A non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression

Abstract

The application discloses a non-orthogonal chirp multicarrier transmission method based on subcarrier interval compression, and belongs to the technical field of wireless communication.The application aims to solve the problem of poor bit error rate performance caused by subcarrier interval interference existing in the prior SEFDM system.The SECDM system based on DFT and phase rotation is established, the chirp subcarrier interval in the orthogonal chirp subcarrier division multiplexing signal is reduced, the distance between the subcarriers in the orthogonal chirp subcarrier division multiplexing system is further compressed, and the transmission rate and the spectral efficiency are improved.The SECDM system of the application replaces the sine and cosine carrier with the chirp carrier, follows the characteristics of the chirp subcarrier, can reduce the influence of ICI under the condition of the same spectral efficiency, and therefore has more superior bit error rate performance than the SEFDM system.The method of the application can be applied to the technical field of wireless communication.

Description

Technical Field

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

[0002] Throughout the 20th century, the rapid development of communications technology has transformed our economic, social, and personal lives. The growth of services and applications facilitated by communications technology is expected to continue, and the added value of mobility has taken this transformation to a new level. Today, wireless communications continue to evolve to provide faster and more stable services to meet people's needs. Spectrum resources, as a crucial medium for information transmission, undoubtedly warrant special attention in communications technology research. Therefore, research into spectrally efficient waveform technology has become a key direction for future communications development.

[0003] Orthogonal Frequency Division Multiplexing (OFDM) is a widely used multicarrier modulation scheme, which is the core of DSL, DAB, WiMax and other communication systems. Its hallmark feature is the use of overlapping but orthogonal subcarriers. Compared with the frequency division multiplexing system using guard band, OFDM has higher bandwidth utilization and better ability to resist channel damage. OFDM converts a high-rate single-carrier signal into multiple overlapping slower subchannels, which helps to resist the delay spread of the channel, thereby having better ability to resist frequency selective fading. OFDM system places its subcarriers at fixed positions, not only ensuring the orthogonality between subcarriers, but also providing high spectral efficiency. Due to the increasing scarcity of spectrum resources, how to further improve the spectral efficiency has become a hot research topic. At present, for multicarrier systems such as OFDM, for example, existing Faster Than Nyquist (FTN), Fast-OFDM, Spectrally Efficient Frequency Division Multiplexing (SEFDM) and other high-spectral-efficiency technologies use different time-frequency domain methods to improve spectral efficiency. FTN is a time-domain technology that aims to reduce the transmission time of the signal and improve the overall spectral efficiency. The Fast-OFDM system sets the subcarrier spacing to half of the OFDM system, and its spectral efficiency is twice that of the OFDM system, but its subcarrier modulation method is limited. It is worth noting that the SEFDM system is a typical high-spectral-efficiency OFDM system, and the main principle is to reduce the subcarrier spacing of the OFDM system in order to achieve the purpose of improving spectral efficiency. Obviously, this further compression of the subcarrier spacing of the OFDM system will lose the orthogonality between the subcarriers, thereby introducing serious inter-carrier interference (ICI) and degrading the bit error rate performance. Therefore, for the SEFDM system, the ICI existing in the system is the main factor affecting its performance. Therefore, it is necessary to propose a new method to solve the problem of poor bit error rate performance of the existing SEFDM system due to the existence of inter-carrier interference. SUMMARY

[0004] The purpose of the present application is to solve the problem of poor bit error rate performance due to the existence of inter-carrier interference in the existing SEFDM system, and to propose a non-orthogonal chirp multicarrier transmission method based on subcarrier spacing compression.

