A non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT

Abstract

A non-orthogonal chirp multi-carrier signal generation method based on multi-channel parallel IDFT belongs to the technical field of chirp multi-carrier signal generation. The present invention solves the problem that the traditional method has high computational complexity and is not conducive to the implementation of the system hardware structure. The present invention adopts multiple N-point short IDFTs to replace a single variable cN-point long IDFT, which not only reduces the computational complexity caused by the large-point IDFT transformation in the signal generation process, but the fixed N-point IDFT is also beneficial to the design and implementation of the system hardware structure, further promoting the digital implementation of non-orthogonal chirp multi-carrier systems, and providing more structural support for the field of non-orthogonal high spectrum efficiency transmission. In addition, by performing post-processing operations on the signal after performing DFT / IDFT at both ends of the transmitter and receiver, the phase error caused by replacing the original single DFT / IDFT with multiple parallel DFT / IDFTs can be compensated. 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 non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT. Background Art

[0002] With the rapid evolution of the information society, advances and innovations in information transmission technology are constantly changing people's lifestyles and production methods. Today, basic data transmission services such as voice calls and text messages are no longer sufficient for interpersonal wireless communications, and the demand for higher data rates is growing. However, the explosive growth of massive amounts of data is exacerbating the already scarce wireless spectrum resources. To address the current difficulties facing communications development, it is necessary to transform existing communications technologies and explore and research new, innovative communications solutions to significantly increase channel capacity within limited spectrum resources, fundamentally resolving the problem of scarce wireless spectrum resources.

[0003] To meet the demands of various high-speed services in modern communications, while also addressing the increasingly scarce spectrum resources, it's crucial to focus on the physical layer of communications, prioritizing research on new technologies with low complexity, high transmission rates, and high spectral efficiency. Currently, a number of new physical layer waveform technologies, based on the mature and commercially available traditional Orthogonal Frequency Division Multiplexing (OFDM) waveform, have emerged, aiming to achieve the highest possible information transmission rates while minimizing bandwidth resources. Fast OFDM (F-OFDM) and Spectrally Efficient Frequency Division Multiplexing (SEFDM) both improve spectral efficiency by relaxing the orthogonality between subcarriers in the frequency domain, placing them closer together and thus utilizing less bandwidth. Truncated OFDM (TOFDM) takes a more direct approach, truncating the full OFDM signal in the time domain, transmitting only a subset of samples to save time and achieve high-speed transmission. Faster than Nyquist (FTN) technology is a time-domain version of SEFDM. By relaxing the orthogonality between symbols in the time domain, it allows signals to be transmitted at rates exceeding the Nyquist limit. Furthermore, FTN technology has been gradually extended to multi-carrier systems, improving spectral efficiency in both the time and frequency domains. All of these technologies utilize non-orthogonal waveform designs and introduce artificial interference, which not only poses significant challenges to communication system design but also significantly degrades system performance. Although various technologies, such as channel coding, nonlinear receiver algorithms, and precoding, have been developed to address the pathologies introduced by non-orthogonality in these systems, performance improvements remain limited. As a new waveform solution, the non-orthogonal chirp multi-carrier multiplexing system leverages the chirp subcarrier's multipath and Doppler resistance and low sensitivity to frequency variations. Compared to non-orthogonal multi-carrier systems using traditional sine and cosine carriers, it offers significant bit error rate performance advantages and can mitigate the inter-subcarrier interference that exists in non-orthogonal systems, making it an effective solution for high-spectral-efficiency waveforms.

[0004] In order to alleviate the problem of transmission performance degradation caused by internal interference in non-orthogonal waveform schemes, researchers have broken through the waveform limitations of traditional communication systems and introduced chirp signals with certain anti-interference capabilities as carriers into non-orthogonal multi-carrier transmission systems. They proposed a non-orthogonal chirp multiplexing system, which compresses the distance between orthogonal chirp subcarriers so that more chirp carriers can be multiplexed within the same time-frequency resources, thereby improving spectrum efficiency.

