High spectral efficiency orthogonal multi-band carrierless amplitude phase modulation and demodulation method

Abstract

The application discloses a high-spectrum-efficiency orthogonal multi-band carrier-free amplitude-phase modulation and demodulation method. The application firstly designs a shaping filter to ensure the orthogonality between subbands in the case that the adjacent subband signal spectrums overlap; specifically, the bit stream of multiple subbands of a transmitting end is subjected to PAM mapping to obtain PAM symbols; the PAM symbols are up-sampled, and then each subband is filtered through a shaping filter to obtain a transmitting digital signal; a matching filter corresponding to each subband is used at a receiving end to subject the received digital signal to matching filtering, and then the digital signal is subjected to down-sampling, equalization and decision, respectively; and finally, the PAM symbols after the decision are subjected to demapping to obtain the bit stream corresponding to each subband; simulation results show that, compared with a traditional orthogonal carrier-free phase modulation, the signal generated by the application has a smaller bandwidth, better error code performance and a larger transmission rate in a bandwidth-limited system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of communication, and particularly relates to a high-spectrum-efficiency orthogonal multiband carrierless amplitude and phase (SEO-m-CAP) modulation and demodulation method. BACKGROUND

[0002] The multiband carrierless amplitude and phase modulation (m-CAP) technology is an advanced modulation technology applied to an intensity modulation / direct detection optical communication system. The m-CAP realizes the modulation of a multiband signal through a plurality of non-overlapping filters in the frequency domain, can realize the orthogonal access of a plurality of users, has a relatively low system complexity, and has a relatively high spectrum efficiency. Since the modulation bandwidth of the optical communication system is limited, if the communication rate bottleneck is to be broken through, the spectrum efficiency of the modulation signal needs to be further improved. One way is to compress the bandwidth of the m-CAP signal, so as to cause the overlap between adjacent subbands. However, this will introduce inter-channel crosstalk, thereby reducing the system performance. Therefore, designing a high-spectrum-efficiency m-CAP modulation scheme with orthogonal subbands has become a research focus. SUMMARY

[0003] The application aims to provide a novel high-spectrum-efficiency orthogonal multiband carrierless amplitude and phase (SEO-m-CAP) modulation and demodulation method.

[0004] The SEO-m-CAP modulation and demodulation method provided by the application comprises designing a new type of shaping filter, so that the orthogonality between subbands can be ensured even in the case that the spectrum of adjacent subband signals is overlapped, that is, the shaping filter satisfies the zero intersymbol interference (ISI) and zero inter-channel crosstalk (ICI) conditions.

[0005] The SEO-m-CAP modulation and demodulation method provided by the application comprises:

[0006] (1) The bit streams of a plurality of subbands at a transmitting end are subjected to PAM (pulse amplitude modulation) mapping to obtain PAM symbols, the PAM symbols are up-sampled, and then each subband is subjected to shaping filtering through a shaping filter and is added to obtain a transmitting digital signal;

[0007] (2) A matching filter corresponding to each subband is used at a receiving end to respectively subject the received digital signal to matching filtering, and then the digital signal is respectively subjected to down-sampling, equalization and decision, and finally the decided PAM symbols are subjected to demapping to obtain the bit stream corresponding to each subband.

[0008] The SEO-m-CAP shaping filter is given by the following formula:

[0009]

[0010]

[0011] wherein g sq (t) represents a root-raised cosine filter, g n (t) represents a shaping filter of the nth sub-band, t is time, T represents a symbol period, and a represents a roll-off factor of the root-raised cosine filter.

[0012] In the present application, the matched filter is determined by the following formula:

[0013] m n (t) = g n (-t), (3)

[0014] wherein m n (t) represents a matched filter of the nth sub-band.

[0015] In the present application, each sub-band transmits a PAM symbol, and the baud rate of each sub-band is 2 / (1+a) times of the sub-band bandwidth.

[0016] In the present application, the bandwidth of each sub-band is:

[0017]

[0018] In the present application, the baud rate of each sub-band is R s =1 / T, i.e., one symbol period is T.

[0019] In the present application, the total bandwidth of the system is:

[0020]

[0021] wherein N represents the total number of sub-bands.

