CN104735017B - A kind of non-orthogonal multi-carrier digital modulation and demodulation method and device - Google Patents

Abstract

The invention discloses a non-orthogonal multi-carrier digital modulation and demodulation method, comprising the following steps: dividing an available channel into several sub-carrier channels; performing source coding, channel coding, mapping, and multiple Carrier modulation and adding guard interval processing to obtain multi-carrier digital signals; convert multi-carrier digital signals into analog signals, then amplify them, and finally transmit them to wireless channels; convert received signals into electrical signals, amplify and convert analog signals Convert to a digital receiving signal; estimate the digital receiving signal through a parameter estimation algorithm to obtain the frequency, amplitude and phase of the multi-carrier, and then complete the demodulation and output the data. The method and device of the present invention overcome the influence of carrier frequency deviation on OFDM and other orthogonal multi-carrier systems, and can not only realize higher frequency spectrum utilization ratio, but also have better anti-Doppler performance.

Description

A non-orthogonal multi-carrier digital modulation and demodulation method and device

technical field

The invention relates to the communication field, in particular to a non-orthogonal multi-carrier digital modulation and demodulation method and device.

Background technique

In wireless communication, limited channel bandwidth, signal multipath interference and Doppler frequency shift affect the development of wireless communication. In order to make full use of channel resources and improve the utilization rate of frequency band, Orthogonal Frequency Division Multiplexing (OFDM) is introduced in communication.

The multi-carriers selected by OFDM technology are mutually orthogonal and the frequency spectrum overlaps. The orthogonality between multiple carriers (assuming the number is N) is described as follows:

where T is the symbol period of OFDM, ω _i and ω _j are the frequencies of the i and jth carriers, i, j ∈ [0,1...N-1]. In the time domain, the orthogonality makes each subcarrier contain an integer multiple of periods in one OFDM symbol period, and the difference between adjacent multi-carriers is several fixed periods; in the frequency domain, at the peak of the frequency spectrum of a subcarrier, The values of other sub-carriers are all zero and the spectrum of each sub-carrier overlaps by 1/2, so the OFDM technology has a high spectrum utilization rate.

Assuming that the data symbols assigned to each subcarrier in the OFDM system are d _i (i=0,1...N-1), the frequency of the i-th multi-carrier is: f _i =f ₀ +i/T, where f ₀ is the frequency of the 0th subcarrier. Assuming the rectangular function rect(t)=1,|t|≤T/2, starting from the time t=t _s , the modulated OFDM signal is:

To simplify the analysis, set t _s to 0, and ignore the rectangular function rect(t), then sample the signal s(t) of (Formula 2) at a sampling rate of N/T to obtain an OFDM digital signal:

At the receiving end, the baseband signal can be demodulated by the orthogonality between subcarriers:

The symbol period of each sub-channel in OFDM technology is larger than the serial signal period before OFDM modulation, coupled with the introduction of guard intervals, the OFDM system has a strong ability to resist multipath interference.

In wireless communication, the Doppler frequency shift of the carrier is unavoidable due to the relative motion between the receiving end and the transmitting end. When carrier frequency offset occurs in OFDM, the orthogonality of each subcarrier is restored at the demodulation end through frequency estimation and compensation, and then demodulation is performed. In practical applications, only when the frequency shift is relatively small relative to the inter-carrier spacing, OFDM can restore the orthogonality through frequency estimation compensation. When the frequency shift is large, the orthogonality between the carriers cannot be restored correctly, making the demodulation The bit error rate at the end increases rapidly. For example, the OFDM system requires the frequency deviation to be less than 4% of the carrier spacing in the channel of additive Gaussian white noise, and the frequency deviation is required to be less than 1% to 2% of the carrier spacing in the fading channel.

From the above analysis, it can be seen that OFDM has the characteristics of high spectrum utilization rate and strong anti-multipath ability, but OFDM requires subcarriers to be strictly orthogonal and sensitive to frequency offset. The Doppler frequency shift is an unavoidable phenomenon in wireless communication, so the Doppler frequency shift becomes an important factor affecting the communication quality and application of OFDM. Furthermore, the carrier frequency offset has become an important factor affecting the application of all orthogonal multi-carrier technologies in the field of communication.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art, to provide a non-orthogonal multi-carrier digital modulation and demodulation method, to overcome the impact of carrier frequency offset on OFDM and other orthogonal multi-carrier systems, at the sending end and the receiving end Neither end requires multi-carrier orthogonality.

