CN104734814B

CN104734814B - A kind of LDPC codings and interpretation method suitable for non-coherent ultra-broad band communication system

Info

Publication number: CN104734814B
Application number: CN201510145176.0A
Authority: CN
Inventors: 梁中华; 臧俊杉; 刘瑾瑾; 李培培
Original assignee: Changan University
Current assignee: Changan University
Priority date: 2015-03-30
Filing date: 2015-03-30
Publication date: 2018-03-13
Anticipated expiration: 2035-03-30
Also published as: CN104734814A

Abstract

The invention discloses a kind of LDPC codings and interpretation method suitable for non-coherent ultra-broad band communication system, it is related to non-coherent ultra-broad band (UWB) communications field, is based particularly on the incoherent UWB communication systems of transmission reference pulse cluster (TRPC).The building method of two kinds of LDPC codes is used in the system by the inventive method, and LDPC code is decoded using BP algorithm, and prior probability need to be tried to achieve for the characteristic of channel using the algorithm.The inventive method is directed to the characteristic of channel of TRPC systems, and channel noise variance is solved using sample value in actual emulation.Simulation result shows, the long convolution code-phase ratio of RS codes, the long convolutional code of system and nonsystematic that the present invention uses at present with non-coherent ultra-broad band communication system, can obtain better performance.

Description

A kind of LDPC codings and interpretation method suitable for non-coherent ultra-broad band communication system

Technical field

The invention belongs to non-coherent ultra-broad band wireless communication technology field, is related to based on the incoherent of transmission reference pulse cluster Channel coding method in ultra-wideband communication system, and in particular to a kind of LDPC suitable for non-coherent ultra-broad band communication system is compiled Code and interpretation method.

Background technology

With the development of radio communication and network technology, merge, ultra wide band (Ultra-wideband, UWB) technology is with low The features such as cost, low-power consumption and good time domain resolution capability, turns into a kind of short-distance wireless communication solution.IEEE 802.15.4a standard uses the UWB schemes based on impulse radio (Impulse radio, IR) standard.IR-UWB systems possess Accurate positioning performance, but it still suffers from the huge challenge of the actual requirements such as low cost, low-power consumption.Therefore, in low bit- rate Occasion, more be using complexity it is relatively low, it is less demanding to sampling rate and do not need channel estimation noncoherent receiver. Wherein, using transmission with reference to (Transmitter Reference, TR) technology autocorrelation receiver due to its is simple in construction, Received much concern without the features such as precisely synchronization and channel estimation, Robust Performance.But TR-UWB systems are carrying out auto-correlation reception When in order to avoid inter-pulse interference caused by multi-path delay spread (Inter-pulse Interference, IPI) is, it is necessary to introduce Long delay line isolates reference pulse and data pulse, and this is for current technical merit to be infeasible.

The it is proposed of reference pulse cluster (Transmitter Reference pulse cluster, the TRPC) system of transmission is just It is to solve the problems, such as the long delay line in TR systems.The reference pulse of TRPC signals and data pulse have more unified, tight The structure gathered.With less delay T between reference pulse and data pulse_dOrder is sent, and the minimum delay is exactly a pulse Width T_p, i.e. T_d=T_p.One reference pulse and a data pulse form a pulse pair, and each pulse is to 2T_dBetween second Sent every repetition.

In TRPC systems, if it is difficult to provide preferable bit error rate performance that signal, which directly transmits, therefore carry out before sending Channel coding improves systematic function.Coded system specified in IEEE 802.15.4a standards is RS codes, but in practice also In the presence of some codes more more preferable than RS code performance, the long convolutional code of such as system, the long convolutional code of nonsystematic.

In recent years, LDPC code is because it is close to the superperformance of shannon limit and as the focus of theoretical circles research.20 The sixties in century, LDPC code are not affected by attention due to being limited by hardware condition, and nowadays LDPC code has obtained widely should With wherein being no lack of the application in communication system coding and decoding and high code check UWB.However, want LDPC code being applied to incoherent In TRPC-UWB systems, there is a problem in that：1st, the parity matrix how to have constructed, avoid becate and ensure submatrix Nonsingularity, be compiled code so as to obtain generator matrix；When the 2nd, entering row decoding using BP algorithm, the priori of known channel is needed Probability.3rd, the prior probability of channel is required, also needs the variance of known multipath channel noise.

