Non-orthogonal chirp multi-carrier signal generation method based on multi-channel parallel IDFT (Inverse Discrete Fourier Transform)

Abstract

The invention discloses a non-orthogonal chirp multi-carrier signal generation method based on multi-channel parallel IDFT (Inverse Discrete Fourier Transform), and belongs to the technical field of chirp multi-carrier signal generation. The method solves the problems that a traditional method is high in calculation complexity and not beneficial to implementation of a system hardware structure. According to the method, a plurality of N-point short IDFT is adopted to replace a single variable cN-point length IDFT, so that the calculation complexity caused by large-point-number IDFT in a signal generation process is reduced, the IDFT with fixed N points is also beneficial to design and implementation of a system hardware structure, digital implementation of a non-orthogonal chirp multi-carrier system is further promoted, and the method has a wide application prospect. And more structural support is provided for the field of non-orthogonal high-spectrum-efficiency transmission. And after the DFT / IDFT is carried out at the receiving end and the transmitting end, the post-processing operation is carried out on the signal, so that the phase error caused by the replacement of the original single DFT / IDFT by the multi-path parallel DFT / IDFT can be compensated. The method provided by the invention can be applied to chirp multi-carrier signal generation.

Description

Technical Field

[0001] The 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, the progress and innovation of information transmission technology are constantly changing people's living habits and production methods. Nowadays, basic data transmission services such as voice calls and text messages can no longer meet the needs of wireless communication between people, and the demand for higher data transmission rate services is increasing. However, the explosive growth of massive data has made the original shortage of wireless spectrum resources even more severe. In order to solve the current difficulties faced by communication development, it is necessary to transform the existing communication technology, explore and research new innovative communication solutions, and achieve the goal of greatly improving channel capacity within limited spectrum resources, fundamentally solving the problem of scarce wireless spectrum resources.

[0003] In order to meet the needs of various high-speed services in modern communications, and considering the increasingly scarce spectrum resources, it is necessary to focus on the physical layer of communications and focus on new technologies with low complexity, high transmission rate and high spectrum efficiency. Nowadays, based on the mature and commercial traditional Orthogonal Frequency Division Multiplexing (OFDM) waveform, a number of new physical layer waveform technologies have been born, aiming to achieve the highest rate of information transmission with the least bandwidth resources. Fast OFDM (F-OFDM) and Spectrally Efficient Frequency Division Multiplexing (SEFDM) both relax the orthogonality between subcarriers in the frequency domain and place the subcarriers closer to occupy less bandwidth to improve spectrum efficiency. Truncated OFDM (TOFDM) uses a more direct approach. It truncates the complete OFDM signal in the time domain and transmits only part of the samples to save transmission time, thereby achieving high-speed transmission. The FasterthanNyquist (FTN) technology is the time domain version of the SEFDM technology. By relaxing the orthogonality between symbols in the time domain, the signal is sent at a rate exceeding the Nyquist limit. In addition, the FTN technology has gradually expanded to multi-carrier systems, achieving the improvement of spectrum efficiency in both the time and frequency domains. The above technologies are all non-orthogonal waveform design schemes, and all introduce artificial interference, which not only brings great challenges to the design of the communication system, but also greatly degrades the communication performance of the system. Although there are various technologies such as channel coding, nonlinear receiver algorithms, and precoding to improve the pathological problems caused by non-orthogonality in the above systems, the degree of performance improvement is still very limited. As a new waveform scheme, the non-orthogonal chirp multi-carrier multiplexing system utilizes the characteristics of chirp subcarriers that are anti-multipath, anti-Doppler, and low sensitivity to frequency changes. Compared with the non-orthogonal multi-carrier system using traditional sine and cosine carriers, it has a great bit error rate performance advantage, and can reduce the interference between subcarriers in non-orthogonal systems to a certain extent. It is one of the effective solutions for high spectral efficiency waveform schemes.

