A flexible spectral-effect chirp multi-carrier signal generation method based on zero insertion and zero padding

Abstract

A flexible spectral efficiency chirp multi-carrier signal generation method based on zero insertion and zero padding belongs to the technical field of chirp multi-carrier signal generation. The present invention solves the problem that the spectrum efficiency of existing non-orthogonal chirp multi-carrier multiplexing technology is limited, as well as the applicability and versatility of the existing non-orthogonal chirp multi-carrier multiplexing system structure are limited. The transmitting and receiving ends of the present invention add zero insertion and zero padding operations after the first phase rotation. By controlling the number of zero insertion and zero padding, the number of points of DFT and IDFT can be adjusted to adjust the bandwidth compression factor in the chirp multi-carrier multiplexing system, thereby providing flexible and variable spectrum efficiency, solving the problem of limited spectrum efficiency range caused by the number of operation points must be an integer and a power of 2 in the chirp multi-carrier signal generation process, further expanding the structural applicability of the chirp multi-carrier multiplexing system, and having greater versatility. The method of the present invention can be applied to chirp multi-carrier signal generation.

Description

Technical Field

[0001] The present invention belongs to the technical field of chirp multi-carrier signal generation, and in particular relates to a flexible spectral effect chirp multi-carrier signal generation method based on zero insertion and zero padding. Background Art

[0002] With the development of wireless technology, mobile communications have made tremendous progress. Today, people's demand for communications is no longer limited to basic services such as calls and text messages. A wide range of data and multimedia services are increasingly available, and new smart terminal devices are becoming increasingly advanced. This high reliance on communications has led to a rapid increase in demand, and the sheer volume of data is overwhelming limited spectrum resources. Given the rapidly increasing demand for communications and the increasingly limited frequency resources, it is imperative to seek and explore communication technologies with higher spectral efficiency. Within the constraints of bandwidth, more efficient transmission technologies should be utilized to meet people's mobile communication needs to the greatest extent possible.

[0003] Orthogonal frequency division multiplexing (OFDM) technology has been widely used and researched as a mainstream communications technology in recent years due to its excellent performance and low implementation complexity. However, with the surge in user data volumes, OFDM has gradually failed to meet this demand. Due to the limitations of subcarrier orthogonality in OFDM, the only way to further improve spectral efficiency is to increase the modulation order. However, higher-order modulation systems are more sensitive to noise and interference. Therefore, increasing spectral efficiency by relaxing orthogonality has gradually become a research focus. Spectrally Efficient Frequency Division Multiplexing (SEFDM) is a multicarrier waveform scheme that achieves higher spectral efficiency by reducing the spacing between subcarriers in an OFDM system. I. Darwazeh and M.R.D. Rodrigue first proposed the concept of SEFDM, which builds on the Fast-OFDM system and further improves spectral efficiency. Similar to how SEFDM systems improve spectral efficiency in the frequency domain by reducing subcarrier spacing, Faster Than Nyquist (FTN), a single-carrier technology, employs a similar concept in the time domain to break the Nyquist orthogonality criterion and achieve higher spectral efficiency without increasing the modulation order. Subsequently, communications researchers expanded their research on single-carrier FTN to the multicarrier domain, further enhancing the theoretical basis of FTN.

[0004] Although the above-mentioned non-orthogonal system transmission improves the spectrum efficiency, it is inevitable that there will be interference between subcarriers or interference between codes, which will affect the overall performance of the system. In order to solve the problem of inter-subcarrier interference in SEFDM system, which affects the system bit error rate performance, researchers have recently started from the signal basis and replaced the sine and cosine function basis in the traditional non-orthogonal system with chirp signals. Taking advantage of the chirp signal's anti-multipath, anti-Doppler, and low sensitivity to frequency changes, a non-orthogonal chirp multi-carrier multiplexing technology was proposed, which further alleviated the interference between subcarriers and provided better bit error rate performance. However, in the existing non-orthogonal chirp multi-carrier multiplexing technology, due to the limitation of the number of transformation points, the spectrum efficiency it can provide is limited. The applicability and versatility of the existing system structure are also limited, which is not conducive to digital implementation. Summary of the Invention

[0005] The purpose of the present invention is to solve the problems of limited spectrum efficiency of existing non-orthogonal chirp multi-carrier multiplexing technology and limited applicability and versatility of existing non-orthogonal chirp multi-carrier multiplexing system structure, and to propose a flexible spectrum-efficient chirp multi-carrier signal generation method based on zero insertion and zero padding.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] According to one aspect of the present invention, a method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding, the method specifically comprising the following steps:

[0008] At the transmitter

[0009] Step S1: A signal source generates a random bit stream sequence v of length N×log2M, where N is the number of subcarriers and M is the digital modulation order;

[0010] Step S2: digitally modulate the random bit stream sequence v to obtain a digitally modulated sequence s. T , where s T =[s0,s1,s2,...,s N-1 ],s0,s1,s2,...,s N-1 The sequence s T The 0th, 1st, 2nd, ..., N-1th elements in ;

[0011] Step S3: sequence s T Perform serial-to-parallel conversion to obtain s=[s0,s1,s2,...,s N-1 ] T , T represents transpose;

[0012] Step S4: Add Q / α-N zeros to the end of s to obtain the zero-filled result.