The content of the invention

It is an object of the invention to which the more preferable LDPC code of performance is used in non-coherent ultra-broad band communication system, solves LDPC Code is during the System build code the problem of, it is proposed that a kind of LDPC suitable for non-coherent ultra-broad band communication system encode and Interpretation method.

To reach above-mentioned purpose, present invention employs following technical scheme：

Comprise the following steps：

1) channel coding, is carried out to signal to be sent using LDPC code, obtains sending signal；

2), signal to be sent is transmitted by UWB channels；

3), receiving terminal receives signal to be sent, and the signal to be sent to receiving is filtered, and obtains reception signal；

4) row decoding, is entered to reception signal using BP algorithm in receiving terminal, calculates the parameters needed for decoding, obtains institute The reception signal needed.

Step (1) detailed process is：

1.1) it is N, to set signal to be sent_fIndividual compact arranged pulse is to composition, and each pulse is to including a ginseng Pulse and a data pulse are examined, according to delay T_dOrder is sent.It is in the transmission signal of transmitting terminal generation：

Wherein, E_bThe emitted energy per bit is represented, N represents the bit number of codeword data bag, N_fRepresent each symbol middle arteries The number to repeating is rushed, g (t) represents energy normalized ultra-wideband pulse, b_n(i) ∈ { ± 1 } is the binary data symbol of transmitting Number, T_SFor symbol period, T_pFor pulse width, m is nonnegative integer, and t is continuous time variable, s_i(t) it is defined as：

1.2) QC-LDPC codes (N, j, k), are constructed using cyclic shift matrices, N represents code length, and j represents row weight, and k represents row Weight.Index matrix P is provided first：

Wherein, P is the index matrix that a dimension is j × k, wherein 0≤s≤j-1,0≤t≤k-1 and a, b are prime numbers, j Less than k；The value of each element in index matrix represents the digit that the submatrix of check matrix moves right；

Check matrix H is：

H dimension is jM × kM, and M=N/k represents the dimension of submatrix；

1.3) H is expressed as form：

H=[A B] (5)

Wherein A is the square formation that dimension is jM × jM, and B dimension is jM × (k-j) M；Then generator matrix G：

G=[(A^-1·B)^T I] (6)

Wherein, square formation A is nonsingular matrix.

1.4), according to generator matrix G, signal to be sent is encoded, generation sends signal.

The square formation A building methods are：

2.1), change index matrix P, obtain new index matrix P₁：

2.2), in the matrix, what z was represented is null matrix, and corresponding check matrix is expressed as：

From H₁In can obtain A₁

Pass through this change, A₁It is nonsingular.

The square formation A building methods are：

3.1), first in exchange equation (5) H each row, make A diagonal entry all 1；

3.2), when switching matrix H row, matrix column weight and ring property keep constant；

3.3) line translation, is entered to switching matrix H：

The first step：From the 1st row to jth M rows, the element 1 below square formation A diagonal is replaced with 0, while check square formation A It is whether nonsingular；If not nonsingular, then repeat the step, until A is nonsingular；

Second step：Generator matrix is obtained from square formation A.

The step 3) concretely comprises the following steps：

In TRPC systems, signal it is encoded and by UWB channels and wave filter after, the signal received is：

Wherein, * represents linear convolution, and n (t) represents additive white Gaussian noise, in IEEE802.15.4a standards, multipath Channel impulse response is expressed as：

Wherein, α_kAnd τ_kThe multiple fading coefficients of K roads multipath component are represented respectively and are reached is delayed；In order to ensure not according with Disturbed between number, it is assumed that T_S≥2N_fT_d+τ_max, wherein τ_maxRepresent the maximum delay of channel.

The step 4) concretely comprises the following steps：

4.1), receiving terminal carries out auto-correlation, obtained judgment variables y to the signal received and the Td delays of itself (i) it is expressed as：

Wherein, T₁And T₂The starting point and terminal in autocorrelation integral section, () are represented respectively^*Represent the conjugation fortune of plural number Calculate；

4.2) prior probability, is obtained, and row decoding is entered using BP algorithm to judgment variables y (i) according to prior probability.

