Time delay Doppler domain waveform design method and device

Abstract

The invention provides a time delay Doppler domain waveform design method and device, and relates to the technical field of time delay Doppler domain waveform design, and the method comprises the steps: sequentially carrying out the serial-parallel conversion and modulation of a bit stream, and obtaining a plurality of time domain data symbols; performing Chirp-Zak conversion on each time domain data symbol, and converting each time domain data symbol into a DD domain to obtain a DD domain data symbol; and sequentially performing inverse discrete Fourier transform and serial-to-parallel transform on the DD domain data symbol to obtain a time domain sending sequence, adding a cyclic prefix to the time domain sending sequence, and performing pulse shaping to obtain a time domain sending signal. According to the invention, the problem of inter-grid interference of the DD domain in the data processing process of the existing DD domain technical scheme in a high-mobility scene is solved, the bit error rate of data transmission is greatly reduced, and the reliability of data transmission is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of delay-Doppler domain waveform design, and in particular to a delay-Doppler domain waveform design method and device. Background Art

[0002] High mobility has a significant impact on communications, including signal frequency deviation and phase shift caused by the Doppler effect, shortened channel coherence time, increased challenges of rapid channel changes, limited spectrum efficiency and transmission capacity, especially the reduced applicability of high-order modulation and limited multi-layer transmission, while increasing the difficulty of synchronization and access. To solve these problems, anti-Doppler technology and dynamic channel estimation and tracking solutions are proposed to meet the communication challenges in high-speed mobile scenarios. The DD domain has advantages in high-mobility scenarios due to its unique channel model and is the focus of research.

[0003] In the existing DD domain technical solutions, although the inter-symbol interference (ISI) and inter-channel interference (ICI) in the time domain can be solved by cyclic prefixes, the inter-grid interference (IGI) on the DD domain grid still exists and will still cause interference during data processing, resulting in poor bit error rate performance of data detection and affecting the reliability of data processing. Summary of the invention

[0004] The purpose of the present invention is to provide a delay-Doppler domain waveform design method and device to improve the above problems. In order to achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0005] In a first aspect, the present application provides a delay-Doppler domain waveform design method, comprising:

[0006] The bit stream is sequentially converted into serial-to-parallel and modulated to obtain a plurality of time-domain data symbols;

[0007] Performing a Chirp-Zak transform on each of the time domain data symbols, converting each of the time domain data symbols into the DD domain to obtain a DD domain data symbol, wherein the Chirp-Zak transform is calculated using a fast Chirp-Zak transform algorithm;

[0008] The DD domain data symbols are sequentially subjected to inverse discrete Fourier transform and serial-to-parallel transform to obtain a time domain transmission sequence, a cyclic prefix is ​​added to the time domain transmission sequence, and pulse shaping is performed to obtain a time domain transmission signal.

[0009] In a second aspect, the present application also provides a delay-Doppler domain waveform design device, comprising:

[0010] A modulation module, used for performing serial-to-parallel conversion and modulation on the bit stream in sequence to obtain multiple time-domain data symbols;

[0011] A transformation module, configured to perform a Chirp-Zak transformation on each of the time domain data symbols, convert each of the time domain data symbols into a DD domain, and obtain a DD domain data symbol, wherein the Chirp-Zak transformation is calculated using a fast Chirp-Zak transformation algorithm;

[0012] The sending module is used to perform inverse discrete Fourier transform and serial-to-parallel transform on the DD domain data symbols in sequence to obtain a time domain sending sequence, add a cyclic prefix to the time domain sending sequence, perform pulse shaping, and obtain a time domain sending signal.

[0013] The beneficial effects of the present invention are as follows: after the Chirp-Zak transform, the data symbols are embedded with partially orthogonal discrete orthogonal chirp sequences in the DD domain, and the orthogonality of the discrete orthogonal chirp sequences can be used to separate the data symbols, thereby optimizing the system's bit error rate performance, especially the bit error rate performance in high mobility scenarios, thereby improving the reliability of the system's high mobility scenario communications.

[0014] Other features and advantages of the present invention will be set forth in the following description, and in part will become apparent from the description, or may be understood by practicing embodiments of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0016] Figure 1 It is a schematic diagram of the process flow of the delay-Doppler domain waveform design method described in an embodiment of the present invention;

[0017] Figure 2 Schematic diagram of DD domain symbol distribution in an embodiment of the present invention;

[0018] Figure 3 A schematic diagram of a data symbol sending sequence in an embodiment of the present invention;

[0019] Figure 4 It is a performance curve diagram in an embodiment of the present invention. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0021] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0022] Embodiment 1:

[0023] This embodiment provides a delay-Doppler domain waveform design method.

[0024] See also Figure 1 , the figure shows that the method includes step S100, step S200, and step S300.

