CN103036669B - A kind of symbol timing synchronization method based on particle filter - Google Patents

Abstract

The present invention relates to a kind of symbol timing synchronization method based on particle filter, particularly relate to a kind of high speed satellite communication system symbol timing synchronization method based on particle filter, belong to signal of communication processing technology field.Input analog baseband signal, after AD sampling, becomes digital signal, and digital signal is first through an interpolation filter, and this filter is according to input signal and the timing offset estimated value that provided by particle filter calculate the value in optimum sampling moment, timing error computing module is sent in the output of interpolation filter, obtains measuring timing error, measures timing error and namely obtains timing offset estimated value through particle filter again will send into interpolation filter to control the interpolation moment, the output x ' (rT of interpolation filter _s) in contained the value x ' (rT) in optimum sampling moment, namely direct output complete sign synchronization.The inventive method, under the prerequisite not increasing sample rate, improves Timing error estimate precision; Utilize particle filter to adjust timing offset, reduce the impact of self noise compared with traditional scheme.

Description

A kind of symbol timing synchronization method based on particle filter

Technical field

The present invention relates to a kind of symbol timing synchronization method based on particle filter, particularly relate to a kind of high speed satellite communication system symbol timing synchronization method based on particle filter, belong to signal of communication processing technology field.

Background technology

Be synchronously research theme and the technical bottleneck of high speed satellite communication system, wherein, the process finding the also tracking code metasymbol optimum sampling moment is sign synchronization always.For high speed satellite communication system, because the character rate of modulation is very high, by the restriction of AD device, the sample rate of AD can not be too high relative to character rate, needs under the sample rate lower relative to character rate, to go out the signal value in optimum sampling moment by Exact recovery.In May, 1986, Gardner proposed a kind of sign synchronization algorithm in the paper of a section " A BPSK/QPSK Timing-Error Detector forSampled Receivers " by name, was called for short Gardner algorithm.In Gardner algorithm, each symbol only needs two sampled points to participate in calculating and just can realize Timed Recovery exactly, and insensitive to carrier phase, can recover prior to carrier auxiliary completion timing.But for high order modulation (such as 16APSK), even if adopt the modification method proposed in the paper of 2008 section " A Modified Gardner Detector for MultilevelPAM/QAM System " by name, systematic function still affects larger by the self noise of Gardner algorithm itself.Suitably the choosing just to become of filter is even more important, only loop filter is used in sign synchronization structure in the past, conventional symbols synchronized algorithm combines with Kalman filter by the paper in November in 2005 one section " Feedforward Symbol TimingRecovery Technique Using Two Samples Per Symbol " by name, obtains more excellent estimated performance.And Kalman filter and extended BHF approach device cannot process the larger situation of LDPC code and filtering error and predicated error, by contrast, the range of application of particle filter is wider, day by day becomes the study hotspot of academia.The paper in September in 2003 one section " Particle filtering " by name has briefly introduced operation principle and the application in a communications system thereof of particle filter.In recent years, particle filter causes the attention of signal transacting and the communications field gradually.Blind equalization, Multiuser Detection, the problems such as the space-time code estimation in fading channel and detection all can be modeled as particle filter problem.Disclosed in May, 2006, particle filter is just applied in channel estimation method by patent " channel estimation methods based on particle filter ".And particle filter method is applied to symbol synchronization system to improve estimated performance by the present invention.The paper of one section that delivers in August, 2005 " A Sequential Monte Carlo Method forAdaptive Blind Timing Estimation and Data Detection " by name, although the method that have employed particle filter estimates that timing error carries out sign synchronization, estimated performance of the present invention cannot be issued in the condition of low sampling rate.

Existing sign synchronization technology has had good estimated performance, but for the high order modulation under low signal-to-noise ratio, its estimated performance is still not ideal enough.

Summary of the invention

The object of the invention is for improving the low defect of existing time-domain symbol synchronized algorithm estimated performance, a kind of symbol timing synchronization method based on particle filter is proposed, under the prerequisite not increasing sample rate and a small amount of increase algorithm complex, realize the sign synchronization of high speed satellite communication.

Based on a symbol timing synchronization method for particle filter, implementation step is as follows:

Step 1, to input a road or two-way analog baseband signal, sample, obtain digital signal; Wherein, sample rate is f _s.

Wherein, for binary modulated, a road analog baseband signal of input is x (t), obtains a railway digital signal x (nT through analog-to-digital conversion _s); For multi-system modulation, the baseband signal of input is two-way analog signal x _i(t) and x _qt (), obtains two paths of signals x after analog-to-digital conversion _i(nT _s) and x _q(nT _s); Sample rate is f _s, the sampling interval is n is the sequence number of sampled point.

Step 2, generation particle.

According to the probability distribution π (it is 0 that π chooses an average usually, the Gaussian distribution that variance is very large) of setting, produce N number of particle sample to each symbol (code element) cycle, the timing offset that N number of particle sample is corresponding is designated as subscript i represents sample sequence number, i=1,2 ..., N, subscript r are symbol period sequence number, r=1,2 ...