Obtain prior probability and specifically include following steps：

5.1), if x is stochastic variable caused by equiprobability, then be can obtain by Bayesian formula：

Wherein, u₀The transmission represented as " 0 " when bit, u₁Represent be send be " 1 " when bit, y representative be to connect The information bit received.P (y/x=u₁) what is represented is when the information sent is u₁When receive y probability, x is that equiprobability produces Stochastic variable；

5.2) u, is set₀Represent value after bit " 0 " is by the channel that removes noise, u₁What is represented is bit " 1 " by this Value after channel；Y is the value received in real system by channel；Then formula (13) is：

Define p (y/x=u₁)=p₁, can be obtained by abbreviation (14)：

5.3) after, being initialized with prior probability, enter row decoding according to BP algorithm, obtain u₀, u₁, variance δ²Depend on The characteristic of channel, it can be worth to by sample.

Compared with the prior art, the invention has the advantages that：

The present invention is directed to the channel coding problem of TRPC-UWB systems, proposes that one kind is applied to non-coherent ultra-broad band communication system The LDPC codings and interpretation method of system.The building method of two kinds of LDPC codes is used in TRPC systems by the inventive method first, so Prior probability is obtained for the characteristic of channel afterwards, also tries to achieve the variance of interchannel noise.Required by more than, carried out using BP algorithm Decoding.Also by the TRPC systems of LDPC codings with being entered using the system of RS codes, the long convolutional code of system and the long convolutional code of nonsystematic Row contrast, draw the system encoded using LDPC code than there is more preferable error code using the system of other existing coded systems Energy.It can be seen that the present invention can be very good to improve the performance of TRPC systems.

Brief description of the drawings

Fig. 1 is the system model applied in the present invention；

Fig. 2 be in the present invention using the TRPC systems of two kinds of LDPC codes with uncoded TRPC systems under the environment of channel 1 Performance comparison figure；

Fig. 3 be in the present invention using the TRPC systems of two kinds of LDPC codes with uncoded TRPC systems under the environment of channel 8 Performance comparison figure；

Fig. 4 is with being grown using RS codes, the long convolutional code of system and nonsystematic in the present invention using the TRPC systems of LDPC code Performance comparison figure of the TRPC systems of convolutional code under the environment of channel 1；

Fig. 5 is with being grown using RS codes, the long convolutional code of system and nonsystematic in the present invention using the TRPC systems of LDPC code Performance comparison figure of the TRPC systems of convolutional code under the environment of channel 8；

Fig. 6 is FB(flow block) of the present invention.

Embodiment

The present invention is described in further detail below in conjunction with the accompanying drawings：

As a shown in Figure 6, application scenarios are given in exemplary Fig. 1, suitable for non-coherent ultra-broad band communication system LDPC is encoded and interpretation method, specifically includes following steps：

Uncoded system is difficult to provide preferable bit error rate performance, and systematic function can be improved using channel coding.Although IEEE 802.15.4a standards define the coded systems such as RS codes, concatenated code, but still have the more preferable code of some performances, such as The long convolutional code of system, the long convolutional code of nonsystematic etc..It is a kind of ideal good code of performance close to shannon limit in view of LDPC code, in recent years All it is applied come many fields in ultra-wideband communications.Therefore use LDPC code as TRPC systems channel coding method with Obtain better performance.

1.2), to improve the becate in the performance of LDPC code reduction check matrix factor figure, using cyclic shift matrices structure QC-LDPC codes (N, j, k) are made, N represents code length, and j represents row weight, and k represents row weight, provides index matrix P first：

Check matrix H is：

H dimension is jM × kM, and M=N/k represents the dimension of submatrix；

1.3) H is expressed as form：

H=[A B] (5)

Wherein, A is the square formation that dimension is jM × jM, and B dimension is jM × (k-j) M；Then generator matrix G：

G=[(A^-1·B)^T I] (6)

Wherein, square formation A is nonsingular matrix.The check matrix of this method construct, both without Fourth Ring or without six rings.But It is that in practice, it is A nonsingular that the QC-LDPC codes of this method construct, which do not ensure that, generator matrix also can not be by upper The method of stating obtains.