[0025] Step S100: performing serial-to-parallel conversion and modulation on the bit stream in sequence to obtain a plurality of time-domain data symbols;

[0026] Assuming that there are N modulated time domain data symbols forming a time domain data symbol sequence, the expression of the time domain data symbol sequence is:

[0027] D={D(0),...,D(N-1)}

[0028] Wherein, D represents a time domain data symbol sequence, D(0) represents the first time domain data symbol, and D(N-1) represents the Nth time domain data symbol.

[0029] Step S200: performing a Chirp-Zak transform on each of the time domain data symbols, converting each of the time domain data symbols into the DD domain to obtain a DD domain data symbol, wherein the Chirp-Zak transform is calculated using a fast Chirp-Zak transform algorithm;

[0030] In this embodiment, the Chirp-Zak transform is referred to as CZT transform, and the definition of CZT transform is:

[0031]

[0032] m=0,...,M D -1,n=0,...,N D -1

[0033] In the formula, represents the value of the DD domain data symbol in the mth row and nth column after D(i) is transformed by CZT, D(i) represents the i-th time domain data symbol, m represents the delay index, n represents the Doppler index, M D Indicates the number of delay indexes, N D represents the Doppler index number, represents the i'th discrete orthogonal chirp sequence, k represents the first index parameter, N represents the number of time-domain data symbols, and j represents an imaginary number.

[0034] Simplifying the above formula, we get the simplified

[0035]

[0036] In the formula, represents the value of the DD domain data symbol in the mth row and nth column after D(i) is transformed by CZT, D(i) represents the i-th time domain data symbol, m represents the delay index, n represents the Doppler index, M D Indicates the number of delay indexes, N D represents the number of Doppler indices, N represents the number of time domain data symbols, represents the i'th discrete orthogonal chirp sequence, f i represents the intermediate variable when D(i) undergoes CZT transformation, C i (·) represents the intermediate variable of the CZT transformation result of D(i), j represents an imaginary number, k represents the first index parameter, i represents the second index parameter, Represents modulo N D operate.

[0037] From the simplified It can be seen that is a sparse matrix with only one non-zero element in each row. Represents the CZT result matrix of the i-th time-domain data symbol D(i).

[0038] When each time-domain data symbol undergoes CZT transformation, it needs to undergo orthogonal Chirp modulation and then discrete Zak transformation, which will significantly increase the complexity of the entire system.

[0039] By observing, we find that the number of delayed indexes M D and the number of Doppler indices ND When fixed, the position of non-zero elements in the CZT result matrix of each time domain data symbol remains unchanged. On this basis, a fast Chirp-Zak transform algorithm, namely FCZT transform, is proposed to improve the computational efficiency through FCZT transform.

[0040] Assume that the number of delay indexes is M D and the number of Doppler indices N D The FCZT transform of fixed, time-domain data symbols is defined as:

[0041]

[0042] In the formula, represents the value of the DD domain data symbol in the mth row and nth column after D(i) is transformed by CZT, i represents the second index parameter, i=0,...,N-1, D(i) represents the i-th time domain data symbol, N represents the number of time domain data symbols, Φ i,DD represents the FCZT transformation matrix of D(i), represents the DFT matrix, represents the element in the pth row and qth column of the DFT matrix, N D represents the Doppler index number, Φ i Represents the matrix Chirp of D(i).

[0043] In this embodiment, the DFT matrix represents a discrete Fourier transform matrix, and the FCZT transform matrix represents a fast Chirp-Zak transform matrix.

[0044] The expression of the matrixed Chirp is:

[0045]

[0046] In the formula, Φ i represents the matrix Chirp of D(i), where D(i) represents the i-th time domain data symbol, represents the i'th discrete orthogonal chirp sequence, M D Indicates the number of delay indexes, N D Indicates the Doppler index number.

[0047] In this embodiment, Chirp-Zak transform is performed on all time-domain data symbols, that is, each time-domain data symbol in the time-domain data symbol sequence D is converted to the DD domain.

[0048] Performing a Chirp-Zak transform on each of the time domain data symbols, converting each of the time domain data symbols into a DD domain, and obtaining a DD domain data symbol, including:

[0049] Get the delay index number and Doppler index number of the DD domain;

[0050] In this embodiment, a DD domain plane is defined, and the expression of the DD domain plane is:

[0051]

[0052] m=0,...,M D -1,n=0,...,N D -1

[0053] M D N D =N,M D =LN D

[0054] Where Γ represents the DD domain plane, m represents the delay index, n represents the Doppler index, and M D Indicates the number of delay indexes, N D represents the Doppler index number, N represents the number of time-domain data symbols, T represents the duration of the symbol, and L represents a positive integer.

[0055] Based on the number of the time domain data symbols, construct a plurality of discrete orthogonal chirp sequences, wherein the discrete orthogonal chirp sequences are obtained by sampling the chirp sequence, and every two of the discrete orthogonal chirp sequences are orthogonal to each other;

[0056] Based on the delay index number and the Doppler index number, convert each of the discrete orthogonal chirp sequences into a matrixed Chirp;

[0057] Define the discrete Fourier transform matrix;

[0058] Calculate a fast Chirp-Zak transform matrix of each of the time domain data symbols based on the discrete Fourier transform matrix, the matrixed Chirp and the Doppler index number;

[0059] Each of the time domain data symbols is converted into the DD domain based on the fast Chirp-Zak transform matrix to obtain a DD domain data symbol.

