (SER) to maximize the expected main lobe integral sidelobe ratio (E-MISR), achieving an online adaptive trade-off between communication quality and positioning accuracy, suitable for fast-changing underwater acoustic channel environments. Attached Figure Description

[0016] Figure 1 This is a flowchart of the present invention;

[0017] Figure 2 Here is a flowchart of the particle swarm optimization algorithm;

[0018] Figure 3 The graph shows the trade-off between E-MISR and pilot data power ratio (PDPR) when the bit error rate (SER) is 0, 0.1, 0.2, and 0.3, respectively. Detailed Implementation

[0019] Specific implementation method one: Combining Figure 1 This embodiment describes a waveform optimization method for integrated communication and positioning based on OFDM cyclic cross-correlation functions. The specific process is as follows:

[0020] Step 1: Acquire the OFDM signal. The OFDM signal uses a comb pilot structure. Perform an inverse Fourier transform on the acquired OFDM signal to obtain the inverse Fourier transform matrix. Based on the inverse Fourier transform matrix Obtain the oversampling factor of sonar emission. OFDM time-domain signal ;

[0021] Step 2: Oversampling factor based on sonar emission OFDM time-domain signal Construct an expectation model of the periodic cross-correlation function (P-CCF) that takes into account decoding errors;

[0022] Step 3: Based on the expected model of the periodic cross-correlation function (P-CCF) considering decoding error constructed in Step 2, calculate the higher-order statistical moments under the M-ary symmetric channel (MSC) model;

[0023] Step 4: Based on the higher-order statistical moments under the M-ary symmetric channel (MSC) model in Step 3, calculate the expectation of the square of the periodic cross-correlation function;

[0024] Step 5: Based on the expectation of the square of the periodic cross-correlation function, construct the expected main lobe integral side lobe ratio (E-MISR) as a quantitative indicator of positioning accuracy, which is a performance evaluation index for time delay estimation.

[0025] An optimization objective is constructed based on the expected main lobe integral side lobe ratio, a performance evaluation metric for time delay estimation.

[0026] Step 6: Solve the optimization objective using the particle swarm optimization algorithm to obtain the optimal set of pilot subcarriers. .

[0027] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that, in step 1, the OFDM signal is acquired using a comb pilot structure; an inverse Fourier transform is performed on the acquired OFDM signal to obtain the matrix after the inverse Fourier transform. Based on the inverse Fourier transform matrix Obtain the oversampling factor of sonar emission. OFDM time-domain signal The specific process is as follows:

[0028] Step 11: To address the rapid time-varying characteristics of the underwater acoustic channel, acquire the baseband OFDM signal. The pilot structure used for the baseband OFDM signal is a comb pilot.

[0029] Let the total number of subcarriers of the baseband OFDM signal be... ;

[0030] Let the set of empty subcarriers be ;

[0031] Let the uniformly distributed sparse pilot spacing be... ;

[0032] Total number of subcarriers includes Data subcarriers and One pilot subcarrier;

[0033] In underwater acoustic localization scenarios, the receiver needs to reconstruct the reference signal through decoding, which introduces the decoding error rate (SER). ;

[0034] ;

[0035] The number of data subcarriers constitutes the data subcarrier set. ;

[0036] The number of pilot subcarriers constitutes the pilot subcarrier set. ;

[0037] The number of pilot subcarriers constitutes the empty subcarrier set. ;

[0038] Define sampling rate , , For oversampling factor, For bandwidth;

[0039] Data subcarrier set Pilot subcarrier set empty subcarrier set As shown in the following formula:

[0040] (1)

[0041] make ;

[0042] ;

[0043] in, This refers to the frequency domain subcarrier index number; It is a constant; , As an intermediate variable;

[0044] Step 12: Perform an inverse Fourier transform on the acquired baseband OFDM signal to obtain the matrix after the inverse Fourier transform. ;

[0045] Step 13: Based on the matrix after inverse Fourier transform Obtain the oversampling factor of sonar emission. OFDM time-domain signal ; indicates as:

[0046] (2)

[0047] in, Oversampling factor representing sonar emission OFDM time-domain signal;

[0048] It is an equivalent frequency domain symbol vector, which includes data symbols, pilot symbols, and zero-padded frequency domain symbols; (The 0 is omitted in the middle) For the first Transmitted symbols on each frequency domain subcarrier It is the frequency domain subcarrier index number. Superscript This indicates the transpose;

[0049] Indicates the first The delay point The time-domain complex exponential basis function of each frequency domain subcarrier; Indicates the first One delay point; ;

[0050] , The imaginary unit, .