[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 have 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 a 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 greatly increases the computational complexity. In addition, the number of IDFT transformation points cN in the traditional method changes with the change of the system parameter c, and the number of IDFT transformation points needs to be adjusted in real time, which is 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 realization of the system hardware structure, and proposes 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 length of the signal source is N×log 2 M's random bit stream sequence v is digitally modulated to obtain the digitally modulated symbol sequence s T ,s T =[s 0 ,s 1 ,s 2 ,...,s N-1 ], where N is the number of subcarriers, M is the digital modulation order, and s 0 ,s 1 ,s 2 ,...,s N-1 Represents the sequence s T The symbol in [] T Represents the transpose of a vector;

[0010] Will s T =[s 0 ,s 1 ,s 2 ,...,s N-1 ] to perform serial-to-parallel conversion, and obtain the sequence s=[s 0 ,s 1 ,s 2 ,...,s N-1 ] T ;

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

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

[0013] For s′=[s′ 0 ,s′ 1 ,s′ 2 ,...,s′ N-1 ] T Perform a zero-filling operation, that is, fill the tail of s′ with (c-1)N zeros to obtain a zero-filled sequence Then reorder the elements in the zero-filled sequence to get the sorted 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 Grouping, the elements of group i are represented as Where 0≤i≤c-1;

[0016] Step 3: Perform N-point IDFT on the c-group elements obtained in step 2, and represent the result of IDFT on the elements of the i-th group 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 for post-processing at the transmitter; the specific process of post-processing at the transmitter is:

[0018] Define the send data matrix in, is a complex number; define the post-processing matrix at the transmitter Transmitter post-processing matrix P 1 The element in the mth row and nth column of Among them, 0≤m≤c-1, 0≤n≤N-1; the data matrix will be sent The nth row in the transmitter post-processing matrix P 1 Multiply the nth column in the 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 Θ 1 H , and the multiplication result is x=[x 0 ,x 1 ,x 2 ,...,x N-1 ] T ;

[0020] Step 5: multiply the result x=[x 0 ,x 1 ,x 2 ,...,x N-1 ] T Perform parallel-to-serial conversion to obtain signal x T =[x 0 ,x 1 ,x 2 ,...,x N-1 ], signal x T Transmitted through a channel;

[0021] On the receiving end

[0022] Step 6: The signal received by the receiving end is expressed as y T =[y 0 ,y 1 ,y 2 ,...,y N-1 ], for the received signal y T Perform serial-to-parallel conversion and obtain y=[y 0 ,y 1 ,y 2 ,...,y N-1 ] T ;

[0023] Set y=[y 0 ,y 1 ,y 2 ,...,yN-1 ] T Multiply by the matrix Θ 1 , and the multiplication result is y′=[y′ 0 ,y′ 1 ,y′ 2 ,...,y′ N-1 ] T ;

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

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

[0026] Step 8: Sequence The elements in 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 represented by 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 Θ 2 After that, the vector to be detected is obtained r = [r 0 ,r 1 ,r 2 ,...,r N-1 ] T , and then for r = [r 0 ,r 1 ,r 2 ,...,r N-1 ] T Test and get s = [s 0 ,s 1 ,s 2 ,...,s N-1 ] T Estimated value of

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

[0030] Furthermore, the phase rotation factor θ 2 H is the matrix Θ 2 The Hermite transpose of the matrix Θ 2 The elements on the main diagonal of are:

[0031]

[0032] Among them, Θ 2 (n,n) is the matrix Θ 2 The element of the nth row and nth column, 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] Matrix Θ 2 All elements on the non-main diagonal of 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 θ 1 H is the matrix Θ 1 The Hermite transpose of the matrix Θ 1 The elements on the main diagonal of are:

[0038]

[0039] Matrix Θ 1 All elements on the non-main diagonal of 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 For 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 the i-th group (i) It is 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 receiving end post-processing matrix Will receive data matrix The nth row in the receiving end post-processing matrix P 2 Multiply the nth column to get r n ′, 0≤n≤N-1, then the post-processing result at the receiving end r′=[r 0 ′,r 1 ′,r 2 ′,...,r N ' -1 ] T .

[0048] Furthermore, the receiving end post-processing matrix P 2 The element in the mth row and nth column of 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 system structure of the chirp multi-carrier multiplexing system in both orthogonal and non-orthogonal situations. By setting different parameters, the switching of orthogonal and non-orthogonal modes can be completed.

[0051] 2. The present invention solves the problem 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 using 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 add 0 to the tail of the signal, reorder and group the 0-added results, and each group of signals after grouping is independently subjected to a fixed-point DFT / IDFT; after DFT / IDFT is performed at both ends of the transmitter and receiver, the signal is post-processed to compensate for the phase error caused by replacing the original single DFT / IDFT with multiple parallel DFT / IDFTs, thereby reducing the computational complexity while ensuring the performance of the system.

