CN103259637A - Transmission method of multi-carrier data - Google Patents

Abstract

Provided is a transmission method of multi-carrier data. According to the transmission method, data are transmitted by means of at least two sub carriers and at least two component channels. The transmission method of the multi-carrier data is characterized in that each component channel for transmitting data comprises multilevel and multi-rate sub carriers which contain harmonic wave deviation modulation sub carriers. Carriers in the same layer are orthogonal in time domain, the spectrum of one sub carrier is overlapped with the spectrum of another sub carrier in the same layer, and the two sub carriers can not be isolated with a segmentation frequency spectrum and by a filter. Signals are combined in a multiply method through the sub carriers which are overlapped in spectrums in the same layer and the sub carriers which are overlapped in spectrums in an adjacent layer, orthogonal component channels or approximate orthogonal component channels can be distinguished through related demodulation, and the number of the component channels is the product of the number of sub carriers in each layer. The transmission method of the multi-carrier data is further characterized in that by means of the Fourier series and a fraction code rate orthogonal function, the number of the component channels with preset bandwidth and time width is increased, new component channels are added on the basis of the existing component channels, and similar performance is achieved with a smaller peak-to-average power ratio compared with the prior art.

Description

Multi-carrier data transmission method

Technical Field

The invention relates to a multi-carrier technology in the communication technology, in particular to a multi-carrier data transmission method which utilizes at least two sub-carriers and sub-channels to transmit data. The sub-channel for transmitting data is composed of a combination of sub-carriers divided into multi-level and multi-code rate including the harmonic offset modulation sub-carrier.

Background

In the field of communication technology, the origin of multi-carrier technology can be traced back to at least the fifth and sixty years of the last century, theoretical discussion can be traced back to earlier stages, the OFDM technology is typical of the multi-carrier technology, and the method for realizing Fast Fourier Transform (FFT) and inverse transform (IFFT) of the OFDM system is rapidly developed since 1971, and is widely applied in the field of communication technology today.

The key point of OFDM system data transmission is that the channel is divided into a plurality of orthogonal sub-channels, the code rate of the data to be transmitted is reduced, and the data to be transmitted is decomposed and loaded on a plurality of sub-carriers for transmission. A complex baseband OFDM signal s (t) can be expressed asEach complex valued subcarrier

The main lobe of the spectrum occupies 2/T bandwidth with equal width, the spectrum between subcarriers has 1/2 overlap, and the main lobe of 2N real-valued subcarrier spectrums occupies the bandwidth (N +1)/T together. The communication system using the OFDM signal has a number of subchannels for transmitting real data of 2N within a bandwidth (N +1)/T, and transmits a number of symbols per T seconds on average of 2N. The measured spectrum utilization is calculated as the number of subchannels (orthogonal functions) divided by 2WT, where T is the signal duration (or symbol duration) and W is the bandwidth occupied by the signal main lobe. The number of subchannels (orthogonal functions) in the form of an OFDM signal is 2N, the bandwidth occupied by the signal main lobe is (N +1)/T, 2N divided by 2 × [ (N +1)/T]X T, it is known that the spectrum utilization rate of a communication system using OFDM signals is N/(N + 1). OFDM signals have many advantages, among which are (1) OFDM signals are composed of a plurality of subcarriers, each subcarrier being orthogonal two by two. Under the condition of a certain bandwidth, the number of subcarriers (namely subchannels) for transmitting data in parallel is increased by prolonging the symbol duration, and the bandwidth of the subchannels is narrowed. Therefore, the OFDM signal form has significant advantages in resisting burst type pulse interference, resisting multipath interference and frequency selective interference; (2) the high spectrum utilization rate can be achieved in the form of N/(N +1) or efficiency by increasing the number N of subcarriers, but the problem of relatively large peak average power is also brought about.

Another technical point of the existing OFDM signal format is that the subcarriers or subchannels of the OFDM signal transmit data in parallel, and the symbol period of each subcarrier, i.e. each subchannel, is equal. I.e. the multi-carrier data transmission of OFDM signals is a parallel transmission of data with a single code rate subchannel. When combined with CDMA techniques, the prior art either assigns each chip of one period of a pseudorandom code sequence on a different subchannel (Multicarrier CDMA); or code sequences are allocated on different sub-carriers (Multicarrier DS-CDMA); alternatively, the data streams are converted from serial to parallel to form an OFDM signal, and then spread with a long spreading code (Multitone CDMA). Based on the bandwidth W occupied by the main lobe or main energy of the spectrum of the data stream and the symbol period T, the spectrum utilization of these techniques cannot reach 1 or exceed 1, i.e. the number of orthogonal functions for loading and transmitting data cannot reach or exceed 2 WT. In addition, it is technically difficult to achieve both the application requiring a long-period spreading code, high spreading gain, and peak average power suppression.

First, therefore, in communication systems employing OFDM signals, the spectral utilization N/(N +1) is infinitely close to 1 as the number of subcarriers (subchannels) increases, but cannot reach and exceed 1. Secondly, the communication system adopting the OFDM signal form needs a larger number of subcarriers when achieving a higher spectrum utilization rate, the spectrum utilization rate increased in the N/(N +1) form is considered according to the comparison of the spectrum utilization rate and the number of the required subcarriers, the efficiency is lower, and meanwhile, the number of subcarriers is large and the peak average power is larger during parallel transmission.

Disclosure of Invention

In response to the deficiencies of the multi-carrier techniques currently employed in communication technologies, there are communication systems in the form of OFDM signals and communication systems in which OFDM signals are combined with CDMA. Namely, the frequency spectrum utilization rate can not reach 1, the comparison efficiency is lower according to the frequency spectrum utilization rate and the number of the needed sub-carriers, and the defects that the number of the sub-carriers is large, the peak average power is large when the sub-carriers are transmitted in parallel and the like are overcome. The invention provides a multicarrier data transmission method including harmonic offset modulation subcarriers, which utilizes a downward Fourier series and a fractional code rate orthogonal function to construct subcarriers, divides a plurality of subcarriers into different code rates and different levels according to certain steps, programs and specifications, and combines the subcarriers to form a data transmission signal.

The multi-carrier data transmission method of the invention can improve the frequency spectrum utilization rate, namely the data transmission capacity, and can reduce the number of sub-carriers under the condition of the same frequency spectrum utilization rate so as to reduce the peak average power ratio. The principle is that the duration T of a given function simultaneously requires that the function constructs a lower Fourier series and fractional code rate orthogonal function under the condition that the energy distribution of a frequency domain is concentrated in a given bandwidth W, and the orthogonal functions are combined to generate more orthogonal functions which simultaneously meet the condition of time limit T and band limit W. The principle is based on the fact that, when orthogonal functions of different levels are combined, the number of approximately orthogonal functions is the product of the numbers of orthogonal functions of different levels, so that the multiplication of the numbers of orthogonal functions and approximately orthogonal functions is multiplied.

In order to achieve the technical purpose, the technical scheme of the invention is that a signal form for transmitting data is a multi-code rate subcarrier combined signal form, and when the signal code rate difference is large, the signal form is represented as a multi-layer form. The meaning of this is that any one subcarrier among a plurality of different subcarriers must be aliased with another subcarrier spectrum, and these subcarriers are a group of subcarriers when the frequency domain cannot be separated by a filter. When the bandwidth of each of two groups of subcarriers differs by more than ten times from the sum of the bandwidths of all the subcarriers of the other group, the two groups of subcarriers are two layers of subcarriers, and the two groups of subcarriers belong to two different layers. Any two groups of subcarriers belong to different layers, namely a multi-layer subcarrier signal form. When the same layer of subcarriers with overlapped frequency spectrums and an adjacent layer of subcarriers with overlapped frequency spectrums are combined in a multiplying mode, the bandwidth of each subcarrier in one layer is more than 10 times larger than the sum of the bandwidths of all subcarriers in the other layer, so that the signals combined in the multiplying mode can be divided into orthogonal or approximately orthogonal subchannels through related demodulation, the number of the subchannels of the combined signals is equal to the product of the number of the subcarriers in each layer, namely, the number of the subchannels is multiplied. The subcarriers of the same layer are orthogonal in time domain, and a certain subcarrier of the same layer must be overlapped with the spectrum of another subcarrier, and cannot be separated by dividing the spectrum and passing through a filter.

The mathematical expression of the sub-carriers is a function, and can be used for independently forming the sub-channels or forming the sub-channels in a multiplication form of more than two sub-carriers, and the mathematical expression of the sub-channels is the product of data multiplied by a function or more than two functions.

The basic signal form for transmitting data in the invention can be expressed as s (t) = s_I(t)cos2πf_ct+s_Q(t)sin2πf_ct, wherein f_cIs the carrier frequency, s_xTypical forms of (t) are signal form one and signal form two, s for signal form one_x(t) can be represented by $s_x\left(t\right)=\left\{{\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}\left\{{\mathrm{\Σ}}_{k=1}^{K\left(x\right)}{{\mathrm{\α}}_k}^{\left(x\right)}\cos (2\mathrm{\π}{f_k}^{\left(x\right)}t+{{\mathrm{\θ}}_k}^{\left(x\right)})\right\},$ x = I or x = Q denotes s_I(t),s_Q(t), L (x) and K (x) are fixed integers, i.e. s_I(t) and s_QL and K in (t) may be different integers. In the formula, ${\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\Σ}}_{l=1}^{L\left(x\right)}\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-i{T}_d^{\left(l\right)\left(x\right)})\right\{{\mathrm{\Σ}}_n{c}_n^{\left(l\right)\left(x\right)}{h}^{\left(l\right)\left(x\right)}(t-{\mathrm{nT}}_c^{\left(l\right)\left(x\right)})\left\}\right\},$ h^(l)(x)(t) is the duration

The time-domain waveform of (a),

is a sequence whose value is optional; $d^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\Σ}}_i{d}_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-i{T}_d^{\left(l\right)\left(x\right)})$ for the first-way data,

for the duration of a data bit, g^(l)(x)(t) is the duration

The time-domain waveform of (a),

is to transmit data;

is expressed in terms of sequence

The frequency value of the change in value of (c),

is expressed in terms of sequence

The phase value of the change is changed,

is expressed in terms of sequence

A function of the change. $\left\{{\mathrm{\Σ}}_{k=1}^{K\left(I\right)}{\mathrm{\α}}_k\cos (2\mathrm{\π}{f_k}^{\left(I\right)}t+{{\mathrm{\θ}}_k}^{\left(I\right)})\right\}$ And $\left\{{\mathrm{\Σ}}_{k=1}^{K\left(Q\right)}{{\mathrm{\α}}_k}^{\left(Q\right)}\cos (2\mathrm{\π}{f_k}^{\left(Q\right)}t+{{\mathrm{\θ}}_k}^{\left(Q\right)})\right\}$ is a harmonic sub-carrier, f_k ^(x)For harmonic subcarrier frequencies, alpha_k ^(x)Is coefficient with optional value, and harmonic subcarrier phase is theta_k ^(x)The value can be arbitrarily selected.

