A chirp multi-carrier transmission method based on windowing and truncation

Abstract

A chirp multi-carrier transmission method based on windowing and truncation belongs to the field of wireless communication technology. The purpose of the present invention is to achieve efficient spectrum utilization while improving the bit error rate performance. The present invention first performs digital modulation and serial-to-parallel conversion on a random bit stream sequence, then performs a discrete Fresnel inverse transform on the conversion result, and after the discrete Fresnel inverse transform result passes through a time domain truncation window, the intercepted signal is converted into parallel and serial, and the parallel-to-serial conversion result is then sent through a channel. The receiving end performs serial-to-parallel conversion, zero padding, discrete Fresnel transformation, and inter-subcarrier interference elimination on the received signal, and then digitally demodulates the signal after interference elimination to restore the original bit stream data. The present invention saves transmission time and improves transmission efficiency by performing windowing and truncation in the time domain, and the bit error rate performance is better than that of existing systems. The method of the present invention can be applied to the field of wireless communication technology.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a chirp multi-carrier transmission method based on windowing and truncation. Background Art

[0002] In the field of wireless communications, the scarcity of spectrum and the demand for high-speed transmission have promoted the research and application of various spectrum-efficient systems. Improving spectrum efficiency is an important direction for future wireless standards. As a multi-carrier modulation scheme, the Orthogonal Frequency Division Multiplexing (OFDM) system achieves efficient utilization of available bandwidth by ensuring that the subcarriers meet the minimum frequency spacing required for mutual orthogonality. The various system advantages of OFDM and its digital implementation based on Fast Fourier Transform (FFT) have greatly stimulated the research of communication technicians on ultra-spectral-efficient OFDM systems. Existing research has proposed various time-domain and frequency-domain technologies, aiming to achieve ultra-spectral-efficient OFDM systems by artificially violating the orthogonality criterion between the subcarriers of the OFDM system. Spectrally Efficient Frequency Division Multiplexing (SEFDM) achieves ultra-efficient spectrum utilization by reducing the subcarrier spacing within OFDM symbols. Similarly, Faster Than Nyquist Signaling (FTN) improves spectrum efficiency by transmitting data of the same bandwidth at a rate exceeding the Nyquist limit. High Compaction Multi-carrier Modulation (HC-MCM), building on the principles of SEFDM and FTN, improves spectrum efficiency by reducing the subcarrier spacing or OFDM transmission time. Truncated OFDM (TOFDM), proposed by Izzat Darwazeh in 2016, truncates OFDM symbols in the time domain, transmitting only a portion of the time samples and discarding the rest. Clearly, the TOFDM symbol duration is shorter than that of OFDM, achieving higher transmission rates and spectrum efficiency.

[0003] However, while the existing system achieves efficient spectrum utilization, the bit error rate performance it can achieve is still relatively limited. Therefore, it is very necessary to propose a new transmission method. Summary of the Invention

[0004] The purpose of the present invention is to improve the bit error rate performance while achieving efficient spectrum utilization, and proposes a chirp multi-carrier transmission method based on windowing and truncation.

[0005] The technical solution adopted by the present invention to solve the above technical problems is:

[0006] A chirp multi-carrier transmission method based on windowing and truncation, the method specifically comprising the following steps:

[0007] At the transmitter

[0008] 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 modulation order;

[0009] Step S2: digitally modulate the random bit stream sequence generated by the signal source to obtain digitally modulated symbols, and represent the digitally modulated symbols in the form of row vectors, i.e., the digitally modulated symbol vector s T =[s0,s1,s2,...,s N-1 ],in,[] T Represents the transpose of a vector, s0,s1,s2,...,s N-1 Respectively represent the 0th, 1st, 2nd, ..., N-1th symbols after digital modulation;

[0010] Step S3: digitally modulated symbol vector s T Perform serial-to-parallel conversion and obtain the conversion result s=[s0,s1,s2,...,s N-1 ] T ;

[0011] Step S4: Perform N-point discrete Fresnel inverse transform on the transformation result s, and express the transformation result as a vector in, is a vector The 0th, 1st, 2nd, ..., N-1th element in ;

[0012] Step S5: After the time domain truncation window, the The first γN data x=[x0,x1,x2,...,x γN-1 ] T , γ is the time truncation factor;

