A GOCDM signal modulation and demodulation method based on generalized Fresnel transform

Abstract

A GOCDM signal modulation and demodulation method based on generalized Fresnel transform is proposed. A generalized Fresnel transform matrix is ​​#imgabs0#Φ N is the N-order traditional Fresnel transformation matrix, I M It is an M-order unit matrix, and the symbol #imgabs1# represents the Kronecker product of the matrix; in the signal modulation method at the transmitting end, the data bits to be transmitted are converted into an MN-dimensional symbol vector x through a serial / parallel conversion module and a bit-symbol mapping module, and a generalized inverse Fresnel transformation is performed on x #imgabs2#. In the signal demodulation method at the receiving end, the signal vector r is sent to a GOCDM symbol detection module to obtain an estimated value of the transmitted symbol vector x #imgabs3# and then #imgabs4# performs mapping from symbols to data bits, etc. The GOCDM communication signal of the present invention has lower requirements on the transmitter power amplifier and the digital / analog conversion unit, and the signal demodulation method can effectively overcome the adverse effects of signal distortion caused by the high-speed movement of the communication machine.

Description

Technical Field

[0001] The invention relates to the field of communication technology, and in particular to a GOCDM signal modulation and demodulation method based on generalized Fresnel transform. Background Art

[0002] In 2016, Ouyang proposed a communication signal design method called OCDM (Orthogonal Chirp Division Multiplexing) based on the traditional Fresnel transform. The communication signal has high spectrum utilization and excellent anti-interference performance, which has attracted widespread attention in the industry. OCDM technology constructs a set of mutually orthogonal linear frequency modulation waves as parallel subcarriers to carry data, and the receiving end restores the original signal through matched filtering. The basis of the OCDM communication system is the discrete Fresnel transform. Specifically, the inverse discrete Fresnel transform (IDFnT) generates the OCDM signal at the transmitter, and the discrete Fresnel transform restores the OCDM signal at the receiver. Therefore, the discrete Fresnel transform is the key to the digital implementation of the OCDM system. However, the peak-to-average ratio of the OCDM signal is very high, which places high requirements on the digital-to-analog conversion module and power amplifier module of the communication machine, and restricts the economy and energy efficiency of the communication machine. The present invention expands the traditional OCDM technology, reduces the peak-to-average ratio of the signal, and improves the transmission reliability of the system. Summary of the invention

[0003] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a generalized GOCDM technology based on generalized Fresnel transform, including a transmitter communication signal modulation method and a receiver signal demodulation method based on the technology. GOCDM technology is an extension and upgrade of traditional OCDM technology, which can obtain a lower signal peak-to-average ratio and higher transmission reliability than traditional OCDM systems, and is also conducive to wireless communication systems to achieve high-speed and reliable communication in fast-moving scenarios.

[0004] The present invention is achieved through the following technical solutions:

[0005] A GOCDM signal modulation and demodulation method based on generalized Fresnel transform includes a signal modulation method and a signal demodulation method. The signal modulation method at the transmitting end includes the following steps:

[0006] S1-1. The data bits to be sent are converted into an MN-dimensional symbol vector x=[x0,...,x n ,...,x MN-1 ] T, where the elements are taken from the emission symbol set Right now M and N are positive integers;

[0007] S1-2. Perform a generalized inverse Fresnel transform on the MN-dimensional symbolic vector x Get MN-dimensional signal vector, where is the generalized inverse Fresnel transformation matrix;

[0008] S1-3. Perform parallel / serial conversion on the signal vector s to obtain the signal sequence s n ,n=.,...,MN-1, and add a cyclic prefix CP (Cyclic Prefix, CP) of length G to get the sequence n=-G,…,0,…,MN-1,and:

[0009]

[0010] sequence That is, it is a generalized orthogonal chirp division multiplexing (GOCDM) baseband signal, which will be transmitted in a baseband equivalent channel; the part after the transmitter digital-to-analog conversion module (including itself), the physical channel and the part before the receiver analog-to-digital conversion module (including itself) are regarded as a whole and defined as the baseband equivalent channel.

