CN104022995A - OFDM (Orthogonal Frequency Division Multiplexing) precise timing synchronous method based on Zadoff-Chu sequence - Google Patents

Abstract

The invention discloses an OFDM (Orthogonal Frequency Division Multiplexing) precise timing synchronous method based on a Zadoff-Chu sequence, which belongs to the technical field of communication and mainly aims at solving the problem of timing deviation caused by the fact that a path with the maximum energy in a multi-path fading channel of an orthogonal frequency division multiplexing system is not a first path. Channel impulse response is estimated through Zadoff-Chu sequence correlation, and a self-adaptive threshold detection algorithm for withstanding residual frequency deviation is established, then the achieving time of the first path is accurately judged, moreover the self-adaptive threshold is modified aiming at the problem that the false alarm probability is increased because of the residual frequency deviation, and verification shows that in a high speed moving multi-path environment, the algorithm detection probability is high, the mean square error is small, the detection probability can be greater than 99% in an SUI-3 channel when the signal to noise ratio is greater than 3dB, and then the method can be applied to a wideband OFDM communication system in the high speed moving environment.

Description

A kind of OFDM accurate timing synchronous method based on Zadoff-Chu sequence

Technical field

The present invention relates to ofdm system Timing Synchronization technology, particularly relate to a kind of OFDM accurate timing synchronous method based on Zadoff-Chu sequence, belong to communication technical field.

Background technology

The features such as OFDM (Orthogonal Frequency Division Multiplexing, orthogonal frequency division multiplexi) is high with its availability of frequency spectrum, and anti-multipath fading ability is strong are used widely in high-speed radio transmission system.Timing Synchronization is one of key issue of ofdm system, at present existing large quantity research.

Under multi-path environment, there are at present many people to propose the Timing Synchronization algorithm based on energy measuring, but the timing point of its acquisition can be subject to the impact of energy maximum diameter and produce skew, can not accurately detect the time of advent in the first footpath, thereby cause the problems such as inaccuracy that channel estimation method hydraulic performance decline and networking application time delay adjust.The method that detects the first footpath under existing multipath channel has: threshold judgement detection method and the synchronized algorithm based on channel estimating etc., wherein:

Document [1]: utilize conjugation symmetrical relevant with postpone the relevant position that obtains timing metric peak value and obtain the first footpath, but this algorithm employing fixed threshold detects, and can not adapt to time varying channel, and poor-performing under Low SNR.Document [2] is asked relevant every the footpath of isolating by receiving signal to local sequence, determine the first path position, but filter parameter setting need to verify repeatedly through filtering, does not have a versatility.Document [3] is according to the ring shift right characteristic estimating timing slip of channel impulse response, but this algorithm need to carry out twice fast Fourier transform, and implementation complexity is high, and timing slip estimates that peak value exists plateau phenomenon.Document [4] adopts permanent envelope zero auto-correlation (Constant Envelope Zero Auto-Correlation, CAZAC) training sequence, there is higher multi-path resolved rate, and according to first footpath time of advent of adaptive threshold detecting, but ignore the impact of frequency deviation on CAZAC serial correlation.Above-mentioned list of references is respectively:

[1] Shi Feng, Wang Chen, Zhou Zhu, etc. a kind of new for repeating the leading OFDM synchronized algorithm [J] of the symmetrical structure of conjugation. National University of Defense technology's journal, 2010,32 (3): 103-108.

[2] Zhang Jie, Cai Peng, Zhang Ping. a kind of OFDM Timing Synchronization algorithm [J] that is applicable to multidiameter fading channel. Beijing University of Post & Telecommunication's journal, 2005,28 (2): 105-108.

[3]Kishore?CN,Reddy?V.A?technique?for?dominant?path?delay?estimation?in?an?OFDM?system?and?its?application?to?frame?synchronization?in?OFDM?mode?of?WMAN[J].EURASIP?Journal?on?Wireless?Communications?and?Networking,2006,2006(2):1-8.

[4]Yang?F,Zhang?X.Robust?Time-Domain?Fine?Symbol?Synchronization?for?OFDM-Based?Packet?Transmission?Using?CAZAC?Preamble[C].2013IEEE?Military?Communications?Conference(MILCOM2013),San?Diego,2013:436-440.

Summary of the invention

For above-mentioned defect, the present invention proposes a kind of OFDM accurate timing synchronous method based on Zadoff-Chu sequence, the method makes full use of the good autocorrelation performance of Zadoff-Chu sequence, by the relation of timing metric function and channel impulse response, adopt adaptive threshold to adjudicate for first footpath time of advent, thereby the problem that the false alarm probability that solution residual frequency departure causes increases, the method does not need time-frequency conversion, be easy to realize, can meet the requirement of high-speed mobile wide-band communication system to synchronization accuracy.

