CN108092931B - Time-delay multi-carrier modulation and demodulation method based on time-frequency pulse shaping - Google Patents

Abstract

The invention discloses a method based on time frequencyThe pulse-forming time-delay multi-carrier modulation and demodulation method is characterized in that a plurality of periodic symbol waveforms capable of carrying information are constructed at a sending end; the symbol waveform is composed of H wavelets, the starting point of each wavelet is required to be placed in the life cycle of the first wavelet, and the symbol waveform is obtained by linear superposition after the starting point of the symbol waveform sequentially moves for a certain time period called time delay; the wavelet is a fundamental wavelet carrying information, and the fundamental wavelet comprises three intervals of waveforms which are respectively in an interval T_θi1Inner prepulse information wave in interval T_θi2Main wave sum without information in interval T_θi3An internal and a back pulse information wave; at a receiving end, the received symbol waveform is equalized, then amplitude information of information carried by the equalized symbol waveform is solved in each front-rear pulse information wave interval in sequence, and then the amplitude information is converted into binary number to complete a signal demodulation process. The invention has the characteristics of higher transmission efficiency, lower demodulation complexity and the like.

Description

Time-delay multi-carrier modulation and demodulation method based on time-frequency pulse shaping

Technical Field

The invention relates to a Modulation technology in digital communication, in particular to a Time-Delay Multi-carrier Modulation and Demodulation method (TFP-TDMC-A Time-Frequency Pulse-Shaping Based Time-Delay Multi-Carriers Modulation and Demodulation for short) Based on Time-Frequency Pulse Shaping, belonging to the technical field of Multi-carrier Modulation in digital communication.

Background

OFDM is a modulation technique in 4G as well as 5G mobile communications. The inventor has proposed a symbol waveform with a special structure and a corresponding modulation and demodulation method in a patent of time-frequency phase-mixing multi-carrier modulation method (application number: 2008101194121), and is called a time-shift orthogonal multi-carrier modulation technique (NMT or TS-NMT for short) later in published documents. The inventor has proved from both theory and experiment that the transmission efficiency is much higher than that of OFDM, and has the advantages of small peak-to-average power ratio, strong frequency shift resistance and no need of cyclic prefix. However, the demodulation complexity of TS-NMT is high, and when the wavenumber of wavelets is large, the demodulation equation set presents a large ill-conditioned behavior, so the inventor has proposed "a time-delay multi-carrier modulation and demodulation method", abbreviated as TDMC (patent application number: 2015100924095). TDMC keeps the characteristics of TS-NMT time delay multi-carrier, greatly simplifies demodulation method on the basis of inheriting the advantage of high transmission efficiency of TS-NMT, but has the defect of error propagation. In digital communication, the structure of a symbol waveform and a pulse shaping technique of the waveform are two important means for improving the efficiency of modulation. In terms of waveform structure, the multi-carrier structure has higher efficiency than the single carrier structure, for example, a composite wave (called QAM) composed of sine and cosine waves is more efficient than a single carrier of single sine or cosine waves, and OFDM composed of multiple QAMs has higher efficiency. The concept of pulse shaping was originally proposed in baseband transmission by nyquist, and demodulation was completed by shaping a transmitted square pulse into a SINC function waveform that does not cause interference at one point by an ideal filter that equalizes a communication system to a 1/(2T) bandwidth at a receiving end. Various pulse shaping methods in the time domain and the frequency domain appear later to meet different performance requirements in the time domain and the frequency domain. It should be noted that in the present invention, TS-NMT and TDMC are modified by using the idea of pulse shaping, and it is proposed that TFP-TDMC also uses multicarrier and pulse shaping as important means for improving transmission efficiency.

Disclosure of Invention

In view of the defects in the prior art, the present invention aims to provide a time-frequency pulse shaping-based time-delay multi-carrier modulation and demodulation method, so that the modulation technology has the characteristics of higher transmission efficiency, low demodulation complexity, etc.

In order to achieve the purpose, the technical scheme of the invention is as follows:

a time-delay multi-carrier modulation and demodulation method based on time-frequency pulse shaping is characterized in that:

at a sending end, binary information is converted into corresponding quantization amplitude and then sequentially given to a front information wave and a back information wave of a base wavelet to form corresponding wavelets to generate H wavelets, all wavelet starting points are required to be placed in the survival period of the first wavelet, all wavelets are sequentially moved for a time delay from the starting point of a symbol waveform and then linearly superposed to form a synthetic wave, namely, a periodic symbol waveform with T as a period is formed to complete a modulation process, namely, the method of sequentially moving for a time delay and then linearly superposed is taken as a time delay rule, different modulation methods have different time delay rules, and the difference is expressed as the rule of the time delay interval of adjacent waveletsDifferent; at a sending end, converting binary information into corresponding quantization amplitude, and sequentially giving a front information wave and a back information wave of the base wavelet to form corresponding wavelets; wherein the quantization amplitude complies with traditional value-taking rules in digital communications; the fundamental wave is composed of waveforms of three sections in which a front information wave, a main wave and a rear information wave are distributed in sequence, and the waveform structures of the front information wave and the rear information wave are completely the same; the wavelets are waveforms formed by respectively changing the amplitudes of a front information wave and a rear information wave of the fundamental wave to enable the front information wave and the rear information wave to respectively carry different binary information and enable the amplitude of the main wave to be unchanged; the three sections of the fundamental wave are respectively T_θ1、T_θ2And T_θ3The term "life time of the wavelet" means that the synthesis interval, in which the three intervals are sequentially combined into one fundamental wavelet, is called the life time of the fundamental wavelet, and the interval of the fundamental wavelet is also called the life time of the wavelet, and is denoted as T_d，T_d＝T_θ1+T_θ2+T_θ3All intervals in the formula are half-open and half-closed intervals, the waveform of each basic wavelet only exists in the corresponding life cycle, and the basic wavelet is not defined or takes a value of 0 outside the life cycle; correspondingly, the tokens associated with different wavelets or base wavelets are distinguished by the subscript i ═ 1, …, H, i.e., T_diIndicating the lifetime of the ith wavelet or base wavelet such that T_di＝T_d(i+1)Or T_di≠T_d(i+1)Generally, take T_di＝T_d(i+1)＝T_d，T_θi1、T_θi2、T_θi3Respectively representing the interval of the ith front information wave, the main wave and the back information wave; and the fundamental wave is divided into two types, namely type 1 fundamental wave and type 2 fundamental wave which are expressed by formula

The corresponding wavelets are classified into type 1 wavelets and type 2 wavelets, and are formulated as

Superscript 1\2 for distinguishing type 1 baseThe wave or type 2 fundamental wave, the symbol "\\" represents the meaning of "or" in the following description, and the following formulas are expressed according to the above expression forms; wherein ω is_kRepresenting the angular frequencies of the wavelet and the fundamental wavelet main information wave and the reference main wave, so that the wavelets with the same angular frequency form a subchannel in the frequency domain, and the center frequency of each subchannel is defined by the angular frequency omega_kDetermining that K is 1, …, K, i.e. K subchannels are formed in total; and each sub-channel is not required to be orthogonal in frequency domain, and the number of co-frequency sub-waves contained in each sub-channel can be equal or unequal, that is, if the number of sub-waves with the same frequency contained in each sub-channel is denoted as L_kK1, …, K, allowing L_k＝L_k+1Or L_k≠L_k+1Angular frequency omega_kThe subscript k and the wavelet subscript i have the following relation: wavelet sub-order i ═ L for each k-th sub-channel_k-1+1,…,L_k-1+L_k；

At the receiving end, firstly, the received waveform is restored to the waveform close to the transmitted waveform or the most suitable demodulation waveform as much as possible through equalization, and then the amplitudes of all wavelets are solved to complete the demodulation process.

Compared with the prior art, the invention has the beneficial effects that:

(1) compared with OFDM and other multi-carriers, TFP-TDMC keeps the characteristics of time-frequency phase mixed multi-carrier modulation method and TDMC high transmission efficiency on transmission efficiency;

(2) compared with the TDMC proposed by the inventor, as the TFP-TDMC information is only carried by the information wave, the amplitude of the main wave of the wavelet is not changed and is known during demodulation, the demodulation of each information wave is independently carried out, and the problem of error propagation is not introduced like the TDMC;

(3) the modulation and demodulation method of the dual overlapping of the packet delay in the TFP-TDMC has the similarity with a 'multi-carrier modulation method of time-frequency phase mixing', but the number of sub-waves contained in each group is reduced, the ill-posed characteristic of an equation set can be effectively reduced, and through the matching of alpha and beta values, the demodulation signal-to-noise ratio can be improved by improving the alpha value, so that the bit number carried by the information wave is increased, but the power of the synthesized wave is not improved.