[0011] The signal demodulation method at the receiving end comprises the following steps:

[0012] S2-1, baseband signal r obtained by the receiver n Described as:

[0013]

[0014] in, is the imaginary unit, b is the time serial number, h i ,l i ,k i are complex numbers, non-negative integers and real numbers, respectively, representing the gain, relative delay (relative to the shortest path) and Doppler frequency shift of the i-th signal propagation path, Signal sequence No. nl i The value of the point, P is the number of paths, ω n is the channel noise;

[0015] S2-2, the received baseband sequence signal r n The cyclic prefix is ​​removed and MN signal points are taken out. Under the expression of formula (1) in step S1-3 and formula (2) in step S2-1, the signal points taken out are r0, r1, ..., rM N-1 ;

[0016] S2-3, after the serial-to-parallel conversion module, the signal points taken out in step S2-2 are converted into a received signal vector r;

[0017] S2-4, the signal vector r is sent to the GOCDM symbol detection module. The function of the GOCDM symbol detection module is to estimate the transmission symbol vector x based on r. The estimation result is recorded as The GOCDM symbol detection module is based on generalized Fresnel transform;

[0018] S2-5, yes The elements in are mapped from symbols to data bits one by one, and the mapping rule corresponds to the bit-to-symbol mapping module in step S1-1 to obtain a data bit vector;

[0019] S2-6, the data bit vector is converted into a data bit sequence by a parallel / serial conversion module;

[0020] Among them, the generalized Fresnel transform is based on the generalized Fresnel transform matrix The transformation of Φ N is the N-order traditional Fresnel transformation matrix, I M is the M-order identity matrix, symbol Represents the Kronecker product of matrices. According to the definition of the Kronecker product, the generalized Fresnel transformation matrix Θ M，N It can be written as the following block matrix:

[0021]

[0022] The corresponding generalized inverse Fresnel transform is based on the generalized inverse Fresnel transform matrix Transformation, generalized inverse Fresnel transformation matrix is the generalized Fresnel transformation matrix Θ M，N The conjugate transposed matrix of .

[0023] Furthermore, the implementation method of the GOCDM symbol detection module comprises the following steps:

[0024] S3-1. Use the existing algorithm to perform channel equalization on the received MN-dimensional signal vector r to obtain the signal vector

[0025] S3-2. Signal vector Perform MN point generalized Fresnel transform Get the MN-dimensional signal vector y;

[0026] S3-3. Vector y = [y0, ..., yi , …, y MN-1 ] T Detect the elements of one by one and get the estimate of the transmitted symbol vector x

[0027] Furthermore, the detection algorithm for detecting elements one by one in step S3-3 adopts maximum likelihood (ML) detection, that is: in, represents the symbol set used by the bit-symbol mapping module in the transmitter, and α represents The elements in .

[0028] Furthermore, the channel equalization is performed in the time domain or the frequency domain, and the equalization algorithm adopts the classic Zero Forcing (Zero Forcing, ZF) equalization or Minimum Mean Square Error (Minimum Mean Square Error) equalization.

[0029] Furthermore, in step S3-2, the signal vector Perform MN point generalized Fresnel transform The method is:

[0030] S3-2-1. Input signal vector Transformed into a signal matrix with M rows and N columns Coming soon vector The elements in are read out sequentially and written into the matrix column by column.

[0031] S3-2-2. Signal Matrix Perform N-point Fresnel transform row by row to obtain the signal matrix Y;

[0032] S3-2-3. Transform the signal matrix Y into an MN-dimensional column vector y, that is, read out the elements in the matrix Y column by column and write them into the vector y in sequence.

[0033] Furthermore, the implementation method of the GOCDM symbol detection module comprises the following steps:

[0034] S4-1. Perform a generalized Fresnel transform on the signal vector r to obtain the signal vector y = Θ M，N r ;

[0035] S4-2, according to the channel path information described by formula (2) in step S2-1 {(h i ,l i ,k i )|i=0,1,...,P-1} calculate the equivalent channel and approximate it as a sparse matrix The calculation formula for the p-th row and q-th column element of is as follows:

[0036]

[0037] in,

[0038]

[0039] Where p,q∈{0,1,...,MN-1}; P is the number of paths; h i ,l i ,k i are complex numbers, non-negative integers and real numbers, respectively, representing the gain, relative delay and Doppler frequency shift of the i-th signal propagation path; and Respectively represent k i The integer part and the decimal part of Indicates the operation of rounding down to an integer; Indicates the modulo operation (i.e., mod M, where M has the same meaning as the above M); B i , C i Is a non-negative integer used to control the approximate accuracy. When B i =C i =0;

[0040] S4-3, according to y obtained in step S4-1 and y obtained in step S4-2 Based on mathematical model The general detection algorithm is used to estimate the transmitted symbol vector x in, is the noise vector, which is the channel noise ω described in formula (2) in step S2-1 n The vector [w0, w1, ..., ω MN-1 ] T The generalized Fresnel transform of ω in formula (2) n is the channel noise, which belongs to the time domain noise, and Belongs to the generalized Fresnel domain noise vector.