Step 3, particle filter initialization.

Step 3.1, the N number of particle sample value produced during note r=1 is wherein the importance weight of each particle is

Step 3.2, each particle importance weight step 3.1 exported is normalized

${\tilde{w}}_1^{\left(i\right)}=\frac{w_1^{\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_1^{\left(i\right)}}=\frac{1}{N}---\left(1\right)$

Step 3.3, calculates timing offset estimated value

${\widehat{\mathrm{\ϵ}}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_1^{\left(i\right)}{\tilde{w}}_1^{\left(i\right)}---\left(2\right)$

Step 4, timing offset estimated value according to current sign filtering interpolation is carried out to the digital signal that step one exports, obtains the filtering interpolation output valve in optimum sampling moment, realize sign synchronization.

Filtering interpolation adopts frequency domain algorithm, and concrete steps are as follows:

Step 4.1, to the x (nT that step one exports _s) signal carries out K point FFT, obtains frequency spectrum R (kf _s/ K).

Step 4.2, to the frequency spectrum R (kf that step 4.1 obtains _s/ K) carry out phase rotating, obtain the frequency domain data R ' (kf removing timing offset _s/ K):

$R^{\′}({\mathrm{kf}}_s/K)=R({\mathrm{kf}}_s/K)\exp (j2\mathrm{\πk}{f}_s{\widehat{\mathrm{\ϵ}}}_{r}T/K)---\left(3\right)$

Step 4.3, to the R ' (kf that step 4.2 exports _s/ K) carry out IFFT, the output x'(nT of interpolation filter under output current symbol period _s), extract the output valve x ' (rT) in wherein optimum sampling moment, T is code-element period, realizes the synchronous of current symbol period.

If multi-system is modulated, the output of interpolation filter is x ' _i(nT _s) and x ' _q(nT _s), then the output valve in optimum sampling moment is x ' _i(r _t) and x ' _q(r _t).

Step 5, filtering interpolation optimum sampling moment output valve according to step 4, calculate measurement timing error u (r) during r>1.

For binary modulated, the measurement timing error of r symbol period is:

$u\left(r\right)=u\left(\mathrm{rT}\right)=x^{\′}(\mathrm{rT}-\frac{1}{2}T)[x^{\′}\left(\mathrm{rT}\right)-x^{\′}(\mathrm{rT}-T)]---\left(4\right)$

For multi-system modulation, the measurement timing error of r symbol period is:

$u\left(r\right)=u\left(\mathrm{rT}\right)$

$=x_1^{\′}(\mathrm{rT}-\frac{1}{2}T)[x_1^{\′}\left(\mathrm{rT}\right)-x_1^{\′}(\mathrm{rT}-T)]+x_Q^{\′}(\mathrm{rT}-\frac{1}{2}T)[x_Q^{\′}\left(\mathrm{rT}\right)-x_Q^{\′}(\mathrm{rT}-T)]---\left(5\right)$

Step 6, particle filter is carried out to the measurement timing error that step 5 obtains, obtain the timing offset estimated value of corresponding symbol period.

Concrete steps are as follows:

Step 6.1, according to the timing error of state equation and r-1 symbol period, tries to achieve the timing offset of N number of particle sample corresponding to r symbol period.

State equation is:

${\mathrm{\ϵ}}_r^{\left(i\right)}={\mathrm{\ϵ}}_{r-1}^{\left(i\right)}+{\mathrm{\μ}}_r^{\left(i\right)}---\left(6\right)$

Wherein, for system noise.

Step 6.2, according to observational equation, set up u (r) with relation;

Observational equation according to u (r) with between S curve obtain, be expressed as

$u\left(r\right)=-(4/T)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)\underset{0}{\overset{1/T}{\∫}}G\left(f\right)G(\frac{1}{T}-f)\sin \mathrm{\πfTdf}{+\mathrm{\γ}}_r^{\left(i\right)}---\left(15\right)$

Wherein, G (f) is filter function, for observation noise.

Step 6.3, calculates the importance weight of each particle in r symbol period;

$w_r^{\left(i\right)}=w_{r-1}^{\left(i\right)}\frac{p\left(u\left(r\right)\right|{\mathrm{\ϵ}}_r^{\left(i\right)})p\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{r-1}^{\left(i\right)})}{\mathrm{\π}\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{0:r-1}^{\left(i\right)},u\left(r\right))}---\left(7\right)$

Wherein, represent the importance weight of N number of particle sample point of r symbol period; represent the probability density of timing error u (r) under condition. represent under condition probability density.

Step 6.4, each particle importance weight of r symbol period step 6.3 exported is normalized: ${\tilde{w}}_r^{\left(i\right)}=\frac{w_r^{\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_r^{\left(i\right)}}---\left(8\right)$

Wherein, represent the normalization importance weight of r the N number of particle sample point of symbol period.

Step 6.5, for eliminating degradation phenomena, carries out resampling to the normalization weights that step 6.4 exports.