(4) The information wave in TFP-TDMC occupies a much smaller interval than the wavelet period, and when the pipeline hardware structure is adopted for demodulation, the demodulation delay can be reduced, which is expected by 5G.

Drawings

FIG. 1 is an illustration of a transmitting end type 1 wavelet of the present invention;

FIG. 2 is an illustration of a transmitting end type 2 wavelet of the present invention;

FIG. 3 illustrates an exemplary type 2 wavelet through a 75 th order filter according to the present invention:

FIG. 4 is an illustration of a first exemplary transmission wave according to the present invention;

FIG. 5 is an illustration of a separate representation of sine and cosine waves of a wavelet pair in a second transmitted wave in accordance with the present invention;

FIG. 6 is an illustration of a synthesis of sine and cosine wavelet pairs in a second transmitted wave in accordance with the present invention;

fig. 7 is an illustration of a third transmission wave according to the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

In the present invention, the term "symbol" is a term specific to a symbol waveform of one period, the period of the symbol being denoted by T, and T being used for each of three modulation methods to be described below₁、T₂And T₃The symbol periods of the characters are represented, and other Pinyin or English letters (including the ones added with upper and lower marks) are called signs; in the following description, all the interval marks may be used as a mark of a time segment or a mark of a time point of an interval starting point depending on the application; the invention changes the amplitude of the information wave before and after the base wave to make them each otherThe basic wavelets carrying information are called wavelets, wherein the basic wavelets carry different binary information but do not carry information because the amplitude of the main wave is unchanged; let i be 1, …, H as a subscript to distinguish between different wavelets and the fundamental wavelets, thus, T_diIndicating the lifetime, T, of the ith wavelet or fundamental wavelet_θi1、T_θi2And T_θi3Respectively representing the interval of the ith front information wave, main wave and back information wave, and using T when different sub-waves are not needed to be distinguished_θ1、T_θ2And T_θ3These three intervals represent all wavelets; in the following formula, f and a are respectively used as subscripts or superscripts in different descriptions to distinguish front and back information waves, the information waves are general names of the front and back information waves, the information waves can be various waveforms such as square waves, raised cosine waves, sine waves or cosine waves, and the like, which are called pulse shaping in digital communication, however, the research of the inventor finds that the square waves and the raised cosine waves are used as the information waves, and a synthetic wave with high efficiency in both frequency domain and time domain is difficult to construct, and in order to simplify the description, in the following specific description, only type 1 and type 2 base waves of the information waves composed of the sine waves and the cosine waves respectively are included, and a designer can select other types of waveforms as the information waves according to different applications according to the following description;

based on the principle, the time-frequency pulse forming-based time-delay multi-carrier modulation and demodulation method is characterized by comprising the following steps of: at the transmitting end, the information is added to each base wavelet to become corresponding wavelet, that is, the quantization amplitude corresponding to the binary number representing the information is given to each base wavelet (as the common technology, the conversion step is omitted below), and then all the wavelets are combined into different synthetic waves to form a symbol waveform, thus completing the modulation process; at a receiving end, firstly, restoring the received waveform to a waveform close to the transmitted waveform or an optimum demodulation waveform as much as possible through equalization, and solving the amplitudes of all wavelets to complete the demodulation process; because the equalization can only obtain a waveform similar to the transmission, in order to distinguish different shapes, subscripts t and r are used for distinguishing a transmitting end from a receiving end, and t \ r is used for representing by an abbreviation of t or r; in the following, x \ y is an abbreviated representation of x or y, and x or y can be replaced by any number and letter;

the basic structure of the fundamental waves of types 1 and 2

Wherein u (t) is as defined above₁)|v(t₂)|w(_t3) The form gives the sequential connection of three waveforms separated by vertical lines marked with "|", u (t)₁)、v(t₂) And w (t)₃) The following general terms refer to three different waveforms, and the listed waveform notation may be substituted for any waveform in the same representation in the formula of the present invention, specifically in formula (1):

and

all the intervals are half-open and half-closed intervals, subscripts 1, 2 and 3 of the intervals give a connection sequence on a time coordinate, superscripts 1\2 are used for distinguishing type 1 or type 2 basewaves,

and

referred to as front or rear information waves, distinguished by subscript f or a respectively,

referred to as the reference dominant wave, i is the index of the different fundamental wavelets, and τ i is the time delay of the ith fundamental wavelet relative to the origin of a symbol (τ when a symbol contains multiple sub-composite waves)_iIs rewritten as

Is indicated as

The fundamental wave is relative to the sub-synthetic waveThe time delay of the point),

meaning that the intervals of the front and back information waves are equal, subscript t \ r represents a sending end or a receiving end, and delay expansion is generated when the sending waveform reaches the receiving end, so that a section of empty interval is reserved for the waveforms of the three intervals of the sending end, and delta tau_i＝τ_i+1-τ_iRepresenting the time delay interval between the (i + 1) th wavelet and the ith wavelet, typically by Δ τ_i＝Δτ_h＝Δτ,i&H1, …, H, notation&Expressing the sum, Δ τ generally refers to the time delay interval, and τ is specified_i+1>τ_i、τ₁＝0、τ_i∈T_d1That is, the origin of the 1 st wavelet coincides with the origin of the symbol, and the origins of the other wavelets are all within the lifetime of the 1 st wavelet, allowing T_di≠T_dh,Δτ_i≠Δτ_hOr T_di＝T_dh＝T_dWhen equal, the subscript may be omitted, and when T ═ 2T_dOr T ═ 2T_dΔ τ, in general, taking T_di＝T_dj,Δτ_i＝Δτ_j，T＝2T_d(ii) a The time delay tau is required in the above formula_iThe use of (b) is specifically explained: definition of tau_iIs the time delay of a base wavelet from a symbol starting point, the time delay of a front information wave is the time delay of the base wavelet, but the time delay of a main wave should be larger than that of the front information wave, the time delay of a back information wave should be larger than that of the front main wave, so that three-section waveforms in the base wavelet should be expressed as

However, such representation is too complicated to read, and therefore, in the present invention, only the time delays between the fundamental waves are distinguished, the time delays of the fundamental waves for all three waveforms in the fundamental waves are not distinguished, and different time delays are distinguished by the sequential connection relationship, that is, the sequential connection relationship given by the symbol "|" of the vertical line in the above expression (1).

For ease of design, the respective regions of type 1 and type 2 waveletsThe same value is used for the interval, so the superscript 1\2, omega of the interval mark can be omitted_kThe angular frequency of main information wave representing wavelet and base wavelet and reference main wave, the wavelets with same angular frequency form a sub-channel in frequency domain, each sub-channel can be orthogonal or non-orthogonal in frequency domain, the same-frequency wavenumbers of sub-channels can be equal or not, and the angular frequency omega_kIs the center frequency of the K-th 1, …, K subchannels, i.e. K subchannels are formed in total; in the following description, the frequency of the information wave is the same as the frequency of the main wave, and the spectrum of the sub-channel is a composite of the information wave and the main wave spectrum; let L be the number of wavelets containing the same frequency in each subchannel_k，L_k＝L_jOr L_k≠L_j，k&j is 1, …, K, meaning that the co-channel sub-wave numbers contained in each sub-channel may be equal or unequal; angular frequency omega_kThe subscript k and the wavelet subscript i have the following relation: the same-frequency wavelet sub-sequence i of k-th sub-channel is L_k-1+1,…,L_k-1+L_kIn all the following descriptions, the subchannel indices will be used for the case where there are sub-composite waves

Or

Denotes k and i,

And

and

and

all of the same; the sending end type 1 wavelet shown in FIG. 1 has a pre-information wave interval T_θt11750, the front information wave is the expansion reserved interval T of the receiving end_θt1275 (meaning)The order of the filter is 75), the main wave interval T_θt214500, the main wave is the expansion reserved interval T of the receiving end_θt2275, the post-information wave interval T_θt31750, the post information wave is the expansion reserved interval T of the receiving end _θt3275, 2, 0.1, wavelet lifetime T_d1＝6225，ω ₁2 pi/750 x 6 x pi/4500 x 0.08378; the transmitting end type 2 wavelet shown in FIG. 2, the front master information wave interval T_θt112750, the front main information wave rear end moves to the section T of the copy part of the front information wave front end_θt11175, the front end of the front main information wave moves to the section T of the copy part of the rear end of the front information wave_θt11375, the front information wave is the expansion reserved interval T of the receiving end_θt12Main wave interval T75_θt24500, the main wave is the expansion reserved interval T of the receiving end_θt2275, the post-master information wave interval T_θt312When the post-main information wave front end moves to the section T of the copied part of the post-main information wave front end, 750_θt311When the post-main information wave front end moves to the section T of the copy part of the post-information wave rear end, 75_θt31375, the rear information wave is the expansion reserved interval T of the receiving end_θt32＝75，α＝2,β＝0.5，

Angular frequency omega of information wave and main wave ₁2 pi/750 2 x 8 x pi/4500 0.08378, wavelet lifetime T_d16225. In the present document, the specific values of the intervals in the various illustrations are represented by dimensionless sampling points, and the corresponding specific values of the frequencies are also calculated values using the points as time units, so that the calculated results can be easily converted into actual time or frequency values by a designer as long as the actual time units of the sampling intervals are given.