[0005] However, in the traditional method, the transmitter uses a single cN-point Inverse Discrete Fourier Transform (IDFT) transform to generate the signal, where c>>1 is a set system parameter related to bandwidth compression. Therefore, the number of points at the transmitter in the traditional method is much larger than the number of subcarriers N, which will greatly increase the computational complexity. In addition, the number of IDFT transformation points cN in the traditional method changes with the system parameter c, and the number of IDFT transformation points needs to be adjusted in real time, which is also not conducive to the implementation of the system hardware structure. Summary of the Invention

[0006] The purpose of the present invention is to solve the problem that the traditional method has high computational complexity and is not conducive to the implementation of the system hardware structure, and to propose a non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT, the method specifically comprising the following steps:

[0008] At the transmitter

[0009] Step 1: The source generates a random bit stream sequence v of length N×log2M, and digitally modulates the sequence v to obtain the digitally modulated symbol sequence s. T , s T =[s0,s1,s2,...,s N-1 ], where N is the number of subcarriers, M is the digital modulation order, s0,s1,s2,...,s N-1 Represents sequence s T The symbol in [] T Represents the transpose of a vector;

[0010] Will s T =[s0,s1,s2,...,s N-1 ] to perform serial-to-parallel conversion and obtain the sequence s=[s0,s1,s2,...,s N-1 ] T ;

[0011] Step 2: Set the sequence s=[s0,s1,s2,...,s N-1 ] T Multiply by the phase rotation factor Θ2 H , and record the multiplication result as s′=[s′0,s′1,s′2,...,s′ N-1 ] T ;

[0012] in,[] HRepresents the Hermite transpose of a matrix;

[0013] For s′=[s′0,s′1,s′2,...,s′ N-1 ] T Perform the zero-filling operation, that is, fill the tail of s′ with (c-1)N zeros to obtain the zero-filled sequence Then reorder the elements in the zero-filled sequence to get the sorting result The sorting result is recorded as

[0014] Wherein, b and c are both positive integers and satisfy α=b / c, b<c;

[0015] Pair Sequence Elements in Group the elements of group i and express them as Where 0≤i≤c-1;

[0016] Step 3: Perform N-point IDFT on the c groups of elements obtained in step 2, and represent the result of IDFT of the elements in group i as x″ (i) =[x″ iN ,x″ iN+1 ,...,x″ (i+1)N-1 ] T ;

[0017] The result x″ of IDFT of each group of elements (i) , 0≤i≤c-1 is used for transmitter post-processing; the specific process of transmitter post-processing is as follows:

[0018] Define the send data matrix in, is a complex number; define the transmitter post-processing matrix The element in the mth row and nth column of the transmitter post-processing matrix P1 is Among them, 0≤m≤c-1, 0≤n≤N-1; the data matrix will be sent Multiply the nth row in the transmitter post-processing matrix P1 by the nth column in the transmitter post-processing matrix P1, and record the multiplication result as x′ n , then we get x′=[x′0,x′1,x′2,...,x′ N-1 ] T ;

[0019] Step 4: Set x′=[x′0,x′1,x′2,...,x′ N-1 ] T Multiply by the phase rotation factor Θ1 H , and the multiplication result is x=[x0,x1,x2,...,x N-1 ] T ;

[0020] Step 5: multiply the result x = [x0, x1, x2, ..., x N-1 ] T Perform parallel-to-serial conversion to obtain signal x T =[x0,x1,x2,...,x N-1 ], signal x T Transmitted through a channel;

[0021] On the receiving end

[0022] Step 6: Express the signal received by the receiving end as y T =[y0,y1,y2,...,y N-1 ], for the received signal y T Perform serial-to-parallel conversion to obtain y=[y0,y1,y2,...,y N-1 ] T ;

[0023] Set y=[y0,y1,y2,...,y N-1 ] T Multiply by matrix Θ1, and get the multiplication result y′=[y′0,y′1,y′2,...,y′ N-1 ] T ;