Another object of the present invention is to provide a non-orthogonal multi-carrier digital modulation and demodulation device.

The purpose of the present invention is achieved through the following technical solutions:

A non-orthogonal multi-carrier digital modulation and demodulation method, comprising the steps in the following order:

S1. Divide available channels into several subcarrier channels according to channel characteristics;

S2. The digital modulation processing unit performs source coding, channel coding, mapping, multi-carrier modulation and guard interval processing on the input data from the outside to obtain multi-carrier digital signals;

Specifically, firstly, after the data from the outside is input into the digital modulation processing unit, source coding, channel coding and mapping processing are respectively performed to improve the reliability and effectiveness of data transmission. Next, the digital modulation processing unit performs serial/parallel conversion on the data, modulates the converted parallel data onto the multi-carrier and adds a guard interval to obtain a digital multi-carrier signal.

S3. The D/A converter converts the multi-carrier digital signal into an analog signal, then amplifies it through the power amplifier, and finally transmits it to the wireless channel by the wireless transmitter;

S4. The wireless receiver converts the received signal into an electrical signal, amplifies it through the preamplifier, and then converts the analog signal into a digital receiving signal through the A/D converter;

The baseband signal is input to the preamplifier and amplified to a size suitable for subsequent processing. Because the signal is attenuated by the wireless channel, the signal received at the receiving end will become smaller, and the amplitude needs to be amplified for subsequent processing. The signal output by the preamplifier is converted into a digital receiving signal through the A/D converter, and then input to the digital demodulation processing unit. The digital demodulation processing unit in the receiving end processes the digital received signal obtained by the A/D converter, including functional modules such as removing guard intervals, parameter estimation, demapping, channel decoding and source decoding, Among them, parameter estimation is the key to realize non-orthogonal digital demodulation. The parameter estimation refers to using a high-performance parameter estimation algorithm to estimate and sort parameters such as frequency, amplitude, and phase to obtain an ordered combination of estimated amplitude and phase values. After the parameter estimation is completed, the digital demodulation processing unit further performs constellation diagram mapping, channel decoding and source decoding to obtain the transmitted data. The power supply at the receiving end supplies energy to all unit modules at the receiving end.

S5. Estimate the digital received signal through a parameter estimation algorithm to obtain the frequency, amplitude and phase of the multi-carrier, and then complete the demodulation and output the data.

Described non-orthogonal multi-carrier digital modulation and demodulation method, concrete steps are as follows:

(1) According to the channel characteristics, the available channels are divided into N sub-carrier channels; the sub-carriers of the signal are:

After coding the transmitted signal and mapping the constellation map, serial-to-parallel conversion is performed to convert the single-channel high-speed data into N-channel parallel low-speed data and modulate it onto the multi-carrier; the modulated multi-carrier signal is:

i∈[0,1...N-1], where A is the carrier amplitude, f is the carrier frequency, and φ is the carrier phase; corresponding to f ₀ <f ₁ <...<f _N-1 , the amplitude and phase value The combination {(A ₀ ,φ ₀ ),(A ₁ ,φ ₁ )...(A _N-1 ,φ _N-1 )} carries the transmission information, that is, the information of the transmission signal is modulated to (A _i ,φ _i )superior;

(2) Perform D/A conversion on the modulated multi-carrier signal s(n) to obtain the analog modulation signal s(t), s(t) is amplified by the power amplifier, and the signal is moved to a suitable wireless channel by the up-conversion module The transmission frequency band is then transmitted by the wireless transmission module;

(3) At the receiving end, the wireless receiver receives the wireless signal and converts it into an electrical signal, and then uses the down-conversion module to move the signal to the baseband. After the baseband signal is amplified by the preamplifier, it performs A/D conversion to obtain a digital reception signal. ;