[0051] The other steps and parameters are the same as in Specific Implementation Method 1.

[0052] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the oversampling factor based on sonar emission is used in step 2. OFDM time-domain signal Construct an expectation model of the periodic cross-correlation function (P-CCF) considering decoding errors; expressed as:

[0053] (3)

[0054] in, For the first The periodic cross-correlation function (P-CCF) values ​​at each delay point;

[0055] The OFDM time-domain signal (reference signal) received by the receiver and reconstructed from the decoded signal. ;

[0056] It is a cyclic shift matrix. ;

[0057] express 3D identity matrix To indicate 3D identity matrix;

[0058] These are DFT basis vectors. , express 0-dimensional vector express 0-dimensional vector;

[0059] The equivalent frequency domain symbol vector for decoding and reconstruction; For the first Decoding and reconstruction symbols on each subcarrier, superscript This indicates the conjugate transpose.

[0060] Other steps and parameters are the same as in specific implementation method one or two.

[0061] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that, in step 3, based on the expected model of the periodic cross-correlation function (P-CCF) considering decoding errors constructed in step 2, the higher-order statistical moments under the M-ary symmetric channel (MSC) model are calculated; the specific process is as follows:

[0062] Step 31: Under actual underwater acoustic channel conditions, due to factors such as noise, multipath fading, and the Doppler effect, incorrect symbol decisions may occur. To characterize this non-ideal detection behavior, an error transition matrix is ​​given. ; indicates as:

[0063] (4)

[0064] in, Indicates the decoding error rate; Indicates the number of elements in the constellation diagram; The sending symbol is He was sentenced to The conditional probability; The constellation chart indicates the first one. One element; The constellation chart indicates the first one. One element; ; ;

[0065] Represented as:

[0066] (5)

[0067] in, Indicates the sending symbol, Indicates the sending symbol; Indicates satisfaction time The probability of;

[0068] satisfy:

[0069] (6)

[0070] Step 32: Based on calculate The higher-order statistical moments under the metasymmetric channel (MSC) model are expressed as:

[0071] (7)

[0072] in, This indicates a demand for expectation; Indicates the absolute value; superscript Indicates conjugate;

[0073] Indicates the kurtosis of a constellation chart. ; It is the frequency domain subcarrier index number. ;

[0074] Indicates factors related to the judgment. This represents the joint fourth moment.

[0075] Error symbols in the remainder The points are evenly distributed among the constellation points.

[0076] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0077] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that, in step 4, the expected value of the square of the periodic cross-correlation function is calculated based on the higher-order statistical moments under the M-ary symmetric channel (MSC) model in step 3; the specific process is as follows:

[0078] Step 41: Calculate the first... The periodic cross-correlation function value at each delay point Square of the modulus ; indicates as:

[0079] (8)

[0080] in, These are DFT basis vectors. , express 0-dimensional vector express 0-dimensional vector;

[0081] These are DFT basis vectors. , express 0-dimensional vector express 0-dimensional vector;

[0082] This refers to the frequency domain subcarrier index number; This refers to the frequency domain subcarrier index number; ; ;

[0083] Indicates the first One delay point, ;

[0084] For Kronecker product; For vectorization operators;

[0085] Superscript Indicates transpose; superscript Indicates conjugate; superscript This indicates the transpose;

[0086] Because the data subcarriers in OFDM signals carry random constellation symbols, and decoding errors follow a random transition characterized by a general error symbol model, It is a random variable and requires a set average to obtain universality;

[0087] Step 42: Calculation Expectations ; indicates as:

[0088] (9)

[0089] in,

[0090] The fourth-order coupling scheme representing subcarrier symbols; ;

[0091] The elements are given by the following formula:

[0092] (10)

[0093] in, Indicates the first Decoded and reconstructed symbols on each subcarrier; Indicates the first Decoded and reconstructed symbols on each subcarrier; Indicates the first Transmitted symbols on each frequency domain subcarrier; Indicates the first Transmitted symbols on each frequency domain subcarrier;

[0094] This is the frequency domain subcarrier index number. ; For frequency domain subcarrier index numbers, ; Indicates the frequency domain subcarrier index number. ; Indicates the frequency domain subcarrier index number. .