[0053] 4. The bandwidth compression factor α of the present invention is b / c, where b and c are both positive integers and are related to the number of zero padding and zero insertion in the reordering process. The values ​​of b and c are selected independently, which expands the setting range of α in two different dimensions and expands the applicable scope of the system structure.

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

[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 It is a working flow chart of a transmitting end of a non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT of the present invention;

[0057] Figure 2 It is a receiving end working flow chart 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 subcarriers in the chirp multi-carrier system when α=1;

[0059] Figure 4 It is the time-frequency distribution diagram of subcarriers of 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 2 The present embodiment describes a method for generating a non-orthogonal chirp multi-carrier signal based on multi-path parallel IDFT, and the method specifically comprises the following steps:

[0063] At the transmitter

[0064] Step 1: The length of the signal source is N×log 2 M's random bit stream sequence v is digitally modulated to obtain the digitally modulated symbol sequence sT ,s T =[s 0 ,s 1 ,s 2 ,...,s N-1 ], where N is the number of subcarriers, M is the digital modulation order, and s 0 ,s 1 ,s 2 ,...,s N-1 Represents the sequence s T The symbol in [] T Represents the transpose of a vector;

[0065] Will s T =[s 0 ,s 1 ,s 2 ,...,s N-1 ] to perform serial-to-parallel conversion, and obtain the sequence s=[s 0 ,s 1 ,s 2 ,...,s N-1 ] T ;

[0066] Step 2: Set the sequence s=[s 0 ,s 1 ,s 2 ,...,s N-1 ] T Multiply by the phase rotation factor Θ 2 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 a zero-filling operation, that is, fill the tail of s′ with (c-1)N zeros to obtain a zero-filled sequence Then reorder the elements in the zero-filled sequence to get the sorted result That is, in the sorting result, each symbol is followed by b-1 zeros, 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 the i-th group as Where 0≤i≤c-1;

[0071] Step 3: Perform N-point IDFT on the c-group elements obtained in step 2, and represent the result of IDFT on the elements of the i-th group 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 for post-processing at the transmitter; the specific process of post-processing at the transmitter is:

[0073] Define the send data matrix in, is a complex number; define the post-processing matrix at the transmitter Transmitter post-processing matrix P 1 The element in the mth row and nth column of Among them, 0≤m≤c-1, 0≤n≤N-1; the data matrix will be sent The nth row in the transmitter post-processing matrix P 1 Multiply the nth column in the 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 Θ 1 H , and the multiplication result is x=[x 0 ,x 1 ,x 2 ,...,x N-1 ] T ;

[0075] Step 5: multiply the result x=[x 0 ,x 1 ,x 2 ,...,x N-1 ] T Perform parallel-to-serial conversion to obtain signal x T =[x 0 ,x 1 ,x 2 ,...,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: The signal received by the receiving end is expressed as y T =[y 0 ,y 1 ,y 2 ,...,y N-1 ], for the received signal y T Perform serial-to-parallel conversion and obtain y=[y 0 ,y 1 ,y 2 ,...,y N-1 ] T ;

[0078] Set y=[y 0 ,y 1 ,y 2 ,...,y N-1 ] T Multiply by the matrix Θ 1 , and the multiplication result is y′=[y′ 0 ,y′ 1 ,y′ 2 ,...,y′ N-1 ] T ;

[0079] Step 7: y′=[y′ 0 ,y′ 1 ,y′ 2 ,...,y′ N-1 ] T Perform a zero-filling operation, that is, fill (c-1)N zeros at the end of y′ to obtain a 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 represented 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 the i-th group 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 Θ 2 After that, the vector to be detected is obtained r = [r 0 ,r 1 ,r 2 ,...,r N-1 ] T , and then for r = [r 0 ,r 1 ,r 2 ,...,r N-1 ] T Perform detection (using detection algorithm to eliminate inter-subcarrier interference) to obtain constellation point s = [s 0 ,s 1 ,s 2 ,...,s N-1 ] T Estimated value of

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

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

[0086] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the phase rotation factor θ 2 H is the matrix Θ 2 The Hermite transpose of the matrix Θ 2 The elements on the main diagonal of are:

[0087]

[0088] Among them, Θ 2 (n,n) is the matrix Θ 2 The element of the nth row and nth column, 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] Matrix Θ 2 All elements on the non-main diagonal of are 0.