The invention is also characterized in that when the data sequence { d }_n ^(I)And { d }_n ^(Q)All equal the constant 1, there is one T all

And

the common multiple of (a) to (b), $\left\{{\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}=\left\{{\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}(t\±\mathrm{NT})c^{\left(l\right)\left(x\right)}(t\±\mathrm{NT})\right\}$ the integer N is true for the number N, $\left\{{\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}$ repeating the process with T as a period; all harmonic subcarriers $\left\{{\mathrm{\Σ}}_{k=1}^{K\left(x\right)}{{\mathrm{\α}}_k}^{\left(x\right)}\cos (2\mathrm{\π}{f_k}^{\left(x\right)}t+{{\mathrm{\θ}}_k}^{\left(x\right)})\right\}$ And each function

And keeping the bit timing synchronization, and keeping the frequency and the phase unchanged in time intervals with the time length being integral multiple of T. The frequency of each harmonic subcarrier is f_k ^(x)The phase being θ_k ^(x)。

The invention is characterized in that the difference between the sub-carrier frequencies of any two harmonics

More than or equal to two times

Bandwidth, i.e. $\left\{{\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}{{\mathrm{\α}}_i}^{\left(x\right)}\cos (2\mathrm{\π}{f}_i^{\left(x\right)}t+{\mathrm{\θ}}_i^{\left(x\right)})$ And $\left\{{\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}{{\mathrm{\α}}_j}^{\left(x\right)}\cos (2\mathrm{\π}{f}_j^{\left(x\right)}t+{\mathrm{\θ}}_j^{\left(x\right)})$ the spectrum of (a) is separable in the frequency domain.

The invention is characterized in that

${\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\Σ}}_{l=1}^{L\left(x\right)}\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-i{T}_d^{\left(l\right)\left(x\right)})\right\{{\mathrm{\Σ}}_n{c}_n^{\left(l\right)\left(x\right)}{h}^{\left(l\right)\left(x\right)}(t-{\mathrm{nT}}_c^{\left(l\right)\left(x\right)})\left\}\right\}$ If L (x) =1 in (1) $s_x\left(t\right)=\left\{{\mathrm{\Σ}}_n{d_n}^{\left(x\right)}{g}^{\left(x\right)}(t-n{T_d}^{\left(x\right)})\right\}\left\{{\mathrm{\Σ}}_n{c_n}^{\left(x\right)}{h}^{\left(x\right)}(t-{\mathrm{nT}}_c^{\left(x\right)})\right\}\left\{{\mathrm{\Σ}}_{k=1}^{K\left(x\right)}{{\mathrm{\α}}_k}^{\left(x\right)}\cos (2\mathrm{\π}{f_k}^{\left(x\right)}t+{{\mathrm{\θ}}_k}^{\left(x\right)})\right\}$ C in (1)_n ^(x)Is a spreading code, s_x(t) a stretching bandwidth greater than its actual occupied bandwidth by at least one d^(x)(t)c^(x)(t) bandwidth frequency interval.

The invention is also characterized in that

At the same time ${\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-{\mathrm{iT}}_d^{\left(l\right)\left(x\right)})$ When L (x) is not less than 2 and g^(l)(x)At least one of (t) isA downward Fourier series or fractional code rate orthogonal function.

The invention is also characterized in that

At the same time ${\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(x\right)}\left(t\right)={\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{\mathrm{\Σ}}_i\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-i{T}_d^{\left(l\right)\left(x\right)}){\mathrm{\Σ}}_n{c_n}^{\left(x\right)}{h}^{\left(x\right)}(t-{\mathrm{nT}}_c^{\left(x\right)})\right\}$ When L is greater thanx) is not less than 2 and g^(l)(x)At least one of (t) is a downward Fourier series or a fractional code rate orthogonal function.

The invention is also characterized in thatAt the same time ${\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\Σ}}_{l=1}^{L\left(x\right)}\left\{{\mathrm{\Σ}}_n\right[{\mathrm{\Σ}}_i{d_n}^{\left(l\right)\left(x\right)}{c}_i^{\left(l\right)\left(x\right)}{h}^{\left(l\right)\left(x\right)}(t-i{T_c}^{\left(l\right)\left(x\right)})\left]g^{\left(l\right)\left(x\right)}(t-n{T_d}^{\left(l\right)\left(x\right)})\right\}$ When L (x) is not less than 2 and h^(l)(x)At least one of (t) is a downward Fourier series or a fractional code rate orthogonal function.

The invention is also characterized in that

At the same time ${\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\Σ}}_{l=1}^{L\left(x\right)}\left\{{\mathrm{\Σ}}_i{d}_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-i{T}_d^{\left(l\right)\left(x\right)})\right[{\mathrm{\Σ}}_n{c}_n^{\left(l\right)\left(x\right)}{h}^{\left(l\right)\left(x\right)}(t-n{T}_c^{\left(l\right)\left(x\right)})\left]\right\}$ When L (x) is not less than 2 and h^(l)(x)(t) or g^(l)(x)At least one of (t) is a downward Fourier series or a fractional code rate orthogonal function.

The invention is also characterized in that $h^{\left(i_1\right)\left(x\right)}\left(t\right)=h^{\left(i_2\right)\left(x\right)}\left(t\right)=...=h^{\left(i_k\right)\left(x\right)}\left(t\right)$ When the temperature of the water is higher than the set temperature, $g^{\left(i_1\right)\left(x\right)}\left(t\right),g^{\left(i_2\right)\left(x\right)}\left(t\right),...,g^{\left(i_k\right)\left(x\right)}\left(t\right)$ two by two unequal and orthogonal in the time domain, spectral aliasing of functions, i.e. each

Must be in contact with a certain pointCannot be separated in the frequency domain by filters. When in use $g^{\left(i_1\right)\left(x\right)}\left(t\right)=g^{\left(i_2\right)\left(x\right)}\left(t\right)=...=g^{\left(i_k\right)\left(x\right)}\left(t\right)$ When the temperature of the water is higher than the set temperature, $h^{\left(i_1\right)\left(x\right)}\left(t\right),h^{\left(i_2\right)\left(x\right)}\left(t\right),...,g^{\left(i_k\right)\left(x\right)}\left(t\right)$ two by two are not equal and are orthogonal in the time domain, ${\mathrm{\Σ}}_n{c}_n^{\left(i_u\right)\left(x\right)}{h}^{\left(i_u\right)\left(x\right)}(t-{{\mathrm{nT}}_c}^{\left(x\right)})$ and ${\mathrm{\Σ}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)$ the spreading code sequences in (1) may be the same or different, eachSpectral aliasing of functions, each of which

Must be in contact with a certain point

Cannot be separated in the frequency domain by filters.

The invention is also characterized in that h^(l)(x)(t), L ═ 1,2, …, L (x), all of h not equal^(l)(x)(t) orthogonal pairwise in the time domain, spectral aliasing of functions, each of which

Must be in contact with a certain pointCannot be separated in the frequency domain by filters.

To be provided with

Is expressed in terms of sequenceFrequency values of change, in

Is expressed in terms of sequence

The phase value of the change is changed,a function representing the variation. S of signal form two_x(t) can be represented by s_x(t) in

Is equal to ${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-i{T}_d^{\left(l\right)\left(x\right)})\right\{{\mathrm{\&Sigma;}}_n[\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;f}\left(c_n^{\left(l\right)\left(x\right)}\right)t+\mathrm{\&phi;}\left(c_n^{\left(l\right)\left(x\right)}\right)]h^{\left(c_n^{\left(l\right)\left(x\right)}\right)}\left(t\right)\left\}\right\}.$

The invention is also characterized in that s is the signal form two_x(t) at a certain harmonic subcarrier α_k ^(x)cos(2πf_k ^(x)t+θ_k ^(x)) Above, when $h^{\left(c_n^{i_1}\right)\left(x\right)}\left(t\right)=h^{\left(c_n^{i_2}\right)\left(x\right)}\left(t\right)=...=h^{\left(c_n^{i_k}\right)\left(x\right)}\left(t\right)$ When the temperature of the water is higher than the set temperature, $g^{\left(i_1\right)\left(x\right)}\left(t\right),g^{\left(i_2\right)\left(x\right)}\left(t\right),...,g^{\left(i_k\right)\left(x\right)}\left(t\right)$ two by two unequal and orthogonal in the time domain, spectral aliasing of functions, each of which

Must be in contact with a certain point

Cannot be separated in the frequency domain by filters. When in use $g^{\left(i_1\right)\left(x\right)}\left(t\right)=g^{\left(i_2\right)\left(x\right)}\left(t\right)=...=g^{\left(i_k\right)\left(x\right)}\left(t\right)$ When the temperature of the water is higher than the set temperature, $h^{\left(c_n^{i_1}\right)\left(x\right)}\left(t\right),h^{\left(c_n^{i_2}\right)\left(x\right)}\left(t\right),...,h^{\left(c_n^{i_k}\right)\left(x\right)}\left(t\right)$ pairwise unequal and orthogonal in time domain, sequence

May or may not be the same, eachSpectral aliasing of functions, each of which

Must be in contact with a certain point

Cannot be separated in the frequency domain by filters.

The invention has the technical effects that the multi-code rate and multi-carrier have fundamental difference with the prior art, and has great superiority in expanding the space dimension of signals and improving the utilization rate of frequency spectrum in the aspect of combining with the CDMA technology or applying with larger code rate difference in other forms. When combined with CDMA techniques, long spreading code, high spreading gain, and small peak-to-average power ratio applications are supported.