[0060] From the expression of the CZT result matrix, we can know that the i-th time domain data symbol and the i+cN-th D After CZT transformation, the distribution position of M time domain data symbols in DD domain is the same, where c represents an integer. Therefore, each time domain data symbol is actually the same as M D The time domain data symbols overlap.

[0061] In this embodiment, each time domain data symbol is converted from the time domain to the DD domain by CZT transformation to obtain a DD domain data symbol X of the time domain data symbol. DD , that is, a new DD domain waveform is obtained, namely, the Orthogonal Chirp Delay-Doppler Division Multiplexing Modulation (CDDM) waveform, so the DD domain data symbol X DD It is the data symbol of CDDM in the DD domain.

[0062] The expression of the DD domain data symbol is:

[0063]

[0064] In the formula, X DD represents the DD domain data symbol, m represents the delay index, n represents the Doppler index, M D Indicates the number of delay indexes, N D represents the number of Doppler indices, N represents the number of time domain data symbols, represents the i'th discrete orthogonal chirp sequence, D(i) represents the i-th time domain data symbol, j represents an imaginary number, k represents a first index parameter, and i represents a second index parameter.

[0065] In this embodiment, the symbol distribution of CDDM in the DD domain is as follows: Figure 2 As shown, Doppler represents Doppler and Delay represents delay.

[0066] From the expression of CZT transformation, it can be seen that after a time domain data symbol is transformed by CZT, it is orthogonal to the time domain data symbol overlapping with it in the DD domain, but it is not orthogonal to the non-overlapping time domain data symbols, because the discrete orthogonal chirp sequence contained in the time domain data symbol transformed to the DD domain is actually part of the complete discrete orthogonal chirp sequence.

[0067] When i<N D When (i.e., the discrete orthogonal chirp sequence located at the first layer), the expression of the time domain data symbol overlapping with the CZT result matrix of the i-th time domain data symbol is:

[0068]

[0069] num=0,1,...,M D -1,m=0,...,M D -1

[0070] Let i num =i+numND , then the above formula can be expressed as:

[0071]

[0072] In the formula, D(i+numN D ) means the i+numNth D time domain data symbols, D(i num ) represents the i-th num time domain data symbols, num represents the third index parameter, i num represents the index parameter of the numth time domain data symbol overlapping with the i-th time domain data symbol, M D Indicates the number of delay indexes, N D represents the Doppler index number, m represents the delay index, N represents the number of time domain data symbols, and j represents an imaginary number.

[0073] For the i-th num1 time domain data symbols and the i-th num2 The inner product of time domain data symbols is:

[0074]

[0075]

[0076] num2=0,1,...,M D -1, num1=0,1,...,M D -1

[0077] i num2 =i+num2N D ,i num1 =i+num1N D

[0078] In the formula, D(i num1 ) represents the i-th num1 time domain data symbols, D(i num2 ) represents the i-th num2 time domain data symbols, num1 and num2 represent the fourth index parameter and the fifth index parameter respectively, i num1 and i num2 They represent the index parameters of the num1th and num2th time domain data symbols overlapping with the i-th time domain data symbol after CZT transformation, m represents the delay index, n represents the Doppler index, M D Indicates the number of delay indexes, N D represents the number of Doppler indices, N represents the number of time-domain data symbols, L represents a positive integer, and j represents an imaginary number.

[0079] When num2≠num1, the inner product of the non-zero parts of the two time domain data symbols is 0, that is, the overlapping time domain data symbols are orthogonal after CZT transformation, but the non-overlapping time domain data symbols do not have this property.

[0080] Step S300: performing inverse discrete Fourier transform and serial-to-parallel transform on the DD domain data symbols in sequence to obtain a time domain transmission sequence, adding a cyclic prefix to the time domain transmission sequence, performing pulse shaping, and obtaining a time domain transmission signal.

[0081] The DD domain data symbols are sequentially subjected to inverse discrete Fourier transform and serial-to-parallel transform to obtain a time domain transmission sequence, including:

[0082] Calculate the index of the time domain data symbol in each grid in the DD domain data symbol;

[0083] The calculation formula for the index of the time domain data symbol in each grid in the DD domain data symbol is:

[0084]

[0085] In the formula, i m,n represents the index of the time domain data symbol in the DD domain data symbol, c' represents the fourth index parameter, M D Indicates the number of delay indexes, N D represents the number of Doppler indexes, m represents the delay index, n represents the Doppler index, Represents modulo N D operate.

[0086] Based on the index, determining an expression in each grid on the DD domain;

[0087] In this embodiment, the number of time domain data symbols and the number of discrete orthogonal chirp sequences are the same, and each time domain data symbol has a one-to-one corresponding discrete orthogonal chirp sequence.

