CN103067135A - Joint modulation coding method for deep-space link residual frequency offset - Google Patents

Abstract

The invention provides a joint modulation coding method for deep-space link residual frequency offset. The joint modulation coding method for the deep-space link residual frequency offset is characterized by comprising the following steps, wherein a step A is that low density parity check (LDPC) coding is carried out to information bits at a transmitting terminal, and at the same time, the order of a coding sequence is changed through an intermediate conversion matrix so that the information bits are enabled to be located at positions where phase deviation is small; a step B is that Feher-patented quadrature phase shift keying (FQPSK) modulation is carried out to the coding sequence, and transmitting signals generated through the modulation are transmitted into an additive white gaussian noise (AWGN) channel; a step C is that the transmitted signals are received at a receiving terminal and demodulated by an MAP to obtain a bit-by-bit logarithmic likelihood ratio LLR, and then the obtained LLR is utilized for carrying out compensation and estimation for phase offset and frequency offset to codes; and a step D is that soft information is sent into a decoder eventually, a posteriori probability of the demodulation is used as a priori probability of decoding, and a belief propagation decoding algorithm based on the soft information is adopted to achieve a decoding process. The joint modulation coding method for the deep-space link residual frequency offset effectively assists in frequency offset compensation, and improves the frequency deviation resistant performance of a system.

Description

Combined modulation coding method under the deep space link residual frequency deviation

Technical field

The present invention relates to a kind of combined modulation coding method, relate in particular to a kind of combined modulation coding method under deep space link residual frequency deviation.

Background technology

In the process of survey of deep space, deep space communication plays a part crucial, the normal operation of only guaranteed deep space communication system just may make the survey of deep space task succeed, and deep space communication is faced with ground communication and the not available particular difficulty of satellite communication, this is because the deep space channel has following characteristics: distance, time delay are large, channel has fading characteristic, operating frequency is high, and available band is wide, interrupt the chain Louis, the uplink and downlink link is asymmetric etc.

The propagation distance of deep space communication is extremely far away, signal energy is along with square decay that is of survey of deep space distance, it is extremely low to receive the pickup electrode low signal-to-noise ratio, and the three-dimensional effects such as the increase of transmission range and Doppler frequency shift, cause the signal of receiving terminal to have large phase place and frequency shift (FS), defy capture especially under low signal-to-noise ratio, the normal operation that guarantee deep space communication needs the channel coding method of high-gain and effective detection means.Therefore, how to guarantee and the reliability that improves deep space communication becomes key issue.The particularity of deep space communication has determined that frequency range that deep space communication adopts, modulation system and coding techniques and protocol architecture etc. and terrestrial wireless communication, satellite communication are different.The technical way that early stage survey of deep space has been adopted and the survey of deep space of following a period of time will be adopted for the problems referred to above comprises: improve carrier frequency, increase the antenna size of ground station and detector to obtain higher transmitting power, adopt power effective and the modulation system of bandwidth efficient and the channel coding method of high-gain, reduce simultaneously the receiving system noise temperature.But, present continuing to increase along with the survey of deep space distance, under the condition that hardware condition limits and machining accuracy is limited of deep space probe, not the main direction of future studies from the angle that strengthens antenna size and raising radio frequency, improve the way of transmitted power and receive restriction.Therefore, must choose suitable modulation system and coded system, problem reliable under deep space communication high attenuation and the long time delay condition to solve, efficient communication.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the invention provides a kind of combined modulation coding method under deep space link residual frequency deviation, may further comprise the steps:

Steps A): at transmitting terminal information bit is carried out the LDPC coding, change simultaneously the order of coded sequence by the intermediate conversion matrix, make information bit be in the little position of phase deviation;

Step B): coded sequence is carried out the FQPSK modulation, transmitting of modulation generation sent into awgn channel;

Step C): receive at receiving terminal and to transmit and it is carried out the MAP demodulation, obtain the log-likelihood ratio (LLR) by bit, utilize the log-likelihood comparison code word that obtains to carry out estimation and the compensation of skew and frequency deviation;

Step D): at last soft information is sent to decoder, with the posterior probability of the demodulation prior probability as decoding, adopts the degree of confidence propagation decoding algorithm based on soft information, realize decode procedure.

Further be improved to described steps A) in, according to the backoff algorithm of frequency deviation, send the order of sequence by the transition matrix adjustment.

Further be improved to described step C) in, the log-likelihood ratio LLR that pursues bit that obtains that passes through and the sample sequence that receives utilize maximum-likelihood criterion that phase difference and frequency deviation are estimated, until satisfy iterated conditional or reach maximum iterations.

Further be improved to described step C) in, in the FQPSK modulation technique, regard the sampled point that represents a described bit as a sub-block.

Further be improved to described step C) in, in the described frequency deviation estimation scheme, come calculated rate by phase place increment in time.

Compared to prior art, it is low to the present invention is directed to the deep space communication received signal to noise ratio, and residual phase and frequency deviation have been set up the combined coding modulating system towards the deep space link to the larger problem of decoding performance impact.FQPSK modulation and LDPC coding are carried out co-design, and in the iterative demodulation loop, embedded estimation and compensation that backoff algorithm is realized phase place and frequency deviation.Simultaneously, the present invention has utilized the characteristic of LDPC coding, changes the code word order of encoding and decoding by adding the intermediate conversion matrix, has effectively assisted compensate of frequency deviation, has increased the anti-frequency deviation performance of system.At last by simulating, verifying the gain of this co-design system on the decoding end error rate, be not more than 0.3 π and frequency deviation 100ppm in the scope of 700ppm in phase deviation, the error rate can reach 10-3 to 10-4.Thereby efficiently solve the problem of weak signal decoding under the deep space communication link residual frequency deviation.