[0013] Where Q is the number of time domain samples and α is the bandwidth compression factor;

[0014] Step S5: Multiply by Θ2 H Get s′, s′=[s′0,s1′,s2′,...,s′ Q / α-1 ] T ;

[0015] Among them, Θ2 H represents the Hermite transpose of the phase rotation factor Θ2;

[0016] Step S6: Insert b-1 zeros between every two adjacent data points of s′, and add cQ-b(Q / α-1)-1 zeros at the end of s′ to obtain the signal vector

[0017] Wherein, b and c are both positive integers, b<c, and α=b / c;

[0018] Step S7: Perform an inverse discrete Fourier transform of the cQ points on the signal vector obtained in step S6 to obtain an inverse discrete Fourier transform result, and then remove the cQ-Q / α time domain data at the end of the inverse discrete Fourier transform result, that is, only retain the first Q / α time domain data in the inverse discrete Fourier transform result, and record the vector composed of the retained time domain data as x′=[x′0,x1′,x2′,...,x′ Q / α-1 ] T ;

[0019] Step S8: Multiply x′ by Θ1 H Get the signal vector [x0,x1,x2,...,x Q-1 ,..,x Q / α-1 ] T , where Θ1 H represents the Hermite transpose of the phase rotation factor Θ1;

[0020] Step S9: discard the signal vector [x0, x1, x2, ..., x Q-1 ,..,x Q / α-1 ] T The Q(1-α) / α data at the end, the vector composed of the retained data is recorded as x=[x0,x1,x2,...,x Q-1 ] T ;

[0021] Step S10: vector x=[x0,x1,x2,...,x Q-1 ]T Perform parallel-to-serial conversion to obtain the parallel-to-serial conversion result x T =[x0,x1,x2,...,x Q-1 ], and x T Send to the additive white Gaussian noise channel;

[0022] On the receiving end

[0023] Step R1: The signal received by the receiving end is expressed as y T =[y0,y1,y2,...,y Q-1 ], for the received signal y T Perform serial-to-parallel conversion to obtain the signal y=[y0,y1,y2,...,y Q-1 ] T ;

[0024] Step R2: perform zero-filling operation on the signal y to obtain a vector [y0,y1,y2,...,y Q-1 ,0,...0] T , that is, add Q(1-α) / α zeros at the end of the signal y;

[0025] Step R3, the [y0,y1,y2,...,y Q-1 ,0,...0] T Multiplying by the phase rotation factor Θ1, we get the vector y′=[y′0,y1′,y′2,...,y′ Q / α-1 ] T ;

[0026] Step R4: In the vector y′=[y′0,y1′,y′2,...,y′ Q / α-1 ] T Insert b-1 zeros between every two adjacent data points, and add cQ-b(Q / α-1)-1 zeros to the tail of the vector y′. The signal vector obtained by inserting and adding zeros is recorded as

[0027]

[0028] Step R5: the signal vector obtained in step R4 Perform discrete Fourier transform of cQ point, and record the signal vector composed of the first Q / α time domain data in the discrete Fourier transform result as r′=[r0′,r1′,r2′,...,r Q ' / α-1 ] T ;

[0029] Step R6: The vector r′ obtained in step R5 is converted into [r0′, r1′, r2′, ..., r Q ' / α-1 ] T Multiply by the phase rotation factor Θ2 to get the vector [r0,r1,r2,...,r Q-1 ,..,r Q / α-1 ] T ;

[0030] Step R7: discard the vector [r0,r1,r2,...,r Q-1 ,..,r Q / α-1 ] T The Q / α-N data at the end are used to obtain the vector to be detected r=[r0,r1,r2,...,r N-1 ] T ;

[0031] Step R8: Use the detection algorithm to detect the vector r = [r0, r1, r2, ..., r N-1 ] T Process and get the estimated value of s

[0032]

[0033] Step R9, estimate the value Perform digital demodulation to obtain an estimate of the random bit stream sequence v That is, the original bit stream data is restored.

[0034] According to another aspect of the present invention, a method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding is provided. The working process of the method at the transmitting end is as follows:

[0035] Step S1: A signal source generates a random bit stream sequence v of length N×log2M, where N is the number of subcarriers and M is the digital modulation order;

[0036] Step S2: digitally modulate the random bit stream sequence v to obtain a digitally modulated sequence s. T , where s T =[s0,s1,s2,...,s N-1 ],s0,s1,s2,...,s N-1 The sequence s T The 0th, 1st, 2nd, ..., N-1th elements in ;

[0037] Step S3: sequence s T Perform serial-to-parallel conversion to obtain s=[s0,s1,s2,...,s N-1 ] T , T represents transpose;

[0038] Step S4: Add Q / α-N zeros to the end of s to obtain the zero-filled result.