[0088] The expression in each grid on the DD domain is:

[0089]

[0090] In the formula, X DD [m,n] represents the DD domain data symbol X DD The value of the mth row and nth column in D(i m,n ) represents the im,nth time domain data symbol, Denotes D(i m,n ) is the intermediate variable of the CZT transformation result, Indicates the i m,n ' discrete orthogonal chirp sequence, M DIndicates the number of delay indexes, N D represents the Doppler index number, and c' represents the sixth index parameter.

[0091] Performing an inverse discrete Fourier transform on the expression in each grid on the DD domain to obtain a transformed data symbol matrix;

[0092] The transformed data symbol matrix is ​​subjected to serial-to-parallel transformation to obtain a time domain transmission sequence.

[0093] The expression of the time domain transmission sequence is:

[0094]

[0095] Where x[k] represents the time domain transmission sequence, Indicates modulo M D operate, Indicates the removal operation. Indicates DD domain data symbol X DD Middle Line The value of the column, k represents the first index parameter, n represents the Doppler index, M D Indicates the number of delay indexes, N D represents the Doppler index number, and j represents an imaginary number.

[0096] A cyclic prefix is ​​added to the time domain transmission sequence, and pulse shaping is performed based on the function g(t) to reduce inter-symbol interference and increase the transmission rate.

[0097] Specifically, the expression of g(t) is:

[0098] Where a(t-nT) represents the combined transformation of a(t), a(t) represents the square root Nyquist pulse, and N D represents the Doppler index number, t represents the time, T represents the duration of the symbol, n represents the Doppler index, and N D represents the number of Doppler indices, and |·| represents the absolute value.

[0099] At the same time, the function g(t) satisfies the following conditions:

[0100]

[0101] In the formula, represents the combined transformation of the function g(t), δ(·) represents the Delta pulse, M D Indicates the number of delay indexes, N Drepresents the Doppler index number, m represents the delay index, n represents the Doppler index, t represents time, T represents the duration of the symbol, and j represents an imaginary number.

[0102] At this time, according to the multi-carrier modulation scheme in the DD domain, the expression of the CDDM time domain transmission signal is:

[0103]

[0104] Where s(t) represents the transmitted signal in the time domain, M D Indicates the number of delay indexes, N D represents the number of Doppler indexes, m represents the delay index, n represents the Doppler index, c' represents the sixth index parameter, j represents an imaginary number, T represents the duration of the symbol, represents the combined transformation of the function g(t), D(i m,n ) represents the i-th m,n time domain data symbols, Denotes D(i m,n ) is an intermediate variable of the CZT transformation result.

[0105] Therefore, in the CDDM multi-carrier communication system, the symbol period of the multi-carrier symbol is The carrier spacing is The time domain data symbols of CDDM are sent in an interleaved manner in the following order: Figure 3 As shown, where M D Indicates the number of delay indexes, N D represents the Doppler index number, and T represents the duration of the symbol.

[0106] After obtaining the time domain transmission signal, it also includes:

[0107] Transmitting the time domain transmission signal through a channel to obtain a time domain reception signal;

[0108] At the receiving end, the expression of the received signal in the time domain is:

[0109]

[0110] Where y(t) represents the received signal in the time domain, t represents time, j represents an imaginary number, P represents the total number of paths, and s(t-τ p ) represents the delay τ p The time domain signal after τ p represents the delay of the pth path, v p (·) represents the Doppler shift of the pth path, z(t) represents the noise, and h p represents the channel gain of the p-th path.

[0111] The time domain received signal is multi-carrier demodulated to obtain DD domain received data symbols, the DD domain received data symbols are subjected to inverse Chirp-Zak transform to obtain the time domain data symbols, a bit stream is obtained through the time domain data symbols, and the inverse Chirp-Zak transform is calculated using an inverse fast Chirp-Zak transform algorithm.

[0112] Performing an inverse Chirp-Zak transform on the DD domain received data symbol to obtain the time domain data symbol, and obtaining a bit stream through the time domain data symbol, including:

[0113] Obtaining a distribution position corresponding to each time domain data symbol in the DD domain received data symbol in the DD domain;

[0114] Based on the conjugate of the discrete orthogonal chirp sequence and the distribution position, the DD domain data symbol is restored to obtain the time domain data symbol;

[0115] The time domain data symbols are sequentially converted from parallel to serial and demodulated to obtain a bit stream.

[0116] In this embodiment, the inverse Chirp-Zak transform is defined as:

[0117]

[0118] In the formula, represents the value of the DD domain data symbol in the mth row and nth column after D(i) is transformed by CZT, D(i) represents the i-th time domain data symbol, m represents the delay index, n represents the Doppler index, M D Indicates the number of delay indexes, N D represents the Doppler index number, express The conjugate of represents the i'th discrete orthogonal chirp sequence, k represents the first index parameter, N represents the number of time-domain data symbols, and j represents an imaginary number.