[0005] The technical scheme adopted by the present application to solve the above technical problems is:

[0006] A non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression, the method specifically comprising the following steps:

[0007] On the sending side

[0008] Step 1: The 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] Then digitally modulate the random bit stream sequence generated by the signal source to obtain the digitally modulated symbol vector s T =[s0,s1,s2,...,s N-1 ],in,[] T Represents the transpose of a vector;

[0010] Step 2: symbol vector s T =[s0,s1,s2,...,s N-1 ] to perform serial-to-parallel conversion and obtain vector s=[s0,s1,s2,...,s N-1 ] T ; And perform zero padding on s, that is, add Q / α-N zeros at the end of s, where Q is the number of time domain samples, Q=ρN, ρ is the oversampling factor, and α is the bandwidth compression factor;

[0011] Step 3: Record the zero-filling result in step 2 as Then fill the result with zero and Θ2 H Multiply them and we get s′=[s′0,s′1,s′2,...,s′ Q / α-1 ] T ;

[0012] Where Θ2 is the phase rotation factor, [] H Represents the Hermite transpose of a matrix;

[0013] Step 4: s′=[s′0,s′1,s′2,...,s′ Q / α-1 ] T Perform IDFT of Q / α point and get x′=[x′0,x′1,x′2,...,x′ Q / α-1 ] T ; Then x′=[x′0,x′1,x′2,...,x′ Q / α-1 ] T With Θ1 H After multiplying and discarding Q(1-α) / α data at the end of the multiplication result, we get x=[x0,x1,x2,...,x Q-1 ] T ;

[0014] wherein Θ1 is a phase rotation factor;

[0015] Step five, x = [x0, x1, x2,..., x Q-1 ] T is converted into parallel serial conversion result x T = [x0, x1, x2,..., x Q-1 ];

[0016] At the receiving end

[0017] Step six, after the signal x T = [x0, x1, x2,..., x Q-1 ] passes through the channel, the signal received at the receiving end is represented as y T = [y0, y1, y2,..., y Q-1 ];the received signal y T is converted into serial parallel conversion result y = [y0, y1, y2,..., y Q-1 ] T , and Q(1-α) / α zeros are added at the end of the serial parallel conversion result to obtain a vector of length Q / αxl

[0018] Step seven, the vector is multiplied by the phase rotation factor Θ1 to obtain multiplication result y' = [y'0, y'1, y'2,..., y' Q / α-1 ] T ; and Q / α-point DFT is performed on the multiplication result y' to obtain vector r' = [r'0, r'1, r'2,..., r' Q / α-1 ] T ;

[0019] Step eight, the vector r' is multiplied by the phase rotation factor Θ2, and Q / α-N data are discarded at the end of the multiplication result to obtain the to-be-detected signal r = [r0, r1, r2,..., r N-1 ] T ;

[0020] Step nine, the to-be-detected signal r = [r0, r1, r2,..., r N-1 ] T is detected to obtain the estimation value of the constellation point s = [s0, s1, s2,..., s N-1 ] T

[0021] Step ten, after the estimation value s = [s0, s1, s2,..., s ] is digitally demodulated, the recovered signal source bit stream sequence is obtained. ​​

[0022] Furthermore, the bandwidth compression factor α is:

[0023] α=Δf′ / Δf

[0024] Wherein, Δf′ is the set subcarrier spacing, and Δf is the subcarrier spacing in the orthogonal chirp division multiplexing system.

[0025] Furthermore, the phase rotation factor θ2 is:

[0026]

[0027] Wherein, Θ2(n,n) is the element in the nth row and nth column of the phase rotation factor Θ2, n=0, 1, ... Q / α-1, e is the base of the natural logarithm, and j is the imaginary unit.

[0028] Furthermore, the expression of the phase rotation factor θ1 is:

[0029]

[0030] Wherein, Θ1(m,m) is the element in the mth row and mth column of the phase rotation factor Θ1, and m=0, 1, ...Q / α-1.

[0031] Furthermore, the transformation matrix of the DFT is:

[0032]

[0033] Among them, F m,n is the element in the mth row and nth column of the transformation matrix F, where F is the transformation matrix of DFT.

[0034] Furthermore, the signal y T for:

[0035] y T =x T +n T

[0036] Among them, n T is the noise sequence introduced by the signal through the channel.