Description of drawings

Fig. 1 is that the cascade system of FQPSK of the present invention and LDPC consists of schematic diagram.

Fig. 2 is the sequence schematic diagram of the transmission of the combined modulation coding method under deep space link residual frequency deviation of the present invention.

Fig. 3 is the FQPSK implementation method principle schematic of the combined modulation coding method under deep space link residual frequency deviation of the present invention.

Fig. 4 is the FQPSK of the combined modulation coding method under deep space link residual frequency deviation of the present invention and the planisphere comparison diagram of QPSK.

Fig. 5 is the phase compensation performance schematic diagram of the combined modulation coding method under deep space link residual frequency deviation of the present invention.

Fig. 6 is the compensate of frequency deviation performance schematic diagram of the combined modulation coding method under deep space link residual frequency deviation of the present invention.

Fig. 7 is the algorithm phase place of the combined modulation coding method under deep space link residual frequency deviation of the present invention and the convergence schematic diagram that frequency deviation is estimated

Fig. 8 is the phase compensation performance schematic diagram after the decoding of the combined modulation coding method under deep space link residual frequency deviation of the present invention.

Fig. 9 is the compensate of frequency deviation performance schematic diagram after the decoding of the combined modulation coding method under deep space link residual frequency deviation of the present invention.

Figure 10 be the combined modulation coding method under deep space link residual frequency deviation of the present invention at the performance comparison schematic diagram with/without the system of intermediate conversion matrix.

Embodiment

The present invention is further described below in conjunction with description of drawings and embodiment.

See also Fig. 1 to Figure 10, the invention provides a kind of under deep space link residual frequency deviation the combined modulation coding method and the cascade system of a kind of FQPSK and LDPC, in its iterative demodulation process, embedded non-data-aided phase place and frequency deviation algorithm for estimating.The demodulation of FQPSK based on BCJR (Bahl-Cocke-Jelinek-Raviv) algorithm for the modification that detects by the symbol maximum a posteriori probability.Especially, the present invention recovers phase place and the soft information LAPPR (log a posteriori probability ratio) by bit of frequency deviation by obtaining from the MAP demodulation in the iterative demodulation process, this soft information is delivered in the estimator of phase place and frequency deviation again.Satisfying compensation precision or reaching in the situation of maximum iteration time, soft information is sent to decoder reliably, utilizes sum-product algorithm SPA (sum-product algorithm) to decipher.The scheme that proposes can effectively utilize the posterior probability that obtains from the MAP demodulation of FQPSK to estimate phase place and frequency deviation, rather than from decoder, obtain, avoided so a large amount of time delays.In addition, the present invention proposes the sequence transition matrix of a low complex degree, it has adjusted the order of the codeword sequence that sends according to the compensate of frequency deviation algorithm, has improved the reliability of information bit.Do like this iterations is reduced greatly simultaneously the performance of error code is improved, this is because the LDPC code does not need decoding when channel condition is good.The cascade system model that the present invention proposes as shown in Figure 1.

Combined modulation coding method under deep space link residual frequency deviation of the present invention may further comprise the steps:

Steps A): at transmitting terminal, information bit is carried out the LDPC coding, change simultaneously the order that sends sequence.Generator matrix in the described cataloged procedure has passed through the conversion of transition matrix, thereby makes the order that sends sequence obtain change, makes information bit be in the quality that information bit is improved in the lower centre position of phase error.

If there is fixedly frequency deviation in the codeword sequence that receives, the phase deviation that is produced by frequency deviation so can be along with the increase of bit linear to be increased, if the present invention adopts the constant phase compensation, all code word samplings only can reach the compensation of zero error at the position of code word mid point phase difference, remaining phase deviation increases gradually to the both sides of code word simultaneously.The present invention proposes an intermediate conversion matrix that is used for conversion, described intermediate conversion matrix makes information bit be positioned at the less position of phase deviation according to the order of the backoff algorithm adjustment transmission sequence of frequency deviation, has improved the quality of information bit.As shown in Figure 2, because a kind of as systematic code of LDPC code sends check bit and information bit simultaneously, when channel condition is enough good, do not need to decipher.Therefore the present invention adjusts the position that sends sequence, makes information bit be in the quality that information bit is improved in the lower centre position of phase error, does like this iterations that not only can reduce decoding and reduces Time Delay of Systems, but also improve the decoding performance of system.

It is U={u that the present invention defines original bit information ₀, u ₁..., u}, the check matrix H of given m * n dimension, m=n-k, after the gaussian elimination conversion, the present invention can obtain:

$H=\left[\begin{array}{cc}{I}_{m\&times;m}& {\left(P_{m\&times;k}\right)}^{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">T</figure-callout>}}\\ 0& 0\end{array}\right]---\left(1\right)$

If H is the row full ranks, will be less than complete zero row in the matrix.After the conversion, the present invention obtains generator matrix:

G＝[P _k×mI _k×k] (2)

The code sequence that the present invention finally obtains LDPC coding is passed through the product of bit information U and generator matrix G:

c＝U·G＝{c ₀，c ₁，...，c _r-1，u ₀，u ₁，...，u _k-1} (3)

It is considered herein that if satisfy following formula then successfully decoded:

G·H ^T＝0 (4)

Equally:

c·H ^T＝u·G·H ^T＝0 (5)

Namely:

$\left\{\begin{array}{c}{c}_o+u_0+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=0\\ {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">c</figure-callout>}}_1+u_0+u_2=0\\ c_o+u_1+u_2=0\end{array}\right.---\left(6\right)$

Given invertible matrix A, if satisfy following formula, and to make the centre position of the numeral sequence of transmission be information bit, and both sides are check bit, and the present invention claims A intermediate conversion matrix.