[0024] Step 7. For y′=[y′0,y′1,y′2,...,y′ N-1 ] T Perform the zero-filling operation, that is, fill (c-1)N zeros at the end of y′ to obtain the zero-filling result

[0025] Reorder the elements in the sequence y′ to get the sorted result And express the sorting result as a sequence

[0026] Step 8: Sequence The elements in the image are divided into c groups, and then the elements of each group are subjected to N-point DFT. The result of DFT of the elements in the i-th group is expressed as r″ (i) =[r″ iN ,r″ iN+1 ,...,r″ (i+1)N-1 ] T , 0≤i≤c-1;

[0027] Perform post-processing on the DFT results of each group of elements at the receiving end;

[0028] Step 9: Multiply the post-processing result of the receiving end by the matrix Θ2 to obtain the vector to be detected r = [r0, r1, r2, ..., rN-1 ] T , then for r=[r0,r1,r2,...,r N-1 ] T Perform the test and get s=[s0,s1,s2,...,s N-1 ] T Estimated value of

[0029] Step 10: Estimated value Perform digital demodulation to obtain That is the restored original bit stream data.

[0030] Furthermore, the phase rotation factor θ2 H is the Hermite transpose of matrix Θ2, and the elements on the main diagonal of matrix Θ2 are:

[0031]

[0032] Where Θ2(n,n) is the element in the nth row and nth column of the matrix Θ2, n = 0, 1, ... N-1, α is the bandwidth compression factor, e is the base of the natural logarithm, and j is the imaginary unit;

[0033] All elements on the non-main diagonal of the matrix Θ2 are 0.

[0034] Furthermore, the bandwidth compression factor is:

[0035] α=Δf′ / Δf

[0036] Wherein, Δf is the subcarrier spacing between chirp carriers when orthogonal, and Δf′ is the subcarrier spacing between chirp carriers when non-orthogonal.

[0037] Furthermore, the phase rotation factor θ1 H is the Hermite transpose of the matrix Θ1, and the elements on the main diagonal of the matrix Θ1 are:

[0038]

[0039] All elements on the non-main diagonal of the matrix Θ1 are 0.

[0040] Furthermore, the channel in step 5 is an additive white Gaussian noise channel.

[0041] Furthermore, the signal y received by the receiving end T for:

[0042] y T =x T +n T

[0043] Among them, n T is the signal x T A noise sequence introduced through a channel.

[0044] Furthermore, the sequence The elements in are divided into c groups, where the element y″ in group i (i) Expressed as:

[0045]

[0046] Furthermore, the DFT results of each group of elements are post-processed at the receiving end, and the specific process is as follows:

[0047] Define the receiving data matrix Define the receiver post-processing matrix Will receive the data matrix Multiply the nth row in the receiving end post-processing matrix P2 by the nth column to get r n ′, 0≤n≤N-1, then the post-processing result at the receiving end is r′=[r0′,r1′,r2′,...,r N ' -1 ] T .

[0048] Furthermore, the element in the mth row and nth column of the receiving end post-processing matrix P2 is Among them, 0≤m≤c-1, 0≤n≤N-1.

[0049] The beneficial effects of the present invention are:

[0050] 1. The present invention proposes a non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT, which realizes the compatibility of the chirp multi-carrier multiplexing system in both orthogonal and non-orthogonal conditions. By setting different parameters, the switching between orthogonal and non-orthogonal modes can be completed.

[0051] 2. The present invention solves the problems of high computational complexity and limited hardware structure design and implementation caused by large-point IDFT transformation in the traditional system structure of non-orthogonal chirp multi-carrier multiplexing by adopting multiple fixed N-point short IDFTs instead of a single variable cN-point long IDFT.

[0052] 3. After the first phase rotation, both ends of the transmitter and receiver of the present invention padded the tail of the signal with zeros, reordered and grouped the padded results, and each group of grouped signals independently performed a fixed-point DFT / IDFT. After the DFT / IDFT was performed at both ends of the transmitter and receiver, the signal was post-processed to compensate for the phase error caused by replacing the original single DFT / IDFT with multiple parallel DFT / IDFTs. This can reduce the computational complexity while ensuring system performance.