The invention will be further explained with reference to the drawings.

Drawings

FIG. 1 is a data transmission method, apparatus and flow chart of the present invention;

fig. 2 is a data receiving method, apparatus and flowchart of the present invention;

FIG. 3 is an example of a function of a downward Fourier series with the number of orthogonal functions exactly equal to 2WT, where the horizontal axis is in 1/T;

FIG. 4 shows that the number of orthogonal functions is equal to

The lower Fourier series function example of (1), wherein the horizontal axis coordinate unit is 1/T;

FIG. 5 is an example of orthogonal functions for fractional code rate, where the horizontal axis is given in T;

fig. 6 shows an example of two-layer two-code-rate subcarrier configuration, where the horizontal axis coordinate unit is T.

Detailed Description

The invention of the technology is to utilize the orthogonal function of the descending Fourier series and the fractional code rate, which is a special type of orthogonal function originally created and constructed by the inventor of the technology according to the method for constructing the orthogonal function. This will now be described below.

The following notations are used.

The complex set is represented as a complex set,is a set of real numbers, and is,

is a natural number set. Real number interval [ -T/2, T/2]The normalized linear space formed by the above whole absolute square multiplicative function f (t) is expressed as

Or L²[-T/2，T/2]f (t) is a real or complex valued function that is easily differentiated by context,

the inner product and norm as defined above are

$\&ForAll;f,g\&Element;{\mathrm{<figure-callout\; id="2"\; label="L\; T"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">L</figure-callout>}}_T^{};$ Inner product ${<f,g>}_T=\underset{-T/2}{\overset{T/2}{\&Integral;}}f\left(t\right)\stackrel{\&OverBar;}{g\left(t\right)}\mathrm{dt};$ Norm of ${\left|\right|f\left|\right|}_T=\sqrt{{<f,f>}_T}$

Wherein,

denotes the complex conjugation of g (t). Using marks when the integration interval is clear without misinterpretation<f，g>And f. Let f, g be orthogonal, if and only if<f，g>Let f ≠ g as 0.

According to the conclusion of complex analysis, the analytic function is not equal to zero

There can only be isolated zeros. Therefore, if

The interval [ -T/2, T/2]Set of upper functions

Is a set of linearly independent functions that are,

it can be orthogonalized using the gram schmidt orthogonalization method.

Defining functions $\mathrm{rect}\left(t\right)=(1/\sqrt{T})[u(t+T/2)-u(t-T/2)],$ Wherein u (t) is a unit step function defined as. The intervals [ a, b ] referred to herein below]The upper functions f (t), all refer to

Where f (t) is 0.

In the interval [ -T/2, T/2]Set of upper and lower cosine trigonometric functions

The function in (1) is even function, sine trigonometric function set

Is an odd function set and thus orthogonal, where 1 refers to u (T + T/2) -u (T-T/2), and u (T) is a unit step function. I.e. the interval [ -T/2, T/2]Thereon is provided with

Thus, it is possible to operate on the intervals [ -T/2, T/2 [ -T/2 [ ]]Set of upper arbitrary functions

The cosine and sine functions are orthogonalized separately,

now, let ${\mathrm{\&psi;}}_0^c\left(t\right)=\mathrm{rect}\left(t\right),$ ${\mathrm{\&psi;}}_1^s\left(t\right)=\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{\tilde{f}}_{1}t/\left|\right|\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{\tilde{f}}_{1}t\left|\right|,$ Order to

${\mathrm{\&psi;}}_n^c\left(t\right)=\frac{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_{n}t-\underset{l=0}{\overset{n-1}{\mathrm{\&Sigma;}}}{<\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_{n}t,{\mathrm{\&psi;}}_l^c\left(t\right)>}_T{\mathrm{\&psi;}}_l^c\left(t\right)}{{\left|\right|\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_{n}t-\underset{l=0}{\overset{n-1}{\mathrm{\&Sigma;}}}{<\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_{n}t,{\mathrm{\&psi;}}_l^c\left(t\right)>}_T{\mathrm{\&psi;}}_l^c\left(t\right)\left|\right|}_T}$

${\mathrm{\&psi;}}_k^s\left(t\right)=\frac{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{\tilde{f}}_{k}t-\underset{l=1}{\overset{k-1}{\mathrm{\&Sigma;}}}{<\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{\tilde{f}}_{k}t,{\mathrm{\&psi;}}_l^s\left(t\right)>}_T{\mathrm{\&psi;}}_l^s\left(t\right)}{{\left|\right|\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{\tilde{f}}_{k}t-\underset{l=1}{\overset{k-1}{\mathrm{\&Sigma;}}}{<\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{\tilde{f}}_{k}t,{\mathrm{\&psi;}}_l^s\left(t\right)>}_T{\mathrm{\&psi;}}_l^s\left(t\right)\left|\right|}_T}$

To obtain [ -T/2, T/2 [ -T/2 [ ]]Set of upper normal orthogonal functions

When f is₁<1/T or

<At the time of 1/T, the alloy is,

ratio of main lobe of spectrum

Or

Closer to the origin, the spectrum moves down towards the low frequency end. After the process of the orthogonalization, the method comprises the steps of,

can be generally expressed as $\{\mathrm{rect}\left(t\right),\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}{f}_{m}t,\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{\tilde{f}}_{l}t;m\&le;n,l\&le;k\}$ Linear combination of (a) if f_i<i/T, i =1,2, …, n or f_l<More than one of l/T, l =1,2, …, k satisfies f_i<i/T or

Thereby to obtain

OrRatio of main lobe of spectrumOr

Closer to the origin, we call

Or

Is a downward Fourier series or an orthogonal function of the downward Fourier series. Orthonormal system comprising orthogonal functions of fourier series down

Referred to as the down-fourier series orthonormal.

A constructive definition of the "fractional-code-rate orthogonal function" is now given. Is provided with

Is [ -T/2, T/2]In the upper orthonormal system, then

Is the interval [ -IT, JT]In the above orthonormal system, I and J are positive integers. Take [ -IT, JT]Upper and F₂In which arbitrary functions are combined with linearly independent functions g_k(t)，

To F₂The medium functions are orthogonalized one by one. Can obtain the product

As follows

${\mathrm{\&psi;}}_k^{(1/(I+J))}\left(t\right)=\frac{j_k\left(t\right)}{\left|\right|j_k\left(t\right)\left|\right|}$

Wherein

$j_1\left(t\right)=g_1\left(t\right)-\underset{i,n}{\mathrm{\&Sigma;}}<g_1\left(t\right),\mathrm{rect}(t+\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}+\mathrm{iT}){\mathrm{\&psi;}}_n(t+\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}+\mathrm{iT})>\left\{\mathrm{rect}(t+\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}+\mathrm{iT}){\mathrm{\&psi;}}_n(t+\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}+\mathrm{iT})\right\}$

$j_k\left(t\right)=g_k\left(t\right)-\underset{l=1}{\overset{k-1}{\mathrm{\&Sigma;}}}<g_k\left(t\right),{\mathrm{\&psi;}}_l^{(1/I+J)}\left(t\right)>{\mathrm{\&psi;}}_l^{(1/(I+J))}\left(t\right)$

$-\underset{i,n}{\mathrm{\&Sigma;}}<g_k\left(t\right),\mathrm{rect}(t+\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}+\mathrm{iT}){\mathrm{\&psi;}}_n(t+\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}+\mathrm{iT})>\left\{\mathrm{rect}(t+\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}+\mathrm{iT}){\mathrm{\&psi;}}_n(t+\frac{\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">T</figure-callout>}}{2}+\mathrm{iT})\right\}$

If T is the basic time unit of symbol duration, we say F₂The middle function is an integer-rate orthogonal function, calledIs a code rate orthogonal function of 1/(I + J),

1/(I + J) is a fraction, and is therefore also referred to as

Is a fractional code rate orthogonal function. In particular, take g_k(t)=[u(t+IT)-u(t-JT)]cos(2πf_kt+θ_k) Take f_kIs F₂At a frequency point within the frequency range of the spectrum of each function, the frequency spectrum of each function is determined

Spectrum of (2) and F₂The spectrum overlapping degree of each function in the spectrum acquisition system is maximized, and the spectrum utilization rate is maximized. In the same manner, F₂A middle function and

shift to the interval [ -IT + (I + J) T, JT + (I + J) T]，[-IT+2(I+J)T,JT+2(I+J)T]Up to [ -IT + (U-1) (I + J) T, JT + (U-1) (I + J) T]In the interval [ -IT, JT + (U-1) (I + J) T]Repeating the above orthogonalization process and repeating the same, and so on, a certain finite interval [ -AT, BT ] can be obtained]In the above, the orthogonal function systems of different code rates, where a and B are positive integers.

The above definition of the orthogonal function of fractional code rate, the meaning of the fraction is relative, i.e. from [ -T/2, T/2]Set of upper functions F₁＝{ψ_n(t) } start, construct duration [ -IT, JT by the gram Schmidt orthogonalization method]Function of (2)

Because of duration [ -IT, JT]Is [ -T/2, T/2]I + J times, and therefore when used to transmit data,the code rate of (1/(I + J). The above process can be easily and directly generalized as [ a ]₀,a₁],[a₁,a₂],[a₂,a₃],…,[a_I-1,a_I]Is a series of time intervals of which,is [ a ]_i-1,a_i]Taking [ a ] from the upper function set or the orthogonal function system₀,a_I]Upper function g_k(t) pairsAnd (4) orthogonalizing. The process is reversible, and the construction of the fraction code rate orthogonal function has a dual mode with a consistent principle. I.e., for [ -T/2, T/2]Set of upper functions F₁={ψ_n(T) }, will [ -T/2, T/2 [ -T/2 }]Divided into I sub-intervals [ a₀,a₁],[a₁,a₂],[a₂,a₃],…,[a_I-1,a_I]Wherein a is₀=-T/2，a_IAnd (= T/2). Fetching areaM [ a ]_i-1,a_i]Function of

i＝1,2,…,I，

In the interval [ a_i-1,a_i]To all [ u (t-a) ]_i-1)-u(t-a_i)]ψ_n(t) (where u (t) is a unit step function) is orthogonalized by the same Km Schmidt method by_n(t)∈F₁. The corresponding orthogonal function set can be obtained

i=1,2,…,I，

The duration of (a) is_i-1,a_i]Thus, it is relative to

So at this time F₁={ψ_n(t) the medium function is a fractional bitrate function, the fractional value being (a)_i-a_i-1) and/T. Therefore, the fractional-rate orthogonal functions in the summary of the present specification and claims refer to orthogonal functions that are determined to overlap each other in time but not have the same duration, according to the above-described method, the above-described direct generalization method, and the method of constructing the dual form inversely.