In TRPC systems, n information packet can be expressed as： Encoded before the data are sent using LDPC code.The generator matrix of LDPC code known to needing is encoded, and generator matrix is by strange Even parity check matrix is transformed, and in the case of known (4), can obtain generator matrix using (5).The main step of LDPC code coding Suddenly it is the parity matrix constructed, generator matrix and can be obtained and avoid becate.

Parity matrix is constructed such as shown in (4) using index matrix (3).To ensure the non-strange of (5) formula neutron matrix A The opposite sex, two methods is employed again check matrix is transformed.First method is to change index matrix such as (7) formula, accordingly Check matrix such as (8) formula ensure to can obtain generator matrix.By entering row-column transform to (5) formula, then second method is Element 1 by being about to below A diagonal replaces with 0, progressively judges whether A is nonsingular, is compiled so as to obtain generator matrix Code.Corresponding export is after being encoded by LDPC：

Here is the two methods being changed to the check matrix, it is therefore an objective to which it is nonsingular to make A, then can be given birth to Code is compiled into matrix G.

First method：

2.1), change index matrix P, obtain new index matrix P₁：

From H₁In obtain A₁

Pass through this change, A₁It is nonsingular, then can obtains generator matrix.The check matrix of this method design No Fourth Ring can be ensured, but still suffer from six rings.

Second method：

3.1), first in exchange equation (6) H each row, make A diagonal entry all 1；

3.3) line translation, is entered to switching matrix H：

Second step：Generator matrix is obtained from square formation A.

In second method, due to being the row of switching matrix and replacing the element 1 in matrix, do not change ring property, Therefore six rings are not present in the check matrix for making to design in this way.

2), signal to be sent is transmitted by UWB channels；After being launched by emitter, it is changed intoSpecifically Shown in expression formula such as formula (1).

3), receiving terminal receives signal to be sent, and the signal to be transmitted to receiving is filtered, and obtains reception signal；

The step 4) concretely comprises the following steps：

Obtain prior probability and specifically include following steps：

Define p (y/x=u₁)=p₁, can be obtained by abbreviation (14)

The algorithm needs the prior probability of known channel, and prior probability formulation process is shown in formula (13)-(16).It can be seen that will Channel noise variance need to first be tried to achieve by obtaining prior probability.Due to actual derivation need to consider the auto-correlation of random signal with mutually Pass acts on, and therefore, it is difficult to draw the complete expression of noise variance, but can be obtained from sample value.In the system of reality In, establish a noisy template and a mould for removing noise using IEEE 802.15.4a channel model standardization programs Plate, then allow a training symbol respectively can be with for calculating noise variance δ by the two templates, resulting value².For Make desired value that there is generality, different number averageds is respectively adopted, such as 100 times, 1000 times or 10000 times, imitative Just close to optimum performance when finding to be averaging for 1000 times during true, therefore choose 1000 times and average to reach good effect Fruit.

The simulation process of the present invention is carried out under channel 1 and the environment of channel 8 respectively.It is illustrated in figure 2 and uses two methods Construct performance comparison analogous diagram of the TRPC systems of LDPC code under the environment of channel 1.It is illustrated in figure 3 and is constructed using two methods Performance comparison analogous diagram of the TRPC systems of LDPC code under the environment of channel 8.The figure of the above two has been carried out pair with uncoded system Than, from simulation curve, the system encoded using LDPC code has larger performance improvement than uncoded system, and using second The system of kind method construct LDPC code using the system of first method than having better performance.Fig. 4 and Fig. 5 is to use first The system of kind method construct LDPC code is with the system using RS codes, the long convolutional code of system and the long convolutional code of nonsystematic in channel 1 With the performance comparison figure of channel 8.The system of LDPC code coding has best performance as seen from the figure.

TRPC-UWB systems described above are only the preferred embodiment of the incoherent UWB communication systems of the present invention, not For limiting the present invention, for those skilled in the art, the present invention can have various modifications and variations, and this method can use In other incoherent UWB communication systems, such as TR systems, NC-PPM systems etc..Within the spirit and principles of the invention, institute Any modification, equivalent substitution and improvements of work etc., should be included in the scope of the protection.