[0053] 4. The bandwidth compression factor α of the present invention is equal to b / c, where b and c are both positive integers and are related to the number of zero padding and insertions during the reordering process. The independent selection of the values ​​of b and c expands the setting range of α in two different dimensions, thereby expanding the applicability of the system architecture.

[0054] 5. The method of the present invention takes into account the two advantages of flexible bandwidth compression factor setting and fixed number of multi-channel IDFT points, provides more structural support for non-orthogonal chirp division multiplexing systems, and further promotes their digital implementation.

[0055] 6. Compared with the traditional SEFDM system, the method proposed in the present invention has better bit error rate performance and can provide higher spectrum efficiency without other performance losses and complex calculation costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is a flowchart of the transmitter operation of a method for generating non-orthogonal chirp multi-carrier signals based on multi-path parallel IDFT of the present invention;

[0057] Figure 2 This is a flowchart of a receiving end operation of a non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT of the present invention;

[0058] Figure 3 It is the time-frequency distribution diagram of the subcarriers of the chirp multi-carrier system when α=1;

[0059] Figure 4 It is the time-frequency distribution diagram of the subcarriers of the chirp multi-carrier system when α = 0.5;

[0060] Figure 5 The bit error rate performance under AWGN channel when N=4;

[0061] Figure 6 It is the bit error rate performance under frequency selective fading channel when N=8. DETAILED DESCRIPTION

[0062] Specific implementation method 1: Combination Figure 1 and Figure 2This embodiment describes a method for generating a non-orthogonal chirp multi-carrier signal based on multi-path parallel IDFT, the method specifically comprising the following steps:

[0063] At the transmitter

[0064] Step 1: The source generates a random bit stream sequence v of length N×log2M, and digitally modulates the sequence v to obtain the digitally modulated symbol sequence s. T , s T =[s0,s1,s2,...,s N-1 ], where N is the number of subcarriers, M is the digital modulation order, s0,s1,s2,...,s N-1 Represents sequence s T The symbol in [] T Represents the transpose of a vector;

[0065] Will s T =[s0,s1,s2,...,s N-1 ] to perform serial-to-parallel conversion and obtain the sequence s=[s0,s1,s2,...,s N-1 ] T ;

[0066] Step 2: Set the sequence s=[s0,s1,s2,...,s N-1 ] T Multiply by the phase rotation factor Θ2 H , and record the multiplication result as s′=[s′0,s′1,s′2,...,s′ N-1 ] T ;

[0067] in,[] H Represents the Hermite transpose of a matrix;

[0068] For s′=[s′0,s′1,s′2,...,s′ N-1 ] T Perform the zero-filling operation, that is, fill the tail of s′ with (c-1)N zeros to obtain the zero-filled sequence Then reorder the elements in the zero-filled sequence to get the sorting result That is, in the sorting result, there are b-1 zeros after each symbol, and the sorting result is recorded as

[0069] Wherein, b and c are both positive integers and satisfy α=b / c, b<c;

[0070] Pair Sequence Elements in Group (can be divided into c groups of data, and the length of each group of data is N), and express the elements of group i as Where 0≤i≤c-1;

[0071] Step 3: Perform N-point IDFT on the c groups of elements obtained in step 2, and represent the result of IDFT of the elements in group i as x″ (i) =[x i ″ N ,x i ″ N+1 ,...,x ( ″ i+1)N-1 ] T ;

[0072] The result x″ of IDFT of each group of elements (i) , 0≤i≤c-1 is used for transmitter post-processing; the specific process of transmitter post-processing is as follows:

[0073] Define the send data matrix in, is a complex number; define the transmitter post-processing matrix The element in the mth row and nth column of the transmitter post-processing matrix P1 is Among them, 0≤m≤c-1, 0≤n≤N-1; the data matrix will be sent Multiply the nth row in the transmitter post-processing matrix P1 by the nth column, and record the multiplication result as x n ′, then we get x′=[x′0,x′1,x′2,...,x′ N-1 ] T ;

[0074] Step 4: Set x′=[x′0,x′1,x′2,...,x′ N-1 ] T Multiply by the phase rotation factor Θ1 H , and the multiplication result is x=[x0,x1,x2,...,x N-1 ] T ;

[0075] Step 5: multiply the result x = [x0, x1, x2, ..., x N-1 ] T Perform parallel-to-serial conversion to obtain signal x T =[x0,x1,x2,...,x N-1 ], that is, non-orthogonal chirp multi-carrier signal, signal x T Transmitted through a channel;

[0076] On the receiving end

[0077] Step 6: Express the signal received by the receiving end as y T =[y0,y1,y2,...,y N-1 ], for the received signal y T Perform serial-to-parallel conversion to obtain y=[y0,y1,y2,...,y N-1 ] T ;

[0078] Set y=[y0,y1,y2,...,y N-1 ] T Multiply by matrix Θ1, and get the multiplication result y′=[y′0,y′1,y′2,...,y′ N-1 ] T ;

[0079] Step 7. For y′=[y′0,y′1,y′2,...,y′ N-1 ] T Perform the zero-filling operation, that is, fill (c-1)N zeros at the end of y′ to obtain the zero-filling result

[0080] Reorder the elements in the sequence y′ to get the sorted result That is, in the sorting result, each symbol is followed by b-1 zeros, and the sorting result is expressed as a sequence

[0081] Step 8: Sequence The elements in are divided into c groups (i.e., the length of each group is N), and then the elements of each group are subjected to N-point DFT. The result of DFT of the elements in group i is expressed as r" (i) =[r″ iN ,r″ iN+1 ,...,r″ (i+1)N-1 ] T , 0≤i≤c-1;

[0082] Perform post-processing on the DFT results of each group of elements at the receiving end;

[0083] Step 9: Multiply the post-processing result of the receiving end by the matrix Θ2 to obtain the vector to be detected r = [r0, r1, r2, ..., r N-1 ] T , then for r=[r0,r1,r2,...,r N-1 ] T Perform detection (using detection algorithm to eliminate inter-subcarrier interference) and obtain constellation point s = [s0, s1, s2, ..., s N-1 ] T Estimated value of

[0084] Step 10: Estimate the constellation points Perform digital demodulation to obtain That is the restored original bit stream data.

[0085] Steps 2 and 3 are equivalent to the process of non-orthogonal chirp subcarrier modulation. By reordering and grouping the IDFT, a multi-path parallel fixed and small number of points IDFT method is used to replace the IDFT operation with too long and variable points in the traditional method, which facilitates the hardware implementation of the system and reduces the computational complexity.

[0086] Specific embodiment 2: This embodiment differs from the specific embodiment 1 in that the phase rotation factor θ2 H is the Hermite transpose of matrix Θ2, and the elements on the main diagonal of matrix Θ2 are:

[0087]

[0088] Where Θ2(n,n) is the element in the nth row and nth column of the matrix Θ2, n = 0, 1, ... N-1, α is the bandwidth compression factor, e is the base of the natural logarithm, and j is the imaginary unit;

[0089] All elements on the non-main diagonal of the matrix Θ2 are 0.

[0090] Other steps and parameters are the same as those in the first embodiment.

[0091] Specific embodiment 3: This embodiment differs from specific embodiment 1 or 2 in that the bandwidth compression factor is:

[0092] α=Δf′ / Δf

[0093] Wherein, Δf is the subcarrier spacing between chirp carriers when orthogonal, and Δf′ is the subcarrier spacing between chirp carriers when non-orthogonal.

[0094] Other steps and parameters are the same as those in the first or second embodiment.