The resampling result of each symbol period is still N number of particle, uses represent the timing offset of the N number of particle sample value after resampling, the weights that after resampling, new particle is corresponding are namely

Step 6.6, asks for the timing offset estimated value after r symbol period resampling

${\widehat{\mathrm{\ϵ}}}_r=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_r^{\′\left(i\right)}{\tilde{w}}_r^{\left(i\right)}---\left(9\right)$

Step 6.7, calculates step 6.6 bring step 4 into, continue step 4 to step 6, until realize the synchronous of all symbol periods.

Beneficial effect

The present invention's " a kind of symbol timing synchronization method based on particle filter ", tool has the following advantages:

1., under the prerequisite not increasing sample rate, improve Timing error estimate precision;

2. utilize particle filter to adjust timing offset, compare the impact that traditional Gardner symbol timing synchronization method reduce further self noise;

3. its estimate variance performance is better than the Gardner symbol timing synchronization method using conventional loop filter;

4. its bit error rate performance is at high s/n ratio (Eb/N ₀>10), when, traditional Gardner sign synchronization algorithm is better than; Improve synchronous estimated accuracy and error rate of system performance.

Accompanying drawing explanation

Fig. 1 is that the system in the present invention's " a kind of symbol timing synchronization method based on particle filter " and embodiment 1 realizes schematic diagram;

When Fig. 2 is different rolloff-factor α in the present invention's " a kind of symbol timing synchronization method based on particle filter " and embodiment 1 and embodiment 2 u (r) with between S curve, abscissa is timing offset ordinate is timing error u (r);

Fig. 3 is when adopting 16APSK modulation system, rolloff-factor to be 0.2 in the embodiment 1 of the present invention's " a kind of symbol timing synchronization method based on particle filter ", the stable state Timing error estimate amount variance comparison diagram of tradition Gardner symbol timing synchronization method and the present invention's " a kind of symbol timing synchronization method based on particle filter ", abscissa is signal to noise ratio, and ordinate is the estimate variance of timing offset;

Fig. 4 is when adopting 32APSK modulation system in the embodiment 2 of the present invention's " a kind of symbol timing synchronization method based on particle filter ", tradition Gardner symbol timing synchronization method and the comparison diagram based on the symbol timing synchronization method bit error rate performance of particle filter, abscissa is signal to noise ratio, and ordinate is the bit error rate of system.

Embodiment

In order to object and the advantage of the inventive method are better described, the embodiment below in conjunction with accompanying drawing and 16APSK, 32APSK two kinds of high-order modulating is described specific embodiment of the invention process.

Embodiment 1

To adopt 16APSK modulation system, matched filter rolloff-factor be 0.2 modulation demodulation system be example, adopt the present invention " a kind of symbol timing synchronization method based on particle filter " realize sign synchronization.

As shown in Figure 1, character rate is the input analog baseband signal x of 1Mbaud _i(t) and x _qt (), after the AD sampling that over-sampling rate is fixed as 200MHz, becomes digital signal x _i(nT _s) and x _q(nT _s), x _i(nT _s) and x _q(nT _s) first through an interpolation filter, this filter is according to input signal and the timing offset estimated value that provided by particle filter calculate the value in optimum sampling moment, timing error computing module is sent in the output of interpolation filter, and obtain u (r), u (r) namely obtains timing offset estimated value through particle filter again will send into interpolation filter to control the interpolation moment, the output x ' (rT of interpolation filter _s) in contained the value x ' (rT) in optimum sampling moment, namely direct output complete sign synchronization.

Step 1, to the two-way character rate of input be 1MBaud, modulation system is 16APSK, rolloff-factor is the analog baseband signal of 0.2, sample, obtain digital signal; Wherein, sample rate is 200MHz.

Wherein, the baseband signal of input is two-way analog signal x _i(t) and x _qt (), obtains two paths of signals x after analog-to-digital conversion _i(nT _s) and x _q(nT _s).

Step 2, generation particle.

According to the probability distribution π of setting, choosing π, to obey average be 0, and variance is the Gaussian distribution of 0.01, and produce N=100 particle sample to each symbol (code element) cycle, the timing offset that 100 particle samples are corresponding is designated as subscript i represents sample sequence number, i=1,2 ..., N, subscript r are symbol period sequence number, r=1,2 ...

Step 3, particle filter initialization.

Step 3.1, the N number of particle sample value produced during note r=1 is wherein the importance weight of each particle is

Step 3.2, each particle importance weight step 3.1 exported is normalized

${\tilde{w}}_r^{\left(i\right)}=\frac{w_r^{\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_1^{\left(i\right)}}=\frac{1}{N}=\frac{1}{100}---\left(1\right)$

Step 3.3, calculates timing offset estimated value

${\widehat{\mathrm{\ϵ}}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_1^{\left(i\right)}{\tilde{w}}_1^{\left(i\right)}=0---\left(2\right)$

Step 4, timing offset estimated value according to current sign filtering interpolation is carried out to the digital signal that step one exports, obtains the filtering interpolation output valve in optimum sampling moment, realize sign synchronization.