[0013] Step S6: Perform parallel-to-serial conversion on the intercepted x to obtain the parallel-to-serial conversion result x T =[x0,x1,x2,...,x γN-1 ]; and send the parallel-to-serial conversion result to the AWGN channel;

[0014] On the receiving end

[0015] Step R1: The signal received by the receiver is expressed as y T =[y0,y1,y2,...,y γN-1 ], for the received signal y T Perform string-to-parallel conversion to obtain y=[y0,y1,y2,...,y γN-1 ] T , and add N(1-γ) zeros at the end of y to get a vector [y0,y1,y2,...,y γN-1 ,0,...0] T ;

[0016] Step R2, vector [y0,y1,y2,...,y γN-1 ,0,...0] T Perform discrete Fresnel transform of N points to obtain the vector to be detected r=[r0,r1,r2,...,r N-1 ] T ;

[0017] Step R3: Use the detection algorithm to eliminate the inter-subcarrier interference in the vector r to be detected, and obtain the signal after the interference is removed.

[0018] Step R4: Perform digital demodulation to obtain That is, the original bit stream data is restored.

[0019] Furthermore, the specific process of the discrete Fresnel inverse transform is:

[0020] Step 1: Compare the conversion result s with Θ2 H Multiply to get s′=[s′0,s′1,s′2,...,s′ N-1 ] T , where s′0,s′1,s′2,...,s′ N-1 is the 0th, 1st, 2nd, ..., N-1th element in the vector s′; Θ2 is the phase rotation factor, [] H Represents the Hermite transpose of a matrix;

[0021] Step 2: Perform N-point IDFT on s′ to obtain x′=[x′0,x1′,x′2,...,x′ N-1 ] T , where x′0,x′1,x′2,...,x′ N-1 is the 0th, 1st, 2nd, …, N-1th element in vector x′;

[0022] Step 3: Compare x′ with Θ1 H Multiply to get in, is a vector The 0th, 1st, 2nd, ..., N-1th elements in ; Θ1 is the phase rotation factor.

[0023] Furthermore, the phase rotation factor θ1 is:

[0024]

[0025] Where m = 1, 2, ... N, Θ1(m, m) is the m-th diagonal element in the phase rotation factor Θ1, j is the imaginary unit, and e is the base of the natural logarithm.

[0026] Furthermore, the phase rotation factor θ2 is:

[0027]

[0028] Where n=1, 2, ... N, Θ2(n, n) is the nth element on the diagonal of the phase rotation factor Θ2.

[0029] Furthermore, the value range of the time truncation factor is 0<γ<1.

[0030] Furthermore, the signal received by the receiver is:

[0031]

[0032] Among them, n T is the noise sequence introduced by the signal through the channel.

[0033] Furthermore, the specific process of the discrete Fresnel transform is:

[0034] Step 1: transform the vector [y0,y1,y2,...,y γN-1 ,0,...0] T Multiplying by the phase rotation factor Θ1, we get y′=[y′0,y′1,y′2,...,y′ N-1 ] T ;

[0035] Step 2: y′=[y′0,y′1,y′2,...,y′ N-1 ] T Perform DFT of N points and get r′=[r′0,r′1,r′2,...,r′ N-1 ] T ;

[0036] Step 3: r′=[r′0,r′1,r′2,...,r′ N-1 ] T Multiplying by the phase rotation factor Θ2, we get the vector to be detected r = [r0, r1, r2, ..., r N-1 ] T .

[0037] Furthermore, the detection algorithm in step R3 is:

[0038]

[0039] Among them, I γN×N is the time domain truncation window, I γN×N ′ is I γN×N is the transpose of , F is the normalized discrete Fourier transform matrix, and ||·|| represents the 2-norm.

[0040] Furthermore, the element in the mth row and nth column of the normalized discrete Fourier transform matrix is:

[0041]

[0042] Furthermore, the time domain truncation window I γN×N The element in row k and column n is:

[0043]

[0044] Where k = 1, 2,…, γN.

[0045] The beneficial effects of the present invention are:

[0046] 1. The present invention proposes a chirp multi-carrier transmission method based on windowing and truncation, which saves transmission time and further improves transmission efficiency by windowing and truncating the signal in the time domain and transmitting only part of the time samples.