[0095] At sampling rate The above equation shows that oversampling introduces additional... Each empty subcarrier must be present. This will be taken into consideration.

[0096] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0097] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that, in step 42... Expectations The solution process is as follows:

[0098] Step 421: Consider the following five cases for derivation. The specific process is as follows:

[0099] Case 1: When there exists any ,have:

[0100] (11)

[0101] Scenario 2: When all ,have:

[0102] (12)

[0103] in, Indicates the joint fourth moment, Indicates factors relevant to the judgment;

[0104] Case 2 Recorded as ;

[0105] Scenario 3: When all ,have:

[0106] (13)

[0107] Case 3 Recorded as ;

[0108] in, Indicates the first The symbols of the pilot subcarriers on each subcarrier, Indicates the first The symbols of the pilot subcarriers on each subcarrier, Indicates the first The symbols of the pilot subcarriers on each subcarrier, Indicates the first The symbol of the pilot subcarrier on each subcarrier;

[0109] Scenario 4: One or three of them correspond to data subcarriers, and the rest correspond to pilot subcarriers; since the odd-order moments of M-PSK / QAM, which has circular symmetry, are zero, we have:

[0110] (14)

[0111] Scenario 5: When For any two corresponding data subcarriers, and the other two corresponding pilot subcarriers, we have:

[0112] (15)

[0113] Case 5 Recorded as ;

[0114] Represents the component matrix; express ; express ; express ; express ;

[0115] Step 422: Calculation ;

[0116] Step 423: Calculation ;

[0117] Step 424: Based on step 422 and step 423 ,get Expectations ; Represented as:

[0118] (16)

[0119] According to equation (16), It depends not only on the decoding error rate It also depends on the modulation order. .

[0120] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0121] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One to Six in that the calculation in step 422 is... The specific process is as follows:

[0122] For the derivation The closed-form expression first analyzes case 2, which contains only data items. Substituting equation (12) into equation (9), we find that when there are only data items... It is given by the following formula:

[0123] (17)

[0124] in, Indicates the contribution of the data subcarrier portion; This indicates the inherent periodicity factor due to the subcarrier arrangement; Indicates the number of data subcarriers;

[0125] (18)

[0126] in, This represents the oversampling factor.

[0127] Therefore, in comb pilot mode, the squared P-CCF expectation (15) containing data subcarriers not only exhibits a main lobe gain loss, but also... Cause Causes periodic interference;

[0128] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0129] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the calculation in step 423 is... The specific process is as follows:

[0130] Consider pilot-related terms, namely cases 3 and 5;

[0131] Step 4231: Pilot subcarrier set based on step 1 Corresponding to Case 3 , in formula (9) Rewritten as:

[0132] (19)

[0133] Step 4232: Based on the situation given in case 5 Substitute formula (15) into formula (9) have to:

[0134] (20)

[0135] Step 4233: Substitute formula (19) and formula (20) into formula (9) to obtain ; indicates as:

[0136] (twenty one)

[0137] in, This represents the contribution of all components including pilot terms; This indicates the contribution of only the pilot term; This represents the contribution of the pilot term and the data term coupling. This represents the contribution of the pilot term and the data term coupling. express The average power of frequency domain subcarrier communication symbols; It is the frequency domain subcarrier index number. .

[0138] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0139] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that, in step 5, the expected main lobe integral side lobe ratio (E-MISR) is constructed as a quantitative indicator of positioning accuracy based on the expectation of the square of the periodic cross-correlation function.

[0140] An optimization objective is constructed based on the expected main lobe integral side lobe ratio, a performance evaluation metric for time delay estimation.

[0141] The specific process is as follows:

[0142] Step 51: Calculate the expected main lobe integral side lobe ratio, a performance evaluation index for time delay estimation, expressed as:

[0143] (twenty two)

[0144] in, The expected main lobe integral side lobe ratio is used as a performance evaluation metric for time delay estimation.