[0039] Where Q is the number of time domain samples and α is the bandwidth compression factor;

[0040] Step S5: Multiply by Θ2 H Get s′, s′=[s′0,s1′,s2′,...,s′ Q / α-1 ] T ;

[0041] Among them, Θ2 H represents the Hermite transpose of the phase rotation factor Θ2;

[0042] Step S6: Insert b-1 zeros between every two adjacent data points of s′, and add cQ-b(Q / α-1)-1 zeros at the end of s′ to obtain the signal vector

[0043] Wherein, b and c are both positive integers, b<c, and α=b / c;

[0044] Step S7: Perform an inverse discrete Fourier transform of the cQ points on the signal vector obtained in step S6 to obtain an inverse discrete Fourier transform result, and then remove the cQ-Q / α time domain data at the end of the inverse discrete Fourier transform result, that is, only retain the first Q / α time domain data in the inverse discrete Fourier transform result, and record the vector composed of the retained time domain data as x′=[x′0,x1′,x2′,...,x′ Q / α-1 ] T ;

[0045] Step S8: Multiply x′ by Θ1 H Get the signal vector [x0,x1,x2,...,x Q-1 ,..,x Q / α-1 ] T , where Θ1 H represents the Hermite transpose of the phase rotation factor Θ1;

[0046] Step S9: discard the signal vector [x0, x1, x2, ..., x Q-1 ,..,x Q / α-1 ] T The Q(1-α) / α data at the end, the vector composed of the retained data is recorded as x=[x0,x1,x2,...,x Q-1 ] T ;

[0047] Step S10: vector x=[x0,x1,x2,...,x Q-1 ] T Perform parallel-to-serial conversion to obtain the parallel-to-serial conversion result xT =[x0,x1,x2,...,x Q-1 ], and x T Sent to an additive white Gaussian noise channel.

[0048] The beneficial effects of the present invention are:

[0049] The present invention adds zero insertion and zero padding operations to both the transmitter and receiver after the first phase rotation. By controlling the number of zero insertion and zero padding, the number of points in the DFT and IDFT can be adjusted to adjust the bandwidth compression factor in the chirp multi-carrier multiplexing system, thereby providing flexible and variable spectrum efficiency. This solves the problem of limited spectrum efficiency range caused by the requirement that the number of operation points must be an integer and a power of 2 during the chirp multi-carrier signal generation process. This further expands the structural applicability of the chirp multi-carrier multiplexing system, making it more versatile, promoting its digital implementation, and providing more structural support for the field of high-spectrum-efficiency transmission. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flowchart of the transmitter operation of a method for generating a flexible spectral-effect chirp multi-carrier signal based on zero insertion and zero padding according to the present invention;

[0051] Figure 2 This is a flowchart of the receiving end of a method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding according to the present invention;

[0052] Figure 3 It is a flow chart of a conventional non-orthogonal chirp multi-carrier multiplexing signal generation method;

[0053] Figure 4 is the bit error rate performance under AWGN channel;

[0054] Figure 5 It is the bit error rate performance under frequency selective fading channel. DETAILED DESCRIPTION

[0055] Specific implementation method 1: Combination Figure 1 and Figure 2 This embodiment describes a method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding, the method specifically comprising the following steps:

[0056] At the transmitter

[0057] Step S1: A signal source generates a random bit stream sequence v of length N×log2M, where N is the number of subcarriers and M is the digital modulation order;

[0058] Step S2: digitally modulate the random bit stream sequence v to obtain a digitally modulated sequence s. T , where s T =[s0,s1,s2,...,s N-1 ],s0,s1,s2,...,s N-1 The sequence s T The 0th, 1st, 2nd, ..., N-1th elements in ;

[0059] Step S3: sequence s T Perform serial-to-parallel conversion to obtain s=[s0,s1,s2,...,s N-1 ] T , T represents transpose;

[0060] Step S4: Add Q / α-N zeros at the end of s (i.e., at the end of s N-1 Fill the back with zero) to get the result of filling with 0

[0061] Where Q is the number of time domain samples and α is the bandwidth compression factor;

[0062] Step S5: Multiply by Θ2 H Get s′, s′=[s′0,s1′,s2′,...,s′ Q / α-1 ] T ;

[0063] Among them, Θ2 H represents the Hermite transpose of the phase rotation factor Θ2;

[0064] Step S6: Insert b-1 zeros between every two adjacent data points of s′ (i.e., insert b-1 zeros between s0′ and s1′, insert b-1 zeros between s1′ and s2′, and so on), and add cQ-b(Q / α-1)-1 zeros at the end of s′ to obtain the signal vector

[0065] Wherein, b and c are both positive integers, b<c, and α=b / c;

[0066] Step S7: Perform an inverse discrete Fourier transform (IDFT) of cQ points on the signal vector obtained in step S6 to obtain an IDFT result. Then, remove the cQ-Q / α time domain data at the end of the IDFT result, that is, only retain the first Q / α time domain data in the IDFT result. The vector composed of the retained time domain data is recorded as x′=[x′0,x1′,x2′,...,x′ Q / α-1 ] T ;