(4) Digital demodulation of digital received signals: use high-performance parameter estimation algorithms to estimate the parameters of digital received signals, and obtain the estimated values of frequency, amplitude and phase of each subcarrier

(5) For the N groups of estimated parameters obtained by the parameter estimation algorithm, according to the estimated frequency The relative size between, for the corresponding estimated magnitude and estimated phase Sorting to obtain N groups of amplitude and phase values that carry information; specifically, the parameter estimation algorithm obtains like Then determine the combination sequence of amplitude and phase as From N groups of estimated parameters can be obtained The combination of estimated values of the parameters carries the transmission information;

(6) Combination of amplitude and phase values Perform operations such as constellation diagram mapping and decoding to obtain transmitted data.

In step (1), the available channels are divided into N subcarrier channels, which are selected according to the channel performance and the parameter estimation algorithm of the receiving end. In the frequency band with poor channel performance, the subcarrier frequency interval is preferably relatively large, and in the place with good channel performance, the subcarrier interval is preferably small; the selected parameter estimation method has a low frequency resolution, and the subcarrier frequency interval can be large; therefore The selected parameter estimation method has high frequency resolution, and the subcarrier frequency spacing can be made small. The system does not require the subcarriers to be strictly orthogonal, but only needs to meet the carrier frequency spacing condition, that is, the frequency spacing of the subcarriers is greater than the maximum frequency shift and greater than or equal to the frequency resolution of the parameter estimation algorithm. When this condition is met, the relative size between the subcarriers will not change when the frequency shift occurs, and the frequency, amplitude and phase can be estimated by the parameter estimation algorithm.

The parameter estimation algorithm is a rational combination parameter estimation algorithm of spectral lines, and the digital receiving signal is obtained After that, the process of obtaining frequency, amplitude and phase is:

A. Signal to point N zero padding to 2N points, and the signal after zero padding Carry out FFT of 2N points;

B. Signal from 2N points The FFT of obtains power spectrum p (k) and phase spectrum D (k);

C. Obtain N spectral peaks from the power spectrum p(k), denoted as k _i , i∈[0,1...N-1], and obtain the estimated angular frequency of each subcarrier according to formula (7):

in Estimated angular frequency from Estimated frequency available and it is easy to obtain the estimated magnitude

D. On the basis of the obtained frequency and amplitude, the estimated phase can be obtained according to the phase spectrum D(k) and formula (8):

in

Another object of the present invention is achieved through the following technical solutions:

A non-orthogonal multi-carrier digital modulation and demodulation device, including a sending module, a receiving module connected to the sending module through a wireless channel, and the sending module includes sequentially connected digital modulation processing units, D/A converters, power An amplifier and a wireless transmitter, the receiving module includes a sequentially connected wireless receiver, preamplifier, A/D converter, and digital demodulation processing unit.

The wireless transmitter includes an up-conversion module and a transmission module. The up-conversion module is selected according to specific applications. The amplified analog signal is transferred to a frequency suitable for wireless channel transmission through the up-conversion module, and then transmitted by the transmission module.

The transmitting module is a radio frequency antenna, or an electro-acoustic transducer. The transmitting module can also be a transmitter of other wireless signals.

The wireless receiver includes a wireless receiving module and a down-conversion module, the wireless receiving module converts the signal received from the wireless channel into an electrical signal, and the down-conversion module moves the electrical signal to obtain a baseband signal, and the down-conversion module can be selected according to specific applications .

The wireless receiving module is an antenna for receiving electromagnetic waves, or an acoustic-electric transducer. The wireless receiving module can also be a receiver of other forms of wireless signals.

The wireless channel is an underwater acoustic channel.

Compared with the prior art, the present invention has the following advantages and beneficial effects:

(1) A frequency-division multi-carrier communication system based on spectrum overlap that can overcome carrier frequency offset is realized.

Since the carrier frequency spectrum of the present invention can be overlapped, and the subcarriers are not required to be strictly orthogonal at the transmitting end and the receiving end, only the carrier frequency interval condition is required to be met, so the present invention can not only achieve a higher spectrum utilization rate, but also has a better Doppler resistance.