Filtering interpolation adopts frequency domain algorithm, and concrete steps are as follows:

Step 4.1, to the x (nT that step one exports _s) signal carries out K=16 point FFT, obtains frequency spectrum R (kf _s/ K).

Step 4.2, to the frequency spectrum R (kf that step 4.1 obtains _s/ K) carry out phase rotating, obtain the frequency domain data R ' (kf removing timing offset _s/ K):

$R^{\′}({\mathrm{kf}}_s/K)=R({\mathrm{kf}}_s/K)\exp (j2\mathrm{\πk}{f}_s{\widehat{\mathrm{\ϵ}}}_{r}T/K)---\left(3\right)$

Step 4.3, to the R ' (kf that step 4.2 exports _s/ K) carry out IFFT, the output x'(nT of interpolation filter under output current symbol period _s), extract the output valve x ' (rT) in wherein optimum sampling moment, T is code-element period, realizes the synchronous of current symbol period.

If multi-system is modulated, the output of interpolation filter is x ' _i(nT _s) and x ' _q(nT _s), then the output valve in optimum sampling moment is x ' _i(r _t) and x ' _q(r _t).

Step 5, filtering interpolation output valve according to step 4, calculate measurement timing error u (r) during r>1.

For high order modulation such as MQAM and MAPSK, need to revise median sample value:

$x_I^{\′\′}(\mathrm{rT}-\frac{1}{2}T)=x_I^{\′}(\mathrm{rT}-\frac{1}{2}T)-\mathrm{\β}[x_I^{\′}(\mathrm{rT}-T)+x_I^{\′}\left(\mathrm{rT}\right)]---\left(4\right)$

$x_Q^{\′\′}(\mathrm{rT}-\frac{1}{2}T)=x_Q^{\′}(\mathrm{rT}-\frac{1}{2}T)-\mathrm{\β}[x_Q^{\′}(\mathrm{rT}-T)+x_Q^{\′}\left(\mathrm{rT}\right)]---\left(5\right)$

Wherein, with for revised median sample value,

β=h (T/2)/h (0)=h (-T/2)/h (0), the impulse response that h (t) is filter;

The measurement timing error of r symbol period is:

$u\left(r\right)=u\left(\mathrm{rT}\right)$

$=x_I^{\′\′}(\mathrm{rT}-\frac{1}{2}T)[x_I^{\′}\left(\mathrm{rT}\right)-x_I^{\′}(\mathrm{rT}-T)]+x_Q^{\′\′}(\mathrm{rT}-\frac{1}{2}T)[x_Q^{\′}\left(\mathrm{rT}\right)-x_Q^{\′}(\mathrm{rT}-T)]---\left(6\right)$

Step 6, particle filter is carried out to the measurement timing error that step 5 obtains, obtain the timing offset estimated value of corresponding symbol period.

Concrete steps are as follows:

Step 6.1, according to the timing error of state equation and r-1 symbol period, tries to achieve the timing offset of N number of particle sample corresponding to r symbol period.

State equation is:

${\mathrm{\ϵ}}_r^{\left(i\right)}={\mathrm{\ϵ}}_{r-1}^{\left(i\right)}+{\mathrm{\μ}}_r^{\left(i\right)}---\left(7\right)$

Wherein, for system noise, setting its obedience average is 0, and variance is the Gaussian distribution of 0.00001.

Step 6.2, according to observational equation, set up u (r) with relation;

Observational equation according to u (r) with between S curve obtain, can be expressed as

$u\left(r\right)=-(4/T)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)\underset{0}{\overset{1/T}{\∫}}G\left(f\right)G(\frac{1}{T}-f)\sin \mathrm{\πfTdf}{+\mathrm{\γ}}_r^{\left(i\right)}---\left(8\right)$

Wherein, G (f) is filter function, for observation noise.

When G (f) is for raised cosine FIR filter,

$u\left(r\right)=\sin (\mathrm{\π\α}/2)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)/\left[\mathrm{\π}(1-{\mathrm{\α}}^2/4)\right]+{\mathrm{\γ}}^{\left(i\right)}---\left(9\right)$

Wherein, α is the rolloff-factor of raised cosine filter, and the S curve that different rolloff-factor is corresponding is shown in Fig. 2.α=0.2 in the present embodiment.