[0037] Preferably, the channel is an AWGN channel.

[0038] Furthermore, the signal to be detected r is expressed as:

[0039] r=Θ2FΘ1Θ1 H F H Θ2 H s+n′=Cs+n′

[0040] Where C is the subcarrier correlation matrix, C = Θ2FΘ1Θ1 H F H Θ2 H , n′ is the noise after demodulation at the receiving end;

[0041] Then the maximum likelihood detection method is used to detect the signal r:

[0042]

[0043] Here, ||·|| represents the two-norm.

[0044] Preferably, the channel is a frequency selective fading channel;

[0045] First, you need to T Insert a cyclic prefix before each symbol, then pass the signal after the cyclic prefix insertion through the frequency selective fading channel, and finally remove the cyclic prefix from the signal received from the channel at the receiving end to obtain the signal y T .

[0046] Furthermore, the signal to be detected r is expressed as:

[0047] r=Φ H ΗΦs+n′=Θ2FΘ1ΗΘ1 H F H Θ2 H s+n′

[0048] Where H is the channel equivalent matrix, Φ is the equivalent subcarrier matrix with dimension Q×N, Φ=Θ2FΘ1, Φ H =Θ2FΘ1,Φ H is the equivalent conjugate subcarrier matrix;

[0049] Then the maximum likelihood detection method is used to detect the signal r:

[0050]

[0051] Here, ||·|| represents the bi-norm, and the superscript -1 represents the inverse of the matrix.

[0052] The beneficial effects of the present invention are:

[0053] The present invention establishes a SECDM system based on DFT and phase rotation. By reducing the chirp subcarrier spacing in the orthogonal chirp division multiplexing signal, the distance between subcarriers in the orthogonal chirp division multiplexing system is further compressed, thereby achieving the purpose of improving transmission rate and spectrum efficiency. At the same time, the SECDM system of the present invention replaces the sine and cosine carriers with chirp carriers, inheriting the characteristics of chirp subcarriers, and can reduce the impact of ICI while maintaining the same spectrum efficiency. Therefore, compared with the SEFDM system, it has superior bit error rate performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a flowchart of the transmitter operation process of the present invention;

[0055] Figure 2 It is a flowchart of the receiver working process of the present invention;

[0056] Figure 3 This is a comparison of the bit error rate performance of SECDM and SEFDM systems when α = 0.7;

[0057] SECDM represents the spectrum-efficient chirp division multiplexing system proposed in the present invention; SEFDM-MLupper represents the upper limit of the bit error rate performance using maximum likelihood detection in the SEFDM system, SECDM-MLupper represents the upper limit of the bit error rate performance using maximum likelihood detection in the system of the present invention, SEFDM-ML represents the bit error rate performance using maximum likelihood detection in the SEFDM system, SECDM-ML represents the bit error rate performance using maximum likelihood detection in the system of the present invention;

[0058] Figure 4 This is a comparison of the bit error rate performance of SECDM and SEFDM systems at different α;

[0059] Singer carrier represents a single carrier system;

[0060] Figure 5 This is a performance comparison chart of SECDM and SEFDM systems in frequency selective fading channels;

[0061] FIG6( a ) is a time-frequency distribution diagram of the SECDM system of the present invention when α=1;

[0062] FIG6( b ) is a time-frequency distribution diagram of the SECDM system of the present invention when α=0.5;

[0063] Figure 6(c) is the time-frequency distribution diagram of the SEFDM system when α = 1;

[0064] FIG6( d ) is a time-frequency distribution diagram of the SEFDM system when α=0.5. DETAILED DESCRIPTION

[0065] Specific implementation method 1: Combination Figure 1 and Figure 2 This embodiment describes a non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression, the method specifically comprising the following steps:

[0066] On the sending side

[0067] Step 1: The 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;