(2) The present invention has low requirements on sub-carriers, is easy to meet, and can make full use of frequency band resources.

Frequency division multi-carrier communication systems have certain requirements for carrier frequency spacing in specific application environments. Compared with OFDM and other communication systems that strictly require subcarrier orthogonality, the carrier frequency spacing conditions of the present invention are easy to meet. Under the condition that the carrier frequency interval is satisfied, the carrier frequency interval can be as small as possible, which fully improves the frequency band utilization of the system.

(3) The present invention is feasible.

The key of the present invention is to realize the parameter estimation of high performance, on the software, existing multiple high-performance parameter estimation algorithm is proposed, comprise the parameter estimation algorithm of time domain and frequency domain; The improvement of the computer can be used as a digital demodulation processing unit to perform high-performance parameter estimation at the receiving end to realize digital demodulation.

(4) The digital modulation and demodulation of the present invention is flexible.

With the improvement of the computing power of modern computers, the computer can be used as a digital modulation processing unit and a digital demodulation processing unit to perform flexible multi-carrier programmable dynamic modulation at the sending end, and perform flexible programmable high-performance parameters at the receiving end It is estimated that the flexibility of the system is improved and the complexity of the system hardware is reduced.

(5) It provides a beneficial solution to overcome carrier frequency offset for wireless multi-carrier communication system.

The present invention only requires bandwidth division to meet the characteristics of carrier frequency interval conditions, so that non-orthogonal multi-carrier communication systems similar to the present invention and orthogonal multi-carrier communication systems such as OFDM can be used after a small amount of modification of the modulation and demodulation rules. The invention directly performs digital demodulation on the received signal, which is beneficial to overcome the influence of carrier frequency deviation.

Description of drawings

Figure 1 is a schematic diagram of spectrum bandwidth division;

Fig. 2 is a schematic structural diagram of a non-orthogonal multi-carrier digital modulation and demodulation device according to the present invention;

Fig. 3 is the functional block diagram of the digital modulation unit of the device described in Fig. 2;

Fig. 4 is the functional block diagram of the digital demodulation unit of device described in Fig. 2;

Fig. 5 is a flow chart of the non-orthogonal multi-carrier digital modulation and demodulation method of the present invention.

Detailed ways

The present invention will be further described in detail below in conjunction with the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

As shown in Figures 2, 3, and 4, a non-orthogonal multi-carrier digital modulation and demodulation device includes a sending module, a receiving module connected to the sending module through a wireless channel, and the sending module includes sequentially connected digital modulation processing units , a D/A converter, a power amplifier, and a wireless transmitter, and the receiving module includes a sequentially connected wireless receiver, a preamplifier, an A/D converter, and a digital demodulation processing unit.

The wireless transmitter includes an up-conversion module and a transmission module. The up-conversion module is selected according to specific applications. The amplified analog signal is transferred to a frequency suitable for wireless channel transmission through the up-conversion module, and then transmitted by the transmission module.

The transmitting module is a radio frequency antenna, or an electro-acoustic transducer. The transmitting module can also be a transmitter of other wireless signals.

The wireless receiver includes a wireless receiving module and a down-conversion module, the wireless receiving module converts the signal received from the wireless channel into an electrical signal, and the down-conversion module moves the electrical signal to obtain a baseband signal, and the down-conversion module can be selected according to specific applications .

The wireless receiving module is an antenna for receiving electromagnetic waves, or an acoustic-electric transducer. The wireless receiving module can also be a receiver of other forms of wireless signals.

The wireless channel is an underwater acoustic channel.

As shown in Figure 5, a non-orthogonal multi-carrier digital modulation and demodulation method includes the steps in the following order:

(1) As shown in Fig. 1, according to channel characteristics, the available channels are divided into several sub-carrier channels. In a frequency band with poor channel performance, the subcarrier frequency interval is preferably relatively large, and in a place with good channel performance, the subcarrier interval is preferably relatively small. Assuming that the channel condition in the frequency band f ₁ ~ f ₂ is poor, and the channel condition in the frequency band f ₃ ~ f ₄ is good, then set K ₁ subcarriers in the frequency band f ₁ ~ f ₂ , and set K subcarriers in the frequency band f ₃ ~ f ₄ K ₂ subcarriers. Wherein, K ₁ <K ₂ . Suppose K ₁ +K ₂ =N, so there are N subcarriers in total.