[0047] 2. The present invention replaces the subcarriers in the TOFDM system with chirp subcarriers. Using chirp subcarriers instead of sine and cosine subcarriers can reduce the impact of ICI under the condition of the same spectral effect.

[0048] 3. The TOCDM system implementation structure proposed in this invention is well compatible with the TOFDM system, enabling smooth switching and mutual compatibility between the TOFDM and TOCDM systems. Simulations have shown that the bit error rate performance of the proposed structure is superior to that of the TOFDM system when the degree of spectrum efficiency improvement is the same. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a working flow chart of the transmitter of the present invention;

[0050] Figure 2 It is a working flow chart of the receiver of the present invention;

[0051] Figure 3 When γ=5 / 8, the bit error rate performance comparison diagram of the present invention and the TOFDM system is shown;

[0052] Figure 4 The figure shows the bit error rate performance comparison between the present invention and the TOFDM system when γ=6 / 8. DETAILED DESCRIPTION

[0053] Specific implementation method 1: Combination Figure 1 and Figure 2 This embodiment describes a chirp multi-carrier transmission method based on windowing and truncation, and the method specifically includes the following steps:

[0054] At the transmitter

[0055] 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 modulation order;

[0056] Step S2: digitally modulate the random bit stream sequence generated by the signal source to obtain digitally modulated symbols, and represent the digitally modulated symbols in the form of row vectors, i.e., the digitally modulated symbol vector s T =[s0,s1,s2,...,s N-1 ],in,[] T Represents the transpose of a vector, s0,s1,s2,...,s N-1 Respectively represent the 0th, 1st, 2nd, ..., N-1th symbols after digital modulation;

[0057] Step S3: digitally modulated symbol vector s T Perform serial-to-parallel conversion and obtain the conversion result s=[s0,s1,s2,...,s N-1 ] T ;

[0058] Step S4: Perform an N-point inverse discrete Fresnel transform (IDFnT) on the conversion result s, and express the transformation result using a vector as in, is a vector The 0th, 1st, 2nd, ..., N-1th element in ;

[0059] Step S5: After the time domain truncation window, the The first γN data x=[x0,x1,x2,...,xγN-1 ] T , γ is the time truncation factor;

[0060] The present invention is a rectangular window I γN×N As the time domain truncation window function, The first γN time samples in the data are transmitted, and the remaining data [x γN ,x γN+1 ,...,x N-1 ] T discarded;

[0061]

[0062] Step S6: Perform parallel-to-serial conversion on the intercepted x to obtain the parallel-to-serial conversion result x T =[x0,x1,x2,...,x γN-1 ], that is, the TOCDM signal of the present invention is obtained; and the parallel-to-serial conversion result is sent to the AWGN (Additive White Gaussian Noise) channel;

[0063] On the receiving end

[0064] Step R1: The signal received by the receiver is expressed as y T =[y0,y1,y2,...,y γN-1 ], for the received signal y T Perform string-to-parallel conversion to obtain y=[y0,y1,y2,...,y γN-1 ] T , and add N(1-γ) zeros at the end of y to get a vector [y0,y1,y2,...,y γN-1 ,0,...0] T ;

[0065] Step R2, vector [y0,y1,y2,...,y γN-1 ,0,...0] T Perform discrete Fresnel transform (DFnT) of N points to obtain the vector to be detected r = [r0, r1, r2, ..., r N-1 ] T ;

[0066] Step R3: Use the detection algorithm to eliminate the inter-subcarrier interference in the vector r to be detected, and obtain the signal after the interference is removed.

[0067] Step R4: Perform digital demodulation to obtain That is, the original bit stream data is restored.

[0068] The Orthogonal Chirp Division Multiplexing (OCDM) system is a multi-carrier transmission scheme using orthogonal chirp signals as subcarriers. Its digital implementation relies on the Discrete Fresnel Transform (DFnT), which can be simply implemented by the Discrete Fourier Transform (DFT) by simply adding additional operations before and after the DFT. Moreover, the OCDM system has demonstrated better bit error rate performance than the OFDM system in various communication scenarios and is often proposed as an alternative to the OFDM system. Drawing on the OCDM system and based on the concept of the TOFDM system, the present invention proposes a high-spectral-efficiency chirp multi-carrier transmission method based on windowing and truncation, and establishes a communication system model based on this method. The established communication system model is called a truncated OCDM system (TOCDM). The method of the present invention performs windowing and truncating on the OCDM symbol in the time domain, transmitting only part of the sample data to achieve efficient spectrum utilization. At the same time, the TOCDM system inherits the characteristics of the chirp subcarrier. The TOCDM system achieves efficient spectrum utilization that is better than the OCDM system, and has better bit error rate performance than the TOFDM system when the truncation window is of equal length or the degree of spectrum efficiency improvement is the same.