[0068] Then digitally modulate the random bit stream sequence generated by the signal source to obtain the digitally modulated symbol vector s T =[s0,s1,s2,...,s N-1 ],in,[] T Represents the transpose of a vector;

[0069] Step 2: symbol vector s T =[s0,s1,s2,...,s N-1 ] to perform serial-to-parallel conversion and obtain vector s=[s0,s1,s2,...,s N-1 ] T ; And perform zero padding on s, that is, add Q / α-N zeros at the end of s, where Q is the number of time domain samples, Q=ρN, ρ is the oversampling factor, and α is the bandwidth compression factor;

[0070] Step 3: Record the zero-filling result in step 2 as Then fill the result with zero and Θ2 H Multiply them and we get s′=[s′0,s′1,s′2,...,s′ Q / α-1 ] T ;

[0071] Where Θ2 is the phase rotation factor, [] H Represents the Hermite transpose of a matrix;

[0072] Step 4: s′=[s′0,s′1,s′2,...,s′ Q / α-1 ] T Perform IDFT (normalized inverse discrete Fourier transform) of Q / α point and get x′=[x′0,x′1,x′2,...,x′ Q / α-1 ] T ; Then x′=[x′0,x′1,x′2,...,x′ Q / α-1 ] T With Θ1 HMultiplication and discarding Q(1-α) / α data at the tail of the multiplication result, x=[x0, x1, x2,..., x Q-1 ] T ;

[0073] wherein Θ1 is a phase rotation factor;

[0074] Step five, x=[x0, x1, x2,..., x Q-1 ] T parallel-serial conversion is performed to obtain parallel-serial conversion result x T =[x0, x1, x2,..., x Q-1 ]; the parallel-serial conversion result is the SECDM signal obtained by the present application;

[0075] At the receiving end

[0076] Step six, after the signal x T =[x0, x1, x2,..., x Q-1 ] passes through a channel, the signal received at the receiving end is represented as y T =[y0, y1, y2,..., y Q-1 ]; the received signal y T is subjected to serial-parallel conversion to obtain serial-parallel conversion result y=[y0, y1, y2,..., y Q-1 ] T , and Q(1-α) / α 0s are added at the tail of the serial-parallel conversion result to obtain a vector of length Q / α×1

[0077] Step seven, the vector is multiplied by the phase rotation factor Θ1 to obtain multiplication result y′=[y′0, y′1, y′2,..., y′ Q / α-1 ] T ; Q / α-point DFT (normalized discrete Fourier transform) is performed on the multiplication result y′ to obtain vector r′=[r′0, r′1, r′2,..., r′ Q / α-1 ] T ;

[0078] Step eight, the vector r′ is multiplied by the phase rotation factor Θ2, and Q / α-N data at the tail of the multiplication result are discarded to obtain the to-be-detected signal r=[r0, r1, r2,..., r N-1 ] T ;

[0079] Step nine, the to-be-detected signal r=[r0, r1, r2,..., r N-1 ] TPerform detection (to eliminate inter-subcarrier interference) and obtain the constellation point s = [s0, s1, s2, ..., s N-1 ] T Estimated value of

[0080] Step 10: Estimated value After digital demodulation, we get This is the recovered source bit stream sequence.

[0081] The method of the present invention has the following advantages:

[0082] 1. The present invention reduces the distance between subcarriers in an orthogonal chirp multi-carrier multiplexing system so that more subcarriers can be accommodated within its bandwidth, thereby carrying more information bits.

[0083] 2. The present invention trades non-orthogonality between subcarriers for high spectrum efficiency and maintains good bit error rate performance.

[0084] 3. In the present invention, the bandwidth compression factor can be selected as 0<α<1, and α can be changed flexibly.

[0085] 4. The present invention replaces the subcarriers in the SEFDM system (Ahmed SI A. Spectrally Efficient FDM Communication Signals and Transceivers: Design, Mathematical Modelling and System Optimization [J].) with chirp subcarriers. Using chirp subcarriers instead of sine and cosine subcarriers can reduce the impact of ICI while maintaining the same spectrum efficiency.