(2) The digital modulation processing unit performs source coding, channel coding, mapping, multi-carrier modulation and guard interval processing on the input data from the outside to obtain multi-carrier digital signals. The module can be realized by combination of DSP and microprocessor, and can also be realized by high-performance computer.

First, after the data is input to the digital modulation processing unit, source coding, channel coding and mapping processing are respectively performed. Since the underwater acoustic channel is a complex time-varying channel, in order to transmit data accurately and quickly, different coding and mapping can be adopted for different channels. For example, in the case of low signal-to-noise ratio, in order to reduce the bit error rate of the system, a combination of forward error correction coding, interleaving and 2ASK modulation can be used.

Then, the digital modulation processing unit performs serial-to-parallel conversion on the data, converts the high-speed serial data stream into N parallel low-speed data streams and modulates them onto multi-carriers to add guard intervals to obtain multi-carrier signals. Let the subcarrier signal be:

The modulated multi-carrier signal is:

Since the solution of the present invention does not require strict orthogonality between multiple carriers, the baseband signal can be modulated on each multiple carrier separately, and joint modulation can also be performed.

(3) Input the multi-carrier signal s(n) obtained by the digital modulation processing unit to the D/A converter to convert it into an analog signal s(t), then amplify it through the power amplifier, and finally amplify it by the electro-acoustic transducer The last s(t) is transmitted into the underwater acoustic channel.

(4) First, the acoustic-electric transducer at the receiving end receives the acoustic signal from the underwater acoustic channel and converts it into an electrical signal. A preamplifier is then used to amplify the electrical signal converted by the wireless receiver to a value suitable for subsequent circuit processing. Finally, the A/D converter performs analog/digital conversion on the amplified signal, converting the analog signal into a digital received signal

(5) digital reception signal obtained by step (4) The high-performance parameter estimation algorithm is used to estimate the frequency, amplitude and phase of the multi-carrier, and then demodulate the transmitted data.

The functional structure of the digital demodulation processing unit to realize estimation demodulation is shown in Figure 4, including functional modules such as removing guard interval, parameter estimation, demapping, channel decoding and source decoding, which can be realized by combining DSP and microprocessor , can also be implemented using a high-performance computer.

Utilizing the parameter estimation algorithm to perform parameter estimation is an important part of the present invention. There are several types of algorithms that can still achieve a certain estimation accuracy in the case of medium and low signal-to-noise ratios: the maximum likelihood method of frequency estimation, and the method of using DFT transform as a rough estimate. Frequency domain estimation algorithm, time domain estimation algorithm based on autocorrelation function and parameter estimation algorithm based on subspace, etc.

In this embodiment, the spectral line rational combination parameter estimation algorithm is taken as an example. This algorithm is a frequency domain estimation algorithm using DFT transform as a rough estimate: the digital received signal is obtained After that, the process of obtaining frequency, amplitude and phase is:

A. Signal to point N zero padding to 2N points, and the signal after zero padding Carry out FFT of 2N points;

B. Signal from 2N points The FFT of obtains power spectrum p (k) and phase spectrum D (k);

C. Obtain N spectral peaks from the power spectrum p(k), denoted as k _i , i∈[0,1...N-1], and obtain the estimated angular frequency of each subcarrier according to formula (7):

in Estimated angular frequency from Estimated frequency available and it is easy to obtain the estimated magnitude

D. On the basis of the obtained frequency and amplitude, the estimated phase can be obtained according to the phase spectrum D(k) and formula (8):

in

The parameter estimation algorithm can obtain Then the parameters are sorted according to the relative size of the estimated frequency. Specifically, if Then determine the combination sequence of amplitude and phase as From N groups of estimated parameters can be obtained The combination of amplitude and phase values carries information about the transmitted data.

Finally, according to the mapping relationship of the system, demap the obtained ordered combination of amplitude and phase values, and then perform channel decoding and source decoding to obtain the transmitted data.