More specifically, 1\2 type waves of the transmitting end and the receiving end are represented as

At the transmitting end

The information wave and the main wave of the type 1 fundamental wave are represented as waveforms of expressions (1-1) and (1-2), respectively:

z(t_(1\3)2-τ_i)＝z(t₂₁-τ_i)＝0

the information wave and the main wave both include two intervals, interval T_θti(1\3)1And T_θti(1\3)2The interval T of the information wave and the main wave_θti(1\3)2And T_θti22The subscript (1\3) is used for distinguishing two abbreviated forms of intervals of front or rear information waves, but on a time axis, the two intervals are respectively distributed at the front end and the rear end of a main wave;

the type 2 fundamental wave information wave and the dominant wave are represented by waveforms of the formulae (1-3) and (1-4)

Scale formula (1-3-1) middle interval T_θti(1\3)12The waveform of (a) is a main information wave,

is sin omega_k(t_(1\3)12-τ_i) A replica of the waveform of the back end portion,

is sin omega_k(t_(1\3)12-τ_i) A replica of the waveform of the front-end portion,

is cos omega_k(t_(1\3)12-τ_i) A replica of the waveform of the back end portion,

is cos omega_k(t_(1\3)12-τ_i) A replica of the waveform to which the front portion corresponds, where T_θti(1\3)1＝T_θti(1\3)11+T_θti(1\3)12+T_θti(1\3)13The waveform of the front and back end parts is similar to the cyclic prefix in OFDM, except that in OFDM, only sin ω is used_k(t_(1\3)12-τ_i) And cos omega_k(t_(1\3)12-τ_i) The section width of the copied part is determined by the channel length, while in the present invention, the section width of the copied part is determined by the order TP of the equalization filter, T is a bidirectional copy in which the front end is copied to the back end and the back end is copied to the front end_θti(1\3)11＝T_θti(1\3)13＝TP/2；

z(t_(1\3)2-τ_i)＝z(t₂₂-τ_i) 0 represents T_θti(1\3)2And T_θti22The value of the waveform in the receiving end is 0, and a reserved interval is expanded for the receiving end;

at a transmitting end, a modulation process of a symbol waveform comprises: firstly, converting binary information into corresponding quantization amplitudes according to a general method of digital communication, sequentially endowing the quantization amplitudes to front and rear information waves of each base wavelet to form a type 1 wavelet or a type 2 wavelet of a transmitting end as described in the following formula (2),

in the formula (2), the reaction mixture is,

respectively the quantized amplitude of the preceding and following information waves,

y belongs to integer field, that is, the amplitude of front and back information wave can select one quantization amplitude from Y grades, which is a universal method in digital communication; note that the main wave in equation (2) is not given quantization amplitude, which indicates that only front and back information waves carry information in one wavelet, and the main wave does not carry information, so that the TFP-TDMC avoids the problem of error propagation in TDMC; alpha and beta are amplitude adjustment parameters which are fixed and unchangeable under the condition that the system operation environment is unchanged after the design is finished, and the designer performs certain adjustment only when needed; in order to improve the signal-to-noise ratio of the information wave, alpha is required to be more than or equal to 1, and only beta is required to be taken so that the amplitude of the main wave does not exceed the maximum value allowed by a system, under different conditions, the different values of alpha and beta are matched to bring larger difference of the power of the synthesized wave, a proper value is selected, alpha is taken as a larger value under the condition of not increasing the power, so that the signal-to-noise ratio of the information wave is increased, and an optimized value can be obtained through computer simulation; t is t_1\3∈T_θti(1\3)Is an abbreviated form, which indicates that different time variables belong to different intervals to indicate different positions of the front and back information waves on the time axis, and is used for indicating the position of the front and back information waves on the time axis

Indicating different quantized amplitudes of the front or back information waves;

further, the composite wave of the transmitting end is composed by selecting one of the following three methods to complete modulation: for convenience of description, in the following description of the three methods, similar symbols to those described above are used, and only symbols given special meanings are additionally described herein, and no special description follows the meaning described above;

the method comprises the following steps: direct addition modulation method based on type 1 wavelet

Specifically, the 1-type wavelets with different time delays are superposed to form a composite wave, as shown in the following formula

τ_i∈T_d1,τ₁0 means that all the H wavelets have their origins in the lifetime of the first wavelet and the time delay interval is equal to the information wave interval, i.e. Δ τ T_θti1＝T_θti3That means that all the information waves occupy the corresponding delay interval sections without overlapping each other, but there is a partial overlap between the information waves and the main wave and between the main wave and the main wave;

the expression of (2) is shown in the formula, and the corresponding basic wavelets are type 1 basic wavelets; as in the first transmit wave illustration of fig. 4: this is a superposition of 7 type 1 wavelets, only the three wavelets 1, 2 and 7 are shown in the figure, which are respectively indicated by solid lines, broken lines and dotted lines, and the information waves are not overlapped; for clarity of illustration, the lifetimes T of the 1 st wavelets are omitted_d16225, all wavelets α -2, β -0.1, a_i1 is ═ 1; the first transmission wave is referred to as equation (2-1).

The method 2 comprises the following steps: modulation method based on type 2 wavelet pair

The method is specifically divided into three steps:

the first step is as follows: constructing same-frequency sine-cosine wavelet pairs on the basis of formulas (1-3), (1-4) (1-3-1) and (1-4-1)

Scale formula (2-3-1) middle interval T_θti(1\3)12The waveform of (a) is a master information wave pair and orthogonal sine and cosine pairs,

is sin omega_k(t_(1\3)12-τ_i) A replica of the waveform of the back end portion,

is sin omega_k(t_(1\3)12-τ_i) A replica of the front-end portion waveform,

is cos omega_k(t_(1\3)12-τ_i) A replica of the waveform of the back end portion,

is cos omega_k(t_(1\3)12-τ_i) A replica of the front-end portion waveform; wherein T is_θti(1\3)1＝T_θti(1\3)11+T_θti(1\3)12+T_θti(1\3)13The partial waveform of the front end and the back end is similar to the cyclic prefix in OFDM, except that in OFDM, only sin omega is used_k(t_(1\3)12-τ_i) And cos omega_k(t_(1\3)12-τ_i) The section width of the copied part is determined by the channel length, while in the present invention, the section width of the copied part is determined by the order TP of the equalization filter, T is a bidirectional copy in which the front end is copied to the back end and the back end is copied to the front end_θti(1\3)11＝T_θti(1\3)13＝TP/2

The second step is that: constructing a type 2 sub-synthetic wave consisting of the same-frequency type 2 sub-wave pairs according to a time delay rule:

representing the lifetime of the first wavelet in the sub-composite wave, with a delay interval equal to the information wave pair interval, i.e.

The sub-synthetic waves all comprise wavelet angular frequencies omega_k；

Let K be 1, …, K then obtain K sub-composite waves of the formula (2-3-3), and all pairs of main information waves with the same time delay in the respective sub-composite waves are defined to be orthogonal in the frequency domain, i.e., for K, j be 1, …, K,

and

interval T_θti(1\3)12Are orthogonal.

The third step: composition type 2 synthetic wave:

the formula (2-3-4) is called as a second transmitting wave; fig. 5 and 6, where fig. 5 is a graphical illustration of a sine and cosine wave separated (not added together) representation of a wavelet pair in a second transmitted wave: the solid line in the figure represents sine wavelets, the dotted line represents cosine wavelets, and the parameter values of each interval are the same as the type 2 wavelets in FIG. 2; FIG. 6 is an illustration of a wavelet pair obtained by adding sine and cosine wavelets in a second transmitted wave, each interval having the same value of parameter as the type 2 wavelet in FIG. 2. The arrangement of wavelets given in the table below may help to understand method 2 more clearly:

the table merely gives an example of the positional relationship among wavelets for pairs of information waves of different frequency bands (note that this is only an example of the positional relationship and is not a description of the complete waveform), where

Representing a sine-cosine pair of information waves, the main pairs of information waves in all columns being orthogonal in frequency domain and superposed without delay, the pairs of information waves in a row in the transverse direction having the same frequency and being arranged in such a way that

Given the superposition of delays (which may actually allow different frequencies to be taken and do not require orthogonality, but are cumbersome to design).