[0095] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the phase rotation factor θ1 H is the Hermite transpose of the matrix Θ1, and the elements on the main diagonal of the matrix Θ1 are:

[0096]

[0097] All elements on the non-main diagonal of the matrix Θ1 are 0.

[0098] The other steps and parameters are the same as those in the first to third embodiments.

[0099] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the channel in step 5 is an additive white Gaussian noise channel.

[0100] The other steps and parameters are the same as those in the first to fourth embodiments.

[0101] 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:

[0102] y T =x T +n T

[0103] Among them, n T is the signal x T A noise sequence introduced through a channel.

[0104] The other steps and parameters are the same as those in the first to fifth embodiments.

[0105] Specific embodiment seven: This embodiment differs from any one of the specific embodiments one to six in that the sequence The elements in are divided into c groups, where the element y″ in group i (i) Expressed as:

[0106]

[0107] The other steps and parameters are the same as those in the first to sixth embodiments.

[0108] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the DFT results of each group of elements are post-processed at the receiving end. The specific process is as follows:

[0109] Define the receiving data matrix Define the receiver post-processing matrix Will receive the data matrix Multiply the nth row in the receiving end post-processing matrix P2 by the nth column to get r n ′, 0≤n≤N-1, then the post-processing result at the receiving end is r′=[r′0,r′1,r′2,...,r′ N-1 ] T .

[0110] The other steps and parameters are the same as those in the first to seventh embodiments.

[0111] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that the elements of the mth row and nth column of the receiving end post-processing matrix P2 are Among them, 0≤m≤c-1, 0≤n≤N-1.

[0112] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0113] Performance simulation and analysis

[0114] The present invention proposes a non-orthogonal chirp multi-carrier method based on multi-path parallel IDFT, which aims to compress the subcarrier spacing in the orthogonal chirp multi-carrier system, thereby saving a certain amount of time-frequency domain resources. The general mathematical expression of the chirp multi-carrier signal can be

[0115]

[0116] Where T is the duration of the symbol, N is the number of subcarriers, s n,l is the constellation point modulated on the nth subcarrier of the lth symbol, g(t) is the pulse shaping function, and the rectangular window function is selected here. α is the bandwidth compression factor, α=ΔfT≤1, Δf is the distance between two adjacent subcarriers, that is, the smaller Δf is, the smaller α is, the more chirp carriers can be multiplexed in a given time-frequency resource block, that is, the higher the spectrum efficiency. In particular, when α=1, the system degenerates into a traditional orthogonal chirp multiplexing system. For convenience, only l=0 is considered. The above continuous signal is sampled at intervals of T / N, that is, t=kT / N. The discrete form of the signal is:

[0117]

[0118] The signal form of the above formula can be completed by discrete Fourier transform and two phase rotation operations.

[0119] Figure 3 and Figure 4 The subcarrier time-frequency distribution diagram of the chirp multi-carrier system when the bandwidth compression factor is 1 and 0.5 respectively is given in Figure 1. As we can see from the figure, when α = 0.5, the distance between the two chirp carriers is closer and there is a vacant time-frequency band. This means that the non-orthogonal chirp multi-carrier method proposed in this invention can reuse more subcarriers within the same time-frequency resources to improve spectrum efficiency.

[0120] According to a non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT proposed in the present invention, the following is adopted: Figure 1 and Figure 2The transmitter and receiver models shown in the figure are used to simulate and analyze the bit error rate performance in AWGN and frequency-selective fading channels, and compared with SEFDM systems and traditional non-orthogonal chirp multicarrier multiplexing systems. The simulations use 4QAM modulation, maximum likelihood detection at the receiver, and different bandwidth compression factors α are set using different values ​​of b and c.

[0121] Depend on Figure 5 and Figure 6 As can be seen, the proposed method for generating non-orthogonal chirp multicarrier signals based on multi-path parallel IDFTs achieves superior bit error rate performance compared to SEFDM systems, depending on the bandwidth compression factor. By replacing a single, variable cN-point long IDFT with multiple fixed N-point short IDFTs, the proposed method not only reduces the computational complexity associated with large-point IDFTs during signal generation, but also facilitates the design and implementation of system hardware architecture, enhancing its practicality.