(6) Output the transmission data to the user.

The above-mentioned embodiment is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited by the above-mentioned embodiment, and any other changes, modifications, substitutions, combinations, Simplifications should be equivalent replacement methods, and all are included in the protection scope of the present invention.

Claims (8)

1. A non-orthogonal multi-carrier digital modulation and demodulation method, characterized in that it comprises the steps in the following order: S1. Divide available channels into several subcarrier channels according to channel characteristics; S2. The digital modulation processing unit performs source coding, channel coding, mapping, multi-carrier modulation and guard interval processing on the input data from the outside to obtain multi-carrier digital signals; S3. The D/A converter converts the multi-carrier digital signal into an analog signal, then amplifies it through the power amplifier, and finally transmits it to the wireless channel by the wireless transmitter; S4. The wireless receiver converts the received signal into an electrical signal, amplifies it through the preamplifier, and then converts the analog signal into a digital receiving signal through the A/D converter; S5. Estimate the digital received signal through the parameter estimation algorithm to obtain the frequency, amplitude and phase of the multi-carrier, and then complete the demodulation and output the data; Specific steps are as follows: (1) According to the channel characteristics, the available channels are divided into N sub-carrier channels; the sub-carriers of the signal are: After coding the transmitted signal and mapping the constellation map, serial-to-parallel conversion is performed to convert the single-channel high-speed data into N-channel parallel low-speed data and modulate it onto the multi-carrier; the modulated multi-carrier signal is: <mrow><mi>s</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mi>&amp;Sigma;</mi><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></msubsup><msub><mi>A</mi><mi>i</mi></msub><mi>c</mi><mi>o</mi><mi>s</mi><mrow><mo>(</mo><mn>2</mn><msub><mi>&amp;pi;f</mi><mi>i</mi></msub><mi>n</mi><mo>+</mo><msub><mi>&amp;phi;</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow> i∈[0,1...N-1], where A is the carrier amplitude, f is the carrier frequency, and φ is the carrier phase; corresponding to f ₀ <f ₁ <...<f _N-1 , by the amplitude phase The value combination {(A ₀ ,φ ₀ ),(A ₁ ,φ ₁ )...(A _N-1 ,φ _N-1 )} carries the transmission information, that is, the information of the transmission signal is modulated to (A _i ,φ _i ) above; (2) Perform D/A conversion on the modulated multi-carrier signal s(n) to obtain the analog modulation signal s(t), s(t) is amplified by the power amplifier, and the signal is moved to a suitable wireless channel by the up-conversion module The transmission frequency band is then transmitted by the wireless transmission module; (3) At the receiving end, the wireless receiver receives the wireless signal and converts it into an electrical signal, and then uses the down-conversion module to move the signal to the baseband. After the baseband signal is amplified by the preamplifier, it performs A/D conversion to obtain a digital reception signal. ; (4) Digital demodulation of digital received signals: use high-performance parameter estimation algorithms to estimate the parameters of digital received signals, and obtain the estimated values of frequency, amplitude and phase of each subcarrier (5) For the N groups of estimated parameters obtained by the parameter estimation algorithm, according to the estimated frequency The relative magnitude between the corresponding estimated magnitudes of and estimated phase Sorting to obtain N groups of amplitude and phase values that carry information; specifically, the parameter estimation algorithm obtains like Then determine the combination sequence of amplitude and phase as From N groups of estimated parameters can be obtained The combination of estimated values of the parameters carries the transmission information; (6) Combination of amplitude and phase values Perform constellation diagram mapping and decoding operations to obtain transmitted data; In step (1), the available channels are divided into N subcarrier channels, which are selected according to the channel performance and the parameter estimation algorithm of the receiving end. 2. non-orthogonal multi-carrier digital modulation and demodulation method according to claim 1, is characterized in that, described parameter estimation