Claims

1. a kind of LDPC codings and interpretation method suitable for non-coherent ultra-broad band communication system, it is characterised in that including following Step：

2), signal to be sent is transmitted by UWB channels；

4) row decoding, is entered to reception signal using BP algorithm in receiving terminal, the parameters needed for decoding are calculated, required for acquisition Reception signal, concretely comprise the following steps：

4.1), receiving terminal is to the signal and the T of itself that receive_dDelay carries out auto-correlation, and obtained judgment variables y (i) is represented For：

<mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mo>&Integral;</mo> <mrow> <msub> <mi>iT</mi> <mi>S</mi> </msub> <mo>+</mo> <msub> <mi>T</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>iT</mi> <mi>s</mi> </msub> <mo>+</mo> <msub> <mi>T</mi> <mn>2</mn> </msub> </mrow> </msubsup> <msub> <mi>r</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <msub> <mi>r</mi> <mi>n</mi> </msub> <mo>*</mo> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>T</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>

Wherein, T₁And T₂The starting point and terminal in autocorrelation integral section, () are represented respectively^*Represent the conjugate operation of plural number；

4.2) prior probability, is obtained, and row decoding is entered using BP algorithm to judgment variables y (i) according to prior probability；

Obtain prior probability and specifically include following steps：

Wherein, u₀The transmission represented as " 0 " when bit, u₁Represent be send be " 1 " when bit, y representative be to receive Information bit, p (y/x=u₁) what is represented is when the information sent is u₁When receive y probability, x be caused by equiprobability with Machine variable；

5.2) u, is set₀Represent value after bit " 0 " is by the channel that removes noise, u₁What is represented is that bit " 1 " passes through the channel Value afterwards；Y is the value received in real system by channel；Then formula (13) is：

<mrow> <mfrac> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>y</mi> <mo>/</mo> <mi>x</mi> <mo>=</mo> <msub> <mi>u</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>p</mi> <mrow> <mo>(</mo> <mi>y</mi> <mo>/</mo> <mi>x</mi> <mo>=</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>y</mi> <mo>/</mo> <mi>x</mi> <mo>=</mo> <msub> <mi>u</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>y</mi> <mo>/</mo> <mi>x</mi> <mo>=</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msqrt> <mi>&sigma;</mi> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>-</mo> <msub> <mi>u</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <mi>&delta;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </msup> </mrow> <mrow> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msqrt> <mi>&sigma;</mi> </mrow> </mfrac> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>r</mi> <mo>-</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <mi>&delta;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>

Define p (y/x=u₁)=p₁, can be obtained by abbreviation (14)

<mrow> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>p</mi> <mn>1</mn> </msub> </mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> </mfrac> <mo>=</mo> <msup> <mi>e</mi> <mfrac> <mrow> <msubsup> <mi>u</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>u</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mn>2</mn> <msub> <mi>yu</mi> <mn>0</mn> </msub> <mo>-</mo> <mn>2</mn> <msub> <mi>yu</mi> <mn>1</mn> </msub> </mrow> <mrow> <mn>2</mn> <msup> <mi>&delta;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mfrac> <mrow> <msubsup> <mi>u</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>u</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mn>2</mn> <msub> <mi>yu</mi> <mn>0</mn> </msub> <mo>-</mo> <mn>2</mn> <msub> <mi>yu</mi> <mn>1</mn> </msub> </mrow> <mrow> <mn>2</mn> <msup> <mi>&delta;</mi> <mn>2</mn> </msup> </mrow> </mfrac> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>

5.3) after, being initialized with prior probability, enter row decoding according to BP algorithm, obtain u₀, u₁, variance δ²Dependent on channel Characteristic, it can be worth to by sample.