G·H ^T＝(G·A)·(A ^-1·H ^T)＝G′·(H′) ^T＝0 (7)

For example, the present invention is given:

$G=\left[\begin{array}{cccccc}1& 1& 0& 1& 0& 0\\ 1& 0& 1& 0& 1& 0\\ 0& 1& 1& 0& 0& 0\end{array}\right],$ $H=\left[\begin{array}{cccccc}1& 0& 0& 1& 1& 0\\ 0& 1& 0& 1& 0& 1\\ 0& 0& 1& 0& 1& 1\end{array}\right]---\left(8\right)$

$A=\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 1& 0& 0& 0\end{array}\right]---\left(9\right)$

Like this, the present invention be multiply by the intermediate conversion matrix with generator matrix and can be got:

$G^{\&prime;}=G\&CenterDot;A=\left[\begin{array}{cccccc}1& 1& 0& 1& 0& 0\\ 1& 0& 1& 0& 1& 0\\ 0& 1& 1& 0& 0& 0\end{array}\right]\&CenterDot;\left[\begin{array}{cccccc}1& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 1& 0& 0& 0\end{array}\right]=\left[\begin{array}{cccccc}1& 0& 0& 1& 0& 1\\ 1& 0& 1& 0& 1& 0\\ 0& 0& 1& 0& 0& 1\end{array}\right]---\left(10\right)$

Then have:

c·(H′) ^T＝u·G′·(H′) ^T＝0 (11)

The condition that satisfies decoding does not change, and still is:

$\left\{\begin{array}{c}{c}_o+{\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">u</figure-callout>}}_0+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=0\\ {\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">c</figure-callout>}}_1+{\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">u</figure-callout>}}_0+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="130107164314.png,130107164349.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=0\\ c_o+{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">u</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="130107164314.png,130107164349.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=0\end{array}\right.---\left(12\right)$

This means, added after the intermediate conversion matrix that decoding is from middle bit, although order has change, the form of decoding is constant, the decoding that the present invention still can be correct.

Step B): coded sequence is carried out the FQPSK modulation.Transmitting after the modulation sent into awgn channel.

Being achieved as follows of FQPSK is described, and its a kind of description is the trellis coding modulation, and the basic principle block diagram of the FQPSK of this description as shown in Figure 3.

I branch road and Q branch road mapping relations can be described with the form that I branch road and Q prop up (0,1) expression formula of circuit-switched data on replaceability ground:

$\left\{\begin{array}{c}{D}_{\mathrm{In}}=\frac{1-d_{\mathrm{In}}}{2}\\ D_{\mathrm{Qn}}=\frac{1-d_{\mathrm{Qn}}}{2}\end{array}\right.---\left(13\right)$

In the formula, the span of this two paths of data is set (0,1).Therefore, can defined label i and the expression formula of the BCD of j be:

$\left\{\begin{array}{c}i=I_3\&times;2^3+I_2\&times;2^2+I_1\&times;2^1+I_0\&times;2^0\\ j={\mathrm{<figure-callout\; id="3"\; label="Q"\; filenames="130107164314.png,130107164407.png"\; state="\{\{state\}\}">Q</figure-callout>}}_3\&times;2^3+{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="130107164314.png,130107164349.png"\; state="\{\{state\}\}">Q</figure-callout>}}_2\&times;2^2+{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">Q</figure-callout>}}_1\&times;2^1+{\mathrm{<figure-callout\; id="0"\; label="Q"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">Q</figure-callout>}}_0\&times;2^0\end{array}\right.---\left(14\right)$

Wherein,

$\left\{\begin{array}{cc}{I}_0=D_{\mathrm{Qn}}\&CirclePlus;D_{Q,n-1},& {\mathrm{<figure-callout\; id="0"\; label="Q"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">Q</figure-callout>}}_0=D_{I,n+1}\&CirclePlus;{\mathrm{<figure-callout\; id="1"\; label="D\; In\; I"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">D</figure-callout>}}_{\mathrm{In}}& \\ I_{}{}_1=D_{Q,n-1}\&CirclePlus;D_{Q,n-2},& {\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">Q</figure-callout>}}_1=D_{\mathrm{In}}\&CirclePlus;D_{I,n-1}=I_2\\ I_2=D_{\mathrm{In}}\&CirclePlus;D_{I,n-1},& {\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="130107164314.png,130107164349.png"\; state="\{\{state\}\}">Q</figure-callout>}}_2=D_{\mathrm{Qn}}\&CirclePlus;D_{Q,n-1}=I_0\\ I_3=D_{\mathrm{In}},& {\mathrm{<figure-callout\; id="3"\; label="Q"\; filenames="130107164314.png,130107164407.png"\; state="\{\{state\}\}">Q</figure-callout>}}_3=D_{\mathrm{Qn}}\end{array}\right.---\left(15\right)$

Like this, just can obtain y _I(t)=s _i(t-nT _s) and y _Q(t)=s _j[t-(n+1/2) T _s].More precisely, for y _I(t), at each symbol time slot (n-1/2) T _sThe T of≤t≤(n+1/2) _sIn, and, for y _Q(t), at each symbol time slot nT _sThe T of≤t≤(n+1) _sIn, the baseband signal of I channel and Q channel is from having 16 signal s _i(t), i=0,1 ..., select in 15 the set.The picture specification of this Mapping implementation is provided by Fig. 3.