[0041] There is no order of precedence between step S4-1 and step S4-2.

[0042] Furthermore, the general detection algorithm in step S4-3 is the message passing algorithm (MP).

[0043] Furthermore, in step S4-1, a generalized Fresnel transform is performed on the signal vector r to obtain a signal vector y=Θ M，N The method of r is:

[0044] S4-1-1, transforming the signal vector r into a signal matrix R with M rows and N columns, that is, reading out the elements in the vector r in sequence and writing them into the matrix R column by column in turn;

[0045] S4-1-2, perform N-point Fresnel transformation on the signal matrix R row by row to obtain the signal matrix Y;

[0046] S4-1-3. Transform the signal matrix Y into an MN-dimensional column vector g, that is, read out the elements in the matrix Y column by column and write them into the vector y in sequence.

[0047] Furthermore, in step S1-2, a generalized inverse Fresnel transform is performed on the MN-dimensional symbolic vector x The method is:

[0048] S1-2-1, transforming the symbol vector x into a symbol matrix X with M rows and N columns, that is, reading out the elements in the vector x in sequence and writing them into the matrix X column by column;

[0049] S1-2-2. Perform N-point inverse Fresnel transform on the signal matrix X row by row to obtain the signal matrix S;

[0050] S-1-2-3. Transform the signal matrix S into an MN-dimensional column vector s, that is, read out the elements in the matrix S column by column and write them into the vector s in sequence.

[0051] The present invention expands the existing Fresnel transform and proposes a generalized Fresnel transform, including a forward transform and an inverse transform. A new communication signal is designed based on the transform, and a new signal demodulation method is proposed to form a new communication system named GOCDM (Generalized OCDM). The GOCDM communication signal has a lower peak-to-average ratio than the traditional OCDM signal, and has lower requirements on the transmitter power amplifier and the digital / analog conversion unit, which is beneficial to reducing the transmitter cost and power consumption; the signal demodulation method can effectively overcome the adverse effects of signal distortion caused by the high-speed movement of the communication machine, and realize highly reliable signal detection, which is particularly suitable for the application scenario of the high-speed movement of the communication machine. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 Graph showing the relationship between the original signal and the image signal in the traditional Fresnel transform in an embodiment of the present invention.

[0053] Figure 2 Graph showing the relationship between the original signal and the image signal in the generalized Fresnel transform in an embodiment of the present invention.

[0054] Figure 3 This is a block diagram of GOCDM equivalent baseband signal generation in an embodiment of the present invention.

[0055] Figure 4 Schematic diagram of equivalent implementation of generalized inverse Fresnel transform in an embodiment of the present invention.

[0056] Figure 5 This is a GOCDM signal modulation block diagram in an embodiment of the present invention.

[0057] Figure 6 It is a block diagram of GOCDM symbol detection method 1 in an embodiment of the present invention.

[0058] Figure 7 Schematic diagram of equivalent implementation of generalized Fresnel transform in an embodiment of the present invention.

[0059] Figure 8 It is a block diagram of the second GOCDM symbol detection method in an embodiment of the present invention.

[0060] Fig. 9 Schematic diagram of comparison of peak-to-average ratios of GOCDM and OCDM according to an embodiment of the present invention.