[0069] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the specific process of the discrete Fresnel inverse transform is as follows:

[0070] Step 1: Compare the conversion result s with Θ2 H Multiply to get s′=[s′0,s′1,s′2,...,s′ N-1 ] T , where s′0,s′1,s′2,...,s′ N-1 is the 0th, 1st, 2nd, ..., N-1th element in the vector s′; Θ2 is the phase rotation factor, [] H Represents the Hermite transpose of a matrix;

[0071] Step 2: Perform N-point IDFT on s′ to obtain x′=[x′0,x′1,x′2,...,x′ N-1 ] T , where x′0,x′1,x′2,...,x′ N-1 is the 0th, 1st, 2nd, …, N-1th element in vector x′;

[0072] Step 3: Compare x′ with Θ1 H Multiply to get in, is a vector The 0th, 1st, 2nd, ..., N-1th elements in ; Θ1 is the phase rotation factor.

[0073] Other steps and parameters are the same as those in the first embodiment.

[0074] This embodiment can be equivalently expressed as:

[0075] Perform discrete Fresnel inverse transform on the conversion result s to obtain vector

[0076]

[0077] Where Φ is the Fresnel matrix, and the element in the k-th row and n-th column of the matrix Φ is:

[0078]

[0079] Specific embodiment three: This embodiment differs from specific embodiment one or two in that the phase rotation factor θ1 is:

[0080]

[0081] Where m = 1, 2, ... N, Θ1(m, m) is the m-th diagonal element in the phase rotation factor Θ1, j is the imaginary unit, and e is the base of the natural logarithm.

[0082] Other steps and parameters are the same as those in the first or second embodiment.

[0083] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the phase rotation factor θ2 is:

[0084]

[0085] Where n=1, 2, ... N, Θ2(n, n) is the nth element on the diagonal of the phase rotation factor Θ2.

[0086] The other steps and parameters are the same as those in the first to third embodiments.

[0087] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the value range of the time truncation factor is 0<γ<1.

[0088] The other steps and parameters are the same as those in the first to fourth embodiments.

[0089] In the present invention, the truncation factor is selected as 0<γ<1, and γ can be changed flexibly; the selection of the truncation window function includes but is not limited to a rectangular window.

[0090] Specific embodiment 6: This embodiment differs from any one of specific embodiments 1 to 5 in that the signal received by the receiver is:

[0091] y T =x T +n T

[0092] Among them, n T is the noise sequence introduced by the signal through the channel.

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

[0094] Specific embodiment 7: This embodiment differs from any one of specific embodiments 1 to 6 in that the specific process of discrete Fresnel transform is as follows:

[0095] Step 1: transform the vector [y0,y1,y2,...,y γN-1 ,0,...0] T Multiplying by the phase rotation factor Θ1, we get y′=[y′0,y′1,y′2,...,y′ N-1 ] T ;

[0096] Step 2: y′=[y′0,y′1,y′2,...,y′ N-1 ] T Perform DFT of N points and get r′=[r′0,r′1,r′2,...,r′ N-1 ] T ;

[0097] Step 3: r′=[r′0,r′1,r′2,...,r N-1 ] T Multiplying by the phase rotation factor Θ2, we get the vector to be detected r = [r0, r1, r2, ..., r N-1 ] T .

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

[0099] This embodiment can be equivalently expressed as:

[0100] Perform discrete Fresnel transform DFnT on y:

[0101] r=Φ H I γN×N 'I γN×N Φs+n′

[0102] Where n′ is the noise sequence after preliminary processing at the receiving end.

[0103] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the detection algorithm in step R3 is:

[0104]

[0105] Among them, I γN×N is the time domain truncation window, I γN×N ′ is I γN×N is the transpose of , F is the normalized discrete Fourier transform matrix, and ||·|| represents the 2-norm.