Step C): receiving terminal receive with the signal of Gaussian noise at first by the MAP demodulation, obtain the log-likelihood ratio LLR (Logarithm Likelihood Ratio) by bit.In the iterative demodulation loop, the LLR that pursues bit that obtains that passes through and the sample sequence that receives utilize maximum-likelihood criterion that phase difference and frequency deviation are estimated, until satisfy iterated conditional or reach maximum iterations.The number of times that phase difference and frequency deviation are compensated is more, and the soft information that obtains is just more reliable.

Briefly, FQPSK modulation is a kind of artificial modulation system of utilizing the accurate permanent envelope that 16 functions slap together, and it is to be based upon on the basis of QPSK, has eliminated again the SPA sudden phase anomalies among the QPSK, and the constellation comparison diagram of FQPSK and QPSK as shown in Figure 4.For example, after list entries is x=(1,1,0,0,1,0,1,0,0,0) process string and conversion, the in the same way sequence xi=(1,0,1,1,0) that the present invention obtains, quadrature xq=(1,0,0,0,0).After through the computing cross-correlation unit, the present invention has obtained the metric numeral of two-way: the I on I road _OutThe Q on=(1,15,6,12,8) and Q road _Out=(13,7,3,2,1).According to this two railway digital, the present invention selects the waveform of appointment to replace corresponding bit from 16 wave functions.Here, the code word waveform on Q road will postpone the half symbols cycle to prevent the jump on the amplitude than I road, just makes modulation waveform keep accurate permanent envelope.

Have the information of n bit to be sent out after setting coding, passed through after the FQPSK modulation, each bit need to replace with Ts sampling of selected waveform.The length of the sequence that need to be sent out like this, is exactly N _s=nT _sThe sequence r={r that receives (0), r (2) ..., r (N _s-1) } be expressed as followsin:

r＝c·e ^jθ+n (16)

Here c=[c ₀, c ₁..., c _Ns-1] ^TIt is the modulation symbol vector in the code word.N=[n ₀, n ₁..., n _Ns-1] ^TBe white Gauss noise independently, average is zero, and variance is N ₀/ 2.θ is the initial phase difference of code word.

$\widehat{\mathrm{\&theta;}}=\arg \underset{\mathrm{\&theta;}}{\max }E\left[P\left(r\right|\mathrm{\&theta;},c)\right]$

$=\arg \underset{\mathrm{\&theta;}}{\max }\underset{c}{\mathrm{\&Sigma;}}\mathrm{Pr}\left(c\right)\frac{1}{{\left(2\mathrm{\&pi;}{\mathrm{\&sigma;}}_n^2\right)}^{N_S/2}}\exp (-\frac{{\left|\right|r-c{e}^{\mathrm{j\&theta;}}\left|\right|}^2}{2{\mathrm{\&sigma;}}_n^2})---\left(17\right)$

In formula (17), if

Value enough little, what formula (17) can be similar to is expressed as:

$E\left[P\left(r\right|\mathrm{\&theta;},c)\right]\&ap;\arg \underset{\mathrm{\&theta;}}{\max }\underset{c}{\mathrm{\&Sigma;}}\mathrm{Pr}\left(c\right)\frac{1}{{\left(2\mathrm{\&pi;}{\mathrm{\&sigma;}}_n^2\right)}^{N_S/2}}(1-\frac{{\left|\right|r-c{e}^{\mathrm{j\&theta;}}\left|\right|}^2}{2{\mathrm{\&sigma;}}_n^2})$ (18)

$=\frac{1}{{\left(2\mathrm{\&pi;}{\mathrm{\&sigma;}}_n^2\right)}^{N_S/2}}E(1-\frac{{\left|\right|r-c{e}^{\mathrm{j\&theta;}}\left|\right|}^2}{2{\mathrm{\&sigma;}}_n^2})$

Therefore, the equivalence of maximum likelihood phase estimation is for making function

Minimum:

$\frac{\&PartialD;E\left({\left|\right|r-c{e}^{\mathrm{j\&theta;}}\left|\right|}^2\right|\hat{r})}{\&PartialD;\mathrm{\&theta;}}=E\left\{c^H(-j)e^{-\mathrm{j\&theta;}}(r-c{e}^{\mathrm{j\&theta;}})\right|\hat{r}\}=0---\left(19\right)$

Therefore have:

$\widehat{\mathrm{\&theta;}}=\mathrm{angle}\{E\left({\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="130107164314.png,130107164349.png"\; state="\{\{state\}\}">c</figure-callout>}}^2\right|\hat{r})/[E\left(c^H\right|\hat{r})\&CenterDot;r\left]\right\}---\left(20\right)$

Because it is constant that the envelope of FQPSK modulation is similar to, be approximately,

$E\left({\mathrm{<figure-callout\; id="2"\; label="c\; m"\; filenames="130107164314.png,130107164349.png"\; state="\{\{state\}\}">c</figure-callout>}}_m^{}\right|\hat{r})\&ap;K,$ m＝0，...，N _s-1 (21)

Generally speaking, can think uncorrelated between any two transmission symbols, therefore:

$E\left(c^H\right|\hat{r})\&ap;{[E\left({\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">c</figure-callout>}}_1\right|\hat{r}),E\left({\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="130107164314.png,130107164349.png"\; state="\{\{state\}\}">c</figure-callout>}}_2\right|\hat{r}),\&CenterDot;\&CenterDot;\&CenterDot;E\left(c_{N_s}\right|\hat{r})]}^{\text{H}}---\left(22\right)$