[0022] In the present application, the spectral efficiency of the system is:

[0023]

[0024] wherein m represents the PAM modulation order.

[0025] In the present application, the shaping filter and the matched filter, the SEO-m-CAP cross filter response is defined as:

[0026]

[0027] In this invention, the Fourier transform of the cross-filter response of the SEO-m-CAP sub-band and the cross-filter response of the (i+1)th sub-band is odd-symmetric about zero frequency, and is expressed by the following formula:

[0028] X i,i+1 (f) = -X i,i+1 (-f), (8)

[0029] Among them, X i,i+1 (f) represents the absolute value of the positive frequency part of the Fourier transform of the cross-filtered response of the i-th subband and the (i+1)-th subband.

[0030] In this invention, the positive frequency part of the Fourier transform of the cross-filter response of the SEO-m-CAP cross-filter response between the i-th sub-band and the (i+1)-th sub-band is related to... Symmetry, the formula is as follows:

[0031]

[0032] In this invention, the SEO-m-CAP cross-filter response, at any sub-band matched filtering point, i.e., at t = kT, satisfies the conditions of zero inter-symbol interference and zero inter-channel interference.

[0033] In this invention, while ensuring the orthogonality of adjacent sub-band shaping filters, partial overlap of the spectrum of adjacent sub-band signals is allowed. Therefore, the overall spectral efficiency is very high, reaching [a certain level]. As the roll-off factor α increases, the center frequency of each subband remains unchanged, the performance of the shaping filter improves, the peak-to-average power ratio (PAPR) decreases, and the increase in the total signal bandwidth is minimal. This results in an increase in the signal-to-noise ratio (SNR) of the received signal. Therefore, when the system modulation bandwidth is limited, compared to conventional m-CAP modulation, this invention allows all shaping filters to have a larger roll-off factor, thereby reducing the transmitted signal PAPR while maintaining a substantially constant total transmitted signal bandwidth. Thus, with the same modulation bandwidth, this invention can achieve a higher transmission rate. Attached Figure Description

[0034] Figure 1 This is a block diagram of the SEO-m-CAP modulation and demodulation system provided in an embodiment of the present invention.

[0035] Figure 2 The first SEO-m-CAP subband shaping filter time-domain diagram provided for an embodiment of the present invention.

[0036] Figure 3 The second SEO-m-CAP subband shaping filter time-domain diagram provided for an embodiment of the present invention.

[0037] Figure 4The third SEO-m-CAP subband shaping filter time-domain diagram provided for an embodiment of the present invention.

[0038] Figure 5 The time-domain diagram of the fourth SEO-m-CAP subband shaping filter provided in this embodiment of the invention.

[0039] Figure 6 Frequency domain diagram of the SEO-m-CAP four-subband shaping filter provided for embodiments of the invention.

[0040] Figure 7 One of the system simulation result graphs provided for the embodiments of the invention is a curve showing the change of bit error rate (BER) with roll-off factor when the peak signal-to-noise ratio (PSNR) is 30dB.

[0041] Figure 8 One of the system simulation result graphs provided for the embodiments of the invention is a curve showing the change of bit error rate with roll-off factor when the signal-to-noise ratio (SNR) is 18dB.

[0042] Figure 9 One of the system simulation result graphs provided for the embodiments of the invention is a curve showing the change of bit error rate with PSNR when the m-CAP roll-off factor is 0.1 and the SEO-m-CAP roll-off factor is 1.

[0043] Figure 10 One of the system simulation result graphs provided for the embodiments of the invention is a curve showing the change of bit error rate with SNR when the m-CAP roll-off factor is 0.1 and the SEO-m-CAP roll-off factor is 1. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] The flowchart shown in the attached diagram is for illustrative purposes only and does not necessarily include all content and operations / steps, nor does it necessarily have to be performed in the order described. For example, some operations / steps can be broken down, combined, or partially merged, so the actual execution order may change depending on the actual situation.