[0106] The other steps and parameters are the same as those in the first to seventh embodiments.

[0107] The detection algorithm of this embodiment can be equivalently expressed as:

[0108]

[0109] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that the element in the mth row and nth column of the normalized discrete Fourier transform matrix is:

[0110]

[0111] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0112] Specific embodiment 10: This embodiment differs from any one of specific embodiments 1 to 9 in that the time domain truncation window I γN×N The element in row k and column n is:

[0113]

[0114] Where k = 1, 2,…, γN.

[0115] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0116] Simulation part

[0117] The system of the present invention was simulated under an AWGN channel and compared with a TOFDM system. During the simulation, the number of subcarriers was set to 8, 4QAM modulation was used, the simulation channel was an AWGN channel, the maximum likelihood detection method was used at the receiving end, and the time domain truncation factor γ was set to 5 / 8 and 6 / 8 respectively.

[0118] Depend on Figure 3 and Figure 4It can be seen that when the time domain truncation factor γ is taken to be the same, the bit error rate performance of the method of the present invention is better than that of the TOFDM system. This means that when achieving the same spectral efficiency, the method of the present invention provides better bit error rate performance and is more robust to the bit error rate performance degradation caused by inter-subcarrier interference caused by the time domain truncation signal.

[0119] The present invention adopts a time domain expression similar to OCDM and adds the influence of the time domain truncation factor γ. The TOCDM signal of the present invention can be expressed as:

[0120]

[0121]

[0122] Among them, S n Represents the data symbol modulated on the nth subcarrier, N represents the number of subcarriers, is the normalization factor, T TOCDM and T OCDM are the symbol durations of TOCDM and OCDM of the present invention, and their relationship is as follows:

[0123] T TOCDM =γT OCDM

[0124] Therefore, the TOCDM signal of the present invention can be expressed as:

[0125]

[0126] The TOCDM signal of the present invention can be obtained by time domain truncation of the OCDM signal, and the window length γT can be used in this process. OCDM This is achieved by using a time domain truncation window.

[0127] The spacing between two adjacent subcarriers in the TOCDM signal of the present invention is consistent with that in the OCDM signal, but compared with the OCDM symbol, the duration of the TOCDM symbol is shortened due to the influence of the time domain truncation factor γ. Therefore, for each TOCDM symbol, it saves (1-γ)T OCDM That is, the TOCDM system achieves an improvement in the spectral efficiency of the OCDM system by approximately 1 / γ times.

[0128] For example, if N = 10 and γ = 0.8, the number of samples transmitted per OCDM symbol is 10, while the number of samples transmitted per TOCDM symbol is only 8. Therefore, five TOCDM symbols carrying the same information can be sent at the same time as four OCDM symbols. However, the TOCDM symbol duration is no longer equal to the inverse of the subcarrier spacing, which means that the TOCDM signal is no longer orthogonal. Compared with the OCDM signal, the TOCDM signal has a higher transmission rate per subcarrier, achieving a further improvement in spectrum efficiency.

[0129] 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 chirp multi-carrier transmission method based on windowing and truncation, 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 modulation order; Step S2: digitally modulate the random bit stream sequence generated by the signal source to obtain digitally modulated symbols, and represent the digitally modulated symbols in the form of row vectors, i.e., the digitally modulated symbol vector s T =[s0,s1,s2,...,s N-1 ],in,[] T Represents the transpose of a vector, s0,s1,s2,...,s N-1 Respectively represent the 0th, 1st, 2nd, ..., N-1th symbols after digital modulation; Step S3: digitally modulated symbol vector s T Perform serial-to-parallel conversion and obtain the conversion result s=[s0,s1,s2,...,s N-1 ] T ; Step S4: Perform N-point discrete Fresnel inverse transform on the transformation result s, and express the transformation result as a vector in, is a vector The 0th, 1st, 2nd, ..., N-1th element in ; Step S5: After the time domain truncation window, the The first γN data x=[x0,x1,x2,...,x γN-1 ] T , γ is the time truncation factor; Step S6: Perform parallel-to-serial conversion on the intercepted x to obtain the parallel-to-serial conversion result x T =[x0,x1,x2,...,x γN-1 ]; and send the parallel-to-serial conversion result to the AWGN channel; On the receiving end Step R1: The signal received by the receiver is expressed as y T =[y0,y1,y2,...,y γN-1 ], for the received signal y T Perform string-to-parallel conversion to obtain y=[y0,y1,y2,...,y γN-1 ] T , and add N(1-γ) zeros at the end of y to get a vector [y0,y1,y2,...,y γN-1 ,0,...0] T ; Step R2, vector [y0,y1,y2,...,y γN-1 ,0,...0] T Perform discrete Fresnel transform of N points to obtain the vector to be detected r=[r0,r1,r2,...,r N-1 ] T ; Step R3: Use the detection algorithm to eliminate the inter-subcarrier interference in the vector r to be detected, and obtain the signal after the interference is removed. Step R4: Perform digital demodulation to obtain That is, the original bit stream data is restored.