Derive as can be known from the definition of LLR:

$L\left(c_m\right|\hat{r})=\ln \frac{\mathrm{Pr}(c_m=+1|\hat{r})}{\mathrm{Pr}(c_m=-1|\hat{r})}=\ln \left(\frac{P\left(c_m^1\right)}{1-P\left(c_m^1\right)}\right)---\left(23\right)$

Therefore

Value be:

$P\left(c_m^1\right)=\frac{e^{L\left({\mathrm{<figure-callout\; id="1"\; label="c\; m"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">c</figure-callout>}}_m^{}\right|\hat{r})}}{1+e^{L\left({\mathrm{<figure-callout\; id="1"\; label="c\; m"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">c</figure-callout>}}_m^{}\right|\hat{r})}}---\left(24\right)$

For the FQPSK modulation, the present invention has:

$E\left(c_m\right|\hat{r})=\underset{m=1}{\overset{N_s}{\mathrm{\&Sigma;}}}{c}_m\&CenterDot;\mathrm{Pr}(c_m=C|\hat{r})$ (25)

$=\tanh \left(\frac{L\left(a_m\right|\hat{r})}{2}\right)+j\tanh \left(\frac{L\left(b_m\right|\hat{r})}{2}\right)$

In the formula, a _mAnd b _mBe the FQPSK modulation signal in the same way and orthogonal component, therefore have:

$E\left(c^H\right|\hat{r})\&CenterDot;r={\left(E\left(c\right|\hat{r})\right)}^H\&CenterDot;r$

$={(\tanh \left(\frac{L\left(a\right|\hat{r})}{2}\right)+j\tanh \left(\frac{L\left(b\right|\hat{r})}{2}\right))}^H\&CenterDot;r---\left(26\right)$

Like this, the estimation of phase place can be expressed as:

$\widehat{\mathrm{\&theta;}}=-\&angle;(K/({(\tanh \left(\frac{L\left(a\right|\hat{r})}{2}\right)+j\tanh \left(\frac{L\left(b\right|\hat{r})}{2}\right))}^H\&CenterDot;r))$

$=\&angle;({(\tanh \left(\frac{L\left(a\right|\hat{r})}{2}\right)+j\tanh \left(\frac{L\left(b\right|\hat{r})}{2}\right))}^H\&CenterDot;r)---\left(27\right)$

According to code modulated principle, each bit after the FQPSK modulation is by the T of selected waveform _sIndividual sampled point replaces, so this T _sThe information that remains a bit of the integral body representative of individual sampled point, therefore: the form of (27) formula can be transformed into:

$\widehat{\mathrm{\&theta;}}=\&angle;({(\tanh \left(\frac{L\left(a\right|\hat{r})}{2}\right)+j\tanh \left(\frac{L\left(b\right|\hat{r})}{2}\right))}^H\&CenterDot;r)=$

$\&angle;(\underset{i}{\mathrm{\&Sigma;}}\underset{j}{\mathrm{\&Sigma;}}(\tanh \left(\frac{L\left(a_i\right|{\hat{r}}_i)}{2}\right)+j\tanh \left(\frac{L\left(b_i\right|\left({\hat{r}}_i\right))}{2}\right))\&CenterDot;r_j)---\left(28\right)$

i＝1，...，n；j＝1，...，i×Ts

When frequency deviation occurring in the code word, utilize said method to estimate that phase difference is not just effective.This is because when having fixedly frequency deviation, can the linear increase along with the increase of code length by the phase difference that frequency deviation causes.If adopting above-mentioned phase compensating method estimates with the frequency deviation codeword sequence whole, can estimate the average of all bit skews, and all bits are compensated this average, thereby the error of causing, this error increases along with the increase of code word size, therefore, said method is not suitable for the situation that has frequency deviation.But because the phase difference that is produced by frequency deviation is linear growth along with the increase of bit length, so phase place that above-mentioned phase compensating method compensates, namely the phase difference average of all bits can just be the phase value of code word mid point, and the sequence after the compensation can reach zero phase difference at point midway.Skew is still very important in the initial sum ending of code word, when especially code word size is very long.In this joint, the present invention adopts the method for a traditional low complex degree to reduce residual frequency deviation to the impact of decoding performance.The waveform sampling that the present invention's handle represents each bit is as a sub-block, and the hypothesis phase place is invariable in this sub-block.

When having a fixing residual frequency deviation, the present invention expresses the sequence that receives again:

$r\left(m\right)=c\left(m\right){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="130107164314.png,130107164349.png"\; state="\{\{state\}\}">e</figure-callout>}}^j+n\left(m\right)---\left(29\right)$

m＝0，...，N _s-1

T is the interval of modulation symbol in the formula, T _sIt is the number of samples of the selected waveform of each bit.F and θ are that initial phase difference and the frequency deviation of receiving sequence is poor.

Definition

Then, the present invention can come calculated rate by a kind of traditional method, namely comes calculated rate by phase place increment in time:

${\hat{f}}_l=\frac{\&angle;x_l(m+d)-\&angle;x_l\left(m\right)}{d\&CenterDot;T}---\left(30\right)$

D is the measurement interval that phase slope calculates in the formula.The calculating of (30) formula is transformed into following form:

${\hat{f}}_l=\frac{\&angle;{x_l}^{*}\left(m\right)x_l(m+d)}{d\&CenterDot;T}---\left(31\right)$

Average to whole codeword sequence, the present invention can obtain one and estimate reliably:

${\hat{f}}_l=\frac{\&angle;\left\{{\mathrm{\&Sigma;}}_{m=1}^{N-d}{x_l}^{*}\left(m\right)x_l(m+d)\right\}}{d\&CenterDot;T}---\left(32\right)$

Step D): at last soft information is sent to decoder, with the posterior probability of the demodulation prior probability as decoding, adopts the degree of confidence propagation decoding algorithm based on soft information, realize decode procedure.