[0061] Fig.10 It is a schematic diagram comparing the bit error performance of GOCDM, OCDM and OFDM in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The traditional OCDM signal is realized by discrete Fresnel transform. The discrete OCDM signal can be expressed as: like Figure 1 As shown, suppose there is an N-dimensional signal vector a = [a0, a1, ..., a N-1 ] T , whose elements are complex numbers, [·] T represents the transpose operation of a vector or matrix. The traditional Fresnel transform of the signal vector is to transform the Fresnel transform matrix Φ N Multiply it by Φ, that is, b = Φ N a, the resulting signal vector b is called the image signal of the original signal a, where Φ N is the Fresnel transformation matrix, which is an N-order square matrix. When N is an even number, Φ N The element in the mth row and nth column of is:

[0063]

[0064] When N is an odd number,

[0065]

[0066] Corresponding to the Fresnel transform, the inverse Fresnel transform can be used with the matrix To describe, here [·]H Represents the conjugate transpose operation of the matrix. Performing an inverse Fresnel transform on the above-mentioned image signal b can yield its original signal a, namely

[0067] The present invention expands the traditional OCDM technology and the traditional Fresnel transform, and proposes a new type of transform, which is named generalized Fresnel transform, including forward transform and inverse transform. The forward transform matrix is Φ N is the N-order traditional Fresnel transformation matrix, I M is the M-order identity matrix, symbol represents the Kronecker product of the matrix. According to the definition of the Kronecker product, the generalized Fresnel transformation matrix Θ M,N It can be written as the following block matrix:

[0068]

[0069] The corresponding generalized inverse Fresnel transformation matrix is That is Θ M,N The conjugate transposed matrix of .

[0070] like Figure 2 As shown, given a MN-dimensional complex signal vector a=[a0,a1,...,a MN-1 ] T , and perform a generalized Fresnel transform to obtain its image signal b = Θ M,N a; object signal b is transformed by generalized inverse Fresnel to get the original signal

[0071]

[0072] Based on the generalized Fresnel transform proposed above, the present invention proposes a novel communication signal modulation method, and names it generalized GOCDM (Generalized Orthogonal Chirp Division Multiplexing). The GOCDM technology can reduce the peak-to-average ratio of the signal while improving the transmission reliability of the system. The GOCDM technology is specifically introduced below, which is mainly based on the signal modulation method and demodulation method of the generalized Fresnel transform mentioned above.

[0073] A GOCDM signal modulation and demodulation method based on generalized Fresnel transform includes a signal modulation method and a signal demodulation method, such as Figure 3 As shown, the signal modulation method at the transmitting end includes the following steps:

[0074] S1-1. According to the application requirements, select a suitable bit-data symbol mapping scheme (constellation diagram), set M and N to appropriate integer values, and divide the data bits to be sent into multiple groups of equal length. Take a group of data bits to be sent and convert them into an MN-dimensional symbol vector x = [x0, ..., x n , …, x MN-1 ] T , where the elements are taken from the emission symbol set Right now M and N are positive integers;

[0075] S1-2. Perform a generalized inverse Fresnel transform on the MN-dimensional symbolic vector x Get MN-dimensional signal vector, where is the generalized inverse Fresnel transformation matrix;

[0076] S1-3. Perform parallel / serial conversion on the signal vector s to obtain the signal sequence s n , n = 0, ..., MN-1, and add a cyclic prefix CP (Cyclic Prefix, CP) of length G to obtain the sequence n=-G,…,0,…,MN-1,and:

[0077]

[0078] sequence That is, the generalized orthogonal chirp division multiplexing (GOCDM) baseband signal, which will be transmitted in the baseband equivalent channel. In engineering applications, the part after the transmitter digital-to-analog conversion module (including itself), the physical channel and the part before the receiver analog-to-digital conversion module (including itself) are regarded as a whole and defined as the baseband equivalent channel.

[0079] Above Figure 3 The generalized inverse Fresnel transform in Figure 3 The generalized inverse Fresnel transform module in ), can directly multiply the generalized inverse Fresnel transform matrix with the input vector, can also be achieved by Figure 4 The method shown is implemented to obtain lower computational complexity, and the specific steps are:

[0080] S1-2-1, transforming the symbol vector x into a symbol matrix X with M rows and N columns, that is, reading out the elements in the vector x in sequence and writing them into the matrix X column by column;

[0081] S1-2-2. Perform N-point inverse Fresnel transform on the signal matrix X row by row to obtain the signal matrix s;

[0082] S-1-2-3. Transform the signal matrix s into an MN-dimensional signal vector s, that is, read out the elements in the matrix S column by column and write them into the vector s in sequence.

[0083] For example: when N=4, M=2, x=[x0, x1, ..., x7] T ,X=[[x0,x1] T , [x2, x3] T , [x4, x5] T , [x6, x7] T ]. S=[[s0,s1] T , [s2, s3] T , [s4, s5] T , [s6, s7] T ],s=[s0,s1,…,s7] T .in:

[0084]

[0085] Signal demodulation refers to the process of estimating the transmitted data from the received signal, which is the basic function of the communication system receiver. The general structure of the receiver of the GOCDM system is as follows: Figure 5 As shown, the figure describes the framework steps of GOCDM signal demodulation.