Fig. 3 and 4 show two function examples, where the number of orthogonal functions is 2WT and (1+ α)2WT, respectively, calculated according to the bandwidth occupied by the main lobe of the spectrum of the function, under the constraint of a bandwidth W and a time interval duration T, and α =1/60 in the example. The spectral efficiency is calculated as the number of orthogonal functions divided by 2WT, the functions in the example are 1 and 1+ α =1+1/60, respectively. The conclusions of fig. 3 hold for all WT values satisfying WT = n · 32, and the conclusions of fig. 4 hold for all WT values satisfying WT = n · 30, n being an integer. This constitutes a class of functions with the number of orthogonal functions being (1+ α)2WT when WT → infinity, and the ratio of out-of-band energy to total energy remains constant and does not decrease as WT increases.

FIG. 5 shows an example of an orthogonal function set with different fractional values, such as [ -T/2, T/2]The last three orthogonal function sets

At the beginning, orthogonal functions of the code rate 1/2, the code rate 1/4 and the code rate 1/8 are constructed in sequence. In this case, s (t) = s_I(t)cos2πf_ct+s_Q(t)sin2πf_cIn t, s_I(t) and s_QThe number of (t) subcarriers is respectively 6, the spectrum utilization rate reaches 96.8%, and 2N =62 subcarriers are needed for achieving the same spectrum utilization rate in the existing OFDM technology.

When the code rate difference is large, the combination of the orthogonal functions of different code rates can form approximately orthogonal subcarriers and subchannels. It is based on the mathematical principle that let { c }_k(T), K =1,2, …, K } is the interval T e [ -T/2, T/2]Functions which are orthogonal or approximately orthogonal, i.e. $k=l\&DoubleRightArrow;{\&Integral;}_{-T/2}^{T/2}{c}_k\left(t\right)c_l\left(t\right)\mathrm{dt}=1,$ $k\&NotEqual;l\&DoubleRightArrow;{\&Integral;}_{-T/2}^{T/2}{c}_k\left(t\right)c_l\left(t\right)\mathrm{dt}\&ap;0;$ {ψ_n(t), N =1,2, …, N } is the interval t e [ -MT/2, MT/2]Functions which are orthogonal or approximately orthogonal, i.e.

$n\&NotEqual;m\&DoubleRightArrow;{\&Integral;}_{-T/2}^{T/2}{\mathrm{\&psi;}}_n\left(t\right){\mathrm{\&psi;}}_m\left(t\right)\mathrm{dt}\&ap;0;$ {f_u(t), U =1,2, …, U } is the interval t e [ -LMT/2, LMT/2]The above orthogonal functions, U, N, M are all large integers. I.e. { f_u(t) } far less than { psi_n(t) } slow change, { ψ_n(t) } is far greater than { c }_k(t) } slow change. Then, when k ≠ l, n ≠ m, and u ≠ v has a true, ${\&Integral;}_{-\mathrm{LMT}/2}^{\mathrm{LMT}/2}{f}_u\left(t\right)f_v\left(t\right){\mathrm{\&psi;}}_n\left(t\right){\mathrm{\&psi;}}_m\left(t\right)c_k\left(t\right)c_l\left(t\right)\mathrm{dt}\&ap;0,$ only when k = l, n = m, and u = v are simultaneously established, ${\&Integral;}_{-\mathrm{LMT}/2}^{\mathrm{LMT}/2}{f}_u\left(t\right)f_v\left(t\right){\mathrm{\&psi;}}_n\left(t\right){\mathrm{\&psi;}}_m\left(t\right)c_k\left(t\right)c_l\left(t\right)\mathrm{dt}=1.$ thus, it is shaped as g_s(t)=f_u(t)ψ_n(t)c_kFunction g of (t)_s(t) total of UXNXK, and two orthogonal. That is to say, when the code rate difference is large and the bandwidth difference is large, the orthogonal functions at different levels are combined, and the number of the generated approximately orthogonal functions can achieve the effect of multiplicative increase. In practical application, { ψ_n(t) the bandwidth occupied by the sum of the spectra of the functions in relation to { f }_u(t) when the bandwidth occupied by the spectrum of each function is an order of magnitude smaller, the residual error is about 110, and so the required { ψ is chosen according to the error constraints_n(t) } and { f_u(t) } relative bandwidth. The selection of the relative bandwidth based on error limits is a well-known principle and well-known method.

The terms "subcarrier" and "subchannel" as used in this specification and the present invention do not refer to a combination of multiple layers of subcarriers forming a subchannel, and their meanings are consistent with well-known definitions and meanings. When the technical specification of the invention refers to a sub-channel composed of a plurality of layers of sub-carriers, the following special meanings are provided.

The meaning of the sub-channel composed of the multi-layer subcarrier combination is that when the mathematical expression of the signal is s (t) = { f₁(t)+f₂(t)+…f_U(t)}{ψ₁(t)+ψ₂(t)+…+ψ_N(t)}{c₁(t)+c₂(t)+…+c_K(t) }, and f₁(t),f₂(t),…,f_U(t) the spectrum of any one of the functions must overlap with the other and cannot be divided in the frequency domain by a filter; psi₁(t),ψ₂(t),…,ψ_N(t) the spectrum of any one of the functions must overlap with the other and cannot be divided in the frequency domain by a filter; c. C₁(t),c₂(t),…,c_K(t) the spectrum of any one of the functions must overlap with the other and cannot be divided in the frequency domain by a filter; s (t) is a signal that consists of the product of three sets of functions, which, for consistency with well-known definitions and terminology,the specification and claims of the present invention call s (t) a signal consisting of the product of three groups of subcarriers. If c is₁(t),c₂(t),…,c_K(t) the bandwidth ratio ψ of each function or subcarrier₁(t),ψ₂(t),…,ψ_N(t) the sum of the sub-carrier bandwidths is more than 10 times larger, psi₁(t),ψ₂(t),…,ψ_N(t) bandwidth ratio f of each function or subcarrier₁(t),f₂(t),…,f_U(t) the sum of the sub-carrier bandwidths is more than 10 times larger, so s (t) is a signal formed by the product of three layers of sub-carriers. Expanding the product of s (t), s (t) = ∑ g_s(t)=∑f_u(t)ψ_n(t)c_k(t), U is more than or equal to 1 and less than or equal to U, N is more than or equal to 1 and less than or equal to N, and K is more than or equal to 1 and less than or equal to K. Each shape as f_u(t)ψ_n(t)c_kThe factor of (t) is the subcarrier of the composite signal s (t), single f_u(t) or ψ_n(t) or c_kNone of (t) is a subcarrier of s (t). The resultant signal s (t) has a total of U × N × K shapes f_u(t)ψ_n(t)c_kThe subcarriers of (t), also called subchannels, may carry data $d_{u,n,k}\left(t\right)={\mathrm{\&Sigma;}}_i{d}_i^{(u,n,k)}{g}^{(u,n,k)}(t-n{T}_i^{(u,n,k)})$ Is modulated at f_u(t)ψ_n(t)c_k(t) on, form d_u,n,k(t)f_u(t)ψ_n(t)c_k(t) transmitting and receiving. Fig. 6 shows an example of layered subcarrier modulation and data transmission, where each layer of subcarriers is an integer rate orthogonal function plus a 1/2 rate orthogonal function.

The relative bandwidth relationship of the sub-channels formed by the combination of the sub-carriers of the multiple layers is that s (t) is between the layers, s_c(t)=c₁(t)+c₂(t)+…+c_K(t) bandwidth ratio s of each subcarrier_ψ(t)=ψ₁(t)+ψ₂(t)+…+ψ_N(t) a bandwidth of more than 10 times wide, s_ψ(t) bandwidth ratio s of each subcarrier_f(t)=f₁(t)+f₂(t)+…f_U(t) is more than 10 times wider. The selection of the relative bandwidth based on error limits is a well-known principle and well-known method.

The present invention is characterized in that, first, the synthesized signal is s (t) = { f₁(t)+f₂(t)}{c₁(t)+c₂(t) } form, i.e. s (t) = f₁(t)c₁(t)+f₂(t)c₁(t)+f₁(t)c₂(t)+f₂(t)c₂(t) form, three-level signals are the same as above, and so on for more than three levels. The sub-carrier spectrums of each layer are overlapped and cannot be separated by a filter. The relative bandwidth relationship between the layers is in accordance with the above-mentioned characteristics of more than 10 times difference. Second, in the signal form of the prior art, s (t) = f₁(t)c₁(t)+f₂(t)c₂(t) form, or s (t) = { f₁(t)+f₂Of the form (t) } c (t), or s (t) = f (t) { c₁(t)+c₂(t) } form, the invention uses a downward Fourier series or a fractional code rate orthogonal function in s (t), namely f (t), f₁(t)、f₂(t) and c (t), c₁(t)、c₂(t) at least one of which is a downward Fourier series or a fractional code rate orthogonal functionAnd (4) counting.

The harmonic subcarrier modulation is a spreading code form disclosed by the technical inventor, and has the advantage that the main lobe of an autocorrelation function is narrower when the harmonic subcarrier modulation is applied to the spreading code. The invention discloses direct sequence spread spectrum harmonic carrier shift modulation published in the journal of electronics and information, 10 th year 2012, and provides a method and a signal example for direct sequence spread spectrum signals and for design, construction and performance of spread spectrum code streams, and relates to a method for transmitting data by using harmonic subcarrier modulation. In the specification and claims, the terms of harmonic subcarrier, stretching bandwidth, and actually occupied bandwidth are consistent with those in the published article.