2. a kind of LDPC codings and interpretation method suitable for non-coherent ultra-broad band communication system according to claim 1, its It is characterised by, the step 1) detailed process is：

1.1) it is N, to set signal to be sent_fIndividual compact arranged pulse is to composition, and each pulse is to including a reference pulse With a data pulse, according to delay T_dOrder is sent, and is in the transmission signal of transmitting terminal generation：

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>s</mi> <mo>~</mo> </mover> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msqrt> <mfrac> <msub> <mi>E</mi> <mi>b</mi> </msub> <mrow> <mn>2</mn> <msub> <mi>N</mi> <mi>f</mi> </msub> </mrow> </mfrac> </msqrt> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <msub> <mi>N</mi> <mi>f</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>&lsqb;</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>iT</mi> <mi>s</mi> </msub> <mo>-</mo> <mn>2</mn> <msub> <mi>mT</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mi>g</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>iT</mi> <mi>s</mi> </msub> <mo>-</mo> <mo>(</mo> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msqrt> <mfrac> <msub> <mi>E</mi> <mi>b</mi> </msub> <mrow> <mn>2</mn> <msub> <mi>N</mi> <mi>f</mi> </msub> </mrow> </mfrac> </msqrt> <munderover> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>s</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>iT</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

Wherein, E_bThe emitted energy per bit is represented, N represents the bit number of codeword data bag, N_fRepresent pulse pair in each symbol The number repeated, g (t) represent energy normalized ultra-wideband pulse, b_n(i) ∈ { ± 1 } be transmitting binary data symbols, T_S For symbol period, T_pFor pulse width, m is nonnegative integer, and t is continuous time variable, s_i(t) it is defined as：

<mrow> <msub> <mi>s</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mover> <mo>=</mo> <mi>&Delta;</mi> </mover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>m</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <msub> <mi>N</mi> <mi>f</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>&lsqb;</mo> <mi>g</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mn>2</mn> <msub> <mi>mT</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mi>g</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mo>(</mo> <mrow> <mn>2</mn> <mi>m</mi> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> <msub> <mi>T</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>

1.2) QC-LDPC codes (N, j, k), are constructed using cyclic shift matrices, N represents code length, and j represents row weight, and k represents row weight, Index matrix P is provided first：

Wherein, P is the index matrix that a dimension is j × k, wherein 0≤s≤j-1,0≤t≤k-1 and a, b are prime numbers, j is less than k；The value of each element in index matrix represents the digit that the submatrix of check matrix moves right；

Check matrix H is：

H dimension is jM × kM, and M=N/k represents the dimension of submatrix；

1.3) H is expressed as form：

H=[A B] (5)

G=[(A^-1·B)^TI] (6)

Wherein, square formation A is nonsingular matrix；

3. a kind of LDPC codings and interpretation method suitable for non-coherent ultra-broad band communication system according to claim 2, Characterized in that, the square formation A building methods are：

2.1), change index matrix P, obtain new index matrix P₁：

From H₁In can obtain A₁

Pass through this change, A₁It is nonsingular.

4. a kind of LDPC codings and interpretation method suitable for non-coherent ultra-broad band communication system according to claim 2, Characterized in that, the square formation A building methods are：

3.1), first in exchange equation (5) H each row, make A diagonal entry all 1；

3.3) line translation, is entered to switching matrix H：

The first step：From the 1st row to jth M rows, the element 1 below square formation A diagonal is replaced with 0, while whether check square formation A It is nonsingular；If not nonsingular, then repeat the step, until A is nonsingular；

Second step：Generator matrix is obtained from square formation A.

5. a kind of LDPC codings and interpretation method suitable for non-coherent ultra-broad band communication system according to claim 2, Characterized in that, the step 3) concretely comprises the following steps：

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>r</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mover> <mi>s</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>*</mo> <mi>h</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>n</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msqrt> <mfrac> <msub> <mi>E</mi> <mi>b</mi> </msub> <mrow> <mn>2</mn> <msub> <mi>N</mi> <mi>f</mi> </msub> </mrow> </mfrac> </msqrt> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>&alpha;</mi> <mi>k</mi> </msub> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>s</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>iT</mi> <mi>s</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>n</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>

Wherein, * represents linear convolution, and n (t) represents additive white Gaussian noise, in IEEE 802.15.4a standards, multipath channel Impulse response is expressed as：

<mrow> <mi>h</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>a</mi> <mi>k</mi> </msub> <mi>&delta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>&tau;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>

Wherein, α_kAnd τ_kThe multiple fading coefficients of K roads multipath component are represented respectively and are reached is delayed；In order to ensure no intersymbol Interference, if T_S≥2N_fT_d+τ_max, wherein τ_maxRepresent the maximum delay of channel.