Step 6.3, calculates the importance weight of each particle in r symbol period;

$w_r^{\left(i\right)}=w_{r-1}^{\left(i\right)}\frac{p\left(u\left(r\right)\right|{\mathrm{\ϵ}}_r^{\left(i\right)})p\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{r-1}^{\left(i\right)})}{\mathrm{\π}\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{0:r-1}^{\left(i\right)},u\left(r\right))}---\left(10\right)$

Because the priori probability density function chosen is importance function, that is,

$\mathrm{\π}\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{0:r-1}^{\left(i\right)},u\left(r\right))=p\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{r-1}^{\left(i\right)})---\left(11\right)$

Therefore, $w_r^{\left(i\right)}=w_{r-1}^{\left(i\right)}p\left(u\left(r\right)\right|{\mathrm{\ϵ}}_r^{\left(i\right)})---\left(12\right)$

Owing to there is observation noise and system noise, and separate between them, therefore,

$p\left(u\left(r\right)\right|{\mathrm{\ϵ}}_r^{\left(i\right)})=p\left({\mathrm{\γ}}_r\right|{\mathrm{\ϵ}}_r^{\left(i\right)})=p(u\left(r\right)-\sin (\mathrm{\π\α}/2)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)/[\mathrm{\π}(1-{\mathrm{\α}}^2/4)\left]\right)---\left(13\right)$

Supposing that observation noise obeys average is the Gaussian Profile of 0, then weight computing is

$w_r^{\left(i\right)}=w_{r-1}^{\left(i\right)}\exp [-\frac{1}{{2\mathrm{\σ}}^2}(u\left(r\right)-\sin (\mathrm{\π\α}/2)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)/[\mathrm{\π}(1-{\mathrm{\α}}^2/4)\left]\right)]---\left(14\right)$

Step 6.4, each particle importance weight of r symbol period step 6.3 exported is normalized:

${\tilde{w}}_r^{\left(i\right)}=\frac{w_r^{\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_r^{\left(i\right)}}---\left(15\right)$

Wherein, represent the normalization importance weight of r the N number of particle sample point of symbol period.

Step 6.5, for eliminating degradation phenomena, carries out resampling to the normalization weights that step 6.4 exports.

The present embodiment adopts systematic sampling method to carry out resampling:

N=100 random number is generated according to following formula,

wherein, q obeys being uniformly distributed of [0,1], m=1, and 2 ..., 100;

If a direct copying a particle for resampling particle.

The resampling result of each symbol period is still N=100 particle, uses represent the timing offset of 100 particle sample values after resampling, the weights that after resampling, new particle is corresponding are namely

Step 6.6, asks for the timing offset estimated value after r symbol period resampling

${\widehat{\mathrm{\ϵ}}}_r=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_r^{\′\left(i\right)}{\tilde{w}}_r^{\left(i\right)}---\left(16\right)$

Step 6.7, calculates step 6.6 bring step 4 into, continue step 4 to step 6, until realize the synchronous of all symbol periods.

Based on the synchronous method in the present invention's " a kind of symbol timing synchronization method based on particle filter ", to employing 16APSK modulation system, rolloff-factor be 0.2 system realize synchronous, traditional Gardner sign synchronization algorithm of Fig. 3 and the variance comparison diagram based on the stable state Timing error estimate amount of the sign synchronization algorithm of particle filter can be drawn, wherein, the normalization bandwidth of loop filter used in traditional Gardner synchronized algorithm is B _lt=10 ^-3.Observe and find, adopt the variance ratio of the stable state Timing error estimate amount of the sign synchronization algorithm based on particle filter to adopt the nearly 8dB of variance performance boost of the stable state Timing error estimate amount of traditional Gardner sign synchronization algorithm.

Embodiment 2

In order to verify this synchronous method further, a kind of method in " symbol timing synchronization method based on particle filter " of the present invention is adopted to realize for the system that there is frequency deviation and skew synchronous.This system adopts STM-4 standard, and information rate is 622.08Mbps, and adopt 32APSK modulation system, character rate is 154MB, and every frame frame head 120 symbols, valid data 3936 symbols, rolloff-factor is 0.5.

Step 1, to the two-way character rate of input be 154MBaud, modulation system is 32APSK, rolloff-factor is the analog baseband signal of 0.5, sample, obtain digital signal; Wherein, sample rate is 1.54GHz.

Wherein, the baseband signal of input is two-way analog signal x _i(t) and x _qt (), obtains two paths of signals x after analog-to-digital conversion _i(nT _s) and x _q(nT _s).

Step 2, generation particle.

According to the probability distribution π of setting, choosing π, to obey average be 0, and variance is the Gaussian distribution of 0.01, and produce N=100 particle sample to each symbol (code element) cycle, the timing offset that 100 particle samples are corresponding is designated as subscript i represents sample sequence number, i=1,2 ..., N, subscript r are symbol period sequence number, r=1,2 ...

Step 3, particle filter initialization.

Step 3.1, the N number of particle sample value produced during note r=1 is wherein the importance weight of each particle is

Step 3.2, each particle importance weight step 3.1 exported is normalized

${\tilde{w}}_1^{\left(i\right)}=\frac{w_1^{\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_1^{\left(i\right)}}=\frac{1}{N}=\frac{1}{100}---\left(1\right)$

Step 3.3, calculates timing offset estimated value

${\widehat{\mathrm{\ϵ}}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_1^{\left(i\right)}{\tilde{w}}_1^{\left(i\right)}---\left(2\right)$

Known

Step 4, timing offset estimated value according to current sign filtering interpolation is carried out to the digital signal that step one exports, obtains the filtering interpolation output valve in optimum sampling moment, realize sign synchronization.