[0145] oversampling factor The value of the periodic cross-correlation function at time 0. oversampling factor The periodic cross-correlation function under the following conditions The value at time;

[0146] The numerator is the maximum estimable delay; the numerator is the expected main lobe power at zero delay, reflecting the target detection intensity; the denominator is the delay. The desired sidelobe power characterizes multipath interference and noise floor.

[0147] Step 52: Construct an optimization objective based on the expected main lobe integral sidelobe ratio, a performance evaluation metric for time delay estimation; the process is as follows:

[0148] The optimization objective is to maximize This is equivalent to minimizing the integral sidelobe level; expressed as:

[0149] (twenty three)

[0150] in, Represents the power vector of the pilot subcarrier The Middle Power; This indicates the upper limit of the total power of the pilot subcarriers; This represents the power vector of the pilot subcarrier; This represents the set of pilot subcarriers.

[0151] E-MISR comprehensively considers four major factors: pilot power, pilot quantity, decoding error, and constellation diagram statistical characteristics, accurately depicting the trade-off between randomness and determinism in underwater acoustic channels.

[0152] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0153] Specific Implementation Method Ten: This implementation method differs from Specific Implementation Methods One through Nine in that, in step 6, the optimization objective is solved based on the particle swarm optimization algorithm to obtain the optimal set of pilot subcarriers. The specific process is as follows:

[0154] Step 61: Let the number of iterations be... ;

[0155] Initialize the particle population; the specific process is as follows:

[0156] Each particle represents an element of the power vector of a pilot subcarrier. , is represented as:

[0157] (twenty four)

[0158] in, Indicates the first The symbols of the pilot subcarriers on each subcarrier, , Indicates the power of the pilot subcarrier; Indicates taking the absolute value;

[0159] Step 62: Calculate the fitness of all particles; the specific process is as follows:

[0160] The reciprocal of the E-MISR index is used as the fitness value. , is represented as:

[0161] (25)

[0162] Introducing a penalty function to obtain the final fitness value , is represented as:

[0163] (26)

[0164] In the formula, This represents the final fitness value after introducing the penalty function. This is the penalty coefficient; This indicates the upper limit of the total power of the pilot subcarriers;

[0165] Substitute the position of each particle into the objective function and calculate the corresponding fitness value to determine the quality of the current solution (fitting maximization / minimization optimization problem).

[0166] Step 63: Update the individual optimal pbest;

[0167] For each particle, compare its current fitness with its own historical best fitness: if the current solution is better, update the particle's individual best position; otherwise, retain the original historical best position.

[0168] Step 64: Update the globally optimal gbest;

[0169] Iterate through the individual optimal solutions of all particles, select the current optimal position and fitness of the entire population, update the global optimal solution, and complete the population information sharing;

[0170] Step 65: Update particle velocity and position;

[0171] Step 66: Let the number of iterations be... Repeat steps 62 to 66 until convergence is achieved, thus obtaining the optimal set of pilot subcarriers. .

[0172] Figure 2 This is the flowchart corresponding to this step.

[0173] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0174] The simulation performance analysis is presented below with reference to the accompanying drawings. To verify the effectiveness of this invention in the integrated waveform design for underwater acoustic communication and positioning, an integrated underwater acoustic OFDM communication and positioning system was constructed, comprising 128 subcarriers, a bandwidth of 1kHz, a center frequency of 7kHz, and an oversampling factor. OFDM symbol length 128ms, cyclic prefix guard interval 60ms. Number of pilot subcarriers. Number of data subcarriers QPSK modulation (kurtosis) is used. The pilot power allocation optimization problem was solved using the particle swarm optimization (PSO) algorithm, with a population size of 30, 50 iterations, and the fitness function being the E-MISR index.