[0067] Step S8: Multiply x′ by Θ1 H Get the signal vector [x0,x1,x2,...,x Q-1 ,..,x Q / α-1 ] T , where Θ1 H represents the Hermite transpose of the phase rotation factor Θ1;

[0068] Step S9: discard the signal vector [x0, x1, x2, ..., x Q-1 ,..,x Q / α-1 ] T The Q(1-α) / α data at the end, the vector composed of the retained data is recorded as x=[x0,x1,x2,...,x Q-1 ] T ;

[0069] Step S10: vector x=[x0,x1,x2,...,x Q-1 ] T Perform parallel-to-serial conversion to obtain the parallel-to-serial conversion result x T =[x0,x1,x2,...,x Q-1 ], that is, flexible spectrum effect chirp multi-carrier signal, and x T Send to the additive white Gaussian noise channel;

[0070] On the receiving end

[0071] Step R1: The signal received by the receiving end is expressed as y T =[y0,y1,y2,...,y Q-1 ], for the received signal y T Perform serial-to-parallel conversion to obtain the signal y=[y0,y1,y2,...,y Q-1 ] T ;

[0072] Step R2: perform zero-filling operation on the signal y to obtain a vector [y0,y1,y2,...,y Q-1 ,0,...0] T , that is, add Q(1-α) / α zeros at the end of the signal y;

[0073] Step R3, the [y0,y1,y2,...,y Q-1 ,0,...0] T Multiplying by the phase rotation factor Θ1, we get the vector y′=[y′0,y1′,y′2,...,y′ Q / α-1 ] T ;

[0074] Step R4: In the vector y′=[y′0,y1′,y′2,...,y′ Q / α-1 ] T Insert b-1 zeros between every two adjacent data points, and add cQ-b(Q / α-1)-1 zeros to the tail of the vector y′. The signal vector obtained by inserting and adding zeros is recorded as

[0075]

[0076] Step R5: the signal vector obtained in step R4 Perform discrete Fourier transform (DFT) of the cQ point, and record the signal vector composed of the first Q / α time domain data in the discrete Fourier transform result as r′=[r0′,r1′,r2′,...,r Q ' / α-1 ] T ;

[0077] Step R6: The vector r′ obtained in step R5 is converted into [r0′, r1′, r2′, ..., r Q ' / α-1 ] T Multiply by the phase rotation factor Θ2 to get the vector [r0,r1,r2,...,r Q-1 ,..,r Q / α-1 ] T ;

[0078] Step R7: discard the vector [r0,r1,r2,...,r Q-1 ,..,r Q / α-1 ] T The Q / α-N data at the end are used to obtain the vector to be detected r=[r0,r1,r2,...,r N-1 ] T ;

[0079] Step R8: Use the detection algorithm to detect the vector r = [r0, r1, r2, ..., r N-1 ] T By processing, the interference between subcarriers can be eliminated and the estimated value of s can be obtained.

[0080] Step R9, estimate the value Perform digital demodulation to obtain an estimate of the random bit stream sequence v That is, the original bit stream data is restored.

[0081] The present invention addresses the problem that the scope of spectrum efficiency is limited due to the conditional restriction of the number of DFT points in the chirp multi-carrier multiplexing system structure, thereby limiting the applicability and versatility of the system structure. A chirp multi-carrier signal generation method with flexible spectrum efficiency is proposed. In the process of adopting DFT and IDFT, zero insertion and zero padding operations are added. Different bandwidth compression factors are set by independently and flexibly controlling the number of zero insertion and zero padding, thereby expanding the scope of spectrum efficiency that can be provided in the system. Compared with the traditional chirp multi-carrier signal generation method, the signal generation method proposed by the present invention is more flexible and more universal, and further promotes the digital realization of the chirp multi-carrier multiplexing system.

[0082] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the number of time domain samples Q is:

[0083] Q=ρN

[0084] Where ρ is the oversampling factor.

[0085] Other steps and parameters are the same as those in the first embodiment.

[0086] Specific embodiment three: This embodiment differs from specific embodiment one or two in that the bandwidth compression factor α is:

[0087] α=Δf / Δf′

[0088] Wherein, Δf is the subcarrier spacing of the chirp multi-carrier when it is non-orthogonal, and Δf′ is the subcarrier spacing of the chirp multi-carrier when it is orthogonal.

[0089] Other steps and parameters are the same as those in the first or second embodiment.

[0090] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the phase rotation factor θ2 is a diagonal matrix having non-zero elements only on the diagonal, and the elements on the diagonal are:

[0091]

[0092] Where n = 0, 1, ... Q / α-1, j is the imaginary unit, e is the base of the natural logarithm, and Θ2(n,n) is the nth element on the diagonal.

[0093] The other steps and parameters are the same as those in the first to third embodiments.