[0086] 5. Compared with the SEFDM system, the SECDM system of the present invention adds a phase rotation operation on the DFT / IDFT module; compared with the orthogonal chirp multiplexing system structure, the SECDM system of the present invention performs a tail padding operation and corrects the phase rotation factor to generate non-orthogonal chirp multi-carrier signals, thereby achieving the purpose of improving spectrum efficiency.

[0087] 6. The SECDM system structure proposed in the present invention can be well compatible with the SEFDM system, achieving smooth switching and mutual compatibility between the SEFDM and SECDM systems, and only requires the addition of a phase rotation factor.

[0088] 7. While maintaining the same spectral efficiency as the SEFDM system, the SECDM system proposed in this invention provides better bit error rate performance in fading channels. Under the same signal power requirements, compared to the SEFDM system, the SECDM system can provide higher spectral efficiency without any other performance loss or complex computational cost.

[0089] 8. Compared with the existing high spectrum efficiency system, the system of the present invention can provide better bit error rate performance at the same spectrum efficiency, and has a certain degree of robustness against channel damage and inter-subcarrier interference.

[0090] 9. The receiving end of the system of the present invention adopts a receiving structure that matches the transmitting end, which is different from the processing method of the traditional non-orthogonal multi-carrier system that uses orthogonal basis correlation to restore the signal.

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

[0092] α=Δf′ / Δf

[0093] Wherein, Δf′ is the set subcarrier spacing (i.e., the subcarrier spacing in the SECDM system of the present invention), and Δf is the subcarrier spacing in the orthogonal chirp division multiplexing system (OUYANG X, ZHAO J. Orthogonal Chirp Division Multiplexing. IEEE Transactions on Communications, 2016, 64(9): 3946-3957.).

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

[0095] Specific embodiment three: This embodiment differs from specific embodiment one in that the phase rotation factor θ2 is:

[0096]

[0097] Wherein, Θ2(n,n) is the element in the nth row and nth column of the phase rotation factor Θ2, n=0, 1, ... Q / α-1, e is the base of the natural logarithm, and j is the imaginary unit.

[0098] Other steps and parameters are the same as those in the first embodiment.

[0099] The phase rotation factor θ2 is a diagonal matrix, that is, except for the elements on the diagonal, all other elements are 0. The present invention can generate a non-orthogonal chirp multi-carrier signal through phase rotation operation and zero-padding operation, thereby achieving the purpose of improving spectrum efficiency.

[0100] Specific embodiment 4: This embodiment differs from specific embodiment 3 in that the expression of the phase rotation factor θ1 is:

[0101]

[0102] Wherein, Θ1(m,m) is the element in the mth row and mth column of the phase rotation factor Θ1, and m=0, 1, ...Q / α-1.

[0103] Other steps and parameters are the same as those in the third embodiment.

[0104] The phase rotation factor Θ1 is a diagonal matrix, that is, except for the elements on the diagonal, all other elements are 0.

[0105] Specific embodiment 5: This embodiment differs from specific embodiment 4 in that the DFT transformation matrix is:

[0106]

[0107] Among them, F m,n is the element in the mth row and nth column of the transformation matrix F, where F is the transformation matrix of DFT.

[0108] Other steps and parameters are the same as those in the fourth embodiment.

[0109] Specific embodiment 6: This embodiment differs from the specific embodiment 1 in that: the signal y T for:

[0110] y T =x T +n T

[0111] Among them, n T is the noise sequence introduced by the signal through the channel.

[0112] Other steps and parameters are the same as those in the first embodiment.

[0113] Specific embodiment seven: This embodiment differs from specific embodiment five in that: the channel is an AWGN channel.

[0114] Other steps and parameters are the same as those in the fifth embodiment.