[0086] The signal demodulation method at the receiving end of the present invention comprises the following steps:

[0087] S2-1. Without loss of generality, assume that both the transmitter and receiver use standard sampling rates, the receiver achieves ideal signal synchronization and has complete channel information, and the GOCDM baseband signal generated by the transmitter is defined by formula (1): In the mobile application scenario, the baseband signal r obtained by the receiver is n Described as:

[0088]

[0089] in, is an imaginary unit, n is the time serial number, h i , l i , k i are complex numbers, non-negative integers and real numbers, respectively, representing the gain, relative delay (relative to the shortest path) and Doppler frequency shift of the i-th signal propagation path, Signal sequence No. nl i The value of the point, P is the number of paths, ω n is the channel noise;

[0090] S2-2, the received baseband sequence signal rn The cyclic prefix in is removed, and MN signal points are taken out. Under the expression of formula (1) in step S1-3 and formula (2) in step S2-1, the signal points taken out are r0, r1, ..., r MN-1 ;

[0091] S2-3, after the serial-to-parallel conversion module, the signal points taken out in step S2-2 are converted into a received signal vector r;

[0092] S2-4, the signal vector r is sent to the GOCDM symbol detection module. The function of the GOCDM symbol detection module is to estimate the transmission symbol vector x based on r. The estimation result is recorded as The GOCDM symbol detection module is based on the generalized Fresnel transform y=Θ M，N r, where Θ M，N is the generalized Fresnel transform matrix, y is the MN-dimensional signal vector;

[0093] S2-5, yes The elements in are mapped from symbols to data bits one by one, and the mapping rule corresponds to the bit-symbol mapping module in step S1-1 to obtain a data bit vector;

[0094] S2-6. The data bit vector is converted into a data bit sequence through a parallel / serial conversion module.

[0095] Figure 4 The GOCDM symbol detection module is the core of the GOCDM receiver. The present invention proposes two implementation methods. Please refer to the following for detailed description.

[0096] Method 1:

[0097] like Figure 6 As shown, the implementation method of the GOCDM symbol detection module includes the following steps:

[0098] S3-1. Use the existing algorithm to perform channel equalization on the received MN-dimensional signal vector r to obtain the signal vector Channel equalization can be performed in the time domain or the frequency domain, and the equalization algorithm can adopt the classic Zero Forcing (ZF) equalization, Minimum Mean Square Error (MMSE) equalization, etc.

[0099] S3-2. Signal vector Perform MN point generalized Fresnel transform Get the MN-dimensional signal vector y.

[0100] S3-3. Vector y = [y0, ..., y i , …, yMN-1 ] T Detect the elements of one by one, and get the estimate of the transmitted symbol vector x The detection algorithm can adopt Maximum Likelihood (ML) detection, that is: here represents the symbol set used by the bit-symbol mapping module at the transmitter, and α represents The elements in .

[0101] Among them, the above signal vector Perform MN point generalized Fresnel transform In addition to direct matrix multiplication, you can also use Figure 7 The method shown is implemented by using the matrix multiplication method, which is more efficient than directly implementing the matrix multiplication method (i.e. ) has lower computational complexity. The specific steps of the equivalent method are:

[0102] S3-2-1. Input signal vector Transformed into a signal matrix with M rows and N columns Coming soon vector The elements in the matrix are read out sequentially and written into the matrix column by column.

[0103] S3-2-2. Signal Matrix Perform N-point Fresnel transform row by row to obtain the signal matrix Y.

[0104] S3-2-3. Transform the signal matrix Y into an MN-dimensional signal vector y, that is, read out the elements in the matrix Y column by column and write them into the vector y in sequence.

[0105] For example: When N=4, M=2, Y=[[y0,y1] T , [y2, y3] T , [y4, y5] T , [y6, y7] T ],y=[y0,y1,…,y7] T .in:

[0106]

[0107] Method 2:

[0108] like Figure 8 As shown, the implementation method of the GOCDM symbol detection module includes the following steps:

[0109] S4-1. Perform a generalized Fresnel transform on the signal vector r to obtain the signal vector y = Θ M，Nr .