[0094] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the phase rotation factor θ1 is a diagonal matrix having non-zero values ​​only on the diagonal, and the values ​​of the elements on the diagonal are:

[0095]

[0096] Where m = 0, 1, ... Q / α-1, Θ1(m, m) is the m-th element on the diagonal.

[0097] The other steps and parameters are the same as those in the first to fourth embodiments.

[0098] Specific embodiment 6: This embodiment differs from any one of specific embodiments 1 to 5 in that the signal y received by the receiving end T for:

[0099] y T =x T +n T

[0100] Among them, n T is the noise sequence introduced by the signal through the channel.

[0101] The other steps and parameters are the same as those in the first to fifth embodiments.

[0102] Specific embodiment seven: This embodiment differs from any one of specific embodiments one to six in that the detection algorithm is a maximum likelihood detection method.

[0103] The other steps and parameters are the same as those in the first to sixth embodiments.

[0104] The transmission process of the Chirp multi-carrier multiplexing system is similar to that of the SEFDM system. Both use block transmission and insert a cyclic prefix (CP) at the beginning of each symbol before entering the fading channel to mitigate the impact of multipath interference. After removing the CP at the receiving end, the received signal sample can be expressed as:

[0105] y=ΗΘ1 H F H Θ2 H s+n=ΗΦs+n

[0106] In particular, when H is the identity matrix, the channel is an additive white Gaussian noise channel. Then according to Figure 2 By following the process shown in , we can get:

[0107] r=Θ2FΘ1ΗΘ1 H F H Θ2 H s+n′=Φ H ΗΦs+n′

[0108] If the detection algorithm selects maximum likelihood detection, the detection is performed according to the following formula to obtain In this way, the original transmitted bit stream sequence is restored;

[0109]

[0110] Specific implementation method eight: combination Figure 1 This embodiment describes a method for generating a flexible spectral chirp multi-carrier signal based on zero insertion and zero padding, and the working process of the method at the transmitting end is as follows:

[0111] Step S1: A signal source generates a random bit stream sequence v of length N×log2M, where N is the number of subcarriers and M is the digital modulation order;

[0112] Step S2: digitally modulate the random bit stream sequence v to obtain a digitally modulated sequence s. T , where s T =[s0,s1,s2,...,s N-1 ],s0,s1,s2,...,s N-1 The sequence s T The 0th, 1st, 2nd, ..., N-1th elements in ;

[0113] Step S3: sequence s T Perform serial-to-parallel conversion to obtain s=[s0,s1,s2,...,s N-1 ] T , T represents transpose;

[0114] Step S4: Add Q / α-N zeros at the end of s (i.e., at the end of s N-1 Fill the back with zero) to get the result of filling with 0

[0115] Where Q is the number of time domain samples and α is the bandwidth compression factor;

[0116] Step S5: Multiply by Θ2 H Get s′, s′=[s′0,s1′,s2′,...,s′ Q / α-1 ] T ;

[0117] Among them, Θ2 H represents the Hermite transpose of the phase rotation factor Θ2;

[0118] Step S6: Insert b-1 zeros between every two adjacent data points of s′ (i.e., insert b-1 zeros between s0′ and s1′, insert b-1 zeros between s1′ and s2′, and so on), and add cQ-b(Q / α-1)-1 zeros at the end of s′ to obtain the signal vector

[0119] Wherein, b and c are both positive integers, b<c, and α=b / c;

[0120] Step S7: Perform an inverse discrete Fourier transform (IDFT) of cQ points on the signal vector obtained in step S6 to obtain an IDFT result. Then, remove the cQ-Q / α time domain data at the end of the IDFT result, that is, only retain the first Q / α time domain data in the IDFT result. The vector composed of the retained time domain data is recorded as x′=[x′0,x1′,x2′,...,x′ Q / α-1 ] T ;

[0121] Step S8: Multiply x′ by Θ1 H Get the signal vector [x0,x1,x2,...,x Q-1 ,..,x Q / α-1 ] T , where Θ1 H represents the Hermite transpose of the phase rotation factor Θ1;

[0122] Step S9: discard the signal vector [x0, x1, x2, ..., x Q-1 ,..,x Q / α-1 ] T The Q(1-α) / α data at the end, the vector composed of the retained data is recorded as x=[x0,x1,x2,...,x Q-1 ] T ;

[0123] Step S10: vector x=[x0,x1,x2,...,x Q-1 ] T Perform parallel-to-serial conversion to obtain the parallel-to-serial conversion result x T =[x0,x1,x2,...,x Q-1 ], that is, flexible spectrum effect chirp multi-carrier signal, and x T Sent to an additive white Gaussian noise channel.

[0124] The numerical selection processes of b and c are independent. By setting b and c, the transmitter expands the selectable range of the bandwidth compression factor α in the chirp multi-carrier multiplexing system in two different dimensions, which facilitates providing flexible and variable spectrum efficiency in the chirp multi-carrier multiplexing system and expands the applicability of the chirp multi-carrier multiplexing system structure.