Filtering interpolation adopts frequency domain algorithm, and concrete steps are as follows:

Step 4.1, to the x (nT that step one exports _s) signal carries out K=32 point FFT, obtains frequency spectrum R (kf _s/ K).

Step 4.2, to the frequency spectrum R (kf that step 4.1 obtains _s/ K) carry out phase rotating, obtain the frequency domain data R ' (kf removing timing offset _s/ K):

$R^{\′}({\mathrm{kf}}_s/K)=R({\mathrm{kf}}_s/K)\exp (j2\mathrm{\πk}{f}_s{\widehat{\mathrm{\ϵ}}}_{r}T/K)---\left(3\right)$

Step 4.3, to the R ' (kf that step 4.2 exports _s/ K) carry out IFFT, the output x'(nT of interpolation filter under output current symbol period _s), extract the output valve x ' (rT) in wherein optimum sampling moment, T is code-element period, realizes the synchronous of current symbol period.

If multi-system is modulated, the output of interpolation filter is x ' _i(nT _s) and x ' _q(nT _s), then the output valve in optimum sampling moment is x ' _iand x ' (rT) _q(rT).

Step 5, filtering interpolation output valve according to step 4, calculate measurement timing error u (r) during r>1.

For high order modulation such as MQAM and MAPSK, need to revise median sample value:

$x_I^{\′\′}(\mathrm{rT}-\frac{1}{2}T)=x_I^{\′}(\mathrm{rT}-\frac{1}{2}T)-\mathrm{\β}[x_I^{\′}(\mathrm{rT}-T)+x_I^{\′}\left(\mathrm{rT}\right)]---\left(4\right)$

$x_Q^{\′\′}(\mathrm{rT}-\frac{1}{2}T)=x_Q^{\′}(\mathrm{rT}-\frac{1}{2}T)-\mathrm{\β}[x_Q^{\′}(\mathrm{rT}-T)+x_Q^{\′}\left(\mathrm{rT}\right)]---\left(5\right)$

Wherein, with for revised median sample value,

β=h (T/2)/h (0)=h (-T/2)/h (0), the impulse response that h (t) is filter;

The measurement timing error of r symbol period is:

$u\left(r\right)=u\left(\mathrm{rT}\right)$

$=x_I^{\′\′}(\mathrm{rT}-\frac{1}{2}T)[x_I^{\′}\left(\mathrm{rT}\right)-x_I^{\′}(\mathrm{rT}-T)]+x_Q^{\′\′}(\mathrm{rT}-\frac{1}{2}T)[x_Q^{\′}\left(\mathrm{rT}\right)-x_Q^{\′}(\mathrm{rT}-T)]---\left(6\right)$

Step 6, particle filter is carried out to the measurement timing error that step 5 obtains, obtain the timing offset estimated value of corresponding symbol period.

Concrete steps are as follows:

Step 6.1, according to the timing error of state equation and r-1 symbol period, tries to achieve the timing offset of N number of particle sample corresponding to r symbol period.

State equation is:

${\mathrm{\ϵ}}_r^{\left(i\right)}={\mathrm{\ϵ}}_{r-1}^{\left(i\right)}+{\mathrm{\μ}}_r^{\left(i\right)}---\left(7\right)$

Wherein, for system noise, setting its obedience average is 0, and variance is the Gaussian distribution of 0.00001.

Step 6.2, according to observational equation, set up u (r) with relation;

Observational equation according to u (r) with between S curve obtain, can be expressed as

$u\left(r\right)=-(4/T)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)\underset{0}{\overset{1/T}{\∫}}G\left(f\right)G(\frac{1}{T}-f)\sin \mathrm{\πfTdf}{+\mathrm{\γ}}_r^{\left(i\right)}---\left(8\right)$

Wherein, G (f) is filter function, for observation noise.

When G (f) is for raised cosine FIR filter,

$u\left(r\right)=\sin (\mathrm{\π\α}/2)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)/\left[\mathrm{\π}(1-{\mathrm{\α}}^2/4)\right]+{\mathrm{\γ}}^{\left(i\right)}---\left(9\right)$

Wherein, α is the rolloff-factor of raised cosine filter, and the S curve that different rolloff-factor is corresponding is shown in Fig. 3.α=0.5 in the present embodiment.