2. A chirp multi-carrier transmission method based on windowing and truncation according to claim 1, characterized in that: The specific process of the discrete Fresnel inverse transform is: Step 1: Compare the conversion result s with Θ2 H Multiply to get s′=[s′0,s′1,s′2,...,s′ N-1 ] T , where s′0,s′1,s′2,...,s′ N-1 is the 0th, 1st, 2nd, ..., N-1th element in the vector s′; Θ2 is the phase rotation factor, [] H Represents the Hermite transpose of a matrix; Step 2: Perform N-point IDFT on s′ to obtain x′=[x′0,x′1,x′2,...,x′ N-1 ] T , where x′0,x′1,x′2,...,x′ N-1 is the 0th, 1st, 2nd, …, N-1th element in vector x′; Step 3: Compare x′ with Θ1 H Multiply to get in, is a vector The 0th, 1st, 2nd, ..., N-1th elements in ; Θ1 is the phase rotation factor.

3. The chirp multi-carrier transmission method based on windowing and truncation according to claim 2, characterized in that: The phase rotation factor θ1 is: Where m = 1, 2, ... N, Θ1(m, m) is the m-th diagonal element in the phase rotation factor Θ1, j is the imaginary unit, and e is the base of the natural logarithm.

4. The chirp multi-carrier transmission method based on windowing and truncation according to claim 3, characterized in that: The phase rotation factor θ2 is: Where n=1, 2, ... N, Θ2(n, n) is the nth element on the diagonal of the phase rotation factor Θ2.

5. The chirp multi-carrier transmission method based on windowing and truncation according to claim 4, characterized in that: The value range of the time truncation factor is 0<γ<1.

6. The chirp multi-carrier transmission method based on windowing and truncation according to claim 5, characterized in that: The signal received by the receiver is: and T =x T +n T Among them, n T is the noise sequence introduced by the signal through the channel.

7. The chirp multi-carrier transmission method based on windowing and truncation according to claim 6, characterized in that: The specific process of the discrete Fresnel transform is: Step 1: transform the vector [y0,y1,y2,...,y γN-1 ,0,...0] T Multiplying by the phase rotation factor Θ1, we get y′=[y′0,y′1,y′2,...,y′ N-1 ] T ; Step 2: y′=[y′0,y′1,y′2,...,y′ N-1 ] T Perform DFT of N points and get r′=[r′0,r′1,r′2,...,r′ N-1 ] T ; Step 3: r′=[r′0,r′1,r′2,...,r′ N-1 ] T Multiplying by the phase rotation factor Θ2, we get the vector to be detected r = [r0, r1, r2, ..., r N-1 ] T .

8. The chirp multi-carrier transmission method based on windowing and truncation according to claim 7, characterized in that: In step R3, the detection algorithm is used to eliminate the inter-subcarrier interference in the vector r to be detected, and the signal after the interference is removed is obtained. The specific process is: Among them, I γN×N is the time domain truncation window, I γN×N ′ is I γN×N is the transpose of , F is the normalized discrete Fourier transform matrix, and ||·|| represents the 2-norm.

9. The chirp multi-carrier transmission method based on windowing and truncation according to claim 8, characterized in that: The element in the mth row and nth column of the normalized discrete Fourier transform matrix is:

10. The chirp multi-carrier transmission method based on windowing and truncation according to claim 9, characterized in that: The time domain truncation window I γN×N The element in row k and column n is: Where k = 1, 2,…, γN.

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