[0122] In summary, the present invention adopts multiple N-point short IDFTs instead of a single variable cN-point long IDFT, which not only reduces the computational complexity caused by the large-point IDFT transformation in the signal generation process, but the fixed N-point IDFT is also beneficial to the design and implementation of the system hardware structure. It further promotes the digital implementation of non-orthogonal chirp multi-carrier systems and provides more structural support for the field of non-orthogonal high spectrum efficiency transmission. After the first phase rotation, the transmitting and receiving ends add 0 to the end of the signal and reorder and group it. Each group of grouped signals independently performs N-point DFT / IDFT; after performing DFT / IDFT at both ends of the transmitting and receiving ends, the signal is post-processed to compensate for the phase error caused by replacing the original single DFT / IDFT with multiple parallel DFT / IDFTs. The method proposed in the present invention solves the problem that the number of DFT / IDFT points in the existing structure of non-orthogonal chirp multi-carrier multiplexing technology needs to be adjusted in real time with system parameters, which is not conducive to hardware implementation, and the computational complexity required for a single large-point IDFT / DFT is high.

[0123] 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 non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT, characterized in that: The method specifically comprises the following steps: At the transmitter Step 1: The source generates a random bit stream sequence v of length N×log2M, and digitally modulates the sequence v to obtain the digitally modulated symbol sequence s. T , s T =[s0,s1,s2,...,s N-1 ], where N is the number of subcarriers, M is the digital modulation order, s0,s1,s2,...,s N-1 Represents sequence s T The symbol in [] T Represents the transpose of a vector; Will s T =[s0,s1,s2,...,s N-1 ] to perform serial-to-parallel conversion and obtain the sequence s=[s0,s1,s2,...,s N-1 ] T ; Step 2: Set the sequence s=[s0,s1,s2,...,s N-1 ] T Multiply by the phase rotation factor Θ2 H , and record the multiplication result as s′=[s0′,s1′,s2′,...,s′ N-1 ] T ; in,[] H Represents the Hermite transpose of a matrix; For s′=[s0′,s1′,s2′,...,s′ N-1 ] T Perform the zero-filling operation, that is, fill the tail of s′ with (c-1)N zeros to obtain the zero-filled sequence Then reorder the elements in the zero-filled sequence to get the sorting result The sorting result is recorded as Wherein, b and c are both positive integers and satisfy α=b / c, b<c; Pair Sequence Elements in Group the elements of group i and express them as Where 0≤i≤c-1; Step 3: Perform N-point IDFT on the c groups of elements obtained in step 2, and represent the result of IDFT of the elements in group i as x″ (i) =[x i ″ N ,x i ″ N+1 ,...,x ( ″ i+1)N-1 ] T ; The result x″ of IDFT of each group of elements (i) , 0≤i≤c-1 is used for transmitter post-processing; the specific process of transmitter post-processing is as follows: Define the send data matrix in, is a complex number; define the transmitter post-processing matrix The element in the mth row and nth column of the transmitter post-processing matrix P1 is Among them, 0≤m≤c-1, 0≤n≤N-1; the data matrix will be sent Multiply the nth row in the transmitter post-processing matrix P1 by the nth column, and record the multiplication result as x n ′, then we get x′=[x0′,x1′,x2′,...,x′ N-1 ] T ; Step 4: Set x′=[x0′,x1′,x2′,...,x′ N-1 ] T Multiply by the phase rotation factor Θ1 H , and the multiplication result is x=[x0,x1,x2,...,x N-1 ] T ; Step 5: multiply the result x = [x0, x1, x2, ..., x N-1 ] T Perform parallel-to-serial conversion to obtain signal x T =[x0,x1,x2,...,x N-1 ], signal x T Transmitted through a channel; On the receiving end Step 6: Express the signal received by the receiving end as y T =[y0,y1,y2,...,y N-1 ], for the received signal y T Perform serial-to-parallel conversion to obtain y=[y0,y1,y2,...,y N-1 ] T ; Set y=[y0,y1,y2,...,y N-1 ] T Multiply by matrix Θ1, and get the multiplication result y′=[y0′,y1′,y2′,...,y′ N-1 ] T ; Step 7: For y′=[y0′,y1′,y2′,...,y′ N-1 ] T Perform the zero-filling operation, that is, fill (c-1)N zeros at the end of y′ to obtain the zero-filling result Reorder the elements in the sequence y′ to get the sorted result And express the sorting result as a sequence Step 8: Sequence The elements in the image are divided into c groups, and then the elements of each group are subjected to N-point DFT. The result of DFT of the elements in the i-th group is expressed as r″ (i) =[r i ' N ′,r i ' N ' +1 ,...,r ( ' i ' +1)N-1 ] T , 0≤i≤c-1; Perform post-processing on the DFT results of each group of elements at the receiving end; Step 9: Multiply the post-processing result of the receiving end by the matrix Θ2 to obtain the vector to be detected r = [r0, r1, r2, ..., r N-1 ] T , then for r=[r0,r1,r2,...,r N-1 ] T Perform the test and get s=[s0,s1,s2,...,s N-1 ] T Estimated value of Step 10: Estimated value Perform digital demodulation to obtain That is the restored original bit stream data.