Be broadly divided into 2 parts:

(1) initialization

If the noise cancellation signal that has that receiving terminal is received is r _n, n=1,2 ..., N, the decision value of the every bit of our initialization is r _nHard decision value x _nIf

Before being the decoding iteration, by the prior information of channel status decision.If

I the bit t that accepts vector r _iThe probabilistic information that obtains by other check equations except j verification formula during value 0/1.

Be initialized to prior information

α _IjBe

Normalized parameter.If

The i bit t that accepts vector _i=0/1 o'clock, the probability of satisfied j check equations.

The external information that to be information node upgrade in iteration each time, we are called pseudo-posterior probability, along with the pseudo-posterior probability of the increase of iterations moves closer to value in maximum a posteriori probability, can whether successfully decodedly adjudicate with it.α _iBe Normalization factor.α _Ij, α _iAll be initialized to α ₀

(2) iterative process

The first step by check-node j to variable node i,

Verification formula c _jIn the known and information node v of other information node distributions _iState is under the condition of a, the probability that verification formula j satisfies.By new probability formula:

$p\left(c_j\right|x_i=a)=\underset{x,x_i=a}{\mathrm{\&Sigma;}}P\left(c_j\right|x)P\left(x\right|x_i=a)---\left(33\right)$

Following formula is to satisfying verification formula j and x _iState is the probable value summation of all x of a condition, obtains x _iState is c under a _jThe conditional probability that satisfies.

In decode procedure, the part mutual independence by between the information node relevant with check-node can get:

$P\left(x\right|x_i=a)=\underset{i^{\&prime;}\&Element;\mathrm{row}\left[j\right]\backslash \left\{i\right\}}{\mathrm{\&Pi;}}{q}_{i^{\&prime;}j}^a---\left(34\right)$

I ' ∈ row[j wherein] i} refer to matrix H j (in the row of 1≤j≤m), row corresponding to non-zero bit i (not containing i) number.

Formula calculates below available:

$r_{\mathrm{ij}}^a=\underset{x,x_i}{\mathrm{\&Sigma;}}P\left(c_j\right|x)\underset{i^{\&prime;}\&Element;\mathrm{row}\left[j\right]\backslash \left\{i\right\}}{\mathrm{\&Pi;}}{q}_{i^{\&prime;}j}^a---\left(35\right)$

In the formula $P\left(c_j\right|x)=\left\{\begin{array}{cc}1& c_j\mathrm{is\; satisfied\; with\; <figure-callout\; id="0"\; label="x"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">x</figure-callout>}\\ 0& \mathrm{else}\end{array}\right..$

Concrete calculating

Use forward direction in the random process/backward recursion algorithm, existing program has provided a kind of method of easy realization.Order Then

$\mathrm{\&delta;}{r}_{\mathrm{ij}}=r_{\mathrm{ij}}^0-{\mathrm{<figure-callout\; id="1"\; label="r\; ij"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{ij}}^{}=\underset{i^{\&prime;}\&Element;\mathrm{row}\left[j\right]\backslash \left\{i\right\}}{\mathrm{\&Pi;}}\mathrm{\&delta;}{q}_{i^{i}j}^a---\left(36\right)$

Proof slightly.Pass through solving equations:

$\left\{\begin{array}{c}{r}_{\mathrm{<figure-callout\; id="1"\; label="ij"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">ij</figure-callout>}}^1+{\mathrm{<figure-callout\; id="0"\; label="r\; ij"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{ij}}^{}=1\\ r_{\mathrm{ij}}^0-{\mathrm{<figure-callout\; id="1"\; label="r\; ij"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{ij}}^{}=\underset{i^{\&prime;}\&Element;\mathrm{row}\left[j\right]\backslash \left\{i\right\}}{\mathrm{\&Pi;}}\mathrm{\&delta;}{q}_{i^{\&prime;}j}^a\end{array}\right.$

Obtain:

$\left\{\begin{array}{c}{r}_{\mathrm{<figure-callout\; id="0"\; label="ij"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">ij</figure-callout>}}^0=\frac{1}{2}[1+\underset{i^{\&prime;}\&Element;\mathrm{row}\left[j\right]\backslash \left\{i\right\}}{\mathrm{\&Pi;}}\mathrm{\&delta;}{q}_{i^{\&prime;}j}^a]\\ {\mathrm{<figure-callout\; id="1"\; label="r\; ij"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">r</figure-callout>}}_{\mathrm{ij}}^{}=\frac{1}{2}[1-\underset{i^{\&prime;}\&Element;\mathrm{row}\left[j\right]\backslash \left\{i\right\}}{\mathrm{\&Pi;}}\mathrm{\&delta;}{q}_{i^{\&prime;}j}^a]\end{array}\right.---\left(37\right)$

Second step by variable node i to check-node j,

To remove c _jOn the information that other check-nodes of outer participation provide, x _iProbability at state a.According to bayesian criterion:

$P(x_i=a|\left\{c_{j^{\&prime;}}\right\},j^{\&prime;}\&Element;\mathrm{col}\left[i\right]\backslash \left\{j\right\})=\frac{P(x_i=a)P\left(\right\{c_{j^{\&prime;}}\},j^{\&prime;}\&Element;\mathrm{col}[i]\backslash \{j\left\}\right|x_i=a)}{P\left(\right\{c_{j^{\&prime;}}\},j^{\&prime;}\&Element;\mathrm{col}[i]\backslash \{j\left\}\right)}---\left(38\right)$

P (x in the following formula _i=a) be prior probability, j ' ∈ row[i] j} refer to matrix H i (in the row of 1≤i≤n), the line number that non-zero bit j ' (not containing j) is corresponding.It is generally acknowledged c _jBetween be separate, joint probability P ({ c _j', j ' ∈ col[i] { j}|x _i=a) can express with product form, that is:

$q_{\mathrm{ij}}^a={\mathrm{\&alpha;}}_{\mathrm{ij}}{P}_i^a\underset{j^{\&prime;}\&Element;\mathrm{col}\left[i\right]\backslash \left\{j\right\}}{\mathrm{\&Pi;}}{r}_{i{j}^{\&prime;}}^a---\left(39\right)$

Be exactly prior probability P (x _i=a), with denominator normalization:

${\mathrm{\&alpha;}}_{\mathrm{ij}}({\mathrm{<figure-callout\; id="1"\; label="q\; ij"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">q</figure-callout>}}_{\mathrm{ij}}^{}+q_{\mathrm{ij}}^0)=1---\left(40\right)$

Then have:

${\mathrm{\&alpha;}}_{\mathrm{ij}}=\frac{1}{{\mathrm{<figure-callout\; id="1"\; label="q\; ij"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">q</figure-callout>}}_{\mathrm{ij}}^{}+{\mathrm{<figure-callout\; id="0"\; label="q\; ij"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">q</figure-callout>}}_{\mathrm{ij}}^{}}$

By what obtain

And external information We can calculate

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="q\; ij"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">q</figure-callout>}}_{\mathrm{ij}}^{}={\mathrm{\&alpha;}}_{\mathrm{ij}}{\mathrm{<figure-callout\; id="1"\; label="p\; i"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">p</figure-callout>}}_i^{}\underset{j^{\&prime;}\&Element;\mathrm{col}\left[i\right]\backslash \left\{i\right\}}{\mathrm{\&Pi;}}{r}_{i{j}^{\&prime;}}^1\\ {\mathrm{<figure-callout\; id="0"\; label="q\; ij"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">q</figure-callout>}}_{\mathrm{ij}}^{}={\mathrm{\&alpha;}}_{\mathrm{ij}}{\mathrm{<figure-callout\; id="0"\; label="p\; i"\; filenames="130107164314.png,130107164340.png"\; state="\{\{state\}\}">p</figure-callout>}}_i^{}\underset{j^{\&prime;}\&Element;\mathrm{col}\left[i\right]\backslash \left\{j\right\}}{\mathrm{\&Pi;}}{r}_{i{j}^{\&prime;}}^0\end{array}\right.---\left(41\right)$

The 3rd step trial and error decoding.Need to obtain the posterior probability of bit i in the decoding stage

The derivation of formula is the same, provides the result to be:

$\left\{\begin{array}{c}{e}_i^0={\mathrm{\&alpha;}}_i\underset{j\&Element;\mathrm{col}\left[i\right]}{\mathrm{\&Pi;}}{r}_{\mathrm{ij}}^0\\ {\mathrm{<figure-callout\; id="1"\; label="e\; i"\; filenames="130107164314.png,130107164333.png"\; state="\{\{state\}\}">e</figure-callout>}}_i^{}={\mathrm{\&alpha;}}_i\underset{j\&Element;\mathrm{col}\left[i\right]}{\mathrm{\&Pi;}}{r}_{\mathrm{ij}}^1\end{array}\right.---\left(42\right)$

It is suitable to select ${\mathrm{\&alpha;}}_i=1/(e_i^0+e_i^1),$ So that $e_i^0+e_i^1=1.$

The decoding judgement at last.If satisfy

, then successfully decoded, output

As effective output valve.Otherwise the continuation iterative process is not if still satisfy when reaching default maximum iteration time

Decoding failure then.

The present invention has proved the impact of performance of the system of proposition by emulation, and along with the increase of iterations, systematic function moves closer to ideal effect.The setting of simulation parameter is referring to table 1.

The system parameter setting of table 1 emulation

What Fig. 5 showed is when having phase deviation, the ber curve of the iterative phase compensation scheme of proposition, and having drawn initial phase deviation among the figure is that 0.1pi is to the situation of 0.3pi.As can be seen from the figure, when phase deviation less than 0.3pi the time, the phase compensation scheme based on maximal possibility estimation that proposes, can obtain very the effect near ideal synchronisation, simultaneously when phase deviation greater than 0.3pi the time, very poor of the performance of system, phase deviation of this explanation this moment has exceeded the compensation range that proposes a plan.That is to say that the effective range that the scheme of proposition can successfully compensate is that remaining phase deviation must not be greater than 0.3pi, for the communication system of reality, this scope can meet the demands fully.

Because the existence of frequency deviation can make phase deviation linear increase along with the increase of bit of whole code word, the constant phase compensation method meeting that last chapters and sections are mentioned causes unacceptable error performance.This means that for the system that will compensate, initial frequency deviation is unsuitable excessive, especially adopts such scheme.In Fig. 6 (a), can see a series of ber curve to the system of 700ppm frequency deviation with 100ppm, the result that comparison diagram 6 (b) compensates by the scheme that proposes.Can find out when initial frequency deviation when being not more than 500ppm that by simulation curve the system after the compensation approaches desirable synchronous very much.Until frequency deviation is when arriving 700ppm, undesirable result has appearred in compensation, but this explanation 700ppm has exceeded the compensation scheme reach.To sum up, the compensate of frequency deviation scheme of the FQPSK of proposition can reach gratifying result, and in wider compensation.