The method 3 comprises the following steps: modulation method of packet delay double overlapping based on 1-type wavelet

The method is to compose a synthetic wave from wavelets of type 1, and to divide all wavelets into U groups, each group of wavelets being

The starting points of the wavelets in the u-th group are sequentially shifted by a time delay in the first previous information wave interval of the group

Referred to as intra-group delay, and further having an intra-group delay interval

Thereby making

The origin of the type 1 wavelet being in the front information wave interval T of the first wavelet of the group_tθi1With internal sequential time delay of one

Post-superposition, the individual information waves within a group being partially overlapping, whereupon

The front information wave of the 1-type wavelet occupies an interval of

This is also called information band, and the main wave and the post-information wave are overlapped and added in the same way, and the post-information wave occupies the interval

This constitutes the u-th composite wave, called the sub-composite wave, which is the first wave; defining interclass delay intervals

Then, each sub-synthesis is sequentially moved by an inter-group time delay interval and then added to form a symbol synthesis wave, which is the second time, the information wave bands of each sub-synthesis wave are not overlapped, but the main wave band is still partially overlapped; in methods 1 and 2, the time delay interval between the wavelets is greater than or equal to the information wave interval, i.e. τ_i+1-τ_i＝Δτ_i≥T_tθi(1\3)And for method 3, the sum U is determined at H>Under the condition of 1. the method comprises the following steps,

the following formula is a sub-composite wave formed by overlapping and adding information waves in the u group:

the corresponding wavelets have the same basic structure as equation (2), except that they follow the subscript

With variations, subscripts

Indicates the u in the group

The sign of the correlation of the individual wavelets,

is the number of sub-waves within a set,

is each wavelet lifetime of the u-th group, but the subscript u may distinguish the positional variation of the wavelet lifetimes of the different groups, T in width_d(u,1)＝T_dBut the position varies with U-1, …, U,

is at the position of

And U is 1, …, varying from U,

indicating that the range of action of the time variable is extended by a period of time longer than the wavelet lifetime

Time-shifting intervals for the information waves within the group and defining

Allow for

Or

In order to reduce the design complexity, the design is typically done in an equal manner,

an interval representing a front information wave of the first wavelet in the u-th group,

meaning that the start points of all wavelets belonging to the u-th group are in the interval

In the above, the superscript f corresponds to the meaning of the front information wave, and it is noted that here, in order not to make the subscript number too much, the subscript f is changed to the superscript f, Δ τ_u＝τ_u+1-τ_uThe time delay interval between groups is also the interval occupied by all information waves of the u-th group; the interval distribution position and the symmetry characteristic of the information waves before and after the wavelet structure are determined, and after the relative position between the current information waves is determined, the starting points of the information waves after all the wavelets in the group are naturally in the interval of the information waves after the first wavelet in the group; all the previous information waves in the group are in the first previous information wave interval and sequentially move by a time delay, and then the whole wavelet corresponding to the previous information wave complies with the time delay rule; the sub-composite wave thus composed is divided into three intervals: the first interval is

A partial overlap interval of the front information wave, which also includes a partial main wave component and is called as the overlap interval of the front information wave and marked as T_u1The second interval is the main wave overlapping region, denoted as T_u2And the third interval is

The post information wave part overlaps the interval, also includes part of main wave component, marked as T_u3；

Then, the sub-synthesized waveforms of all groups are sequentially shifted by a time delay tau_u(U-1, …, U) are added to form the final composite wave, as shown in the following equation

Based on the symmetry of the wave structure of the front and back information, the grouping of the wavelets will naturally result in the front and back informationThe same grouping of waves, so that the expressions (2-4-1) and (2-4-2) do not particularly use a representation for distinguishing between preceding and following information waves, H being the total wavenumber, where τ_uIs a group u delay, so that the information waves of the wavelets in each group have a delay in turn

Making the information waves in the u-th group partially overlapped, but the information waves between the groups are not overlapped, and only the main waves still keep partially overlapped; the formula (2-4-2) is called as a third transmitting wave; third transmission wave illustration as shown in fig. 7: two sets of overlapping information waves are shown, each set comprising 5 partially overlapping information waves, two adjacent sets of information waves do not overlap, only the information waves in the sets overlap, the time delay interval of the information waves in the sets is 150 points, the two sets of sub-waves have the same angular frequency omega_u1In practice, each group may have a different frequency, which is not clearly visible in the figure, the wavelets are not added up in order to make the wavelet distribution clearly visible in the figure, and only the first two groups are shown, and two groups of sub-composite waves may be arranged in the remaining interval, which are omitted for clarity of the drawing. For the above three methods, the symbol periods are T respectively₁、T₂、T₃。

At a receiving end, firstly, restoring the waveform subjected to channel distortion to be close to a transmitting waveform as much as possible or balancing the waveform to be a waveform suitable for demodulation through balancing; in general digital communication, equalization needs to follow the principle of obtaining the maximum signal-to-noise ratio of demodulation or the minimum distortion of a waveform, the invention allows the adoption of various existing equalization methods, but follows the principle of receiving the minimum distortion of the waveform or the most suitable demodulation of the waveform, the expanded width of an information wave is ensured not to exceed the wavelet interval, and the specific expanded width is determined by training; the specially proposed band-limited inverse filter equalization method of the present invention is an equalization method for achieving the above-mentioned purpose by controlling the parameters of the equalization filter.

Specifically, the mathematical expression of the band-limited inverse filtering equalization method is expressed as

HP(u)＝BP(u)/H(u) (3-1)

hp(t)＝IFFT[BP(u)/H(u)] (3-2)

Equations (3-1) and (3-2) are the frequency and time domain representations, respectively, of band-limited inverse filtering, where S_r(u)/H (u) represents inverse filtering, which has a certain ill-conditioned property, and the addition of the filter BP (u) effectively reduces the ill-conditioned property, u and t are frequency domain and time domain variables respectively,

and

representing equalized frequency-domain and time-domain waves, S_t(u) and s_t(t) symbol waveforms, S, representing frequency and time domain transmissions, respectively_r(u) and s_r(t) represents the received symbol waveform in frequency domain and time domain, respectively, H (u), and N (u) are the channel transfer function or channel model, low pass or band pass filter, and noise in frequency domain, respectively, h (t) and bp (t) are the channel impulse response and impulse response of band pass or low pass filter, respectively, in time domain, are the convolved symbols,

is a deconvolution symbol, [ N (u)/H (u)]BP (u) and

is a frequency domain time domain representation of the equalized noise term. The present invention requires the filter bp (u) to have symmetry, and requires the bandwidth of the filter to be smaller than the system-limited bandwidth to reduce the ill-conditioned nature of the inverse filtering, and does not limit other specific forms, such as the FIR or FIR filter, or other specially designed pulse or spectrum shaping filters, and also requires the filter to have symmetry, and the shaping filters are also called equalization filtering filters in the followingA machine; due to the band-limiting effect of the filter, so that s_r(t) relative to s_t(t) in the time domain, the spreading widths of the waveforms caused by them are collectively called shaping spreading or equalization spreading, for FIR filters, the shaping spreading is equal to the order of the filter, for specially designed filters the shaping width is determined by the design parameters, for convenience of description, this parameter is also called the order, denoted TP, as illustrated in fig. 3 for the wavelet of type 2 passing through a 75 th order filter: front end extended wave interval T of front information wave_θr1175, the former master information wave interval T_θr12750, the rear end of the front information wave is spread the wave interval T_θr1375, main interval T without expansion_θr214500, its extension interval T_θr2275, front end spreading wave section T of rear information wave_θr3175, the post-master information wave interval T_θr32750, rear end spreading wave section T of rear information wave_θr33Three spreading waveforms can be seen in three spreading intervals, called tail waveforms, α is 2, β is 0.5, a_i1, due to the trailing waveform, some high-frequency components are added in the side lobe of the wavelet spectrum, but the central angular frequency is not changed by omega_k＝2×6×π/4500＝0.08378；

After equalization, the corresponding base wavelet waveform and base wavelet of the receiving end

The equation (4-1) corresponds to the equation (1-1), and the difference is only that the reserved empty interval of each segment of waveform is occupied by the expanded trailing waveform, so that the waveform can only be an approximate sine/cosine wave, and correspondingly, the subscript t representing the transmitting end in the equation is changed into the subscript r representing the receiving end.