[0125] Specific embodiment 9: This embodiment differs from specific embodiment 8 in that the number of time domain samples Q is:

[0126] Q=ρN

[0127] Where ρ is the oversampling factor;

[0128] The bandwidth compression factor α is:

[0129] α=Δf / Δf′

[0130] Wherein, Δf is the subcarrier spacing of the chirp multi-carrier when it is non-orthogonal, and Δf′ is the subcarrier spacing of the chirp multi-carrier when it is orthogonal.

[0131] Other steps and parameters are the same as those in the eighth embodiment.

[0132] Specific embodiment ten: This embodiment differs from specific embodiments eight or nine in that the phase rotation factor θ2 is a diagonal matrix having non-zero elements only on the diagonal, and the elements on the diagonal are:

[0133]

[0134] Where n = 0, 1, ... Q / α-1, j is the imaginary unit, e is the base of the natural logarithm, and Θ2(n,n) is the nth element on the diagonal.

[0135] The phase rotation factor θ1 is a diagonal matrix with non-zero values ​​only on the diagonal, and the elements on the diagonal are:

[0136]

[0137] Where m = 0, 1, ... Q / α-1, Θ1(m, m) is the m-th element on the diagonal.

[0138] Other steps and parameters are the same as those in the eighth or ninth embodiment.

[0139] Equivalence Proof

[0140] The general mathematical expression of a multi-carrier signal with a chirp signal as the carrier is:

[0141]

[0142] Where T is the duration of the symbol, N is the number of subcarriers, s n,lis the modulation symbol modulated on the nth subcarrier of the lth multicarrier symbol, g(t) is the pulse shaping function, here a rectangular window function is chosen. α = ΔfT ≤ 1, where α is the bandwidth compression factor, which measures the spectral efficiency provided by the chirp multicarrier multiplexing system; Δf is the distance between two adjacent subcarriers. The smaller Δf, the smaller α, and the higher the spectral efficiency. In particular, when α = 1, the system degenerates into a traditional OCDM system, while when α < 1, it becomes a non-orthogonal chirp multicarrier multiplexing system.

[0143] For convenience, only l = 0 is considered. The above continuous signal is sampled at intervals of T / Q, that is, t = kT / Q, where Q = ρN, and ρ is an oversampling factor.

[0144] The discrete form of this signal is:

[0145]

[0146] The signal form of formula (2) can be completed by discrete Fourier transform and two phase rotation operations. The transmitter structure of the existing chirp multi-carrier multiplexing system is as follows: Figure 3 As shown, the specific process is: multiply by Θ2 H , perform Q / α point IDFT, multiply by Θ1 H .

[0147] Figure 3 In the process shown, the DFT input Q / α must be a positive integer. If the fast DFT algorithm (FFT) is used, the number of points must generally be a power of 2. This limits the range of choices for α, and thus the range of options for spectral efficiency, and also reduces the practicality of the system architecture.

[0148] The operation of the IDFT part can be expressed as:

[0149]

[0150] Among them, U=[u′0,u1′,...u′ Q-1 ], any multi-carrier signal form similar to formula (3) can be expressed as:

[0151]

[0152] Among them, U′=[u0′,u1′,...u′ Q-1 ,...u′ L-1 ], is the normalization factor, Ω is the L×L IDFT matrix, whose elements can be expressed as:

[0153]

[0154] According to the transmitter structure proposed in the present invention, the input signal of IDFT can be expressed as:

[0155]

[0156] Where S is Figure 3 The input signal of IDFT is 0≤i<L, L=cQ, α=b / c, b, c are both positive integers and b<c. According to the signal form, U′=[u′0,u1′,...u′ Q-1 ,...u′ L-1 ] can also be expressed as:

[0157]

[0158] Let l = bl′, Then we get:

[0159]

[0160] According to the above proof process, the process of the chirp multi-carrier multiplexing signal generation method can be expressed as:

[0161]

[0162] So far, the equivalence between the flexible spectral effect chirp multi-carrier signal generation method based on zero insertion and zero padding proposed in the present invention and the traditional chirp multi-carrier multiplexing signal generation method has been explained, and they can be flexibly selected according to different needs.

[0163] Experimental part

[0164] The bit error rate performance of the transmitter and receiver models of the present invention was simulated and analyzed in AWGN and frequency-selective fading channels, and compared with SEFDM systems and traditional non-orthogonal chirp multicarrier multiplexing systems. During the simulation, the number of subcarriers was set to 8, 4QAM modulation was used, and maximum likelihood detection was employed at the receiver. Different b and c values ​​were set to achieve different bandwidth compression factors, α.

[0165] Depend on Figure 4 and Figure 5It can be seen that under different choices of bandwidth compression factors, the bit error rate performance of the chirp multi-carrier signal generation method proposed in the present invention is consistent with that of the traditional non-orthogonal chirp multi-carrier multiplexing system, and is superior to the SEFDM system. It can provide higher spectrum efficiency without other performance losses and complex computational costs. Moreover, the method proposed in the present invention can control the bandwidth compression factor α by independently setting the numerical values ​​of b and c, so as to provide flexible spectrum efficiency and enhance the practicality of the system structure. When providing the same spectrum efficiency, the above results reflect the performance advantages of the multi-carrier system with the chirp signal as the carrier. At the same time, simulation verifies the feasibility of the method proposed in the present invention.