[0110] S4-2, according to the channel path information described by formula (2) in step S2-1 {(h i , l i , k i )|i=0,1,…,P-1} calculate the equivalent channel and approximate it as a sparse matrix The calculation formula for the p-th row and q-th column element of is as follows:

[0111]

[0112] in,

[0113]

[0114] Where p,q∈{0,1,...,MN-1}; P is the number of paths; h i ,l i ,k i are complex numbers, non-negative integers and real numbers, respectively, representing the gain, relative delay and Doppler frequency shift of the i-th signal propagation path; and Respectively represent k i The integer part and the decimal part of Indicates the operation of rounding down to an integer; Indicates modular operation (i.e. mod M); B i , C i Is a non-negative integer used to control the approximate accuracy. When B i =C i =0;

[0115] S4-3, according to y obtained in step S4-1 and y obtained in step S4-2 Based on mathematical model is the noise vector, and the general detection algorithm is used to obtain the estimate of the transmitted symbol vector x The general detection algorithm may adopt a message passing algorithm (MP) or the like. Here, is the generalized Fresnel domain noise vector, which is the channel noise ω described in formula (2) in step S2-1 n The vector [w0, w1, ..., w MN-1 ] T The generalized Fresnel transform of

[0116] There is no order of precedence between step S4-1 and step S4-2.

[0117] As mentioned above, the signal vector r is transformed by the generalized Fresnel transform to obtain the signal vector y = Θ M，N r The transformation matrix Θ can be M，N It can be directly multiplied with the vector r, or it can be achieved by Figure 7 The method shown is implemented equivalently to reduce the computational overhead. The specific steps of the latter are:

[0118] S4-1-1, transforming the signal vector r into a signal matrix R with M rows and N columns, that is, reading out the elements in the vector r in sequence and writing them into the matrix R column by column in turn;

[0119] S4-1-2, perform N-point Fresnel transformation on the signal matrix R row by row to obtain the signal matrix Y;

[0120] S4-1-3. Transform the signal matrix Y into an MN-dimensional column vector y, that is, read out the elements in the matrix Y column by column and write them into the vector y in sequence.

[0121] The present invention proposes a generalized Fresnel transform, including a forward transform and an inverse transform. Based on the transform, a communication technology defined as GOCDM is creatively proposed, which mainly includes a communication signal modulation method at the transmitter and a signal demodulation method at the receiver. The GOCDM system is an extension and upgrade of the traditional OCDM technology. It can obtain a lower signal peak-to-average ratio and higher transmission reliability than the traditional OCDM system, and is also conducive to the wireless communication system to achieve high-speed and reliable communication in fast-moving scenarios.

[0122] Fig. 9 A comparison of the Peak to Average Power Ratio (PAPR) of GOCDM and OCDM under Monte Carlo simulation is given. Here, the symbol length of GOCDM and OCDM is the same, which is 128 samples (excluding the cyclic prefix), and the constellation diagram of the bit-symbol mapping used is 4-QAM (Quadrature Amplitude Modulation). Fig. 9 The horizontal axis is the reference peak-to-average ratio, and the vertical axis is the probability that the peak-to-average ratio exceeds the reference peak-to-average ratio, which is given by Fig. 9 It can be seen that the peak-to-average ratio of the GOCDM signal is significantly lower than that of the OCDM signal. When the N value is small, the peak-to-average ratio advantage of GOCDM is particularly obvious.

[0123] Fig.10The error performance comparison of GOCDM, OCDM and OFDM in a mobile underwater acoustic channel is given. The main parameters of the system are as follows: the carrier frequency is 24kHz, the bandwidth is 3.2kHz, the symbol length is 128 (excluding the cyclic prefix), among which N=16 and M=8 of GOCDM, the constellation diagram used for bit-symbol mapping is 4-QAM, the symbol duration is 55 milliseconds (excluding the cyclic prefix), the cyclic prefix duration is 15 milliseconds, the relative movement speed between the communication transceivers is 40 kilometers per hour, and the underwater sound speed is 1500 meters per second. There are 10 physical paths in the channel, and the attenuation coefficient of each path is independent of each other, and the Doppler frequency shift of each path is also independent of each other. Fig.10 The GOCDM-MMSE in the above is the GOCDM error performance obtained by combining the detection method 1 proposed by the present invention with the classic MMSE algorithm, and the GOCDM-MP is the GOCDM error performance obtained by combining the detection method 2 proposed by the present invention with the existing message passing (MP) algorithm. Fig.10 It can be seen that the performance of GOCDM-MP is significantly better than that of GOCDM-MMSE. The fundamental reason is that the MP algorithm is an iterative algorithm with decision feedback, and its success rate is higher than that of MMSE detection without decision feedback. Under the premise of using the same general detection algorithm, the error performance of GOCDM is better than that of the traditional OCDM system and the widely used OFDM system, and has higher communication reliability.