Step 6.3, calculates the importance weight of each particle in r symbol period;

$w_r^{\left(i\right)}=w_{r-1}^{\left(i\right)}\frac{p\left(u\left(r\right)\right|{\mathrm{\ϵ}}_r^{\left(i\right)})p\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{r-1}^{\left(i\right)})}{\mathrm{\π}\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{0:r-1}^{\left(i\right)},u\left(r\right))}---\left(10\right)$

Because the priori probability density function chosen is importance function, that is,

$\mathrm{\π}\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{0:r-1}^{\left(i\right)},u\left(r\right))=p\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{r-1}^{\left(i\right)})---\left(11\right)$

Therefore,

$w_r^{\left(i\right)}=w_{r-1}^{\left(i\right)}p\left(u\left(r\right)\right|{\mathrm{\ϵ}}_r^{\left(i\right)})---\left(12\right)$

Owing to there is observation noise and system noise, and separate between them, therefore,

$p\left(u\left(r\right)\right|{\mathrm{\ϵ}}_r^{\left(i\right)})=p\left({\mathrm{\γ}}_r\right|{\mathrm{\ϵ}}_r^{\left(i\right)})=p(u\left(r\right)-\sin (\mathrm{\π\α}/2)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)/[\mathrm{\π}(1-{\mathrm{\α}}^2/4)\left]\right)---\left(13\right)$

Supposing that observation noise obeys average is the Gaussian Profile of 0, then weight computing is

$w_r^{\left(i\right)}=w_{r-1}^{\left(i\right)}\exp [-\frac{1}{{2\mathrm{\σ}}^2}(u\left(r\right)-\sin (\mathrm{\π\α}/2)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)/[\mathrm{\π}(1-{\mathrm{\α}}^2/4)\left]\right)]---\left(14\right)$

Step 6.4, each particle importance weight of r symbol period step 6.3 exported is normalized:

${\tilde{w}}_r^{\left(i\right)}=\frac{w_r^{\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_r^{\left(i\right)}}---\left(15\right)$

Wherein, represent the normalization importance weight of r the N number of particle sample point of symbol period.

Step 6.5, for eliminating degradation phenomena, carries out resampling to the normalization weights that step 6.4 exports.

The present embodiment adopts systematic sampling method to carry out resampling:

N=100 random number is generated according to following formula,

wherein, q obeys being uniformly distributed of [0,1], m=1, and 2 ..., 100;

If a direct copying a particle for resampling particle.

The resampling result of each symbol period is still N=100 particle, uses represent the timing offset of 100 particle sample values after resampling, the weights that after resampling, new particle is corresponding are namely

Step 6.6, asks for the timing offset estimated value after r symbol period resampling

${\widehat{\mathrm{\ϵ}}}_r=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_r^{\′\left(i\right)}{\tilde{w}}_r^{\left(i\right)}---\left(16\right)$

Step 6.7, calculates step 6.6 bring step 4 into, continue step 4 to step 6, until realize the synchronous of all symbol periods.

Fig. 4 is under this systems, and setting frequency deviation is 3MHz, when skew is π/12, and traditional Gardner sign synchronization algorithm and the comparison diagram based on the sign synchronization algorithm bit error rate performance of particle filter.From Fig. 3 and Fig. 4, the bit error rate performance based on the sign synchronization algorithm of particle filter is better than the bit error rate performance of traditional Gardner sign synchronization algorithm, and advantage is especially obvious under conditions of high signal/noise ratio.

The above is preferred embodiment of the present invention, and the present invention should not be confined to the content disclosed in this embodiment and accompanying drawing.Every do not depart from spirit disclosed in this invention under the equivalence that completes or amendment, all fall into the scope of protection of the invention.

Claims (4)

1. based on a symbol timing synchronization method for particle filter, it is characterized in that: performing step is as follows:

Step 1, to input a road or two-way analog baseband signal, sample, obtain digital signal;

Wherein, for binary modulated, a road analog baseband signal of input is x (t), obtains a railway digital signal x (nT through analog-to-digital conversion _s); For multi-system modulation, the baseband signal of input is two-way analog signal x _i(t) and x _qt (), obtains two paths of signals x after analog-to-digital conversion _i(nT _s) and x _q(nT _s); Sample rate is f _s, the sampling interval is n is the sequence number of sampled point;

Step 2, generation particle;

According to the probability distribution π of setting, produce N number of particle sample to each symbol period, the timing offset that N number of particle sample is corresponding is designated as subscript i represents sample sequence number, i=1,2 ..., N, subscript r are symbol period sequence number, r=1,2,

Step 3, particle filter initialization;

Step 3.1, the N number of particle sample value produced during note r=1 is wherein the importance weight of each particle is

Step 3.2, each particle importance weight step 3.1 exported is normalized

${\tilde{w}}_1^{\left(i\right)}=\frac{w_1^{\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_1^{\left(i\right)}}=\frac{1}{N}---\left(1\right)$

Step 3.3, calculates timing offset estimated value

${\widehat{\mathrm{\ϵ}}}_1=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_1^{\left(i\right)}{\tilde{w}}_1^{\left(i\right)}---\left(2\right)$

Step 4, timing offset estimated value according to current sign filtering interpolation is carried out to the digital signal that step one exports, obtains the filtering interpolation output valve in optimum sampling moment, realize sign synchronization;

Filtering interpolation adopts frequency domain algorithm, and concrete steps are as follows:

Step 4.1, to the x (nT that step one exports _s) signal carries out K point FFT, obtains frequency spectrum R (kf _s/ K);

Step 4.2, to the frequency spectrum R (kf that step 4.1 obtains _s/ K) carry out phase rotating, obtain the frequency domain data R ' (kf removing timing offset _s/ K):