[0046] It should be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0047] The primary applications of short-distance high-speed optical transmission are access networks and data center optical interconnects. Data center transmission distances range from approximately 0.5 to 10 km, while optical access network transmission distances range from approximately 20 to 50 km. Unlike long-distance optical transmission networks, where capacity-distance product is the primary metric, cost control is a major consideration in short-distance applications. Although technologies such as optical IQ modulation and coherent detection have achieved great success in long-distance transmission, they are less suitable for short-distance applications. Currently, the main solutions for short-distance communication are direct intensity modulation and direct detection, employing higher-order modulation formats to maximize single-channel transmission capacity and using parallel transmission methods to improve the overall capacity of short-distance communication.

[0048] Carrierless amplitude and phase (CAP) modulation is a variation of quadrature amplitude modulation (QAM). Due to its reduced system complexity, it is widely used in digital subscriber lines. CAP modulation technology can achieve higher-order signal modulation by using analog or digital filters, reducing system structure and computational complexity. For short-distance communication scenarios, CAP-based direct detection systems offer significant advantages in data transmission rate and cost control.

[0049] Multi-band carrier-free amplitude-phase modulation (m-CAP) is a modulation technique suitable for multi-user communication. m-CAP modulates multi-band signals using multiple non-overlapping frequency-domain filters, enabling orthogonal access for multiple users with low system complexity and high spectral efficiency. Since optical communication systems have limited modulation bandwidth, further improving the spectral efficiency of the modulated signal is necessary to overcome communication rate bottlenecks. One approach is to compress the bandwidth of the m-CAP signal, causing overlap between adjacent sub-bands. However, this introduces inter-channel crosstalk, degrading system performance. Therefore, designing a high-spectral-efficiency m-CAP modulation scheme with orthogonal sub-bands has become a key research focus.

[0050] This invention proposes a novel high-spectral-efficiency orthogonal multiband carrierless amplitude and phase (SEO-m-CAP) modulation and demodulation technique. In this invention, each subband transmits PAM symbols, and the baud rate of each subband is 2 / (1+α) times its bandwidth. This invention allows partial overlap of the signal spectra of adjacent subbands while ensuring the orthogonality of the shaping filters, thus achieving high overall spectral efficiency. As the roll-off factor α increases, the center frequency of each subband remains unchanged, the performance of the shaping filters improves, and the peak-to-average power ratio (PAPR) of the signal decreases. Since the increase in the total signal bandwidth is minimal, the signal-to-noise ratio (SNR) of the received signal is effectively improved. Therefore, when the system modulation bandwidth is limited, compared to traditional m-CAP modulation, this invention allows the roll-off factor of all shaping filters to be set to 1, thereby reducing the transmitted signal PAPR while maintaining a substantially constant total transmitted signal bandwidth. Therefore, with the same modulation bandwidth, this invention can achieve a higher transmission rate.

[0051] The following detailed description of some embodiments of the present invention is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0052] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating an SEO-m-CAP modulation and demodulation method provided by the present invention. This method can be applied to systems transmitting real-valued signals, specifically, to intensity modulation / direct detection (IM / DD) optical communication systems, such as... Figure 1 As shown, the modulation and demodulation technique includes steps S101 to S107.

[0053] Step S101: Perform PAM mapping on the binary data of each sub-band.

[0054] Step S102: Upsample the PAM symbols of each sub-band obtained in S101, i.e., insert S-1 zeros between every two symbols, where S represents the upsampling factor. It should be noted that the upsampling factor increases with the number of sub-bands, and the minimum upsampling factor is N+1, where N represents the number of sub-bands.

[0055] Step S103: The upsampled signal is subjected to shaping filtering through a shaping filter. The shaping filter is as follows:

[0056]

[0057]

[0058] Among them, gsq (t) represents the root-raised cosine filter, g n (t) represents the shaping filter of the nth subband, t represents time, T represents the symbol period, and α represents the roll-off coefficient of the root-raised cosine filter.

[0059] The transmitted digital signal is obtained by summing the signals after shaping and filtering each sub-band, which can be expressed as:

[0060]

[0061] In the formula, g n (t) represents the shaping filter of the nth subband, u n (t) represents the signal after upsampling in the nth subband.