[0124] The above detailed description is a specific description of a feasible embodiment of the present invention. The embodiment is not intended to limit the patent scope of the present invention. Any equivalent implementation or modification that does not deviate from the present invention should be included in the patent scope of this case.

Claims

1. A GOCDM signal modulation and demodulation method based on generalized Fresnel transform, characterized in that: It includes a signal modulation method and a signal demodulation method, wherein the GOCDM is a generalized GOCDM, which is the abbreviation of Generalized Orthogonal Chirp Division Multiplexing, indicating generalized orthogonal chirp division multiplexing; The signal modulation method at the transmitting end comprises the following steps: S1-1. The data bits to be sent are converted into an MN-dimensional symbol vector x=[x0, ..., x n , …, x MN-1 ] T , where the elements are taken from the emission symbol set Right now M and N are positive integers; S1-2. Perform a generalized inverse Fresnel transform on the MN-dimensional symbolic vector x Get the MN-dimensional signal vector s, where is the generalized inverse Fresnel transformation matrix; S1-3. Perform parallel / serial conversion on the signal vector s to obtain the signal sequence s n , n = 0, ..., MN-1, and add a cyclic prefix CP of length G to obtain the sequence And there are: sequence That is, a generalized orthogonal chirp multiplexing (GOCDM) baseband signal, which will be transmitted in a baseband equivalent channel; the transmitter digital-to-analog conversion module and its subsequent parts, the physical channel, the receiver analog-to-digital conversion module and its previous parts are regarded as a whole and defined as the baseband equivalent channel; The signal demodulation method at the receiving end comprises the following steps: S2-1, the baseband sequence signal r obtained by the receiver n Described as: in, is an imaginary unit, n is the time serial number, h i , l i , k i are complex numbers, non-negative integers and real numbers, respectively, representing the gain, relative delay and Doppler frequency shift of the i-th signal propagation path, P is the number of paths, Signal sequence No. nl i The value of the point, ω n is the channel noise; S2-2, the received baseband sequence signal r n The cyclic prefix in is removed, and MN signal points are taken out. Under the expression of formula (1) in step S1-3 and formula (2) in step S2-1, the signal points taken out are r0, r1, ..., r MN-1 ; S2-3, after the serial-to-parallel conversion module, the signal point taken out in step S2-2 is converted into a received signal vector r; S2-4, the signal vector r is sent to the GOCDM symbol detection module. The function of the GOCDM symbol detection module is to estimate the transmission symbol vector x based on r. The estimation result is recorded as The GOCDM symbol detection module is based on generalized Fresnel transform; S2-5, yes The elements in are mapped from symbols to data bits one by one, and the mapping rule corresponds to the bit-symbol mapping module in step S1-1 to obtain a data bit vector; S2-6, the data bit vector is converted into a data bit sequence by a parallel / serial conversion module; Among them, the generalized Fresnel transform is based on the generalized Fresnel transform matrix Θ M，N The transformation of Among them, Φ N is the N-order traditional Fresnel transformation matrix, I M is the M-order identity matrix, symbol Represents the Kronecker product of matrices. According to the definition of the Kronecker product, the generalized Fresnel transformation matrix Θ M，N It can be written as the following block matrix: The corresponding generalized inverse Fresnel transform is based on the generalized inverse Fresnel transform matrix Transformation, generalized inverse Fresnel transformation matrix is the generalized Fresnel transformation matrix Θ M，N The conjugate transposed matrix of .