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

[0091] Specific implementation method three: This implementation method is different from specific implementation methods one or two 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] The other steps and parameters are the same as those in the first or second embodiment.

[0095] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the phase rotation factor θ 1 H is the matrix Θ 1 The Hermite transpose of the matrix Θ 1 The elements on the main diagonal of are:

[0096]

[0097] Matrix Θ 1 All elements on the non-main diagonal of are 0.

[0098] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0099] Specific implementation mode five: This implementation mode is different from any one of specific implementation modes one to four 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 Specific Embodiments 1 to 4.

[0101] Specific implementation method 6: This implementation method is different from any one of the specific implementation methods 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 For signal x T A noise sequence introduced through a channel.

[0104] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0105] Specific implementation method 7: This implementation method is different from the specific implementation methods 1 to 6 in that the sequence The elements in are divided into c groups, where the element y″ in the i-th group (i) It is expressed as:

[0106]

[0107] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

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

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

[0110] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0111] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that the receiving end post-processing matrix P 2 The element in the mth row and nth column of 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 certain 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, and 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 reused 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. From the figure, we can see that when α=0.5, the distance between the two chirp carriers is closer and there is a vacant time-frequency band, which means that the non-orthogonal chirp multi-carrier method proposed in the present invention can reuse more subcarriers in 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 2 The transmitter and receiver models shown in the figure are used to simulate and analyze the bit error rate performance in AWGN channel and frequency selective fading channel, and compared with SEFDM system and traditional non-orthogonal chirp multi-carrier multiplexing system. In the simulation process, 4QAM modulation is adopted, and the maximum likelihood detection method is adopted at the receiving end. Different b and c are set to complete the setting of different bandwidth compression factors α.

[0121] Depend on Figure 5 and Figure 6It can be seen that under different selections of bandwidth compression factors, the bit error rate performance of the non-orthogonal chirp multi-carrier signal generation method based on multi-path parallel IDFT proposed in the present invention is better than that of the SEFDM system. The method proposed in the present invention not only reduces the computational complexity caused by the large number of IDFT transformations in the signal generation process, but also the fixed number of IDFTs is conducive to the design and implementation of the system hardware structure, thereby enhancing the practicality of the system structure.

[0122] In summary, 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 also the fixed N-point IDFT is 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 two ends of the transmitter and receiver add 0 to the tail of the signal and reorder and group it. Each group of signals after grouping is independently subjected to N-point DFT / IDFT; after the DFT / IDFT is performed at both ends of the transmitter and receiver, 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 the system parameters, which is not conducive to hardware implementation, and the high computational complexity required for a single large-point IDFT / DFT.

[0123] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for generating non-orthogonal chirp multi-carrier signals 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 with a length of N×log2M, and digitally modulates the sequence v to obtain a 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 the 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 a zero-filling operation, that is, fill the tail of s′ with (c-1)N zeros to obtain a zero-filled sequence Then reorder the elements in the zero-filled sequence to get the sorted 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 Grouping, the elements of group i are represented as Where 0≤i≤c-1; Step 3: Perform N-point IDFT on the c-group elements obtained in step 2, and represent the result of IDFT on the elements of the i-th group 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 for post-processing at the transmitter; the specific process of post-processing at the transmitter is: Define the send data matrix in, is a complex number; define the post-processing matrix at the transmitter The element in the mth row and nth column of the post-processing matrix P1 at the transmitter is Among them, 0≤m≤c-1, 0≤n≤N-1; the data matrix will be sent The nth row in the transmitter post-processing matrix P1 is multiplied by the nth column in the transmitter post-processing matrix P1, and the multiplication result is recorded 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: The signal received by the receiving end is expressed 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 a zero-filling operation, that is, fill (c-1)N zeros at the end of y′ to obtain a zero-filling result Reorder the elements in the sequence y′ to get the sorted result And represent the sorting result as a sequence Step 8: Sequence The elements in 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 represented by 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 , and 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 Digital demodulation is performed 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, characterized 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: Wherein, 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, characterized in that: 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, characterized in that: The phase rotation factor θ1 H is the Hermite transpose of the matrix Θ1. 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 For 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 the i-th group (i) It is 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 receiving end post-processes the DFT results of each group of elements, and the specific process is as follows: Define the receiving data matrix Define the receiving end post-processing matrix Will receive the data matrix The nth row in the receiving end post-processing matrix P2 is multiplied by the nth column to obtain 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.

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