[0119] In this embodiment, when the number of delay indexes is M D and the number of Doppler indices N D When fixed, the FCZT transformation matrix Φ of the i-th time domain data symbol i,DD The positions of the non-zero elements of remain unchanged, using P i The FCZT transformation matrix Φ represents the i-th time domain data symbol i,DD The positions of the non-zero elements in , where (m i,j' ,n i,j' ) represents Φ i,DDAt the position of the non-zero element in the j'th row, P is the set of non-zero element positions of the FCZT transformation matrix of all time domain data symbols, P = {P0, ..., P N-1},P i represents the position of the non-zero elements of the FCZT transformation matrix of the i-th time-domain data symbol, i=0,...,N-1, N represents the number of time-domain data symbols.

[0120] At this time, based on the orthogonality of discrete orthogonal chirp sequences, an inverse fast Chirp-Zak transform algorithm, namely, IFCZT transform, can be used in the DD domain to perform an inverse Chirp-Zak transform.

[0121] The IFCZT transform is defined as:

[0122]

[0123] Where D(i) represents the i-th time domain data symbol, M D represents the number of delay indexes, m represents the delay index, express The conjugate of represents the i'th discrete orthogonal chirp sequence, It represents the CZT result matrix of the time domain data symbol sequence D after the i-th time domain data symbol is transformed by CZT. The distribution of non-zero elements in .

[0124] Therefore, based on the IFCZT transform, when the channel estimation is completed, the orthogonality calculation is performed directly in the DD domain based on the separability of the data symbols and the chirp is used to more quickly restore the time domain data symbol sequence and realize data detection.

[0125] In this embodiment, the IFCZT transformation can quickly restore the DD domain data symbols to the original time domain data symbol sequence. However, due to the influence of the DD domain dual-selection channel, there will be errors when directly using the IFCZT transformation for data recovery.

[0126] In this embodiment, assuming that the channel estimation has been completed and the channel parameters of the path with the maximum channel gain have been obtained, a method is also provided to improve the IFCZT transform so that the time domain data symbols can still be accurately restored after the data symbols pass through the DD domain dual-selection channel, that is, the Chirp-Zak inverse transform is performed by improving the IFCZT transform to achieve data recovery, which specifically includes steps A100, A200, A300 and A400:

[0127] Step A100: Obtaining a DD domain recovery data matrix;

[0128] Step A200: constructing an extended matrix based on the DD domain;

[0129] The extended matrix Φ ext The expression is:

[0130]

[0131] In the formula, Φ ext [l,r] represents the extended matrix Φ ext The value of the lth row and the rth column in , where r represents the seventh index parameter, Indicates the r+bNth D The intermediate variable of the CZT transform result of the time domain data symbol, Indicates the first (r+bN D )' discrete orthogonal chirp sequence, b represents the seventh index parameter, M D Indicates the number of delay indexes, N D represents the Doppler index number, and l represents the eighth index parameter.

[0132] But even after extension, the time domain data symbols are still not completely orthogonal, because the original discrete orthogonal chirp sequence is multiplied by the modulated time domain data symbol, and after passing through the channel, it is also multiplied by the channel coefficient. Different channel coefficients will also destroy the orthogonality to a certain extent. However, after channel estimation, the path with the largest channel coefficient can be selected, and dividing it by the channel parameters of the path can minimize the interference caused by multipath.

[0133] Step A300: Based on the channel parameters and the extended expansion matrix, the DD domain restored data matrix is ​​restored by inverse Chirp-Zak transform to obtain the time domain data symbols;

[0134] Through channel estimation, the channel parameter H of the path with the maximum channel gain is obtained path , and H path (m)∈H path , where H path (m) represents the mth value in the channel parameter Hpath, including the channel gain of the path and the phase rotation of the mth data symbol.

[0135] According to the FCZT transformation matrix Φ of the i-th time domain data symbol i,DD, the position of each time domain data symbol in the DD domain can be determined. At the receiving end, after the received signal is demodulated and converted to the DD domain, the original position of each time domain data symbol in the DD domain is known. Therefore, the position of the time domain data symbol under the path with the largest channel response after passing through the multipath channel can be determined, that is, the position after a certain delay and Doppler shift. At this time, the formula for recovering the DD domain recovery data matrix, that is, the definition of the improved IFCZT transform is:

[0136]

[0137] Where D(i) represents the i-th time domain data symbol, Y DD,i (m) represents the position of the i-th time domain data symbol in the received signal under the m-th delay index under the path with the maximum channel response, Represents the extended matrix Φ ext middlemM D Line The value of the column, Represents modulo N D Operation, M D Indicates the number of delay indexes, N D represents the number of Doppler indices, N represents the number of time domain data symbols, express The conjugate of represents the i'th discrete orthogonal chirp sequence, m represents the delay index, and i represents the second index parameter.

[0138] Step A400: Perform parallel-to-serial conversion and demodulation on the time domain data symbols in sequence to obtain a bit stream.