[0062] Step S104: At the receiving end, perform matched filtering on the received signal using the matched filter corresponding to each sub-band to obtain the independent signal corresponding to each sub-band. The matched filter of the nth sub-band can be expressed as:

[0063] m n (t)=g n The signal after matched filtering for each subband (-t) can be expressed as:

[0064]

[0065] Here, r(t) represents the received signal.

[0066] Step S105: Downsample the signal after matched filtering for each sub-band.

[0067] Step S106: Equalize and decide on the downsampled PAM symbols.

[0068] Step S107: Demap the PAM symbols after the decision to obtain the binary data corresponding to each subband.

[0069] Assuming the channel response is ideal, i.e., h(t) = δ(t), then the downsampled signal can be expressed as:

[0070]

[0071] Among them, I k,i This indicates the transmitted PAM symbol, k represents the time index, and i represents the subband index; Let represent the cross-filtering response of the i-th subband and the j-th subband. From this, the zero ISI and zero ICI conditions for interference-free transmission in an ideal channel can be obtained as follows:

[0072]

[0073]

[0074] Performing a Fourier transform on the above equation yields:

[0075]

[0076]

[0077] Among them, X ij (f) represents x ij The continuous-time Fourier transform of (f). This is the frequency domain form of the zero ISI and zero ICI conditions.

[0078] The following will demonstrate that the SEO-m-CAP shaping filter proposed in this invention satisfies the zero ISI and zero ICI conditions.

[0079] The frequency domain expression of the root-raised cosine filter is:

[0080]

[0081] Furthermore, the frequency domain form of the shaping filter described in this invention can be obtained as follows:

[0082]

[0083] According to the definition of cross-filter response, its frequency domain form can be obtained as follows:

[0084]

[0085] Furthermore, it can be proven that the shaped filter proposed in this invention satisfies the zero ISI condition.

[0086] prove:

[0087] When i = 1 It is a raised cosine filter that satisfies the zero ISI condition.

[0088] When i>1

[0089]

[0090] make For all We have

[0091] for We have

[0092]

[0093] thereby

[0094] for Then there is

[0095]

[0096] so

[0097] In summary

[0098] To prove that the shaped filter proposed in this invention satisfies the zero ICI condition, two lemmas concerning the cross-filter response will be introduced below.

[0099] Lemma 1: The Fourier transform of the cross-filtered response of adjacent subbands is odd-symmetric about zero frequency, and can be expressed by the following formula:

[0100] X i,i+1 (f) = -X i,i+1 (-f)

[0101] Lemma 2: The positive frequency part of the Fourier transform of the cross-filtered response of adjacent subbands is related to... Symmetry, that is:

[0102]

[0103] It is easy to see that Lemma 1 holds given the frequency domain expression of a shaped filter. We will now prove Lemma 2.

[0104] prove:

[0105] In particular, we will first prove the case where i = 1, that is, prove... Satisfying Lemma 2

[0106] on the one hand,

[0107]

[0108] on the other hand,

[0109]

[0110] The case where i > 1 will be proven below.

[0111]

[0112] In summary, for all i≥1, about symmetry.

[0113] Furthermore, using the two lemmas above, the zero ICI condition can be proved.

[0114] if

[0115] but

[0116] If |ij|=1, let j=i+1 without loss of generality. in

[0117] By Lemma 1 and Lemma 2, we have

[0118]

[0119] therefore

[0120] so

[0121] In summary, the SCO-m-CAP shaping filter of this invention satisfies the zero ISI and zero ICI conditions, and its orthogonality is proven.

[0122] For example, the foregoing embodiments will be further described in conjunction with specific application scenarios. The novel SEO-m-CAP provided in this application is applied to a bandwidth limiting system, where the bandwidth limiting effect is simulated using an FIR low-pass filter. In this embodiment, the number of sub-bands is set to 4. In this embodiment, the upsampling factor is set to 8, and the low-pass filter's -3dB bandwidth is 0.5π rad / s.

[0123] For example, the time-domain waveforms of the four sub-band shaping filters are as follows: Figures 2-5 As shown, the frequency domain transformation is as follows Figure 6 As shown in the diagram, the time-domain waveform of the filter reveals that subband shaping filters with higher center frequencies exhibit greater fluctuations, corresponding to a monotonically increasing center frequency of the sin and cosine functions. From a frequency perspective, the center frequency of each subband is fixed, and the intersection center of two adjacent subbands is located at a specific position.