algorithm is spectral line rational combination parameter estimation algorithm, obtains digital reception signal After that, the process of obtaining frequency, amplitude and phase is: A. Signal to point N zero padding to 2N points, and the signal after zero padding Carry out FFT of 2N points; B. Signal from 2N points The FFT of obtains power spectrum p (k) and phase spectrum D (k); C. Obtain N spectral peaks from the power spectrum p(k), denoted as k _i , i∈[0,1...N-1], and obtain the estimated angular frequency of each subcarrier according to formula (7): <mrow><msub><mover><mi>&amp;omega;</mi><mo>^</mo></mover><mi>i</mi></msub><mo>=</mo><mfrac><mrow><mi>p</mi><mrow><mo>(</mo><msub><mi>k</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>-</mo><mi>p</mi><mrow><mo>(</mo><msub><mi>k</mi><mi>i</mi></msub><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mi>&amp;mu;</mi><mo>&amp;times;</mo><mo>&amp;lsqb;</mo><mi>p</mi><mrow><mo>(</mo><msub><mi>k</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>-</mo><mi>p</mi><mrow><mo>(</mo><msub><mi>k</mi><mi>i</mi></msub><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>&amp;rsqb;</mo><mo>+</mo><mi>v</mi><mo>&amp;times;</mo><mi>p</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mrow> in Estimated angular frequency from Estimated frequency available and it is easy to obtain the estimated magnitude D. On the basis of obtaining the estimated frequency and estimated amplitude, the estimated phase can be obtained according to the phase spectrum D(k) and formula (8): <mrow><msub><mover><mi>&amp;phi;</mi><mo>^</mo></mover><mi>i</mi></msub><mo>=</mo><mfrac><mrow><msubsup><mi>&amp;Sigma;</mi><mrow><msub><mi>k</mi><mi>i</mi></msub><mo>=</mo><msub><mi>k</mi><mi>i</mi></msub><mo>-</mo><mn>1</mn></mrow><mrow><msub><mi>k</mi><mi>i</mi></msub><mo>=</mo><msub><mi>k</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><mi>D</mi><mo>(</mo><msub><mi>k</mi><mi>i</mi></msub><mo>)</mo><mo>-</mo><mfrac><mrow><mo>(</mo><msub><mover><mi>&amp;omega;</mi><mo>^</mo></mover><mi>i</mi></msub><mo>-</mo><msub><mi>k</mi><mi>i</mi></msub><msub><mi>&amp;omega;</mi><mi>s</mi></msub><mo>)</mo><mo>(</mo><mi>N</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>)</mo></mrow></mrow><mrow><mn>2</mn><msub><mi>k</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn></mrow></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow></mrow> in 3. a kind of non-orthogonal multi-carrier digital modulation and demodulation device for the non-orthogonal multi-carrier digital modulation and demodulation method described in claim 1 or 2, it is characterized in that: comprise sending module, pass wireless channel and A receiving module connected to the sending module, the sending module includes a sequentially connected digital modulation processing unit, a D/A converter, a power amplifier, and a wireless transmitter, and the described receiving module includes a sequentially connected wireless receiver, a preamplifier , A/D converter, digital demodulation processing unit. 4. The non-orthogonal multi-carrier digital modulation and demodulation device according to claim 3, characterized in that: the wireless transmitter includes an up-conversion module and a transmitting module, and the up-conversion module is selected according to specific applications, and after power amplification The analog signal is moved to a frequency suitable for wireless channel propagation through the up-conversion module, and then transmitted by the transmitting module. 5. The non-orthogonal multi-carrier digital modulation and demodulation device according to claim 4, characterized in that: the transmitting module is a radio frequency antenna, or an electro-acoustic transducer. 6. The non-orthogonal multi-carrier digital modulation and demodulation device according to claim 3, characterized in that: the wireless receiver includes a wireless receiving module and a down-conversion module, and the wireless receiving module converts the received signal from the wireless channel The signal is converted into an electrical signal, and the down-conversion module moves the electrical signal to obtain a baseband signal, and the down-conversion module can be selected according to specific applications. 7. The non-orthogonal multi-carrier digital modulation and demodulation device according to claim 6, wherein the wireless receiving module is an antenna for receiving electromagnetic waves, or an acoustic-electric transducer. 8. The non-orthogonal multi-carrier digital modulation and demodulation device according to claim 3, wherein said wireless channel is an underwater acoustic channel.