Based on the duality of the time domain and the frequency domain known in the technical field of engineering, the orthogonal function constructing method used by the invention is also suitable for constructing the orthogonal function from the frequency domain. The process of constructing the orthogonal function is such that the duration of the signal is equal to the basic time unit T, duration [ -T/2, T/2]Constructing a lower Fourier series on the basis of the above-mentioned data, and₁T/2,L₁T/2]constructing orthogonal function of fractional code rate on interval, repeating the process at [ -NI [)₁T/2,ML₁T/2]And constructing different fraction code rate orthogonal functions on the interval. As a variable replacement, order

The above process can be repeated from the frequency range [ -W, W]Initially, a downward Fourier series is constructed, followed by construction of [ -I ]₁W,L₁W]Frequency interval fractional code rate orthogonal function, and [ -NI₁W,ML₁W]And (3) orthogonal functions of different fraction code rates in frequency intervals.

Based on the dual relation between the frequency domain and the time domain, the method for transmitting data by modulating the harmonic subcarrier uses the form of the harmonic subcarrier signal, which comprises the step of directly constructing the harmonic subcarrier signal from the frequency domain. The signal configuration and signal form thereof are as follows. Constructing a frequency spectrum limited in a frequency interval f E [ - (k +1) W, -kW]∪[kW,(k+1)W]Of (2) a signal

Note the book

Has a spectrum of

l＝1,2,…,L(x)，k＝0,1,2,…,K(x)。Only in the case where f is in the form of [ - (k +1) W, -kW ] < U [ kW, (k +1) W]May not be equal to zero in the interval, otherwise must be equal to zero, i.e. $f\&NotElement;[-(k+1)W,-\mathrm{kW}]\&cup;[\mathrm{kW},(k+1)W]\&DoubleRightArrow;{\mathrm{\&Phi;}}_l^{\left(k\right)}\left(f\right)=0$ . Band-limited signals constructed directly from the frequency domain, since strictly band-limited signals must be of infinite duration

Are referred to as being time-aligned according to principles well-known in the art of communication technology

Truncating and windowing functions

Is focused for a time length

The present invention is characterized in that

Integral multiple of the common multiple T of, all harmonic sub-carriers $\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}$ And each function

Bit timing synchronization is maintained, the harmonic sub-carriers maintain the frequency and phase unchanged, and the change of the harmonic sub-carrier frequency and phase occurs at integral multiple time points of T.

Based on the known principle in the engineering technical field, the dual relation of frequency and time, two variables of Fourier transform and two domain variables related to Fourier series can be interchanged to form the dual relation. The variables T and f, the basic unit of the variables, the unit of the length of the interval, and the start-stop values T and W of the interval are not limited and fixed, and are understood as dual quantities of Fourier transform and Fourier series according to the well-known principle in the engineering technical field. Spectral aliasing, the expression that the frequency domain cannot be separated by a filter, and the expression in dual form should be understood as meaning that the durations overlap and cannot be separated in time.

In the signal example, the signal implementation scheme, the signal sending and receiving method and the signal sending and receiving steps, based on the known principle in the engineering technical field, the dual relation of frequency and time, the dual relation formed by the Fourier transform on two variables and two variable domains related to Fourier series can be mutually transformed. The method of converting the frequency into time, the corresponding signal form and the corresponding sub-carrier configuration, and transmitting data by using the corresponding and dual form signals and sub-carriers is also the technical method disclosed by the invention.

The signals having the above-described features of the present invention may be combined to form a combined signal. The combination method includes setting N signals as s based on the same time scale and time axis_n(t)=s_I,n(t)cos2πf_c,nt+s_Q,n(t)sin2πf_c,nForm t, N ═ 1,2, …, N, where s₁(t),s₂(t),…,s_NAt least one of (t) is a signal having the above-described feature of the present invention. Selection f_c,1,f_c,2,…,f_c,nLet each s_n(t) spectra are in different frequency bands without mutual interference, and are combined to form

The assembly method further comprises the step of₁(t),s₂(t),…,s_N(t) the phase relationship, i.e. the time-relative delay relationship, is changed, combined

The data transmission method and the data reception method according to the present invention are implemented as follows. The related devices comprise multipliers, adders and matched filters, and the devices and implementation methods are well known in the technical field of communication, and the related demodulation and related operation methods are well known in the technical field of communication.

Selecting a function in the form of an OFDM signal, a descending Fourier series and a fractional code rate orthogonal function, and constructing a subcarrier function g in the signal expression^(l)(x)(t) and h^(l)(x)(t)、

. The shaping and modifying method comprises the known methods of windowing function, adding frequency protection isolation frequency band, prefix and suffix, etc., so that the function can be transmitted on the channel when being used as a signal, and the technical requirement of signal transmission is met. Selected for transmitting data as a function of sub-carriers, i.e. $s_x\left(t\right)=\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}$ All functions g in (1)^(l)(x)(t) and h^(l)(x)(t) and

the present invention has the features described above. The description of the present specification with respect to the signal composition and the transmission and reception methods is described with respect to the subcarriers and functions before shaping and modification, and the correspondence and processing methods before and after signal shaping and modification in the implementation are well known in the field of communication technology.

First, information to be transmitted is mapped into a data sequence d_n ^(I)And { d }_n ^(Q)Will { d }_n ^(x)Divide into L (x) data sequences { d }_n ^(l)(x)L =1,2, …, L (x), each data sequence having a symbol duration ofWill be provided withFormed on sub-carriers by multiplier loading

Then through a multiplier and c^(l)(x)(t) multiplication by d^(l)(x)(t)c^(l)(x)(t) adding all d^(l)(x)(t)c^(l)(x)(t) synthesis by adder

Multiplication of harmonic sub-carriers by multipliers $\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}$ As s_x(t)，s_I(t) multiplication by a multiplier of the carrier cos2 π f_ct is formed by $s_I\left(t\right)\cos 2\mathrm{\&pi;}{f}_{c}t=\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(I\right)}{d}^{\left(l\right)\left(I\right)}\left(t\right)c^{\left(l\right)\left(I\right)}\left(t\right)\right\}\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(I\right)}{\mathrm{\&alpha;}}_k\cos (2\mathrm{\&pi;}{f_k}^{\left(I\right)}t+{{\mathrm{\&theta;}}_k}^{\left(I\right)})\right\}\cos 2\mathrm{\&pi;}{f}_{c}t.$ In the same way, the data sequence d_n ^(Q)Generating a signal $s_Q\left(t\right)\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{f}_{c}t=\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(Q\right)}{d}^{\left(l\right)\left(Q\right)}\left(t\right)\right\}\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(Q\right)}{{\mathrm{\&alpha;}}_k}^{\left(Q\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(Q\right)}t+{{\mathrm{\&theta;}}_k}^{\left(Q\right)})\right\}\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}{f}_{c}t,$ And finally s_I(t) and s_Q(t) forming a transmission signal s (t) = s by an adder_I(t)cos2πf_ct+s_Q(t)sin2πf_cAnd t, transmitting the signal to a receiving end through a channel. The data transmission method, the device and the flow chart are shown in the attached figure 1.

In receiving, the excitation received by the receiving end is r (t) = s (t) + j (t) + n (t), where s (t) is a signal, n (t) is background noise, and j (t) is various other interference signals. The receiving end demodulates the data by a successive stripping demodulation mode.

First multiply r (t) by the multiplier with the carrier cos2 π f_ct and cos2 π f_ct, separation output s_I(t) and s_Q(t) of (d). The invention is characterized in that the difference between any two harmonic subcarrier frequencies

More than two times

Bandwidth, i.e. $\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}{{\mathrm{\&alpha;}}_j}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_j}^{\left(x\right)}t+{{\mathrm{\&theta;}}_j}^{\left(x\right)})$ And $\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(I\right)}{\mathrm{\&alpha;}}_k\cos (2\mathrm{\&pi;}{f_k}^{\left(I\right)}t+{{\mathrm{\&theta;}}_k}^{\left(I\right)})\right\}$ is separable in the frequency domain, so s_I(t) and s_Q(t) are multiplied by multipliers respectively

And $\{{\mathrm{\&Sigma;}}_{k=1}^K{{\mathrm{\&alpha;}}_k}^{\left(Q\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(Q\right)}t+{{\mathrm{\&theta;}}_k}^{\left(Q\right)}),$ pass through a filter and output respectively ${\mathrm{\&Sigma;}}_{l=1}^{L\left(I\right)}{d}^{\left(l\right)\left(I\right)}\left(t\right)c^{\left(l\right)\left(I\right)}\left(t\right)$ And ${\mathrm{\&Sigma;}}_{l=1}^{L\left(Q\right)}{d}^{\left(l\right)\left(Q\right)}\left(t\right)c^{\left(l\right)\left(Q\right)}\left(t\right)$ then useMultiplying by c through a multiplier^(j)(I)(t) outputting d by correlator or matched filter correlation^(j)(I)(t), the equivalence of matched filters and correlation operations is a well-known principle. To be provided with

Multiplying by c through a multiplier^(j)(Q)(t) output d^(j)(Q)(t), j ═ 1,2, …, L (x). Then with d^(j)(I)(t) multiplication by a multiplier

By correlation operation of correlator or matched filter, sequentially outputting { d }_n ^(j)(I)H at d^(j)(Q)(t) multiplication by a multiplier

Output { d in sequence_n ^(j)(Q)}. All sequences d_n ^(j)(I) And { d }_n ^(j)(Q)J-1, 2, …, L (x), synthesizing the original transmit data sequence d_n}. A known equivalent of this procedure is to

Multiplied by a multiplierBy correlation operation of correlator or matched filter, sequentially outputting { d }_n ^(j)(x)J ═ 1,2, …, L (x). The data receiving method, the device and the flow chart are shown in figure 2.

Referring to FIG. 3, take [ -T/2, T/2]Set of upper trigonometric functions

In which the orthogonal cosine function set

And is not changed. For sine function

Orthogonalizing according to the Grameschmidt orthogonalization method to obtain

Let N equal to 16, λ₁＝0.7，λ₂＝1.6，λ₃＝2.4，λ₄＝3.2，λ₅＝4，λ₆＝4.8，λ₇When n is not less than 8 and not more than 16, the value is lambda_nN-1. Can obtain the product

The spectrum is shown in FIG. 3, in which the abscissa unit is 1/T, and the numbers 1,2, …, 16 mean

Spectrum of (a).