[0124] For example, to study the performance of SEO-m-CAP in a peak-limited system, the peak signal-to-noise ratio (PSNR) is set to 30 dB. The bit error rate (BER) of the simulated system as a function of the roll-off factor is shown in the curve below. Figure 7 As shown, the peak-to-average power ratio (PAPR) of the modulated signal decreases as the roll-off factor increases. With a fixed peak power, the average energy of the transmitted signal increases with the roll-off factor. For traditional m-CAP modulated signals, the transmitted signal bandwidth increases linearly with the roll-off factor. Due to bandwidth limitations, the last sub-band of the received m-CAP signal is severely damaged, resulting in a low SNR and an overall increase in the bit error rate. The m-CAP modulation performance is optimal when the roll-off factor is 0.1. In contrast, with SEO-m-CAP, the center frequency of each sub-band remains unchanged, the total bandwidth increases only slightly, while the average power of the transmitted signal increases, thus improving the overall system performance. The SEO-m-CAP performance is optimal when the roll-off factor is 1.

[0125] For example, to study the performance of SEO-m-CAP in a peak power limited system, the peak signal-to-noise ratio (PSNR) is set to 30 dB. The simulated system's bit error rate (BER) as a function of the roll-off factor is shown in the curve below. Figure 7 As shown. On the one hand, as the roll-off factor increases, the peak-to-average power ratio (PAPR) of the modulated signal decreases. Therefore, when the peak power is fixed, the average energy of the transmitted signal increases with the increase of the roll-off factor. On the other hand, the shaping filter used in digital systems is a truncated FIR filter, and the error caused by truncation decreases with the increase of the roll-off factor. This is because as the roll-off factor increases, the time-domain decay of the shaping filter becomes faster, and more energy is concentrated within the truncated rectangular window. For conventional m-CAP modulated signals, the transmitted signal bandwidth increases linearly with the roll-off factor. Due to bandwidth limitations, the last subband of the received m-CAP signal is severely damaged, resulting in a low SNR and an overall increase in the bit error rate. The m-CAP modulation performance is optimal when the roll-off factor is 0.1. In contrast, when the roll-off factor increases, the center frequency of each subband in SEO-m-CAP remains unchanged, the total bandwidth increases only slightly, while the average power of the transmitted signal increases, thus improving the overall system performance. The SEO-m-CAP performance is optimal when the roll-off factor is 1. The minimum bit error rate of SEO-m-CAP is less than that of m-CAP.

[0126] Furthermore, to optimize the performance of the SEO-m-CAP in the average power-limited system, the signal-to-noise ratio (SNR) was set to 18 dB. The simulated system's bit error rate (BER) as a function of the roll-off factor is shown in the curve below. Figure 8 As shown. Since the SNR is fixed, the PAPR reduction from increasing the roll-off factor has no effect here. The factor affecting system performance is the performance of the truncated FIR filter. For m-CAP, the system performance is optimal when the roll-off factor is 0.1; for SEO-m-CAP, the performance is optimal when the roll-off factor is 0.3. The minimum bit error rate of SEO-m-CAP is lower than that of m-CAP. Therefore, under average power constraints, increasing the roll-off factor provides limited performance gain for SEO-m-CAP.

[0127] For example, according to Figure 7 The numerical simulation results shown illustrate the study of system performance changes by setting the m-CAP roll-off factor to 0.1 and the SEO-m-CAP roll-off factor to 1, and varying the PSNR. Figure 9 As shown, the system performance of both modulation methods improves with increasing PSNR. SEO-m-CAP consistently outperforms m-CAP.

[0128] Furthermore, according to Figure 8 The numerical simulation results shown illustrate the effects of setting the m-CAP roll-off factor to 0.1 and the SEO-m-CAP roll-off factor to 0.3, and varying the SNR to study system performance changes. The numerical simulation results are as follows: Figure 10 As shown, the system performance of both modulation methods improves with increasing SNR. SEO-m-CAP consistently outperforms m-CAP. Figure 9 Compared to the results in, Figure 10 The performance improvement of SEO-m-CAP compared to m-CAP is relatively small. This is because, at the same PSNR, the PAPR of SEO-m-CAP with a roll-off factor of 1 is lower than that of m-CAP with a roll-off factor of 0.1. Therefore, at the same PSNR, the SNR of SEO-m-CAP is higher than that of m-CAP, resulting in a significant performance difference.