[0139] In this embodiment, the restored time domain data symbol is obtained by the above formula, that is, the original time domain data symbol sequence D is obtained. The above formula is the definition of the improved IFCZT transform, and the delay index number M D , Doppler index number N D When the number N of data symbols is determined, when data detection is performed on the data symbols, the extended expansion matrix part can be calculated in advance without consuming real-time computing resources.

[0140] In this embodiment, the step A100 further includes steps A101, A102, A103, and A104:

[0141] Step A101: performing matched filtering on the time domain received signal based on the orthogonal characteristic of the discrete orthogonal chirp sequence to obtain a filtered signal;

[0142] The expression of the filtered signal is:

[0143] ym (t) = ∫y(t-τ)a * (-τ)dτ

[0144] In the formula, y m (t) represents the filtered signal, t represents time, τ represents the delay, a * (·) represents the conjugate of the square root Nyquist pulse, and y(t-τ) represents the time domain received signal after a time delay of τ.

[0145] Step A102: sampling the filtered signal to obtain a discrete representation;

[0146] For the filtered signal y m (t) The interval is The sampling of M is used to obtain the discrete representation y[k], where M D represents the delay index number, and T represents the duration of the time slot.

[0147] Step A103: removing a cyclic prefix from the discrete representation to obtain a discrete representation without the cyclic prefix;

[0148] Step A104: performing serial-to-parallel conversion and discrete Fourier transform on the discrete representation after removing the cyclic prefix, restoring the discrete representation to the DD domain, and obtaining a DD domain restored data matrix.

[0149] In this embodiment, after serial-to-parallel conversion, N D Point discrete Fourier transform, get the DD domain recovery data matrix Y DD :

[0150]

[0151] Where Y DD [m,n] represents the DD domain recovery data matrix Y DD The value of the mth row and nth column in h p represents the channel gain of the pth path, It means that after the pth path, X DD The value of [m,n], X DD [m,n] represents the DD domain data symbol X DD The value of the mth row and nth column in the DD domain, z[m,n] represents the noise of the mth row and nth column in the DD domain, k p represents the Doppler shift of the pth path in the DD domain grid, l p represents the delay offset of the pth path in the DD domain grid, represents the delay index of the data symbol passing through the pth path, represents the Doppler index of the data symbol passing through the pth path, M D Indicates the number of delay indexes, ND represents the number of Doppler indices, m represents the delay index, n represents the Doppler index, j represents an imaginary number, T represents the duration of the symbol, and v p represents the Doppler shift of the pth path, τ p represents the delay of the pth path, Represents modulo N D operation, and P represents the total number of paths.

[0152] And when hour, X DD [m,n] represents the DD domain data symbol X DD The value of the mth row and nth column in hour, Indicates DD domain data symbol X DD Middle Line The value of the column.

[0153] Embodiment 2:

[0154] This embodiment provides a delay-Doppler domain waveform design device, the device comprising:

[0155] A modulation module, used for performing serial-to-parallel conversion and modulation on the bit stream in sequence to obtain multiple time-domain data symbols;

[0156] A transformation module, configured to perform a Chirp-Zak transformation on each of the time domain data symbols, convert each of the time domain data symbols into a DD domain, and obtain a DD domain data symbol, wherein the Chirp-Zak transformation is calculated using a fast Chirp-Zak transformation algorithm;

[0157] The sending module is used to perform inverse discrete Fourier transform and serial-to-parallel transform on the DD domain data symbols in sequence to obtain a time domain sending sequence, add a cyclic prefix to the time domain sending sequence, perform pulse shaping, and obtain a time domain sending signal.

[0158] The transformation module comprises:

[0159] A first acquisition unit, configured to acquire a delay index number and a Doppler index number in a DD domain;

[0160] A construction unit, configured to construct a plurality of discrete orthogonal chirp sequences based on the number of the time domain data symbols, wherein the discrete orthogonal chirp sequences are obtained by sampling the chirp sequence, and each two of the discrete orthogonal chirp sequences are orthogonal to each other;

[0161] A first conversion unit, configured to convert each of the discrete orthogonal chirp sequences into a matrixed Chirp based on the delay index number and the Doppler index number;

[0162] A definition unit for defining a discrete Fourier transform matrix;

[0163] A first calculation unit, configured to calculate a fast Chirp-Zak transform matrix of each of the time domain data symbols based on the discrete Fourier transform matrix, the matrixed Chirp and the Doppler index number;

[0164] The second conversion unit is used to convert each of the time domain data symbols into the DD domain based on the fast Chirp-Zak transform matrix to obtain a DD domain data symbol.

[0165] The sending module comprises:

[0166] A second calculation unit, used to calculate the index of the time domain data symbol in each grid in the DD domain data symbol;

[0167] A third computing unit, configured to determine an expression in each grid on the DD domain based on the index;

[0168] A first transform unit is used to perform an inverse discrete Fourier transform on the expression in each grid on the DD domain to obtain a transformed data symbol matrix;

[0169] The second transformation unit is used to perform serial-to-parallel transformation on the transformation data symbol matrix to obtain a time domain transmission sequence.