[0166] The structure of the non-orthogonal chirp multi-carrier multiplexing system of the present invention is well compatible with SEFDM systems, achieving smooth switching and mutual compatibility between the two systems, requiring only the addition of phase rotation factors. Furthermore, the chirp multi-carrier multiplexing system achieves system structure compatibility in both orthogonal and non-orthogonal modes, enabling switching between orthogonal and non-orthogonal modes by setting different parameters.

[0167] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding, characterized in that: The method specifically comprises the following steps: At the transmitter Step S1: A signal source generates a random bit stream sequence v of length N×log2M, where N is the number of subcarriers and M is the digital modulation order; Step S2: digitally modulate the random bit stream sequence v to obtain a digitally modulated sequence s. T , where s T =[s0,s1,s2,...,s N-1 ],s0,s1,s2,...,s N-1 The sequence s T The 0th, 1st, 2nd, ..., N-1th elements in ; Step S3: sequence s T Perform serial-to-parallel conversion to obtain s=[s0,s1,s2,...,s N-1 ] T , T represents transpose; Step S4: Add Q / α-N zeros to the end of s to obtain the zero-filled result. Where Q is the number of time domain samples and α is the bandwidth compression factor; Step S5: Multiply by Θ2 H Get s′, s′=[s′0,s1′,s2′,...,s′ Q / α-1 ] T ; Among them, Θ2 H represents the Hermite transpose of the phase rotation factor Θ2; Step S6: Insert b-1 zeros between every two adjacent data points of s′, and add cQ-b(Q / α-1)-1 zeros at the end of s′ to obtain the signal vector Wherein, b and c are both positive integers, b<c, and α=b / c; Step S7: Perform an inverse discrete Fourier transform of the cQ points on the signal vector obtained in step S6 to obtain an inverse discrete Fourier transform result, and then remove the cQ-Q / α time domain data at the end of the inverse discrete Fourier transform result, that is, only retain the first Q / α time domain data in the inverse discrete Fourier transform result, and record the vector composed of the retained time domain data as x′=[x′0,x1′,x2′,...,x′ Q / α-1 ] T ; Step S8: Multiply x′ by Θ1 H Get the signal vector [x0,x1,x2,...,x Q-1 ,..,x Q / α-1 ] T , where Θ1 H represents the Hermite transpose of the phase rotation factor Θ1; Step S9: discard the signal vector [x0, x1, x2, ..., x Q-1 ,..,x Q / α-1 ] T The Q(1-α) / α data at the end, the vector composed of the retained data is recorded as x=[x0,x1,x2,...,x Q-1 ] T ; Step S10: vector x=[x0,x1,x2,...,x Q-1 ] T Perform parallel-to-serial conversion to obtain the parallel-to-serial conversion result x T =[x0,x1,x2,...,x Q-1 ], and x T Send to the additive white Gaussian noise channel; On the receiving end Step R1: The signal received by the receiving end is expressed as y T =[y0,y1,y2,...,y Q-1 ], for the received signal y T Perform serial-to-parallel conversion to obtain the signal y=[y0,y1,y2,...,y Q-1 ] T ; Step R2: perform zero-filling operation on the signal y to obtain a vector [y0,y1,y2,...,y Q-1 ,0,...0] T , that is, add Q(1-α) / α zeros at the end of the signal y; Step R3, the [y0,y1,y2,...,y Q-1 ,0,...0] T Multiplying by the phase rotation factor Θ1, we get the vector y′=[y′0,y1′,y′2,...,y′ Q / α-1 ] T ; Step R4: In the vector y′=[y′0,y1′,y′2,...,y′ Q / α-1 ] T Insert b-1 zeros between every two adjacent data points, and add cQ-b(Q / α-1)-1 zeros to the tail of the vector y′. The signal vector obtained by inserting and adding zeros is recorded as Step R5: the signal vector obtained in step R4 Perform discrete Fourier transform of cQ point, and record the signal vector composed of the first Q / α time domain data in the discrete Fourier transform result as r′=[r0′,r1′,r2′,...,r Q ' / α-1 ] T ; Step R6: The vector r′ obtained in step R5 is converted into [r0′, r1′, r2′, ..., r Q ' / α-1 ] T Multiply by the phase rotation factor Θ2 to get the vector [r0,r1,r2,...,r Q-1 ,..,r Q / α-1 ] T ; Step R7: discard the vector [r0,r1,r2,...,r Q-1 ,..,r Q / α-1 ] T The Q / α-N data at the end are used to obtain the vector to be detected r=[r0,r1,r2,...,r N-1 ] T ; Step R8: Use the detection algorithm to detect the vector r = [r0, r1, r2, ..., r N-1 ] T Process and get the estimated value of s Step R9, estimate the value Perform digital demodulation to obtain an estimate of the random bit stream sequence v That is, the original bit stream data is restored.