$R^{\′}(k{f}_s/K)=R(k{f}_s/K)\exp (j2\mathrm{\π}{f}_s{\widehat{\mathrm{\ϵ}}}_{r}T/K)---\left(3\right)$

Step 4.3, to the R ' (kf that step 4.2 exports _s/ K) carry out IFFT, the output x'(nT of interpolation filter under output current symbol period _s), extract the output valve x ' (rT) in wherein optimum sampling moment, T is code-element period, realizes the synchronous of current symbol period;

Step 5, filtering interpolation optimum sampling moment output valve according to step 4, calculate measurement timing error u (r) during r>1;

For binary modulated, the measurement timing error of r symbol period is:

$u\left(r\right)=u\left(\mathrm{rT}\right)=x^{\′}(\mathrm{rT}-\frac{1}{2}T)[x^{\′}\left(\mathrm{rT}\right)-x^{\′}(\mathrm{rT}-T)]---\left(4\right)$

Step 6, particle filter is carried out to the measurement timing error that step 5 obtains, obtain the timing offset estimated value of corresponding symbol period;

Concrete steps are as follows:

Step 6.1, according to the timing error of state equation and r-1 symbol period, tries to achieve the timing offset of N number of particle sample corresponding to r symbol period;

State equation is:

${\mathrm{\ϵ}}_r^{\left(i\right)}={\mathrm{\ϵ}}_{r-1}^{\left(i\right)}+{\mathrm{\μ}}_r^{\left(i\right)}---\left(6\right)$

Wherein, for system noise;

Step 6.2, according to observational equation, set up u (r) with relation;

Observational equation according to u (r) with between S curve obtain, be expressed as

$u\left(r\right)=-(4/T)\sin \left(2\mathrm{\π}{\mathrm{\ϵ}}_r^{\left(i\right)}\right)\underset{0}{\overset{1/T}{\∫}}G\left(f\right)G(\frac{1}{T}-f)\sin \mathrm{\πfTdf}+{\mathrm{\γ}}_r^{\left(i\right)}---\left(15\right)$

Wherein, G (f) is filter function, for observation noise;

Step 6.3, calculates the importance weight of each particle in r symbol period;

$w_r^{\left(i\right)}=w_{r-1}^{\left(i\right)}\frac{p\left(u\left(r\right)\right|{\mathrm{\ϵ}}_r^{\left(i\right)})p\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{r-1}^{\left(i\right)})}{\mathrm{\π}\left({\mathrm{\ϵ}}_r^{\left(i\right)}\right|{\mathrm{\ϵ}}_{0:r-1}^{\left(i\right)},u\left(r\right))}---\left(7\right)$

Wherein, represent the importance weight of N number of particle sample point of r symbol period; represent the probability density of timing error u (r) under condition; represent under condition probability density; be the priori probability density function chosen, be importance function;

Step 6.4, each particle importance weight of r symbol period step 6.3 exported is normalized:

${\tilde{w}}_r^{\left(i\right)}=\frac{w_r^{\left(i\right)}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{w}_r^{\left(i\right)}}---\left(8\right)$

Wherein, represent the normalization importance weight of r the N number of particle sample point of symbol period;

Step 6.5, carries out resampling to the normalization weights that step 6.4 exports;

represent the timing offset of the N number of particle sample value after resampling, the weights that after resampling, new particle is corresponding are

Step 6.6, asks for the timing offset estimated value after r symbol period resampling

${\widehat{\mathrm{\ϵ}}}_r=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_r^{\′\left(i\right)}{\tilde{w}}_r^{\left(i\right)}---\left(9\right)$

Step 6.7, calculates step 6.6 bring step 4 into, continue step 4 to step 6, until realize the synchronous of all symbol periods.

2. a kind of symbol timing synchronization method based on particle filter according to claim 1, is characterized in that: π is Gaussian distribution, 0 average, large variance.

3. a kind of symbol timing synchronization method based on particle filter according to claim 1, is characterized in that: $-0.5<{\mathrm{\&epsiv;}}_r^{\left(i\right)}\&le;0.5.$

4. a kind of symbol timing synchronization method based on particle filter according to claim 1, is characterized in that: if multi-system modulation, the output of interpolation filter is x ' _i(nT _s) and x ' _q(nT _s), the output valve in optimum sampling moment is x ' _iand x ' (rT) _q(rT); The measurement timing error of r symbol period is:

$\begin{array}{c}u\left(r\right)=u\left(\mathrm{rT}\right)\\ =x_I^{\&prime;}(\mathrm{rT}-\frac{1}{2}T)[x_I^{\&prime;}\left(\mathrm{rT}\right)-x_I^{\&prime;}(\mathrm{rT}-T)]+x_Q^{\&prime;}(\mathrm{rT}-\frac{1}{2}T)[x_Q^{\&prime;}\left(\mathrm{rT}\right)-x_Q^{\&prime;}(\mathrm{rT}-T)].\end{array}$