The information wave and the main wave of the type 1 fundamental wave are expressed by the formulas (4-1-1) and (4-1-2)

The information wave and the main wave of the type 2 fundamental wave are expressed by the formulas (4-1-3) and (4-1-4)

Wherein the content of the first and second substances,

and

are no longer partial replicas of sine and cosine waves, but instead are deformation waves with time delay spread of these replicas;

wherein the content of the first and second substances,

the corresponding wavelet is

A in the formula (4-2)_fiAnd a_aiIs the actual amplitude; the composite wave of a symbol at the receiving end is composed of wavelets shown in (4-2); specifically, for different transmitted symbol waveforms shown by the formulas (2-1), (2-3-4) and (2-4-2), corresponding different symbol composite wave waveform structures exist after equalization is performed on a receiving end, so that the following three demodulation methods are correspondingly adopted; the receiving waveforms of different structures are respectively as follows: compared with the transmitting wave, the subscript t is changed into r, and other marks have the same meaning;

the first method comprises the following steps: received waves corresponding to the first type of transmitted waves:

the corresponding wavelets and the fundamental waves are shown as formulas (4-2) and (4-1);

and the second method comprises the following steps: received wave corresponding to second transmitted wave

Wherein the content of the first and second substances,

and

no longer are partial replicas of sine and cosine waves, but instead are deformation waves with extended time delay of those replicas, with only intervals

The waveforms in (a) are orthogonal,

and

is the actual amplitude of the wavelet at the receiving end, sinceA certain difference is caused between the quantization amplitude and the noise and the balance error, and finally the quantization amplitude is classified into the corresponding quantization amplitude according to a certain principle (such as 4 SHE 5 input);

the main wave pair is changed into approximate sine wave and cosine wave with time delay expansion from sine wave and cosine wave

And the third is that: received wave corresponding to third transmitted wave

For the three received waveforms, there are three demodulation methods, which are respectively:

the method comprises the following steps: for coherent demodulation of the first received wave, specifically,

in the interval T_θri1And T_θri3Respectively performing operations in the following steps:

the expression (6-1-3) means that the main wave part which does not carry information is subtracted in the information wave interval, and only the information wave which carries information is left, wherein the mark x in the expressions (6-1-1) and (6-1-2) is a vector dot product;

when i is 1, …, H, the amplitude of the information wave before and after each wavelet corresponding to the symbol waveform can be obtained by repeating the equations (6-1-1) and (6-1-2), that is, the demodulation of the first type of received wave is completed;

the method 2 comprises the following steps: for the demodulation of the second type of received wave, the specific steps are as follows:

the first step is as follows: dividing the waveform of formula (4-3-1) into

Section, front

Each section interval in a section is T_rθi1After, after

Each section interval in a section is T_rθi3Wherein, the first

The waveform within a segment may be represented as

Is the corresponding dominant wave component;

the second step is that: subtracting the main wave component in (6-2-1)

Thus, in the formula (6-2-2)

Intermediate interval T of segment_rθi(1\3)2Is a combination of K orthogonal pairs of sine-cosine waves,

the third step: fast Fourier operation is performed on the waveform shown in the formula (6-2-2)

K front or back information wave amplitudes can be obtained

Superscripts f and a indicate the front or back information wave, respectively; order to

Repeating the formulas (6-2-1) to (6-2-3) to obtain all information wave amplitudes;

the method 3 comprises the following steps: for the packet demodulation of the third type of received wave, specifically, the following four steps are performed:

the first step is as follows: the received wave represented by the formula (5-3-1)

Carrying out segmentation interception to obtain waveforms of 2U groups of sections, wherein the front U group of sections comprises all front information waves and main wave components in corresponding intervals, and the rear U group of sections corresponds to all rear information waves and main wave components in corresponding intervals; each group of segment waveforms is expressed as follows

Wherein the superscript f \ a indicates the front or back information wave, T_ruThe interval representing the waveform of the u-th group of segments

The information wave interval before and after the wavelet is

The second step is that: in the interval

All main wave components are removed:

the third step: obtaining a demodulation equation set

In the intervalPerforming coherent operation as shown in the following formula:

order to

Repeating the formula (6-3-3) to obtain the coherent operation column vector

Further form a linear equation system

This is called the demodulation equation set, where

For the magnitude column vector to be solved,

in order to coherently operate on the column vectors,

in order to demodulate the matrix, the demodulation matrix,

the subscripts in the above formulas are all increased by u as group differences;

of a matrixThe element is obtained by coherent operation of the fundamental wave obtained by training and a part of waveforms corresponding to other fundamental waves in the interval; where, x is the vector point-by-sign, ω_kAnd ω_jIndicating that different information waves may have different angular frequencies, k&j＝1,…,K；。

The fourth step: solving the equation set shown in equation (6-3-4)

Obtaining amplitude vectors of the U-th group of front/back information waves, enabling U to be 1, … and U, and repeatedly performing the formulas (6-3-3) and (6-3-4) to obtain the amplitude vectors of the front/back information waves of all groups;

further, in order to implement demodulation, when the amplitude of information carried by a symbol waveform is solved, firstly, the correlation parameters of a fundamental wave required for demodulation and a demodulation matrix required for demodulation of a third received wave need to be obtained through training; specifically, the obtaining of the relevant parameters of the training base wavelet is obtained through band-limited inverse filtering training; meanwhile, because the same-frequency wavelets have the same training result, each subchannel only takes one base wavelet, and because the training is carried out on a single base wavelet, the time delay tau of each wavelet does not need to be considered_iThe subscripts i and k may be modified

And

or

And

the same applies to the following training steps;

the band-limited inverse filtering training is characterized in that:

(1) training for 1\2 type base wavelets: for K1, …, K, the following is done:

selecting a 1\2 type base wavelet from the k-th sub-channel

Let 1\2 type base wave

Is formulated as

Then in the interval

From

Is separated out

Rear information wave

And a reference main wave

t₂∈T_θrk2Three sections of waveforms are used for completing the training of a fundamental wave;

making K equal to 1, … and K, and repeating the first step to obtain the trained waveforms of the 1\2 type base wavelets of all the sub-channels;

(2) training of demodulation matrix required for demodulation of third received wave

The demodulation matrix in the rewritten equation (6-3-4) is as follows

And

the angular frequencies of the wavelets in the u-th group, i.e. different indices, to indicate the crossing between the information waves

As long as it is obtained

Can form a demodulation matrix to obtain

Is mainly to do

A about

The operation of (1); for this purpose, the following matrix is constructed

Elements in a matrix

Is that

To (1) a

And (4) sampling points, wherein 0 in the matrix is a time delay interval in the front of the wavelet, and in order to form the matrix, the tail part of the right side of each row needs to be correspondingly supplemented with 0.

Further, the band-limited filteringThe device BP (u) is designed according to the following principle: i. filter bandwidth W of the filter_bpW ≦ W, W is the symbol bandwidth, and W is_bp>>W_sc，W_scThe order TP of the filter determines the trailing length of an information wave, if the TP is large, the trailing is lengthened, the time delay interval is enlarged, the number of sub-waves in a symbol is reduced, and the transmission rate is influenced, so that the problem of engineering compromise is solved, and the optimal value can be selected through computer simulation.

The specific implementation method of the technical scheme of the invention comprises the following steps:

the technical principle and some key technologies of implementation of the present invention are further described below by taking an implementation of the TFP-TDMC for wireless broadband access as an example; the scheme mainly describes special technical problems in the implementation of the TFP-TDMC, and conventional technologies in digital communication are not explained in detail.

The following embodiments are all referenced to the 802.11a international standard. The following environmental parameters are specifically taken: when the channel bandwidth of 5MHz, the number of subcarriers is 52, the data carrier is 48, the OFDM symbol duration is 16 mus, the guard interval is 3.2 mus, the occupied bandwidth is 4.15MHz, the modulation method is 64QAM, and the highest transmission rate is 13.5 Mbps.

The first example is an explanation of an embodiment example of a second transmitting and receiving composite wave composed of type 2 wavelets:

1. the system gives the conditions:

system sampling rate f_s120 MHz; if the order of the equalization filter is 20, the total expansion point number of the waveform is 20 points, the corresponding time value of the total expansion tailing is 0.167us, the expansion point numbers at two ends are respectively 10 points, and the corresponding time values are respectively 0.083 us;

2. arrangement of wavelet intervals:

let the symbol period of OFDM be T_O＝T_O1+ CP is (16+3.2) ═ 19.2us, CP is cyclic prefix (or time isolation zone), the wavelet interval of TFP-TDMC:

T_d＝T_θ1+T_θ2+T_θ3＝T_O＝(16+3.2)＝19.2us

T_θ1＝T_θ11+T_θ12+T_θ13＝T_O/10＝1.92us

T_θ11+T_θ13＝0.167us,T_θ12＝1.92-0.167＝1.75us

wavelet lifetime T_d＝T_O，T_θ1、T_θ2、T_θ3The front information wave, the main wave and the back information wave are respectively intervals, the information wave interval is 1/10 of the OFDM symbol interval, T_θ1＝T_θ11+T_θ12+T_θ13＝T_O1.92us (/ 10 ═ T_θ11+T_θ130.167us is the extension interval),

3. the relationship between the coherent demodulation signal-to-noise ratio and the demodulation interval,

according to the literature, the relation between the signal-to-noise ratio of coherent demodulation and the demodulation interval and amplitude under the condition of narrow-band white noise can be formulated

Meaning that the signal-to-noise ratio SNR is proportional to the product of the interval and the amplitude. Thus, a wavelet (i.e., a sine or cosine wave) of OFDM is related to the coherent demodulation signal-to-noise ratio of an information wave of TFP-TDMC as follows:

there is the ratio of the coherent demodulation signal-to-noise ratio of OFDM and TPF-TDMC single wavelet

γ＝SNR_TPF/SNR_O＝T_θ12α²/T_O1＝0.109α² (7‐2)

Description of the drawings: t is_O1、T_θ12Respectively, OFDM and TPF-TDMC coherent demodulation interval, a_OAnd a_TFPRespectively OFDM wavelet and TPF-TDMC information wave amplitude, n₀Is the power spectral density, SNR, of the noise_OAnd SNR_TFPRespectively, the signal-to-noise ratio of OFDM and TPF-TDMC coherent demodulation; it can be seen that increasing T is required to improve the signal-to-noise ratio of TPF-TDMC coherent demodulation_θ12α²Or, when T is reduced_θ12The signal-to-noise ratio can be kept unchanged by increasing alpha.