[0175] When the bit error rate (SER) is 0, 0.1, 0.2, and 0.3, the trade-off curves between E-MISR and pilot data power ratio (PDPR) are shown below. Figure 3 As shown in the attached figures, the comb-shaped pilot structure proposed in this invention exhibits excellent expected main lobe integral sidelobe ratio performance under different decoding error conditions. As the PDPR increases from 0.5 to 2, the E-MISR rapidly decreases and tends to converge, indicating that appropriately increasing the pilot power can effectively suppress sidelobe rise caused by decoding errors and improve positioning accuracy. When the channel conditions are good (SER=0), the system... At this point, the E-MISR performance is close to optimal (approximately 8 dB). As the decoding error increases (SER = 0.1 to 0.3), the E-MISR curve generally rises, but... The average convergence to a low level (approximately 8 dB when SER=0.3) indicates that by optimizing the pilot power configuration, the method of this invention can maintain robust positioning performance even under adverse channel conditions. Subsequently, the marginal effect of further increasing pilot power on improving E-MISR diminishes. At this point, a balance should be struck between communication rate and positioning accuracy, and an appropriate power ratio should be selected.

[0176] Figure 3 The results show that the waveform design method based on OFDM cyclic cross-correlation function proposed in this invention can effectively cope with the challenges brought by underwater acoustic channel decoding errors by reasonably configuring the comb pilot power, and achieve joint optimization of communication and positioning performance. It is suitable for practical application scenarios such as cooperative positioning of autonomous underwater vehicles and positioning of underwater IoT nodes.

[0177] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. An OFDM cyclic cross-correlation function-based integrated communication and positioning waveform optimization method, characterized by: The specific process of the method is as follows: Step 1: obtaining an OFDM signal, the pilot structure adopted by the OFDM signal being a comb-shaped pilot; performing inverse Fourier transform on the obtained OFDM signal to obtain an inverse Fourier transform matrix ; based on the inverse Fourier transform matrix , obtaining an OFDM time domain signal under an oversampling factor of sonar transmission ; Step 2: Over-sampling factor based on sonar emission OFDM time domain signal under , a periodic cross-correlation function expectation model considering decoding error is constructed; Step 3: Based on the expected model of the periodic cross-correlation function considering decoding error constructed in Step 2, calculate the higher-order statistical moments under the M-ary symmetric channel model; Step 4: Based on the higher-order statistical moments under the M-ary symmetric channel model in Step 3, calculate the expectation of the square of the periodic cross-correlation function; Step 5: Based on the expectation of the square of the periodic cross-correlation function, construct the expected main lobe integral side lobe ratio as a performance evaluation index for time delay estimation; An optimization objective is constructed based on the expected main lobe integral side lobe ratio, a performance evaluation metric for time delay estimation. Step 6: Solve the optimization objective based on a particle swarm optimization algorithm to obtain an optimal pilot subcarrier set .

2. The communication and positioning integrated waveform optimization method based on OFDM cyclic cross-correlation function according to claim 1, characterized in that: The OFDM signal obtained in the step 1 adopts a comb pilot structure; inverse Fourier transform is performed on the obtained OFDM signal to obtain an inverse Fourier transform matrix ; based on the inverse Fourier transform matrix , an OFDM time domain signal under an oversampling factor of the sonar emission is obtained ; The specific process is as follows: Step 11: Acquire the baseband OFDM signal. The pilot structure used for the baseband OFDM signal is a comb pilot. Let the total number of subcarriers of the baseband OFDM signal be ; The set of null subcarriers is denoted by ; Let the uniform distribution of sparse pilot interval is ; Total number of subcarriers includes Data subcarriers and One pilot subcarrier; Introducing decoding error rate ; ； The number of data subcarriers constitutes the data subcarrier set. ; The number of pilot subcarriers constitutes the pilot subcarrier set. ; The number of pilot subcarriers constitutes the empty subcarrier set. ; Define sampling rate , , For oversampling factor, For bandwidth; Data subcarrier set Pilot subcarrier set empty subcarrier set As shown in the following formula: (1) make ; ； in, This refers to the frequency domain subcarrier index number; It is a constant; , As an intermediate variable; Step 12: Perform an inverse Fourier transform on the acquired baseband OFDM signal to obtain the matrix after the inverse Fourier transform. ; Step 13: Based on the matrix after inverse Fourier transform Obtain the oversampling factor of sonar emission. OFDM time-domain signal ; indicates as: (2) in, Oversampling factor representing sonar emission OFDM time-domain signal; It is an equivalent frequency domain symbol vector, which includes data symbols, pilot symbols, and zero-padded frequency domain symbols; , For the first Transmitted symbols on each frequency domain subcarrier It is the frequency domain subcarrier index number. Superscript This indicates the transpose; Indicates the first The delay point The time-domain complex exponential basis function of each frequency domain subcarrier; Indicates the first One delay point; ; , The imaginary unit, .