[0115] Specific embodiment eight: This embodiment differs from specific embodiment seven in that: the signal to be detected r is expressed as:

[0116] r=Φ H Φs+n′=Θ2FΘ1Θ1 H F H Θ2 Hs+n′=Cs+n′

[0117] Where Φ is the equivalent subcarrier matrix with dimension Q×N, Φ H is the equivalent conjugate subcarrier matrix, C is the subcarrier correlation matrix, C = Θ2FΘ1Θ1 H F H Θ2 H , n′ is the noise after demodulation at the receiving end;

[0118] The element in row k and column n of Φ is:

[0119]

[0120] Where, k = 1, 2, ..., Q, n = 1, 2, ..., N;

[0121] Then the maximum likelihood detection method is used to detect the signal r:

[0122]

[0123] Here, ||·|| represents the two-norm.

[0124] Other steps and parameters are the same as those in the seventh embodiment.

[0125] Select the maximum likelihood detection method to detect the signal r and get

[0126]

[0127] Applying the Cauchy inequality to the above equation, we get:

[0128]

[0129] Among them, σ max for The maximum singular value of ; the inequality condition leads to a performance upper bound for maximum likelihood detection, which can be expressed as:

[0130]

[0131] The SECDM system of the present invention is compared and analyzed with the SEFDM system. During the simulation, the number of subcarriers is set to 4, 4QAM modulation is adopted, the simulation channel is an AWGN channel, the maximum likelihood detection method is adopted at the receiving end, and the bandwidth compression factor α is set to 0.7, 0.8, and 0.9 respectively.

[0132] Depend on Figure 3It can be seen that when the bandwidth compression factor α is taken to be the same, the bit error rate performance of the SECDM system proposed in this invention is better than that of the SEFDM system. This means that when achieving the same spectral efficiency, the SECDM system provides better bit error rate performance and is more robust to bit error rate performance degradation caused by inter-subcarrier interference caused by non-orthogonality between subcarriers.

[0133] Depend on Figure 4 It can be seen that as the bandwidth compression factor decreases, that is, as the compression degree increases, the performance of both systems degrades. However, under different choices of bandwidth compression factors, the bit error rate performance of the SECDM system proposed in this invention is better than that of the SEFDM system.

[0134] Specific embodiment 9: This embodiment differs from specific embodiment 5 in that: the channel is a frequency selective fading channel;

[0135] First, you need to T A cyclic prefix (CP) is inserted before each symbol of , and the signal after the cyclic prefix is ​​inserted passes through a frequency selective fading channel. Finally, the receiving end removes the cyclic prefix from the signal received from the channel and obtains the signal y T .

[0136] Other steps and parameters are the same as those in the fifth embodiment.

[0137] Before transmission over a fading channel, a cyclic prefix (CP) is inserted at the beginning of each SECDM symbol to mitigate the effects of multipath interference.

[0138] Specific embodiment ten: This embodiment differs from specific embodiment nine in that: the signal to be detected r is expressed as:

[0139] r=Φ H ΗΦs+n′=Θ2FΘ1ΗΘ1 H F H Θ2 H s+n′

[0140] Where Φ is the equivalent subcarrier matrix of dimension Q×N, Φ=Θ2FΘ1, Φ H =Θ2FΘ1,Φ H is the equivalent conjugate subcarrier matrix, H is the channel equivalent matrix (representing the entire process of adding a cyclic prefix to the transmitting end signal, the signal passing through the channel, and the receiving end removing the cyclic prefix from the received signal);

[0141] Then the maximum likelihood detection method is used to detect the signal r:

[0142]

[0143] Here, ||·|| represents the bi-norm, and the superscript -1 represents the inverse of the matrix.

[0144] Other steps and parameters are the same as those in the ninth embodiment.