The function example has orthogonal functions in 32 time intervals of [ -T/2, T/2], the spectrum of the 32 orthogonal functions has a main lobe in [ -16W, 16W ], and W is 1/T. The number of orthogonal functions is exactly equal to 2 WT.

Referring to fig. 4, the method is as described in fig. 3, let N =15, λ₁=0.7，λ₂=1.6，λ₃=2.4，λ₄=3.2，λ₅=4，λ₆=4.8，λ₇=5.6，λ₈=6.4，λ₉λ is =7.2, n is more than or equal to 10 and less than or equal to 15_nAnd n-2. Can obtain the productThe spectrum is shown in FIG. 4a, where the horizontal axis is 1/T. Then [ -T, T [ -T]On $g\left(t\right)=\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}\frac{14.5}{T}t$ To pair $\{\mathrm{rect}\left(t\right),\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}\frac{n-1}{T}t,\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}\frac{{\mathrm{\&lambda;}}_n}{T}t;1\&le;n\&le;15\}$ And (4) orthogonalizing. Obtaining a 1/2 code rate orthogonal function psi^(1/2)(t) FIG. 4b is^(1/2)(t) spectrum.

Over the time interval [ -T, T ], there are 61 orthogonal functions in this example, the main lobe of the spectrum is within [ -15W,15W ], W = 1/T. The number of orthogonal functions is equal to (1+ α)2WT, α =1/60> 0.

See FIG. 5, from [ -T/2, T/2]The last three orthogonal function sets $\{\mathrm{rect}\left(t\right),\left(\sqrt{2/T}\right)\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}(1/T)t,\left(\sqrt{2/T}\right)\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">sin</figure-callout>}2\mathrm{\&pi;}(0.5/T)t\}$ At the beginning, wherein

u (t) is a unit step function. Firstly adding a 1/2 code rate orthogonal function ${\mathrm{\&psi;}}_c^{(1/2)}\left(t\right)=\{u(t+T)-u(t-T)\}\&CenterDot;\left(\sqrt{1/T}\right)\cos 2\mathrm{\&pi;}(1.5/T)t,$ Obtaining the interval [ -T, T]Seven functions rect (T + T/2) of the upper quadrature, $\mathrm{rect}(t-T/2),\left(\sqrt{2/T}\right)\cos 2\mathrm{\&pi;}(1/T)(t+T/2),$ $\left(\sqrt{2/T}\right)\cos 2\mathrm{\&pi;}(1/T)(t-T/2),$ $\left(\sqrt{2/T}\right)\sin 2\mathrm{\&pi;}(0.5/T)(t+T/2),$

and

move the above seven orthogonal functions to [ -2T,0 []And [0,2T]To use $\{u(t+2T)-u(t-2T)\}\&CenterDot;\left(\sqrt{1/T}\right)\cos 2\mathrm{\&pi;}(1.75/T)t$ Orthogonalizing the code to obtain a 1/4 code rate orthogonal function ${\mathrm{\&psi;}}_c^{(1/4)}\left(t\right)$ Then move to [ -4T,0 [)]And [0,4T]To use $\{u(t+4T)-u(t-4T)\}\&CenterDot;\left(\sqrt{1/T}\right)\cos 2\mathrm{\&pi;}(1.875/T)t,$ At [ -4T,4T]The orthogonalization is carried out to obtain the 1/8 code rate orthogonal function

FIG. 5 shows the waveform of a data sequence when binary data are modulated by integer-code-rate orthogonal functions, 1/2-code-rate orthogonal functions, 1/4-code-rate orthogonal functions and 1/8-code-rate orthogonal functions respectively and transmitted in parallel. Mathematical representation of the signal being equivalent to $s_x\left(t\right)=\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}$ In (1), ${\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\&equiv;1,$ c^(l)(x)(t) ≡ 1, i.e. equivalently $s_x\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}_n^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-{\mathrm{nT}}_d^{\left(l\right)\left(x\right)}),$ Wherein, L (x) =6, g^(1)(x)(t)=rect(t-T/2)， $g^{\left(2\right)\left(x\right)}\left(t\right)=\mathrm{rect}(t-T/2)\sqrt{2}\cos 2\mathrm{\&pi;}(1/T)(t-T/2),$ $g^{\left(3\right)\left(x\right)}\left(t\right)=\mathrm{rect}(t-T/2)\sqrt{2}\sin 2\mathrm{\&pi;}(0.5/T)(t-T/2),$ $g^{\left(4\right)\left(x\right)}\left(t\right)={\mathrm{\&psi;}}_c^{(1/2)}(t-T),g^{\left(5\right)\left(x\right)}\left(t\right)={\mathrm{\&psi;}}_c^{(1/4)}(t-2T),$ $g^{\left(6\right)\left(x\right)}\left(t\right)={\mathrm{\&psi;}}_c^{(1/8)}\left(t\right),$ $T_d^{\left(1\right)\left(x\right)}=T_d^{\left(2\right)\left(x\right)}=T_d^{\left(3\right)\left(x\right)}=T,$ $T_d^{\left(4\right)\left(x\right)}=2T$ $T_d^{\left(5\right)\left(x\right)}=4T,$ $T_d^{\left(6\right)\left(x\right)}=8T.$ The 6 orthogonal functions are used, and the main lobe occupies the bandwidth of [ -2W,2W]The spectral utilization is equal to 96.875%. The existing OFDM technology requires 2N =62 subcarriers to achieve the same spectrum utilization.

Referring to FIG. 6, a rect with superscript is defined^(T)(t)， $t\&Element;[-T/2,T/2]\&DoubleRightArrow;{\mathrm{rect}}^{\left(T\right)}\left(t\right)=1/\sqrt{T},$ $t\&NotElement;[-T/2,T/2]\&DoubleRightArrow;{\mathrm{rect}}^{\left(T\right)}\left(t\right)=0.$ Definition of $g^{\left(2T\right)}\left(t\right)=[u(t+T)-u(t-T)]\left(\sqrt{1/T}\right)\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA00003070077100011.png,HDA00003070077100031.png"\; state="\{\{state\}\}">cos</figure-callout>}2\mathrm{\&pi;}(1/2T)t.$ The time domain waveform and phase relationship of the binary data when modulated is shown in fig. 6.

The method of the present invention is used for expanding the communication capacity of a conventional code division multiple access (single carrier code division multiple access) system with the number of users being L.

The signal form of the l-th user in the original system is s (t) = d (t) c_l(t), d (t) is a data stream, c_l(t)=∑_nc_l,nh(t-nT_c) Is a code stream, where c_l,nIs the spreading code assigned to the l-th user, and the spreading waveform h (t) is a rectangular function. The method of the present invention is now used to reconstruct data streams and code streams. Firstly, reconstructing the spread spectrum code stream c of the first user_l(t) using two different code rates $c_l^{\left(T_c\right)}\left(t\right)=\underset{n}{\mathrm{\&Sigma;}}{c_{l,n}}^{\left(1\right)}{\mathrm{rect}}^{\left(T_c\right)}(t-n{T}_c-\frac{T_c}{2})$ And $c_l^{\left({2T}_c\right)}\left(t\right)=\underset{n}{\mathrm{\&Sigma;}}{c_{l,n}}^{\left(2\right)}{g}^{\left({2T}_c\right)}(t-2n{T}_c-T_c),$ {c_l，n ⁽¹⁾and { c }and_l，n ⁽²⁾The same or different spreading codes can be used.

Four user data streams are formed with a symbol period of T_dIs/are as follows

And a symbol period of 2T_dIs/are as followsAre respectively as $d_1^{\left(T_d\right)}\left(t\right)=\underset{n}{\mathrm{\&Sigma;}}{x}_n\mathrm{rec}{t}^{\left(T_d\right)}(t-\frac{T_d}{2}-n{T}_d),$ $d_2^{\left(T_d\right)}\left(t\right)=\underset{n}{\mathrm{\&Sigma;}}{y}_n{\mathrm{rect}}^{\left(T_d\right)}(t-\frac{T_d}{2}-n{T}_d),$ $d_1^{\left({2T}_d\right)}\left(t\right)=\underset{n}{\mathrm{\&Sigma;}}{\tilde{x}}_n{g}^{\left({2T}_d\right)}(t-2n{T}_d-T_d),$ And $d_2^{\left({2T}_d\right)}\left(t\right)=\underset{n}{\mathrm{\&Sigma;}}{\tilde{y}}_n{g}^{\left({2T}_d\right)}(t-2n{T}_d-T_d),$ wherein,is an arbitrary sequence of data. S for transmitting data_I(t) and s_Q(t) are all $\{d_1^{\left(T_d\right)}\left(t\right)+d_1^{\left({2T}_d\right)}\left(t\right)\}{c}_l^{\left(T_c\right)}\left(t\right)+\{d_2^{\left(T_d\right)}\left(t\right)+d_2^{\left({2T}_d\right)}\left(t\right)\}{c}_l^{\left({2T}_c\right)}\left(t\right)$ Form (a). Thus, the user subchannel expansion is up to 3 times in terms of I, Q quadrature modulation.

In the above embodiments, based on the principle known in the engineering technology field, the dual relationship between frequency and time, the two variables of the fourier transform and the two variable domains related to the fourier series may be interchanged to form the dual relationship. The frequency conversion into time, the corresponding signal form and the corresponding sub-carrier configuration, and the method of transmitting data by using the corresponding and dual signal and sub-carrier should also be regarded as a simple transformation of the technical method disclosed by the present invention and fall into the protection scope of the present patent.

In the above embodiments, based on the principle of digitizing analog quantities known in the engineering field, based on the method of digitizing analog quantities known in the engineering field, the signals represented by analog quantities in the description are digitized, the corresponding signal forms and the corresponding subcarrier configurations, and the method of transmitting data by using the corresponding digitized signals and digitized subcarriers should also be regarded as a simple transformation of the technical method disclosed in the present invention and fall within the protection scope of the present patent.