4. Effect of alpha, beta on TFP-TDMC wavelet power and relation to OFDM wavelet power

Since the information wave and the main wave are both sine and cosine waves, and the amplitude of the wave is normalized to 1, the power of one wavelet is

Wherein, T_θ1、T_θ2、T_θ3、T_dThe intervals of the pre-information wave, the main wave, the post-information wave and the wavelet lifetime are respectively. The amplitude normalization value makes the OFDM wavelet power be

T_O＝T_dIs the symbol period and is also the interval occupied by the wavelet. Taking the sum of normalized values in amplitude_O＝T_dUnder the condition of (1), 1/10 indicating that the information wave interval is the OFDM symbol interval and the power of the two is equal, there are

Let T_θ1＝T_θ3＝T_O/10,T_θ2＝T_d-2T_θ1＝(4/5)T_OThen there is

0.2α²+0.8β²＝1 (7-4)

Since the main wave does not carry information and a high signal-to-noise ratio of the information wave is desired, the value of β is reduced while the value of α is increased. If γ of the formula (7-2) is 1, α is guaranteed²9.173, it can ensure that the information wave carries 3 bits as one sub-channel of OFDM; however, according to the formula (7-4), β²(1-1.83)/0.8, which results in β being an imaginary number; for this purpose, 0.2 α is used²<1，α²<5, e.g. by taking alpha²4.9, then beta²This corresponds to an amplitude reduction of about one time by 0.025, which reduces the number of carrying bits by 1, so that each information wave carries 2 bits and an information wave pair carries 4 bits.

4. Forming a second received wave

According to the above analysis, the following parameters were used:

(1) each section of the wavelet

T_d＝T_θ1+T_θ2+T_θ3＝T_O(16+3.2)＝19.2us

T_θ1＝T_θ11+T_θ12+T_θ13＝T_O/10＝1.92us

T_θ11+T_θ13＝0.167us,T_θ12＝1.92-0.167＝1.75us

Wherein, the main information wave interval is 1.6us, and the two ends of the main information wave interval are respectively added with a 0.083us interval and a 0.083us expansion interval for storing the copy waveform of sine and cosine, so that the information wave interval is T_θri1＝T_θri32.0332us, main wave interval T_θri2＝12.766us

(2) Amplitude parameter: alpha is alpha²4.9, β 0.05, information wave quantization width 2²The number of the grades is 4,

(3) construction of symbols

i. Number of wavelets N in a frequency band_w＝T_d/T_θ1-1-10-1-9; according to equation (7-3), the power of one wavelet of TFP-TDMC is equal to the power of one wavelet of OFDM (1/2 corresponding to the power of one subchannel), and thus the power of one band is equal to the power of 5 subchannels of OFDM;

number of bands: the condition is that the power of the TFP-TDMC and OFDM wavelet pair is equal; the condition that the OFDM comprises 52 sub-channels is regulated according to the design and the standard of the interval and the values of alpha and beta, corresponding to TFP-TDMC, the frequency range number is 52/5 and 10.4, and 10 frequency ranges are taken;

frequency arrangement of the center of each band:

the first frequency band has a central angular frequency of

The angular frequencies of the other frequency bands being 2 omega respectively₁,3ω₁,…,10ω₁

The configuration of the waveform: rewriting outputWave receiving formula

Wherein the content of the first and second substances,

5. demodulation (omit training and equalization)

The first step is as follows: subtracting the dominant wave component in the received wave:

the second step is that: performing fast Fourier operation

K front or back information wave amplitudes can be obtained

Superscripts f and a indicate the front or back information wave, respectively; order to

Repeating the first step and the second step to obtain all information wave amplitudes;

6. analysis of transmission rate and spectral efficiency

(1) TFP-TDMC: since the information wave pairs are densely populated in the composite wave, the transmission rate of one information wave pair interval is the transmission rate of the entire symbol. According to the analysis of wavelet power and signal-to-noise ratio of information wave, one information wave pair carries 4 bits, 40 bits in total are carried in 10 frequency bands, and the transmission rate R is (10 x 4 bits)/T_θ1＝40/1.92us＝20.83Mbps；

(2) OFDM: transmission rate of 13.5Mbps

(3) And (3) comparison: the transmission rate of the second received wave of the TFP-TDMC is 1.5 times that of OFDM.

(4) Analysis of spectral efficiency: OFDM occupies 52 sub-channels, while TFP-TDMC occupies only 10 sub-channels, so the spectral efficiency of TFP-TDMC is 7.8 times that of OFDM.

The second example is an implementation case of a third sending and receiving synthetic wave for the wavelet type 1 configuration:

the system setting conditions are the same as the first example described above.

1. Composition of synthetic wave

(1) Wavelet region:

(2) each interval in the composite wave

Time delay interval of information wave in group

Meaning that a group contains 100 wavelets, the inter-group delay interval Δ τ_u＝2×T _θri12 × 4 ═ 8us, the number of groups in one composite wave is 2;

(3) selection of values of α and β: for a single wavelet, the smaller beta is, the smaller the wavelet power is, but for different synthesized waves, because each wavelet has time delay, the larger alpha can be obtained under the condition of ensuring that the power of the synthesized wave is unchanged due to the fact that the values of alpha and beta and the positive and negative changes of the alpha and beta are different, so that the improvement of the signal-to-noise ratio of the information wave is facilitated, and the optimization in a certain degree can be obtained through computer simulation; to reduce space, the following gives a case: α -16 and β -12, the composite wave power is 51.854, the power of OFDM is 52;

then there are

Corresponding to 18 decibels of the audio signal,

in digital communication, for each 6 db improvement of the noise ratio, one bit is added, that is, the information wave of the TFP-TDMC can carry 2 more bits than one sine wave of the OFDM, and carries 5 bits in total, and then the transmission rate of 100 information waves is (5 × 100)/8 × 62.5Mbps, which is 4.6 times of the OFDM standard.

(4) With the interval, the values of alpha and beta and the number of bits carried by the information wave, a composite wave can be created according to the formulas (2-4-1) and (2-4-2);

2. analysis of transmission rate and spectral efficiency

The transmission rate of the third waveform of TFP-TDMC is (5 × 100)/8 ═ 62.5Mbps, which is 4.6 times that of the OFDM standard.

Spectral efficiency: if all wavelets are at the same frequency, the spectral zero bandwidth is 0.042MHz, the spectral efficiency is 62.5/0.042 ═ 1.5Mbps/Hz, and if 52 wavelets are at the same frequency, the spectral efficiency is 62.5/(0.042 × 52) ═ 28.8bps/Hz

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (3)