2. The method for generating non-orthogonal chirp multi-carrier signals based on multi-path parallel IDFT according to claim 1, wherein: The phase rotation factor Θ2 H is the Hermite transpose of matrix Θ2, and the elements on the main diagonal of matrix Θ2 are: Where Θ2(n,n) is the element in the nth row and nth column of the matrix Θ2, n = 0, 1, ... N-1, α is the bandwidth compression factor, e is the base of the natural logarithm, and j is the imaginary unit; All elements on the non-main diagonal of the matrix Θ2 are 0.

3. The method for generating non-orthogonal chirp multi-carrier signals based on multi-path parallel IDFT according to claim 2, wherein: The bandwidth compression factor is: α=Δf′ / Δf Wherein, Δf is the subcarrier spacing between chirp carriers when orthogonal, and Δf′ is the subcarrier spacing between chirp carriers when non-orthogonal.

4. The method for generating non-orthogonal chirp multi-carrier signals based on multi-path parallel IDFT according to claim 3, wherein: The phase rotation factor Θ1 H is the Hermite transpose of the matrix Θ1, and the elements on the main diagonal of the matrix Θ1 are: All elements on the non-main diagonal of the matrix Θ1 are 0.

5. The method for generating non-orthogonal chirp multi-carrier signals based on multi-path parallel IDFT according to claim 4, characterized in that: The channel in step 5 is an additive white Gaussian noise channel.

6. The method for generating non-orthogonal chirp multi-carrier signals based on multi-path parallel IDFT 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 signal x T A noise sequence introduced through a channel.

7. The method for generating non-orthogonal chirp multi-carrier signals based on multi-path parallel IDFT according to claim 6, characterized in that: The sequence The elements in are divided into c groups, where the element y″ in group i (i) Expressed as: .

8. The method for generating non-orthogonal chirp multi-carrier signals based on multi-path parallel IDFT according to claim 7, characterized in that: The DFT results of each group of elements are post-processed at the receiving end, and the specific process is as follows: Define the receiving data matrix Define the receiver post-processing matrix Will receive the data matrix Multiply the nth row in the receiving end post-processing matrix P2 by the nth column to get r n ′, 0≤n≤N-1, then the post-processing result at the receiving end is r′=[r0′,r1′,r2′,...,r N ' -1 ] T .

9. The method for generating non-orthogonal chirp multi-carrier signals based on multi-path parallel IDFT according to claim 8, characterized in that: The element of the mth row and nth column of the receiving end post-processing matrix P2 is Among them, 0≤m≤c-1, 0≤n≤N-1.

Images