In the above embodiments, the combination of all the signals with the above features to form the signal form includes that N waveforms are s based on the same time scale and time axis_n(t)=s_I,n(t)cos2πf_c,nt+s_Q,n(t)sin2πf_c,nt form of signal, N =1,2, …, N, where s₁(t),s₂(t),…,s_N(t) at least one of the signals having the above-described features of the present invention; selection f_c,1,f_c,2,…,f_c,nLet each s_n(t) spectra are in different frequency bands without mutual interference, and are combined to form

The assembly method further comprises the step of₁(t),s₂(t),…,s_N(t) the phase relationship, i.e. the time-relative delay relationship, is changed, combined

These combinations should also be regarded as simple variations of the technical means disclosed in the present invention and fall within the scope of protection of the present patent。

In the above embodiments, the signal and the data transmission method are constituted by direct combination of signals having equivalent characteristics. Multilayer signal and data transmission method consisting of direct superposition of signals with equivalent characteristics. Including the method of transmitting data by combining at least one signal having the above-described features of the present invention with other types of signals as described in the specification. It should also be considered as a simple variation of the disclosed technical method and fall within the scope of the patent.

Claims (11)

1. A multi-carrier data transmission method is characterized by comprising a sending step and a receiving step, wherein the sending step comprises the step of mapping information to be sent into a data sequence { d }_n ^(I)And { d }_n ^(Q)Then will { d }_n ^(x)Divide into L (x) data sequences

Where x is one of I or Q, L =1,2, …, L (x), each data sequence having a symbol duration of

Will be provided with

Multiplied by a multiplier

Become into $d^{\left(l\right)\left(x\right)}\left(t\right)=d_n^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-{\mathrm{nT}}_d^{\left(l\right)\left(x\right)}),$ And c^(l)(x)(t) multiplying by a multiplier to form d^(l)(x)(t)c^(l)(x)(t) adding all d^(l)(x)(t)c^(l)(x)(t) synthesis by adder

Multiplication of harmonic sub-carriers by multipliers ${\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos ({{2\mathrm{\&pi;f}}_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})$ To obtain $\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos ({{2\mathrm{\&pi;f}}_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}$ As s_x(t) in which s_I(t) multiplication by a multiplier of the carrier cos2 π f_ct is formed by $s_I\left(t\right)\cos 2\mathrm{\&pi;}{f}_{c}t=\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(I\right)}{d}^{\left(l\right)\left(I\right)}\left(t\right)c^{\left(l\right)\left(I\right)}\left(t\right)\right\}\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(I\right)}{\mathrm{\&alpha;}}_k\cos ({{2\mathrm{\&pi;f}}_k}^{\left(I\right)}t+{{\mathrm{\&theta;}}_k}^{\left(I\right)})\right\}\cos 2\mathrm{\&pi;}{f}_{c}t,$ The data sequence d is also repeated_n ^(Q)} generating a signal s_Q(t) multiplication by a multiplier of the carrier sin2 π f_ct is formed by $s_Q\left(t\right)\sin {2\mathrm{\&pi;f}}_{c}t=\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(Q\right)}{d}^{\left(l\right)\left(Q\right)}\left(t\right)c^{\left(l\right)\left(Q\right)}\left(t\right)\right\}\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(Q\right)}{{\mathrm{\&alpha;}}_k}^{\left(Q\right)}\cos ({{2\mathrm{\&pi;f}}_k}^{\left(Q\right)}t+{{\mathrm{\&theta;}}_k}^{\left(Q\right)})\right\}$ sin2πf_ct, last s_I(t) and s_Q(t) forming a transmission signal s (t) = s by an adder_I(t)cos2πf_ct+s_Q(t)sin2πf_ct, sending the data to a receiving end through a channel;

the receiving step comprises demodulating the excitation r (t) = s (t) + j (t) + n (t) received by the receiving end by a successive stripping demodulation mode, wherein s (t) is a signal, n (t) is background noise, and j (t) is other various interference signals; the excitation r (t) is first multiplied by the receiver's internally recovered carrier cos2 π f by a multiplier_ct and sin2 π f_ct, respectively outputting s through filters_I(t) and s_Q(t)；s_I(t) and s_Q(t) are multiplied by multipliers respectively $\left\{{\mathrm{\&Sigma;}}_{K=1}^{K\left(I\right)}{\mathrm{\&alpha;}}_k\cos ({{2\mathrm{\&pi;f}}_k}^{\left(I\right)}t+{{\mathrm{\&theta;}}_k}^{\left(I\right)})\right\}$ And $\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(Q\right)}{{\mathrm{\&alpha;}}_k}^{\left(Q\right)}\cos ({{2\mathrm{\&pi;f}}_k}^{\left(Q\right)}t+{{\mathrm{\&theta;}}_k}^{\left(Q\right)})\right\},$ pass through a filter and output respectively ${\mathrm{\&Sigma;}}_{l=1}^{L\left(I\right)}{d}^{\left(l\right)\left(I\right)}\left(t\right)c^{\left(l\right)\left(I\right)}\left(t\right)$ And ${\mathrm{\&Sigma;}}_{l=1}^{L\left(Q\right)}{d}^{\left(l\right)\left(Q\right)}\left(t\right)c^{\left(l\right)\left(Q\right)}\left(t\right);$ then use ${\mathrm{\&Sigma;}}_{l=1}^{L\left(I\right)}{d}^{\left(l\right)\left(I\right)}\left(t\right)c^{\left(l\right)\left(I\right)}\left(t\right)$ Multiplying by c through a multiplier^(j)(I)(t) outputting d by correlator or matched filter correlation^(j)(I)(t) in the presence of

Multiplying by c through a multiplier^(j)(Q)(t) output d^(j)(Q)(t), j =1,2, …, L (x), and further d^(j)(I)(t) multiplication by a multiplier

By correlation operation of correlator or matched filter, sequentially outputting { d }_n ^(j)(I)H at d^(j)(Q)(t) multiplication by a multiplier

Output { d in sequence_n ^(j)(Q)1,2, …, L (x), all sequences d_n ^(j)(I)And { d }_n ^(j)(Q)Synthesize the original transmitted data sequence d_n}；

The method utilizes at least two subcarriers and subchannels to transmit data, the signal form for transmitting data is a multi-code rate subcarrier combined signal form including harmonic offset modulation subcarriers, any one subcarrier between a plurality of different subcarriers must be mixed with another subcarrier in spectrum, when the frequency domain can not be separated by a filter, the subcarriers are a group of subcarriers, when the bandwidth of each of one group of the two groups of subcarriers is more than ten times different from the sum of the bandwidths of all the subcarriers of the other group, the two groups of subcarriers belong to two different layers, any two groups of the subcarriers belong to different layers, the subcarriers are in a multilayer subcarrier signal form, the mathematical expression of the subcarriers is a function, the subcarriers can be independently formed, or the subchannels are formed in a mode of multiplying more than two subcarriers, the mathematical expression of the subchannels is the product of data multiplied by a function or more than two functions, the mathematical expression of the basic signal form s (t) of the data transmitted by the method is in the form

s(t)＝s_I(t)cos2πf_ct+s_Q(t)sin2πf_ct，

Wherein f is_cIs the carrier frequency, s_xThe form (t) includes signal form one and signal form two, s of signal form one_x(t) is in the form

$s_x\left(t\right)=\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos ({{2\mathrm{\&pi;f}}_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\},$

${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}\left({t-\mathrm{iT}}_d^{\left(l\right)\left(x\right)}\right)\right\{{\mathrm{\&Sigma;}}_n{c}_n^{\left(l\right)\left(x\right)}{h}^{\left(l\right)\left(x\right)}(t-{\mathrm{nT}}_c^{\left(l\right)\left(x\right)})\left\}\right\},$

SignalS of form two_x(t) is represented by the formula s_x(t) in

Is equal to

${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}\left({t-\mathrm{iT}}_d^{\left(l\right)\left(x\right)}\right)\right\{{\mathrm{\&Sigma;}}_n[\cos 2\mathrm{\&pi;f}\left(c_n^{\left(l\right)\left(x\right)}\right)t+\mathrm{\&phi;}\left(c_n^{\left(l\right)\left(x\right)}\right)]h^{\left(c_n^{\left(l\right)\left(x\right)}\right)}\left(t\right)\left\}\right\},$

Wherein x ═ I denotes s_I(t), x = Q represents s_Q(t), L (x) and K (x) are fixed integers, i.e. s_I(t) and s_QL and K in (t) may be any integer, and h^(l)(x)(t) is the duration

The time-domain waveform of (a),

is a sequence whose value is optional; $d^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_i{d}_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}\left({t-\mathrm{iT}}_d^{\left(l\right)\left(x\right)}\right)$ for the first-way data,

for the duration of a data bit, g^(l)(x)(t) is the duration

The time-domain waveform of (a),

is to transmit data;

is expressed in terms of sequence

The frequency value of the change in value of (c),

is expressed in terms of sequence

The phase value of the change is changed,

is expressed in terms of sequence

As a function of the change in the amount of the change, $\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(I\right)}{\mathrm{\&alpha;}}_k\cos ({{2\mathrm{\&pi;f}}_k}^{\left(I\right)}t+{{\mathrm{\&theta;}}_k}^{\left(I\right)})\right\}$ and

are the sub-carriers of the harmonics,

for the harmonic sub-carrier frequencies it is,is a coefficient and has an optional value, and the harmonic subcarrier has a phase of

And the numerical value can be arbitrarily selected;

the subcarriers of the same layer are orthogonal in a time domain, and a certain subcarrier of the same layer must be overlapped with the spectrum of another subcarrier and cannot be isolated by a frequency division spectrum and a filter; when the same layer of subcarriers with overlapped frequency spectrums and another layer of subcarriers with overlapped frequency spectrums are combined in a multiplying mode, the bandwidth of each subcarrier in one layer is more than 10 times larger than the sum of the bandwidths of all subcarriers in the other layer, so that the combined signals in the multiplying mode can be divided into orthogonal or approximately orthogonal subchannels through related demodulation, and the number of the subchannels of the combined signals is equal to the product of the number of the subcarriers in each layer.