2. A GOCDM signal modulation and demodulation method based on generalized Fresnel transform according to claim 1, characterized in that: The implementation method of the GOCDM symbol detection module comprises the following steps: S3-1. Perform channel equalization on the received MN-dimensional signal vector r to obtain the signal vector S3-2. Signal vector Perform MN point generalized Fresnel transform Get the MN-dimensional signal vector y; S3-3. Vector y = [y0, ..., y i , …, y MN-1 ] T Detect the elements of one by one and get the estimate of the transmitted symbol vector x 3. A GOCDM signal modulation and demodulation method based on generalized Fresnel transform according to claim 2, characterized in that: The detection algorithm for detecting elements one by one in step S3-3 adopts maximum likelihood detection, that is: in, represents the symbol set used by the bit-symbol mapping module in the transmitter, and α represents The elements in .

4. The GOCDM signal modulation and demodulation method based on generalized Fresnel transform according to claim 2, characterized in that: The channel equalization in step S3-1 is performed in the time domain or the frequency domain, and the equalization algorithm adopts the classic zero-forcing equalization or the minimum mean square error equalization.

5. The GOCDM signal modulation and demodulation method based on generalized Fresnel transform according to claim 2, characterized in that: In step S3-2, the signal vector Perform MN point generalized Fresnel transform The method is: S3-2-1. Input signal vector Transformed into a signal matrix with M rows and N columns Coming soon vector The elements in the matrix are read out sequentially and written into the matrix column by column. S3-2-2. Signal Matrix Perform N-point Fresnel transform row by row to obtain the signal matrix Y; S3-2-3. Transform the signal matrix Y into an MN-dimensional signal vector y, that is, read out the elements in the matrix Y column by column and write them into the vector y in sequence.

6. The GOCDM signal modulation and demodulation method based on generalized Fresnel transform according to claim 1, characterized in that: The implementation method of the GOCDM symbol detection module comprises the following steps: S4-1. Perform a generalized Fresnel transform on the signal vector r to obtain the signal vector y = Θ M，N r; S4-2, according to the channel path information described by formula (2) in step S2-1 {(h i , l i , k i )|i=0,1,…,P-1} calculate the equivalent channel and approximate it as a sparse matrix The calculation formula for the p-th row and q-th column element of is as follows: in, p,q∈{0,1,…,MN-1}; P is the number of paths; h i , l i , k i are complex numbers, non-negative integers and real numbers, respectively, representing the gain, relative delay and Doppler frequency shift of the i-th signal propagation path; and Respectively represent k i The integer part and the decimal part of Indicates the operation of rounding down to an integer; Indicates modulo M operation; B i , C i Is a non-negative integer used to control the approximate accuracy. When B i =C i =0; S4-3, according to y obtained in step S4-1 and y obtained in step S4-2 Based on mathematical model The general detection algorithm is used to estimate the transmitted symbol vector x in, is the noise vector, which is the channel noise ω described in formula (2) in step S2-1 n The vector [w0, w1, ..., w MN-1 ] T The generalized Fresnel transform of There is no order of precedence between step S4-1 and step S4-2.

7. A GOCDM signal modulation and demodulation method based on generalized Fresnel transform according to claim 6, characterized in that: The general detection algorithm in step S4-3 is the message passing algorithm MP.

8. The GOCDM signal modulation and demodulation method based on generalized Fresnel transform according to claim 6, characterized in that: In step S4-1, a generalized Fresnel transform is performed on the signal vector r to obtain a signal vector y=Θ M，N The method of r is: S4-1-1, transforming the signal vector r into a signal matrix R with M rows and N columns, that is, reading out the elements in the vector r in sequence and writing them into the matrix R column by column in turn; S4-1-2, perform N-point Fresnel transformation on the signal matrix R row by row to obtain the signal matrix Y; S4-1-3. Transform the signal matrix Y into an MN-dimensional signal vector y, that is, read out the elements in the matrix Y column by column and write them into the vector y in sequence.

9. The GOCDM signal modulation and demodulation method based on generalized Fresnel transform according to claim 1, characterized in that: In step S1-2, a generalized inverse Fresnel transform is performed on the MN-dimensional symbolic vector x. The method is: S1-2-1, transforming the symbol vector x into a symbol matrix X with M rows and N columns, that is, reading out the elements in the vector x in sequence and writing them into the matrix X column by column; S1-2-2. Perform N-point inverse Fresnel transform on the signal matrix X row by row to obtain the signal matrix S; S-1-2-3. Transform the signal matrix S into an MN-dimensional signal vector s, that is, read out the elements in the matrix S column by column and write them into the vector s in sequence.

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