[0129] It should be noted that in this invention, each sub-band transmits PAM symbols, and the baud rate of each sub-band is 2 / (1+α) times the sub-band bandwidth. This invention allows partial overlap of the signal spectra of adjacent sub-bands while ensuring the orthogonality of the shaping filters, thus achieving a very high overall spectral efficiency. As the roll-off factor α increases, the center frequency of each subband in this invention remains unchanged. The performance of the truncated FIR shaping filter improves, the peak-to-average power ratio (PAPR) of the signal decreases, and the increase in the total signal bandwidth is minimal. This results in an increase in the signal-to-noise ratio (SNR) of the received signal. Therefore, when the system modulation bandwidth is limited, compared with conventional m-CAP modulation, the roll-off factor of all shaping filters in this invention can be set to 1, thereby reducing the PAPR of the transmitted signal and improving the SNR of the transmitted signal while keeping the total bandwidth of the transmitted signal essentially unchanged. Therefore, with the same modulation bandwidth, the transmission rate of this invention can be higher.

[0130] It should be understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. It should be noted that, herein, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0131] The sequence numbers of the above embodiments of the present invention are merely for descriptive purposes and do not represent the superiority or inferiority of the embodiments. The above descriptions are only specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A high spectral efficiency orthogonal multi-band carrier-less amplitude phase (SEO-m-CAP) modulation and demodulation method, characterized in that, The application relates to a method for transmitting and receiving a signal in a multi-subband system, comprising the following steps: (1) a bit stream of a plurality of subbands at a transmitting end is subjected to PAM mapping to obtain PAM symbols; the PAM symbols are up-sampled, and then each subband is subjected to shaping filtering through a shaping filter and is added to obtain a transmitting digital signal; (2) a matching filter corresponding to each subband is used at a receiving end to subject a received digital signal to matching filtering, and then the signal is subjected to down-sampling, equalization and decision, and finally the PAM symbols after decision are subjected to demapping to obtain a bit stream corresponding to each subband; wherein the shaping filter is given by the following formula: where g sq (t) denotes a root raised cosine filter, g n (t) denotes a shaping filter of the nth subband, t denotes time, T denotes a symbol period, and a denotes a roll-off factor of the root raised cosine filter.

2. The modulation method according to claim 1, characterized by, the matching filter is determined by the following formula: m n (t) = g n (-t) where m n (t) denotes the matched filter of the nthsubband.

3. The modulation method according to claim 2, wherein each subband has a bandwidth of:

4. The modulation / demodulation method according to claim 3, wherein, Each sub-band baud rate is R s = 1 / T, i.e. one symbol period is T.

5. The modulation method according to claim 4, wherein the total bandwidth of the system is: wherein N represents the total number of subbands.

6. The modulation method according to claim 5, wherein, the spectral efficiency of the system is: wherein m represents the PAM modulation order.

7. The modulation method according to claim 6, wherein, the shaping filter and the matching filter, a cross filtering response is defined as:

8. The modulation method according to claim 7, wherein, the cross filtering response, a Fourier transform of a cross filtering response of the i-th subband and the i+1-th subband is odd about zero frequency, and is expressed by the following formula: X i,i+1 (f) = -X i,i+1 (-f) wherein X i,i+1 (f) a Fourier transform of the cross-over filter response of the i-th sub-band to the i+1-th sub-band.

9. The modulation method according to claim 7, wherein, The cross-filter response, the Fourier transform positive frequency part of the cross-filter response of the i-th sub-band and the i+1-th sub-band is about Symmetry, the formula is expressed as follows:

10. The modulation method according to claim 9, wherein, the cross filtering response, a signal after matching filtering of any subband satisfies a zero inter-symbol interference (ISI) and a zero inter-channel interference (ICI) condition at a sampling point, i.e. t=kT.

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