2. The method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding according to claim 1, characterized in that: The number of time domain samples Q is: Q=ρN Where ρ is the oversampling factor.

3. The method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding according to claim 2, characterized in that: The bandwidth compression factor α is: α=Δf / Δf′ Wherein, Δf is the subcarrier spacing of the chirp multi-carrier when it is non-orthogonal, and Δf′ is the subcarrier spacing of the chirp multi-carrier when it is orthogonal.

4. The method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding according to claim 3, wherein: The phase rotation factor θ2 is a diagonal matrix with non-zero elements only on the diagonal, and the elements on the diagonal are: Where n = 0, 1, ... Q / α-1, j is the imaginary unit, e is the base of the natural logarithm, and Θ2(n,n) is the nth element on the diagonal.

5. The method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding according to claim 4, characterized in that: The phase rotation factor θ1 is a diagonal matrix with non-zero values ​​only on the diagonal, and the elements on the diagonal are: Where m = 0, 1, ... Q / α-1, Θ1(m, m) is the m-th element on the diagonal.

6. The method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding according to claim 5, characterized in that: The signal y received by the receiving end T for: and T =x T +n T Among them, n T is the noise sequence introduced by the signal through the channel.

7. The method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding according to claim 6, characterized in that: The detection algorithm is a maximum likelihood detection method.

8. A method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding, characterized in that: The working process of the method at the sending end is: Step S1: A signal source generates a random bit stream sequence v of length N×log2M, where N is the number of subcarriers and M is the digital modulation order; Step S2: digitally modulate the random bit stream sequence v to obtain a digitally modulated sequence s. T , where s T =[s0,s1,s2,...,s N-1 ],s0,s1,s2,...,s N-1 The sequence s T The 0th, 1st, 2nd, ..., N-1th elements in ; Step S3: sequence s T Perform serial-to-parallel conversion to obtain s=[s0,s1,s2,...,s N-1 ] T , T represents transpose; Step S4: Add Q / α-N zeros to the end of s to obtain the zero-filled result. Where Q is the number of time domain samples and α is the bandwidth compression factor; Step S5: Multiply by Θ2 H Get s′, s′=[s′0,s1′,s2′,...,s′ Q / α-1 ] T ; Among them, Θ2 H represents the Hermite transpose of the phase rotation factor Θ2; Step S6: Insert b-1 zeros between every two adjacent data points of s′, and add cQ-b(Q / α-1)-1 zeros at the end of s′ to obtain the signal vector Wherein, b and c are both positive integers, b<c, and α=b / c; Step S7: Perform an inverse discrete Fourier transform of the cQ points on the signal vector obtained in step S6 to obtain an inverse discrete Fourier transform result, and then remove the cQ-Q / α time domain data at the end of the inverse discrete Fourier transform result, that is, only retain the first Q / α time domain data in the inverse discrete Fourier transform result, and record the vector composed of the retained time domain data as x′=[x′0,x1′,x2′,...,x′ Q / α-1 ] T ; Step S8: Multiply x′ by Θ1 H Get the signal vector [x0,x1,x2,...,x Q-1 ,..,x Q / α-1 ] T , where Θ1 H represents the Hermite transpose of the phase rotation factor Θ1; Step S9: discard the signal vector [x0, x1, x2, ..., x Q-1 ,..,x Q / α-1 ] T The Q(1-α) / α data at the end, the vector composed of the retained data is recorded as x=[x0,x1,x2,...,x Q-1 ] T ; Step S10: vector x=[x0,x1,x2,...,x Q-1 ] T Perform parallel-to-serial conversion to obtain the parallel-to-serial conversion result x T =[x0,x1,x2,...,x Q-1 ], and x T Sent into an additive white Gaussian noise channel.

9. The method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding according to claim 8, characterized in that: The number of time domain samples Q is: Q=ρN Where ρ is the oversampling factor; The bandwidth compression factor α is: α=Δf / Δf′ Wherein, Δf is the subcarrier spacing of the chirp multi-carrier when it is non-orthogonal, and Δf′ is the subcarrier spacing of the chirp multi-carrier when it is orthogonal.

10. The method for generating a flexible spectral effect chirp multi-carrier signal based on zero insertion and zero padding according to claim 9, characterized in that: The phase rotation factor θ2 is a diagonal matrix with non-zero elements only on the diagonal, and the elements on the diagonal are: Where n = 0, 1, ... Q / α-1, j is the imaginary unit, e is the base of the natural logarithm, and Θ2(n,n) is the nth element on the diagonal. The phase rotation factor θ1 is a diagonal matrix with non-zero values ​​only on the diagonal, and the elements on the diagonal are: Where m = 0, 1, ... Q / α-1, Θ1(m, m) is the m-th element on the diagonal.

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