1. A time-delay multi-carrier modulation and demodulation method based on time-frequency pulse shaping is characterized in that:

at a sending end, binary information is converted into corresponding quantization amplitude and then sequentially given to a front information wave and a back information wave of a base wavelet to form corresponding wavelets, H wavelets are generated, all wavelet starting points are required to be placed in the survival period of the first wavelet, all wavelets are sequentially moved by different time delays from the starting point of a symbol waveform and then linearly superposed to form a synthetic wave, namely, a periodic symbol waveform with T as a period is formed to complete a modulation process, namely, the method of sequentially moving by one time delay and then linearly superposed is called as a time delay rule, different modulation methods have different time delay rules, and the difference is mainly expressed as different time delay intervals of adjacent wavelets; the fundamental wave is composed of waveforms corresponding to respective corresponding sections of a front information wave, a main wave and a rear information wave which are distributed in sequence, and the waveform structures of the front information wave and the rear information wave are consistent; the wavelets are waveform structures formed by respectively changing the amplitudes of the front information wave and the rear information wave of the fundamental wave so that the front information wave and the rear information wave respectively carry different binary information and the amplitude of the main wave is kept unchanged; front information wave of the fundamental waveThe sections corresponding to the main wave and the post information wave are respectively T_θ1、T_θ2And T_θ3Expressing that the three intervals are combined into a fundamental wavelet or a wavelet interval in turn, namely the life cycle of the fundamental wavelet/wavelet, and is marked as T_d，T_d＝T_θ1+T_θ2+T_θ3All intervals in the formula are half-open and half-closed intervals, the waveform corresponding to each base wavelet only exists in the life cycle corresponding to each base wavelet, and the base wavelets outside the life cycle are not defined or take the value of 0; the tokens associated with different fundamental wavelets are distinguished by the subscript i ═ 1, …, H, then T_diRepresents the lifetime of the ith base wavelet, such that T_di＝T_d(i+1)Or T_di≠T_d(i+1)Taking T_di＝T_d(i+1)＝T_dAnd T is_θi1、T_θi2、T_θi3Respectively representing the sections corresponding to the ith front information wave, the main wave and the back information wave; the symbol "\\" means "or";

more specifically, the fundamental waves are divided into two types, i.e., type 1 fundamental wave and type 2 fundamental wave, which are formulated as

The corresponding wavelets are classified into type 1 wavelets and type 2 wavelets, and are formulated as

Wherein the superscript 1\2 is used to distinguish type 1 basewaves or type 2 basewaves, where ω is_kRepresenting the angular frequency of the main wave of the wavelet and the fundamental wave, so that the wavelets with the same angular frequency form a sub-channel on the frequency domain, and the center frequency of each sub-channel is formed by the angular frequency omega of the main wave_kDetermining that K is 1, …, K, i.e. K subchannels are formed in total; and each sub-channel is not required to be orthogonal in frequency domain, so that the same-frequency wavelets contained in each sub-channel are equal or unequal, that is, if the wavelets with the same frequency contained in each sub-channel are denoted by L_kK1, …, K, allowing L_k＝L_k+1Or L_k≠L_k+1Angular frequency omega_kThe subscript k and the wavelet subscript i have the following relation: i.e. the wavelet index i of each k-th sub-channel is L_k-1+1,…,L_k-1+L_k；

The fundamental wave can be uniformly expressed by formula (1)

In the formula, the vertical line symbol "|" represents

And

three waveforms are connected in sequence, the interval corresponding to each waveform is a half-open half-close interval, subscripts 1, 2 and 3 of the three waveforms give the connection sequence on a time coordinate, namely the three waveforms are expressed by a formula

Representation of affiliation of time variables

So that the front and rear information waves are distinguished by subscripts f, a, respectively, i.e.

In the form of a front information wave,

in order to be the rear information wave,

for the reference dominant wave, i denotes the subscript, τ, of the different fundamental waves_iThe delay of the ith base wavelet relative to a symbol starting point is used for distinguishing various waves of a transmitting end and a receiving end by subscripts t and rThe shape and the time parameters of the shape and the time,

the interval representing the front information wave and the rear information wave is equal, and the width of the interval is taken according to the following principle: is provided with

c≤1，

Determining through computer simulation; delta tau_i＝τ_i+1-τ_iRepresenting the time delay interval between the (i + 1) th wavelet and the (i) th wavelet, and defining tau_i+1>τ_i，τ₁0 and τ_i∈T_d1That is, the starting point of the 1 st wavelet is coincident with the starting point of the symbol, and the starting points of other wavelets are all in the life cycle of the 1 st wavelet, allowing T_di≠T_dj,Δτ_i≠Δτ_jOr T_di＝T_dj,Δτ_i＝Δτ_j,i&j-1, …, H, notation&To indicate the sum, when taken equal, the subscripts are omitted and when T is 2T_dOr T ═ 2T_d- Δ τ, taking T_di＝T_dj,Δτ_i＝Δτ_j，T＝2T_d；

The performance of the base wavelet at the sending end and the receiving end is different, specifically:

at the transmitting end, the information wave and the main wave of the type 1 wavelet are embodied as waveforms of the following formulas (1-1) and (1-2): namely, it is

z(t_(1\3)2-τ_i)＝z(t₂₂-τ_i) 0 represents T_θti(1\3)2And T_θti22The value of the waveform in the receiving end is 0, and a reserved interval is expanded for the receiving end;

the information wave and the main wave both include two intervals, interval T_θti(1\3)1And T_θti(1\3)2The interval T of the information wave and the main wave_θti(1\3)2And T_θti22The subscript (1\3) is used for distinguishing two kinds of interval abbreviation forms of front or back information waves;

the type 2 fundamental wave information wave and the dominant wave are represented by waveforms of the following formulae (1-3) and (1-4):

scale formula (1-3-1) middle interval T_θti(1\3)12The waveform of (a) is a main information wave,

is sin omega_k(t_(1\3)12-τ_i) A replica of the waveform to which the trailing portion corresponds,

is sin omega_k(t_(1\3)12-τ_i) A replica of the waveform to which the front end portion corresponds,

is cos omega_k(t_(1\3)12-τ_i) A replica of the waveform to which the trailing portion corresponds,

is cos omega_k(t_(1\3)12-τ_i) A replica of the waveform to which the front portion corresponds, where T_θti(1\3)1＝T_θti(1\3)11+T_θti(1\3)12+T_θti(1\3)13，T_θti(1\3)11＝T_θti(1\3)13＝TP/2；

z(t_(1\3)2-τ_i)＝z(t₂₂-τ_i) 0 represents T_θti(1\3)2And T_θti22The value of the waveform in the equalization filter is 0, the reserved interval is expanded for a receiving end, and TP is the order of the equalization filter;

ω in the above formula_kThe wavelets with the same angular frequency form a sub-channel on a frequency domain, each sub-channel is orthogonal or non-orthogonal on the frequency domain, so that the same frequency sub-wave number contained in each sub-channel is equal or not, wherein the central frequency of the kth sub-channel is formed by the angular frequency omega_kDeciding that K subchannels are formed in total;

at the receiving end, the received base wavelet is represented as

Wherein the information wave and the main wave of the type 1 fundamental wave are expressed as the following formulas (1-5-1) and (1-5-2), respectively:

wherein, the information wave and the main wave of the type 2 fundamental wave are expressed as the formulas (1-5-3) and (1-5-4) respectively

Wherein the content of the first and second substances,

scale formula (1-5-5) middle interval T_θri(1\3)12The waveform of (a) is a main information wave,

is that

The spread wave of (a) is generated,

is that

The spread wave of (a) is generated,

is that

The spread wave of (a) is generated,

is that

The spreading wave of (1).

2. The time-frequency pulse shaping-based time-delay multi-carrier modulation and demodulation method according to claim 1, characterized in that:

in the modulation process of the transmitting end, firstly, binary information is converted into corresponding quantization amplitudes according to a general method of digital communication, each quantization amplitude is sequentially given to a front pulse information wave and a rear pulse information wave of each base wavelet, so as to form 1 type wavelets or 2 type wavelets of the transmitting end as shown in the following formula (2),

in the formula (2), the reaction mixture is,

the information pulse amplitude quantization method comprises the steps that quantization amplitudes corresponding to front or rear information waves are respectively, Y belongs to an integer field, and Z is a quantization amplitude level number, namely the amplitude of front and rear information pulses can select one quantization amplitude from Y levels; alpha and beta are amplitude adjustment parameters, and alpha is taken>1, the value of beta only needs to ensure that the dominant wave amplitude does not exceed the allowable value of the system, the specific values of alpha and beta are relatively unchanged, and the values are changed only when the working state of the system needs to be adjusted, and are generally determined by computer simulation;

specifically, the modulation process at the transmitting end adopts any one of the following three methods:

the method comprises the following steps: modulation method based on type 1 wavelet direct addition

Specifically, the 1-type wavelets are superimposed according to a time-delay rule to form a synthetic wave, as shown in the following formula

τ_i∈T_d1,τ₁0 means that all the H wavelets have their origins in the lifetime of the first wavelet and the time delay interval is equal to the information wave interval, i.e. Δ τ T_θti1＝T_θti3,H＝(T_di-T_θti3)/T_θti1(ii) a The formula (2-1) is called a first transmission wave;

the expression of (2) is shown in the formula, and the corresponding basic wavelets are type 1 basic wavelets;

the method 2 comprises the following steps: modulation method based on type 2 wavelet pair

The method is specifically divided into three steps:

the first step is as follows: constructing same-frequency sine-cosine wavelet pairs on the basis of formulas (1-3), (1-4), (1-3-1) and (1-4-1)

Scale formula (2-3-1) middle interval T_θti(1\3)12The inner waveform is the master information wave pair,

is sin omega_k(t_(1\3)12-τ_i) A replica of the waveform of the back end portion,

is sin omega_k(t_(1\3)12-τ_i) A replica of the front-end portion waveform,

is cos omega_k(t_(1\3)12-τ_i) A replica of the waveform of the back end portion,

is cos omega_k(t_(1\3)12-τ_i) A replica of the front-end portion waveform; wherein, in the interval T_θti(1\3)12The main information wave pair in the system is a same-frequency sine and cosine orthogonal wavelet pair;

the second step is that: constructing a type 2 sub-synthetic wave consisting of the same-frequency type 2 sub-wave pairs according to a time delay rule:

representing the lifetime of the first wavelet in the sub-composite wave, with a delay interval equal to the information wave pair interval, i.e.