2. A multi-carrier data transmission method as claimed in claim 1, characterized in that when the data sequence { d } is present_n ^(I)And { d }_n ^(Q)All equal the constant 1, there is one T all

And

the common multiple of (a) to (b), $\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}=\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}(t\&PlusMinus;\mathrm{NT})c^{\left(l\right)\left(x\right)}(t\&PlusMinus;\mathrm{NT})\right\}$ is true for an integer N, where N is any integer, $\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}$ repeating the process with T as a period; all harmonic subcarriers $\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}$ And each functionAnd keeping the bit timing synchronization, and keeping the frequency and the phase unchanged in time intervals with the time length being integral multiple of T.

3. A method for multi-carrier data transmission as claimed in claim 1, characterized in that the difference between the frequencies of any two harmonic sub-carriers in the signal

More than or equal to two times ${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)$ Bandwidth, i.e. $\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}{\mathrm{\&alpha;}}_i^{\left(x\right)}\cos ({2\mathrm{\&pi;f}}_i^{\left(x\right)}t+{\mathrm{\&theta;}}_i^{\left(x\right)})$ And $\left\{{\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)\right\}{\mathrm{\&alpha;}}_j^{\left(x\right)}\cos ({{2\mathrm{\&pi;f}}_j}^{\left(x\right)}t+{{\mathrm{\&theta;}}_j}^{\left(x\right)})$ the spectrum of (a) is separable in the frequency domain.

4. A method for multi-carrier data transmission as claimed in claim 1, characterized in that the data is transmitted in a signal

${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}\left({t-\mathrm{iT}}_d^{\left(l\right)\left(x\right)}\right)\right\{{\mathrm{\&Sigma;}}_n{c}_n^{\left(l\right)\left(x\right)}{h}^{\left(l\right)\left(x\right)}\left({t-\mathrm{nT}}_c^{\left(l\right)\left(x\right)}\right)\left\}\right\}$ If L (x) =1 in (1) $s_x\left(t\right)=\left\{{\mathrm{\&Sigma;}}_n{d_n}^{\left(x\right)}{g}^{\left(x\right)}\left({{t-\mathrm{nT}}_d}^{\left(x\right)}\right)\right\}\left\{{\mathrm{\&Sigma;}}_n{c_n}^{\left(x\right)}{h}^{\left(x\right)}\left({t-\mathrm{nT}}_c^{\left(x\right)}\right)\right\}\{{\mathrm{\&Sigma;}}_{k=1}^K{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\}$ C in (1)_n ^(x)Is a spreading code, then s_x(t) a stretching bandwidth greater than its actual occupied bandwidth by at least one d^(x)(t)c^(x)(t) bandwidth frequency interval.

5. A method for multi-carrier data transmission as claimed in claim 1, characterized in that the data is transmitted in a signal

$\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}\&equiv;1,$ And is

${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}\left({t-\mathrm{iT}}_d^{\left(l\right)\left(x\right)}\right)$ When L (x) is not less than 2 and g^(l)(x)At least one of (t) is a downward Fourier series or a fractional code rate orthogonal function.

6. A method for multi-carrier data transmission as claimed in claim 1, characterized in that the data is transmitted in a signal

$\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}\&equiv;1,$ At the same time

${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{\mathrm{\&Sigma;}}_i\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}\left({t-\mathrm{iT}}_d^{\left(l\right)\left(x\right)}\right){\mathrm{\&Sigma;}}_n{c_n}^{\left(x\right)}{h}^{\left(x\right)}\left({t-\mathrm{nT}}_c^{\left(x\right)}\right)\right\}$ When L (x) is not less than 2 and g^(l)(x)At least one of (t) is a downward Fourier series or a fractional code rate orthogonal function.

7. A method for multi-carrier data transmission as claimed in claim 1, characterized in that the data is transmitted in a signal

$\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos ({{2\mathrm{\&pi;f}}_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}\&equiv;1,$ At the same time

${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}\left\{{\mathrm{\&Sigma;}}_n\right[{\mathrm{\&Sigma;}}_i{d_n}^{\left(l\right)\left(x\right)}{c}_i^{\left(l\right)\left(x\right)}{h}^{\left(l\right)\left(x\right)}\left({t-\mathrm{iT}}_c^{\left(l\right)\left(x\right)}\right)\left]g^{\left(l\right)\left(x\right)}\left({t-\mathrm{nT}}_d^{\left(l\right)\left(x\right)}\right)\right\}$ Then, L (x)Not less than 2 and h^(l)(x)At least one of (t) is a downward Fourier series or a fractional code rate orthogonal function.

8. A multi-carrier data transmission method according to claim 1,

when in signal $\left\{{\mathrm{\&Sigma;}}_{k=1}^{K\left(x\right)}{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos ({{2\mathrm{\&pi;f}}_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}\&equiv;1,$ At the same time

${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}{d}^{\left(l\right)\left(x\right)}\left(t\right)c^{\left(l\right)\left(x\right)}\left(t\right)={\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}\left\{{\mathrm{\&Sigma;}}_i{d}_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}\left({t-\mathrm{iT}}_d^{\left(l\right)\left(x\right)}\right)\right[{\mathrm{\&Sigma;}}_n{c}_n^{\left(l\right)\left(x\right)}{h}^{\left(l\right)\left(x\right)}\left({t-\mathrm{nT}}_c^{\left(l\right)\left(x\right)}\right)\left]\right\}$ When L (x) is not less than 2 and h^(l)(x)(t) or g^(l)(x)At least one of (t) is a downward Fourier series or a fractional code rate orthogonal function.

9. A method for multi-carrier data transmission as claimed in claim 1, characterized in that the data is transmitted in a signal $h^{\left(i_1\right)\left(x\right)}\left(t\right)=h^{\left(i_2\right)\left(x\right)}\left(t\right)=...=h^{\left(i_k\right)\left(x\right)}\left(t\right)$ When the temperature of the water is higher than the set temperature, $g^{\left(i_1\right)\left(x\right)}\left(t\right),g^{\left(i_2\right)\left(x\right)}\left(t\right),...,g^{\left(i_k\right)\left(x\right)}\left(t\right)$ two by two unequal and orthogonal in the time domain, spectral aliasing of functions, i.e. each

Must be in contact with a certain point

Cannot be separated in the frequency domain by filters. When in use $g^{\left(i_1\right)\left(x\right)}\left(t\right)=g^{\left(i_2\right)\left(x\right)}\left(t\right)=...=g^{\left(i_k\right)\left(x\right)}\left(t\right)$ When the temperature of the water is higher than the set temperature, $h^{\left(i_1\right)\left(x\right)}\left(t\right),h^{\left(i_2\right)\left(x\right)}\left(t\right),...,h^{\left(i_k\right)\left(x\right)}\left(t\right)$ two by two are not equal and are orthogonal in the time domain, ${\mathrm{\&Sigma;}}_n{c}_n^{\left(i_u\right)\left(x\right)}{h}^{\left(i_u\right)\left(x\right)}(t-n{T}_c^{\left(x\right)})$ and ${\mathrm{\&Sigma;}}_n{c}_n^{\left(i_v\right)\left(x\right)}{h}^{\left(i_v\right)\left(x\right)}(t-n{T}_c^{\left(x\right)})$ sequence of (1)

And

can be arbitrarily taken from

Spectral aliasing of functions, each of which

Must be in contact with a certain point

Cannot be separated in the frequency domain by filters.

10. A method for multi-carrier data transmission as claimed in claim 1, characterized in that h^(l)(x)(t), L ═ 1,2, …, L (x), all of h not equal^(l)(x)(t) orthogonal pairwise in the time domain, spectral aliasing of functions, each of which

Must be in contact with a certain point

Cannot be separated in the frequency domain by filters.

11. A method for multi-carrier data transmission according to claim 1, characterized in that when the data is transmitted in a single carrier

Is shown as ${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-i{T}_d^{\left(l\right)\left(x\right)})\right\{{\mathrm{\&Sigma;}}_n[\cos 2\mathrm{\&pi;f}\left(c_n^{\left(l\right)\left(x\right)}\right)t+\mathrm{\&phi;}\left(c_n^{\left(l\right)\left(x\right)}\right)]h^{\left(c_n^{\left(l\right)\left(x\right)}\right)}\left(t\right)\left\}\right\}$ When the signal is expressed ${\mathrm{\&Sigma;}}_{l=1}^{L\left(x\right)}\left\{d_i^{\left(l\right)\left(x\right)}{g}^{\left(l\right)\left(x\right)}(t-i{T}_d^{\left(l\right)\left(x\right)})\right\{{\mathrm{\&Sigma;}}_n[\cos 2\mathrm{\&pi;f}\left(c_n^{\left(l\right)\left(x\right)}\right)t+\mathrm{\&phi;}\left(c_n^{\left(l\right)\left(x\right)}\right)]h^{\left(c_n^{\left(l\right)\left(x\right)}\right)}\left(t\right)\left\}\right\}\left\{{{\mathrm{\&alpha;}}_k}^{\left(x\right)}\cos (2\mathrm{\&pi;}{f_k}^{\left(x\right)}t+{{\mathrm{\&theta;}}_k}^{\left(x\right)})\right\}$ In (1) $h^{\left(c_n^{i_1}\right)\left(x\right)}\left(t\right)=h^{\left(c_n^{i_2}\right)\left(x\right)}\left(t\right)=...=h^{\left(c_n^{i_k}\right)\left(x\right)}\left(t\right)$ When the temperature of the water is higher than the set temperature,

two by two unequal and orthogonal in the time domain, spectral aliasing of functions, each of which

Must be in contact with a certain point

Spectral aliasing of (a), which cannot be separated by a filter in the frequency domain; when in use $g^{\left(i_1\right)\left(x\right)}\left(t\right)=g^{\left(i_2\right)\left(x\right)}\left(t\right)=...=g^{\left(i_k\right)\left(x\right)}\left(t\right)$ When the temperature of the water is higher than the set temperature,

pairwise unequal and orthogonal in time domain, sequence

Can be arbitrarily taken $h^{\left(c_n^{i_1}\right)\left(x\right)}\left(t\right),h^{\left(c_n^{i_2}\right)\left(x\right)}\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;,h^{\left(c_n^{i_k}\right)\left(x\right)}\left(t\right)$ Spectral aliasing of functions, each of which

Must be in contact with a certain point

Cannot be separated in the frequency domain by filters.

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