[0170] The delay-Doppler domain waveform design device also includes a transmission module and a demodulation module;

[0171] A transmission module, used for transmitting the time domain transmission signal through a channel to obtain a time domain reception signal;

[0172] A demodulation module is used to perform multi-carrier demodulation on the time domain received signal to obtain DD domain received data symbols, perform inverse Chirp-Zak transform on the DD domain received data symbols to obtain the time domain data symbols, and obtain a bit stream through the time domain data symbols. The inverse Chirp-Zak transform is calculated using an inverse fast Chirp-Zak transform algorithm.

[0173] It should be noted that, regarding the device in the above embodiment, the specific manner in which each module performs the operation has been described in detail in the embodiment of the method, and will not be elaborated here.

[0174] The demodulation module comprises:

[0175] A second acquisition unit is used to acquire a distribution position corresponding to each time domain data symbol in the DD domain received data symbol in the DD domain;

[0176] A recovery unit, configured to recover the DD domain data symbol based on the conjugate of the discrete orthogonal chirp sequence and the distribution position to obtain the time domain data symbol;

[0177] The demodulation unit is used to perform parallel-to-serial conversion and demodulate the time domain data symbols in sequence to obtain a bit stream.

[0178] Embodiment 3:

[0179] This embodiment is applied to high-speed mobile communication scenarios. To verify the reliability of the present invention in high-speed mobile scenarios, this embodiment is simulated. The simulation channel modeling adopts the extended vehicle channel model, and the Doppler shift is generated by Jake's channel model. Considering that the channel estimation has been completed, the experimental simulation parameters are as follows: M D =512,N D =32, T=66.7μs, carrier frequency is 5GHz, mobile speed is 500km / h, and data modulation method is QPSK.

[0180] Figure 4 The performance curves of Orthogonal Frequency Division Multiplexing (OFDM), Orthogonal Chirp Division Multiplexing (OCDM), Chirp-Convolved Data Transmission (CCDT), Affine Frequency Division Multiplexing (AFDM), Orthogonal Time Frequency Space (OTFS), Orthogonal Delay-Doppler Division Multiplexing (ODDM), and Orthogonal Chirp Delay-Doppler Division Multiplexing (CDDM) proposed in the present invention with the variation of Eb / N0 under the simulation parameters, where CCDT and AFDM are both extended waveforms of OCDM. Eb / N0 represents the ratio of bit energy to noise power spectral density, which is used to measure the performance of a digital communication system under a given signal noise environment.

[0181] from Figure 4It can be seen that OFDM has poor communication performance in high-mobility scenarios and is difficult to apply in high-mobility scenarios. Chirp-based OCDM, CCDT, and AFDM perform significantly better than OFDM in high-mobility scenarios, but there is still a performance gap compared to OTFS, ODDM, and CDDM based on DD domain communication. This is because DD domain channels can provide good path resolution in high-mobility scenarios. CDDM performs better than OTFS and ODDM, and has a performance gain of about 1dB compared to ODDM at a bit error probability BER of 10-6. This is because the DD domain orthogonal chirp sequence brought by the Chirp-Zak transform can accurately separate the signals.

[0182] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0183] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A delay-Doppler domain waveform design method, characterized in that: include: The bit stream is sequentially converted into serial-to-parallel and modulated to obtain a plurality of time-domain data symbols; Performing a Chirp-Zak transform on each of the time domain data symbols, converting each of the time domain data symbols into the DD domain to obtain a DD domain data symbol, wherein the Chirp-Zak transform is calculated using a fast Chirp-Zak transform algorithm; The DD domain data symbols are sequentially subjected to inverse discrete Fourier transform and serial-to-parallel transform to obtain a time domain transmission sequence, a cyclic prefix is ​​added to the time domain transmission sequence, and pulse shaping is performed to obtain a time domain transmission signal.

2. The delay-Doppler domain waveform design method according to claim 1, characterized in that , performing Chirp-Zak transform on each of the time domain data symbols, converting each of the time domain data symbols into the DD domain, and obtaining a DD domain data symbol, including: Get the delay index number and Doppler index number of the DD domain; Based on the number of the time domain data symbols, construct a plurality of discrete orthogonal chirp sequences, wherein the discrete orthogonal chirp sequences are obtained by sampling the chirp sequence, and every two of the discrete orthogonal chirp sequences are orthogonal to each other; Based on the delay index number and the Doppler index number, convert each of the discrete orthogonal chirp sequences into a matrixed Chirp; Define the discrete Fourier transform matrix; Calculate a fast Chirp-Zak transform matrix of each of the time domain data symbols based on the discrete Fourier transform matrix, the matrixed Chirp and the Doppler index number; Each of the time domain data symbols is converted into the DD domain based on the fast Chirp-Zak transform matrix to obtain a DD domain data symbol.