3. The communication and positioning integrated waveform optimization method based on OFDM cyclic cross-correlation function according to claim 2, characterized in that: The oversampling factor based on sonar emission in step 2 OFDM time-domain signal Construct an expectation model of the periodic cross-correlation function considering decoding error; expressed as: (3) in, For the first The periodic cross-correlation function values ​​at each delay point; The OFDM time-domain signal received by the receiver after decoding and reconstruction. ; It is a cyclic shift matrix. ; express 3D identity matrix To indicate 3D identity matrix; These are DFT basis vectors. , express 0-dimensional vector express 0-dimensional vector; The equivalent frequency domain symbol vector for decoding and reconstruction; For the first Decoded and reconstructed symbols on each subcarrier, superscript This indicates the conjugate transpose.

4. The communication and positioning integrated waveform optimization method based on OFDM cyclic cross-correlation function according to claim 3, characterized in that: In step 3, based on the expected model of the periodic cross-correlation function considering decoding error constructed in step 2, the higher-order statistical moments under the M-ary symmetric channel model are calculated; the specific process is as follows: Step 31: Given the error transition matrix ; indicates as: (4) in, Indicates the decoding error rate; Indicates the number of elements in the constellation diagram; The sending symbol is He was sentenced to The conditional probability; The constellation chart indicates the first one. One element; The constellation chart indicates the first one. One element; ; ; Represented as: (5) in, Indicates the sending symbol, Indicates the sending symbol; Indicates satisfaction time The probability of; satisfy: (6) Step 32: Based on calculate The higher-order statistical moments under the metasymmetric channel model are expressed as: (7) in, Indicates the expectation; Indicates the absolute value; superscript Indicates conjugate; Indicates the kurtosis of a constellation chart. ; It is the frequency domain subcarrier index number. ; Indicates factors related to the judgment. This represents the joint fourth moment.

5. The communication and positioning integrated waveform optimization method based on OFDM cyclic cross-correlation function according to claim 4, characterized in that: In step 4, the expected value of the square of the periodic cross-correlation function is calculated based on the higher-order statistical moments under the M-ary symmetric channel model in step 3; the specific process is as follows: Step 41: Calculate the first... The periodic cross-correlation function value at each delay point Square of the modulus ; indicates as: (8) in, These are DFT basis vectors. , express 0-dimensional vector express 0-dimensional vector; These are DFT basis vectors. , express 0-dimensional vector express 0-dimensional vector; This refers to the frequency domain subcarrier index number; This refers to the frequency domain subcarrier index number; ; ; Indicates the first One delay point, ; For Kronecker product; For vectorization operators; Superscript Indicates transpose; superscript Indicates conjugate; superscript This indicates the transpose; Step 42: Calculation Expectations ; indicates as: (9) in, The fourth-order coupling scheme representing subcarrier symbols; ; The elements are given by the following formula: (10) in, Indicates the first Decoded and reconstructed symbols on each subcarrier; Indicates the first Decoded and reconstructed symbols on each subcarrier; Indicates the first Transmitted symbols on each frequency domain subcarrier; Indicates the first Transmitted symbols on each frequency domain subcarrier; This is the frequency domain subcarrier index number. ; This is the frequency domain subcarrier index number. ; Indicates the frequency domain subcarrier index number. ; Indicates the frequency domain subcarrier index number. .