Fig. 7 has shown in the scheme that proposes, the convergence that phase place and compensate of frequency deviation are estimated.In the iteration loop, the frequency deviation of estimating each time and phase place all are last phase potential difference and the frequency deviations after the last estimation compensation, so, for desirable bucking-out system, the estimation of phase difference and frequency deviation should little by little level off to zero, along with the increase of simulation times, the effect of estimation can be become better and better.From simulation result, when initial phase difference was 0.1pi, along with the increase of iterations, the estimation of phase place converged on 10 gradually ^-7Below, when phase difference is 0.2pi, converge to accordingly 10 ^-6Below, and when initial phase difference was 0.3pi, estimation can only converge to 10 ^-2Below.For estimation and the bucking-out system of frequency deviation, effect can be more stable under little frequency deviation.On the other hand, primary estimated value is less than initial frequency deviation value, this is because the present invention has taked a kind of approximate addition when adding frequency deviation, the present invention regards the waveform sampling point that represents a bit as a sub-block, be phase difference the present invention on each sub-block be similar to regard that phase place is constant as, the actual frequency deviation that therefore estimates is less than the added initial frequency deviation of the present invention.Initial frequency deviation is greater than 700ppm the time, and the compensation of system restrains hardly, has surpassed the compensation range that system can reach this moment.

Fig. 8 and Fig. 9 have shown that cascade LDPC deciphers phase place afterwards and the compensation result of frequency deviation.Chart understands that the scheme that proposes can obtain comparatively satisfied error performance under the environment of low signal-to-noise ratio, although under low signal-to-noise ratio, being difficult to very much synchronously before the decoding of FQPSK system guarantees.

Figure 10 has shown in frequency deviation and has equaled in the situation of 300ppm, with system and the systematic function comparison diagram that does not have the intermediate conversion matrix of intermediate conversion matrix.From simulation result, with the system of intermediate conversion matrix can be in the situation of average 4 decodings decoding success, and do not have the system of intermediate conversion matrix under identical condition, to need at least 10 times decoding just can reach identical result.In Figure 10, can find two differences between the different system.This shows that the intermediate conversion matrix of use is the effective method of avoiding the impact of residual frequency deviation.

It is low to the present invention is directed to the deep space communication received signal to noise ratio, and residual phase and frequency deviation have been set up the combined coding modulating system towards the deep space link to the larger problem of decoding performance impact.FQPSK modulation and LDPC coding are carried out co-design, and in the iterative demodulation loop, embedded estimation and compensation that backoff algorithm is realized phase place and frequency deviation.Simultaneously, the present invention has utilized the characteristic of LDPC coding, changes the code word order of encoding and decoding by adding the intermediate conversion matrix, has effectively assisted compensate of frequency deviation, has increased the anti-frequency deviation performance of system.At last by simulating, verifying the gain of this co-design system on the decoding end error rate, be not more than 0.3 π and frequency deviation 100ppm in the scope of 700ppm in phase deviation, the error rate can reach 10-3 to 10-4.Thereby efficiently solve the key issue of deep space communication weak signal decoding.

Above content is the further description of the present invention being done in conjunction with concrete preferred implementation, can not assert that implementation of the present invention is confined to these explanations.For the general technical staff of the technical field of the invention, without departing from the inventive concept of the premise, can also make some simple deduction or replace, all should be considered as belonging to protection scope of the present invention.

Claims (5)

1. combined modulation coding method under the deep space link residual frequency deviation is characterized in that: may further comprise the steps:

Steps A): at transmitting terminal information bit is carried out the LDPC coding, change simultaneously the order of coded sequence by the intermediate conversion matrix, make information bit be in the little position of phase deviation;

Step B): coded sequence is carried out the FQPSK modulation, transmitting of modulation generation sent into awgn channel;

Step C): receive at receiving terminal and to transmit and it is carried out the MAP demodulation, obtain the log-likelihood ratio (LLR) by bit, utilize the log-likelihood comparison code word that obtains to carry out estimation and the compensation of skew and frequency deviation;

Step D): at last soft information is sent to decoder, with the posterior probability of the demodulation prior probability as decoding, adopts the degree of confidence propagation decoding algorithm based on soft information, realize decode procedure.

2. according to claim 1 described combined modulation coding method under deep space link residual frequency deviation is characterized in that: described steps A), according to the backoff algorithm of frequency deviation, send the order of sequence by the transition matrix adjustment.

3. according to claim 1 described combined modulation coding method under deep space link residual frequency deviation, it is characterized in that: described step C), the log-likelihood ratio LLR that pursues bit that obtains that passes through and the sample sequence that receives, utilize maximum-likelihood criterion that phase difference and frequency deviation are estimated, until satisfy iterated conditional or reach maximum iterations.

4. according to claim 1 described combined modulation coding method under deep space link residual frequency deviation is characterized in that: described step C), in the FQPSK modulation technique, regard the sampled point that represents a described bit as a sub-block.

5. according to claim 1 described combined modulation coding method under deep space link residual frequency deviation, it is characterized in that: described step C), the phase difference that is caused by fixing frequency deviation can be along with the increase of code length linear increasing, in the described frequency deviation estimation scheme, come calculated rate by phase place increment in time.

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