[0145] When the channel condition is a frequency selective fading channel, a cyclic prefix (CP) needs to be inserted at the beginning of each SECDM symbol before transmission through the fading channel to mitigate the impact of multipath interference. After removing the CP at the receiving end, the sampling of the SECDM signal can be expressed as:

[0146] y=ΗΦs+n=ΗΘ1 H F H Θ2 H s+n

[0147] Then follow Figure 2 By operating the process, we can get:

[0148] r=Φ H ΗΦs+n′=Θ2FΘ1ΗΘ1 H F H Θ2 H s+n′

[0149] The detection algorithm still selects the maximum likelihood detection, and the detection is performed according to the following formula to obtain This restores the original transmitted bit stream sequence.

[0150]

[0151] The SECDM system of the present invention was simulated in a multipath channel and compared with the SEFDM system. During the simulation, the number of subcarriers was set to 8, 4QAM modulation was used, the multipath delay was set to [0, 1, 2], and the path gain was [0, -5, -6] dB. The maximum likelihood detection method was used at the receiving end, and the bandwidth compression factor α was set to 0.6, 0.7, and 0.8, respectively.

[0152] Depend on Figure 5It can be seen that under different choices of bandwidth compression factors, the bit error rate performance of the SECDM system proposed in the present invention is better than that of the SEFDM system. Moreover, as the bandwidth compression factor α decreases, that is, as the degree of compression increases, the trend of SECDM being better than SEFDM becomes more obvious. This means that when the SECDM system proposed in the present invention maintains the same spectral efficiency as the SEFDM system, the system of the present invention can provide better bit error rate performance, providing a new solution for high spectral efficiency systems. Moreover, under the same signal power requirements, the SECDM of the present invention can provide higher spectral efficiency compared to the SEFDM system. It can be seen from this that the SECDM system of the present invention is an effective waveform design that combines high spectral efficiency and low bit error rate.

[0153] Figure 6(a) to Figure 6(d) The following plots show the subcarrier time-frequency distribution for SECDM and SEFDM systems for different α values. As shown in the figure, as the bandwidth compression factor α decreases, that is, as the degree of bandwidth compression increases, the spectral efficiency improves by a factor of 1 / α. In particular, while subcarriers in a SECDM system still occupy the entire bandwidth, compared to traditional orthogonal chirp multicarrier systems, more subcarriers are allowed to fit within the bandwidth, thus still achieving spectrum conservation.

[0154] 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 transmission method based on subcarrier spacing compression, characterized in that: The method specifically comprises the following steps: On the sending side Step 1: The 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; Then digitally modulate the random bit stream sequence generated by the signal source to obtain the digitally modulated symbol vector s T =[s0,s1,s2,...,s N-1 ],in,[] T Represents the transpose of a vector; Step 2: symbol vector s T =[s0,s1,s2,...,s N-1 ] to perform serial-to-parallel conversion and obtain vector s=[s0,s1,s2,...,s N-1 ] T ; And perform post-padded zero processing on s, that is, add Q / α-N zeros at the end of s, where Q is the number of time domain samples, Q=ρN, ρ is the oversampling factor, and α is the bandwidth compression factor; Step 3: Record the zero-filling result in step 2 as Then fill the result with zero and Θ2 H Multiply them and we get s′=[s′0,s′1,s′2,...,s′ Q / α-1 ] T ; Where Θ2 is the phase rotation factor, [] H Represents the Hermite transpose of a matrix; Step 4: s′=[s′0,s′1,s′2,...,s′ Q / α-1 ] T Perform IDFT at Q / α point and get x′=[x′0,x′1,x′2,...,x′ Q / α-1 ] T ; Then x′=[x′0,x′1,x′2,...,x′ Q / α-1 ] T With Θ1 H After multiplying and discarding Q(1-α) / α data at the end of the multiplication result, we get x=[x0,x1,x2,...,x Q-1 ] T ; Where Θ1 is the phase rotation factor; Step 5: Set x=[x0,x1,x2,...,x Q-1 ] T Perform parallel-to-serial conversion to obtain the parallel-to-serial conversion result x T =[x0,x1,x2,...,x Q-1 ]; On the receiving end Step 6: Signal x T =[x0,x1,x2,...,x Q-1 ]After passing through the channel, the signal received by the receiver is represented as y T =[y0,y1,y2,...,y Q-1 ]; will receive signal y T Perform serial-to-parallel conversion to obtain the serial-to-parallel conversion result y=[y0,y1,y2,...,y Q-1 ] T , and add Q(1-α) / α zeros to the end of the string-to-parallel conversion result to obtain a vector of length Q / α×1 Step 7: Vector Multiplying by the phase rotation factor Θ1, the multiplication result y′=[y′0,y′1,y′2,...,y′ Q / α-1 ] T ; Then perform DFT of Q / α points on the multiplication result y′ to obtain the vector r′=[r′0,r′1,r′2,...,r′ Q / α-1 ] T ; Step 8: Multiply the vector r′ by the phase rotation factor Θ2, and discard Q / α-N data at the end of the multiplication result to obtain the signal to be detected r=[r0,r1,r2,...,r N-1 ] T ; Step 9: For the detection signal r=[r0,r1,r2,...,r N-1 ] T Perform detection and obtain the constellation point s=[s0,s1,s2,...,s N-1 ] T Estimated value of Step 10: Estimated value After digital demodulation, we get This is the recovered source bit stream sequence.