3. The delay-Doppler domain waveform design method according to claim 1, characterized in that , the DD domain data symbols are sequentially subjected to inverse discrete Fourier transform and serial-to-parallel transform to obtain a time domain transmission sequence, including: Calculate the index of the time domain data symbol in each grid in the DD domain data symbol; Based on the index, determining an expression in each grid on the DD domain; Performing an inverse discrete Fourier transform on the expression in each grid on the DD domain to obtain a transformed data symbol matrix; The transformed data symbol matrix is ​​subjected to serial-to-parallel transformation to obtain a time domain transmission sequence.

4. The delay-Doppler domain waveform design method according to claim 1, characterized in that , after obtaining the time domain transmission signal, it also includes: Transmitting the time domain transmission signal through a channel to obtain a time domain reception signal; The time domain received signal is multi-carrier demodulated to obtain DD domain received data symbols, the DD domain received data symbols are subjected to inverse Chirp-Zak transform to obtain the time domain data symbols, a bit stream is obtained through the time domain data symbols, and the inverse Chirp-Zak transform is calculated using an inverse fast Chirp-Zak transform algorithm.

5. The delay-Doppler domain waveform design method according to claim 4, characterized in that , performing an inverse Chirp-Zak transform on the DD domain received data symbol to obtain the time domain data symbol, and obtaining a bit stream through the time domain data symbol, including: Obtaining a distribution position corresponding to each time domain data symbol in the DD domain received data symbol in the DD domain; Based on the conjugate of the discrete orthogonal chirp sequence and the distribution position, the DD domain data symbol is restored to obtain the time domain data symbol; The time domain data symbols are sequentially converted from parallel to serial and demodulated to obtain a bit stream.

6. A delay-Doppler domain waveform design device, characterized in that: include: A modulation module, used for performing serial-to-parallel conversion and modulation on the bit stream in sequence to obtain multiple time-domain data symbols; A transformation module, configured to perform a Chirp-Zak transformation on each of the time domain data symbols, convert each of the time domain data symbols into a DD domain, and obtain a DD domain data symbol, wherein the Chirp-Zak transformation is calculated using a fast Chirp-Zak transformation algorithm; The sending module is used to perform inverse discrete Fourier transform and serial-to-parallel transform on the DD domain data symbols in sequence to obtain a time domain sending sequence, add a cyclic prefix to the time domain sending sequence, perform pulse shaping, and obtain a time domain sending signal.

7. The delay-Doppler domain waveform design device according to claim 6, characterized in that: The transformation module comprises: A first acquisition unit, configured to acquire a delay index number and a Doppler index number in a DD domain; A construction unit, configured to construct a plurality of discrete orthogonal chirp sequences based on the number of the time domain data symbols, wherein the discrete orthogonal chirp sequences are obtained by sampling the chirp sequence, and each two of the discrete orthogonal chirp sequences are orthogonal to each other; A first conversion unit, configured to convert each of the discrete orthogonal chirp sequences into a matrixed Chirp based on the delay index number and the Doppler index number; A definition unit for defining a discrete Fourier transform matrix; A first calculation unit, configured to calculate a fast Chirp-Zak transform matrix of each of the time domain data symbols based on the discrete Fourier transform matrix, the matrixed Chirp and the Doppler index number; The second conversion unit is used to convert each of the time domain data symbols into the DD domain based on the fast Chirp-Zak transform matrix to obtain a DD domain data symbol.

8. The delay-Doppler domain waveform design device according to claim 6, characterized in that: The sending module comprises: A second calculation unit, used to calculate the index of the time domain data symbol in each grid in the DD domain data symbol; A third computing unit, configured to determine an expression in each grid on the DD domain based on the index; A first transform unit is used to perform an inverse discrete Fourier transform on the expression in each grid on the DD domain to obtain a transformed data symbol matrix; The second transformation unit is used to perform serial-to-parallel transformation on the transformation data symbol matrix to obtain a time domain transmission sequence.

9. The delay-Doppler domain waveform design device according to claim 6, characterized in that: The delay-Doppler domain waveform design device also includes a transmission module and a demodulation module; A transmission module, used for transmitting the time domain transmission signal through a channel to obtain a time domain reception signal; A demodulation module is used to perform multi-carrier demodulation on the time domain received signal to obtain DD domain received data symbols, perform inverse Chirp-Zak transform on the DD domain received data symbols to obtain the time domain data symbols, and obtain a bit stream through the time domain data symbols. The inverse Chirp-Zak transform is calculated using an inverse fast Chirp-Zak transform algorithm.

10. The delay-Doppler domain waveform design device according to claim 9, characterized in that: The demodulation module comprises: A second acquisition unit is used to acquire a distribution position corresponding to each time domain data symbol in the DD domain received data symbol in the DD domain; A recovery unit, configured to recover the DD domain data symbol based on the conjugate of the discrete orthogonal chirp sequence and the distribution position to obtain the time domain data symbol; The demodulation unit is used to perform parallel-to-serial conversion and demodulate the time domain data symbols in sequence to obtain a bit stream.

Images