6. The communication and positioning integrated waveform optimization method based on OFDM cyclic cross-correlation function according to claim 5, characterized in that: In step 42 Expectations The solution process is as follows: Step 421: Consider the following five cases for derivation. The specific process is as follows: Case 1: When there exists any ,have: (11) Scenario 2: When all ,have: (12) in, Indicates the joint fourth moment, Indicates factors relevant to the judgment; Case 2 Recorded as ; Scenario 3: When all ,have: (13) Case 3 Recorded as ; in, Indicates the first The symbols of the pilot subcarriers on each subcarrier, Indicates the first The symbols of the pilot subcarriers on each subcarrier, Indicates the first The symbols of the pilot subcarriers on each subcarrier, Indicates the first The symbol of the pilot subcarrier on each subcarrier; Scenario 4: One or three of them correspond to data subcarriers, and the rest correspond to pilot subcarriers; There are: (14) Scenario 5: When For any two corresponding data subcarriers, and the other two corresponding pilot subcarriers, we have: (15) Case 5 Recorded as ; Represents the component matrix; express ; express ; express ; express ; Step 422: Calculation ; Step 423: Calculation ; Step 424: Based on step 422 and step 423 ,get Expectations ; Represented as: (16)。 7. The integrated waveform optimization method for communication and positioning based on OFDM cyclic cross-correlation function according to claim 6, characterized in that: The calculation in step 422 The specific process is as follows: First, we analyze case 2, which contains only data items. Substituting equation (12) into equation (9), we find that when there are only data items... It is given by the following formula: (17) in, This indicates the contribution of the data subcarrier portion; This indicates the inherent periodicity factor due to the subcarrier arrangement; Indicates the number of data subcarriers; (18) in, This represents the oversampling factor.

8. The integrated waveform optimization method for communication and positioning based on OFDM cyclic cross-correlation function according to claim 7, characterized in that: The calculation in step 423 ; The specific process is as follows: Step 4231: Pilot subcarrier set based on step 1 Corresponding to Case 3 , Rewritten as: (19) Step 4232: Based on the situation given in case 5 Substitute formula (15) into have to: (20) Step 4233: Substitute formula (19) and formula (20) into formula (9) to obtain ; indicates as: (21) in, This represents the contribution of all terms including pilot terms; This indicates the contribution of only the pilot term; This represents the contribution of the coupling between the pilot term and the data term; This represents the contribution of the coupling between the pilot term and the data term; express The average power of frequency domain subcarrier communication symbols; It is the frequency domain subcarrier index number. .

9. The communication and positioning integrated waveform optimization method based on OFDM cyclic cross-correlation function according to claim 8, characterized in that: In step 5, the expected main lobe integral side lobe ratio is constructed based on the expectation of the square of the periodic cross-correlation function. An optimization objective is constructed based on the expected main lobe integral side lobe ratio, a performance evaluation metric for time delay estimation. The specific process is as follows: Step 51: Calculate the expected main lobe integral side lobe ratio, a performance evaluation index for time delay estimation, expressed as: (22) in, The expected main lobe integral side lobe ratio is used as a performance evaluation metric for time delay estimation. oversampling factor The value of the periodic cross-correlation function at time 0. oversampling factor The periodic cross-correlation function under the following conditions The value at time; Step 52: Construct an optimization objective based on the expected main lobe integral sidelobe ratio, a performance evaluation metric for time delay estimation; the process is as follows: The optimization objective is to maximize This is equivalent to minimizing the integral sidelobe level; expressed as: (23) in, Represents the power vector of the pilot subcarrier The Middle Power; This indicates the upper limit of the total power of the pilot subcarriers; This represents the power vector of the pilot subcarrier; This represents the set of pilot subcarriers.

10. The communication and positioning integrated waveform optimization method based on OFDM cyclic cross-correlation function according to claim 9, characterized in that: In step 6, the optimization objective is solved based on the particle swarm optimization algorithm to obtain the optimal set of pilot subcarriers. The specific process is as follows: Step 61: Let the number of iterations be... ; Initialize the particle population; the specific process is as follows: Each particle represents an element of the power vector of a pilot subcarrier. , represented as: (24) in, Indicates the first The symbols of the pilot subcarriers on each subcarrier, , Indicates the power of the pilot subcarrier; Indicates taking the absolute value; Step 62: Calculate the fitness of all particles; the specific process is as follows: The reciprocal of the E-MISR index is used as the fitness value. , represented as: (25) Introducing a penalty function to obtain the final fitness value , represented as: (26) In the formula, This represents the final fitness value after introducing the penalty function. This is the penalty coefficient; This indicates the upper limit of the total power of the pilot subcarriers; Step 63: Update the individual optimal pbest; Step 64: Update the globally optimal gbest; Step 65: Update particle velocity and position; Step 66: Let the number of iterations be... Repeat steps 62 to 66 until convergence is achieved, thus obtaining the optimal set of pilot subcarriers. .

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