2. The non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression according to claim 1, characterized in that: The bandwidth compression factor α is: α=Δf′ / Δf Wherein, Δf′ is the set subcarrier spacing, and Δf is the subcarrier spacing in the orthogonal chirp division multiplexing system.

3. The non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression according to claim 1, characterized in that: The phase rotation factor θ2 is: Wherein, Θ2(n,n) is the element in the nth row and nth column of the phase rotation factor Θ2, n=0, 1, ... Q / α-1, e is the base of the natural logarithm, and j is the imaginary unit.

4. The non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression according to claim 3, characterized in that: The expression of the phase rotation factor θ1 is: Wherein, Θ1(m,m) is the element in the mth row and mth column of the phase rotation factor Θ1, and m=0, 1, ...Q / α-1.

5. The non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression according to claim 4, characterized in that: The transformation matrix of the DFT is: Among them, F m,n is the element in the mth row and nth column of the transformation matrix F, where F is the transformation matrix of DFT.

6. The non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression according to claim 1, characterized in that: The signal y T for: and T =x T +n T Among them, n T is the noise sequence introduced by the signal through the channel.

7. The non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression according to claim 5, characterized in that: The channel is an AWGN channel.

8. The non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression according to claim 7, characterized in that: The signal to be detected r is expressed as: r=Θ2FΘ1Θ1 H F H Θ2 H s+n′=Cs+n′ Where C is the subcarrier correlation matrix, C = Θ2FΘ1Θ1 H F H Θ2 H , n′ is the noise after demodulation at the receiving end; Then the maximum likelihood detection method is used to detect the signal r: Here, ||·|| represents the two-norm.

9. The non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression according to claim 5, characterized in that: The channel is a frequency selective fading channel; First, you need to T Insert a cyclic prefix before each symbol, then pass the signal after the cyclic prefix insertion through the frequency selective fading channel, and finally remove the cyclic prefix from the signal received from the channel at the receiving end to obtain the signal y T .

10. The non-orthogonal chirp multi-carrier transmission method based on subcarrier spacing compression according to claim 9, characterized in that: The signal to be detected r is expressed as: r=Φ H ΗΦs+n′=Θ2FΘ1ΗΘ1 H F H T2 H s+n′ Where H is the channel equivalent matrix, Φ is the equivalent subcarrier matrix with dimension Q×N, Φ=Θ2FΘ1, Φ H =Θ2FΘ1,Φ H is the equivalent conjugate subcarrier matrix; Then the maximum likelihood detection method is used to detect the signal r: Here, ||·|| represents the bi-norm, and the superscript -1 represents the inverse of the matrix.

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