The sub-synthetic waves all comprise wavelet angular frequencies omega_k(ii) a Let K be 1, …, K then obtain K sub-composite waves of the formula (2-3-3), which defines that all pairs of sub-information waves with the same time delay in different sub-composite waves are orthogonal in the frequency domain, i.e., for K, j be 1, …, K,

and

the pair of master information waves contained in (1) is orthogonal;

the third step: composition type 2 synthetic wave:

the formula (2-3-4) is called as a second transmitting wave;

the method 3 comprises the following steps: modulation method of packet delay double overlapping based on 1-type wavelet

The method is to form a synthetic wave from wavelets of type 1, and specifically, to divide all wavelets into groups of U1, …, U, where each group of wavelets is

The starting points of the wavelets in the u-th group are sequentially shifted by a time delay in the first previous information wave interval of the group

Balance

The time delay in the group of the ith wavelet in the u group is called

Is an inter-group delay interval, thereby

The origin of the wavelets of type 1 being in the front information wave interval T of the first wavelet of the group_tθi1Therein is thus

The information wave of the 1-type wavelet occupies an interval of

The wave is called an information wave band, and meanwhile, the main wave and the post information wave are overlapped and added according to the same time delay rule, so that a u-th combined wave is formed, which is called a sub-combined wave and is the first wave; provision for

The sub-combinations are sequentially separated for the time delay interval between groups

Moving a time delay and adding them to form a composite wave of symbols, this being the second term

Group delay, and make the information bands of the sub-composite waves not overlap, but make the main band still partially overlap, and the inter-group delay interval

The following formula is a sub-composite wave formed by overlapping and adding the time delays of the wavelets in the u group:

the corresponding wavelet has the same basic structure as the wavelet in equation (2-1) except that it follows the subscript

With variations, subscripts

Indicates the u in the group

The sign of the correlation of the individual wavelets,

the wavenumbers within a group are equal in width for different groups of wavelet lifetimes, but the position of the wavenumbers in different groups varies with the subscript U1, …, U, i.e., U

Is at the position of

And U is 1, …, varying from U,

is the u-th group

The time delay of the individual wavelets is,

an interval representing a front information wave of the first wavelet in the u-th group,

means that all the information wave origins of the wavelets belonging to the u-th group are in the interval

In the interior of said container body,

will represent subscripts of the front information wave_fIs changed into a superscript_fAnd specify

Recording the time shift interval of information wave in the u-th group

And stipulate

Indicating equal spacing of information waves within a group, then

The section of the u-th group of the sub-synthetic waves; the symmetry characteristics of the information wave before and after the base wave structure are determined, and the description is simultaneously suitable for the information wave after the base wave structure; the start of the information waves after all wavelets in the set also being in the interval of the information waves after the first wavelet in the set

And

respectively representing the intervals of the first sub-wavefront information wave and the rear information wave in the group, and the superscripts f and a respectively correspond to the meanings of the front information wave and the rear information wave; each sub-composite wave is divided into three intervals: the first interval is

A front information wave time delay overlapping interval, which also contains part of main wave components and is called front information wave overlapping interval and marked as T_u1The second interval is the main wave overlapping region, denoted as T_u2And the third interval is

The post-information wave time delay overlapping interval also contains partial main wave component, which is marked as T_u3；

Then, the sub-synthesized waveforms of all groups are separated in sequence

Moving one delay by one delay and adding them together to form the final composite wave, as shown in the following formula

The formula (2-4-2) is called as a third transmitting wave; the periods of the above three transmission waves are respectively T₁、T₂And T₃Represents;

after the transmission wave passes through the channel, the waveform will change, and after proper equalization, the waveform is specifically represented as:

corresponding to three kinds of transmission waves transmitted by the transmitting end, there are three kinds of reception waves after the receiving end is equalized:

the first method comprises the following steps: received waves corresponding to the first type of transmitted waves:

the corresponding wavelet:

wherein, a_fi\a_aiα is the actual amplitude of the preceding or following information wave;

and the second method comprises the following steps: received wave corresponding to second transmitted wave

And

all are deformation waves with time delay expansion,

and

is the actual amplitude of the wavelet at the receiving end;

and the third is that: received wave corresponding to third transmitted wave

Wherein, the sub-synthetic wave:

the corresponding wavelet has the same basic structure as equation (4-2), but the range of the time quantum varies with the change of the subscript.

3. The time-frequency pulse shaping-based time-delay multi-carrier modulation and demodulation method according to claim 2, characterized in that:

there are corresponding respective demodulation methods for the three received waveforms: namely, it is

The method comprises the following steps: for coherent demodulation of the first received wave, specifically,

in the interval T_θri1And T_θri3Respectively performing operations in the following steps:

wherein the content of the first and second substances,

in the formulae (5-1-1) and (5-1-2), the notation x is a vector dot product; wherein

The main wave component in the interval is obtained;

repeating the equations (5-1-1) and (5-1-2) for i, j ∈ {1, …, H }, and obtaining the amplitude of the information wave before and after each wavelet corresponding to the symbol waveform, thereby completing demodulation of the first type of received wave;

the method 2 comprises the following steps: for the demodulation of the second type of received wave, the specific steps are as follows:

the first step is as follows: dividing the waveform of formula (4-3-1) into

Section, front

Each section interval in a section is T_rθi1After, after

Each section interval in a section is T_rθi3Wherein, the first

The waveform within a segment may be represented as

Is the corresponding dominant wave component;

the second step is that: subtracting the main wave component in (5-2-1)

Thus, in the formula (5-2-2)

Intermediate interval T of segment_rθi(1\3)2Is a combination of K orthogonal pairs of sine-cosine waves,

the third step: fast Fourier operation is performed on the waveform shown in the formula (5-2-2)

Repeating the formula (5-2-3) for K equal to 1, … to obtain K front or back information wave amplitudes

Superscripts f and a indicate the front or back information wave, respectively; order to

Repeating the formulas (5-2-1) to (5-2-3) to obtain all information wave amplitudes;

the method 3 comprises the following steps: for the packet demodulation of the third type of received wave, the following four steps are specifically performed:

the first step is as follows: the received wave represented by the formula (4-4-1)

Carrying out segmentation interception to obtain waveforms of 2U groups, namely waveforms of front U groups and rear U groups, wherein the front U groups comprise all front information waves and main waves in corresponding intervals, and the rear U groups correspond to all rear information waves and main waves in corresponding intervals; each group of segment waveforms is expressed as follows

Wherein the superscript f \ a represents the front or rear information wave, T_ruThe interval representing the waveform of the u-th group of segments

The information wave interval before and after the wavelet is

The second step is that: in the interval

All main wave components are removed:

the action interval representing the time variable is in the front information wave interval of the u group section;

the third step: obtaining a demodulation equation set

In the interval

Performing coherent operation as shown in the following formula:

order to

Repeating the formula (5-3-3) to obtain the column vector related to the coherent operation of the front information wave

Further forming a linear system of equations for the front information wave

This is called the demodulation equation set for the front information wave, where,

for the magnitude column vector to be solved,

in order to coherently operate on the column vectors,

in order to demodulate the matrix, the demodulation matrix,

according to the symmetry of the front and rear information waves, the formula (5-3-3) is changed into:

order to

Repeating the formula (5-3-5) to obtain the column vector related to the post-information wave coherent operation

Further form a linear equation system

Wherein the content of the first and second substances,

for the magnitude column vector to be solved,

in order to coherently operate on the column vectors,

in order to demodulate the matrix, the demodulation matrix,

obtaining a demodulation equation set related to the post information wave; the combined writing of formulae (5-3-4) and (5-3-6) is:

the subscripts in the above formulas are each increased by u as a group difference,

and ω_jIndicating that different information waves may have different angular frequencies, k&j＝1,…,K；

The elements of the matrix are obtained by training and are obtained by carrying out coherent operation on the fundamental wave and a part of waveforms corresponding to all fundamental waves including the fundamental wave in the interval; wherein, x is a vector point-by-symbol;

the fourth step: solving the system of equations shown in equation (5-3-7)

Obtaining the amplitude vectors of all the front and back information waves of the u-th group;

let U be 1, …, U, repeat the magnitude vector of the preceding and following information waves of all groups.

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