In order to achieve the above object, concrete technical scheme of the present invention is as follows:

An OFDM accurate timing synchronous method based on Zadoff-Chu sequence, its key is to carry out according to following steps:

Step S1, according to calculate the timing metric functional value that d baseband equivalence receives signal place, and using | M (d) | d point corresponding while getting maximum is as thick synchronous point wherein:

N _pfor the cycle of Zadoff-Chu sequence, and N _p=N/2 is also even number, and N is system subcarrier number; Local Zadoff-Chu sequence definition is j is imaginary unit, and r is positive integer, and r and N _prelatively prime; C ^*(n) be local Zadoff-Chu sequence C _ncomplex conjugate; R (d+n) is the sampled value that d+n baseband equivalence receives signal;

Step S2: according to the thick synchronous point in step S1 system is carried out to frequency deviation estimation, obtains frequency departure ε, and according to r ' (n)=r (n) e ^{-j2 π ε}baseband equivalence is received to signal and carry out compensate of frequency deviation;

Step S3: according to calculate the timing metric functional value at d baseband equivalence reception signal place after compensate of frequency deviation;

Step S4: in scope, select to meet | M'(d) | > V ' _tand minimum d as best Timing Synchronization point n _gfor the length of Cyclic Prefix, V ' _tfor judging threshold.

In order to realize adaptive threshold judgement, decision threshold V ' _tv _t+ Δ V, wherein:

$V_T=\sqrt{P_{\mathrm{fa}}^{-1/J}-1\underset{d=1}{\overset{J}{\mathrm{\Σ}}}{\left|M\left(d\right)\right|}^2};$

$\mathrm{\ΔV}=\frac{1}{N_p}\left|e^{-\mathrm{j\π}/N_p}\frac{1-e^{\mathrm{j\π}{\mathrm{\Δ\ϵ}}_{\max }}}{1-e^{-\mathrm{j\π}(2-{\mathrm{\Δ\ϵ}}_{\max })/N_p}}\right|*\left|M{\hat{d}}_{\mathrm{coarse}}\right|;$

Δ ε _maxfor the maximum residual frequency departure of system, in practical application, can be taken as maximum doppler frequency, the number that J is energy sampled point, P _fafor the false alarm probability of system.

As preferably, the number J=N of described energy sampled point _g.

As preferably, local Zadoff-Chu sequence middle r is made as 1.

Remarkable result of the present invention is:

The present invention is directed to energy maximum diameter under multipath channel and be not the problem that ofdm system timing accuracy that the first footpath causes declines, a kind of new time synchronization method based on Zadoff-Chu sequence has been proposed, first the method utilizes the good autocorrelation performance of Zadoff-Chu sequence to obtain the estimated value of channel impulse response, then adopt the time of advent in adaptive threshold technology for detection the first footpath, and the problem that causes false alarm probability to increase for residual frequency departure is revised adaptive threshold, by checking, this paper method detection probability in multipath channel is high, mean square error is little, can be used for the wideband OFDM communication system under high-speed mobile environment.

Brief description of the drawings

Fig. 1 is method step figure of the present invention;

Fig. 2 is training symbol structural representation;

Fig. 3 is the schematic diagram of Timing Synchronization in Different Diameter;

Fig. 4 is the MSE curve chart of channel impulse response estimation;

Fig. 5 is under SUI3 channel, the detection probability comparative analysis figure of various algorithms;

Fig. 6 is under SUI5 channel, the detection probability comparative analysis figure of various algorithms;

Fig. 7 is under SUI3 channel, the MSE result comparative analysis figure of various algorithms;

Fig. 8 is under SUI5 channel, the MSE result comparative analysis figure of various algorithms.

Embodiment

Below in conjunction with drawings and Examples, the invention will be further described:

As shown in Figure 1, a kind of OFDM accurate timing synchronous method based on Zadoff-Chu sequence, by local Zadoff-Chu sequence definition is first j is imaginary unit, and r is positive integer, and r and N _prelatively prime, conventionally r is made as to 1, N here _pfor the cycle of Zadoff-Chu sequence, and N _p=N/2 is also even number, and N is system subcarrier number;

For Zadoff-Chu sequence, its auto-correlation function is:

$R_m=\underset{n=0}{\overset{N_p-1}{\mathrm{\Σ}}}{C}_n{C}_{(n+m)\mathrm{mod}{N}_p}^{*}=\underset{n=0}{\overset{N_p-m-1}{\mathrm{\Σ}}}{C}_n{C}_{(n+m)}^{*}+\underset{n-N_p-m}{\overset{N_p-1}{\mathrm{\Σ}}}{C}_n{C}_{(n+m)}^{*}=\left\{\begin{array}{c}{N}_p,m=0\\ 0,m\≠0\end{array}\right.$

Mod in above formula represents delivery, having secondary lobe by the circulation auto-correlation of the known Zadoff-Chu sequence of above formula is 0 characteristic, in addition, Zadoff-Chu sequence also has the feature of low peak average ratio, permanent envelope, and its FFT conversion or a Zadoff-Chu sequence, these characteristics are widely used in ofdm system Zadoff-Chu sequence.

In the present embodiment, the structure of training symbol as shown in Figure 2, according to the feature of Fig. 2 training symbol, can utilize its repeatability that comprises data sequence and correlation properties to carry out timing slip estimation, and therefore, this method concrete steps are:

Step S1, according to calculate the timing metric functional value that d baseband equivalence receives signal place, and using | M (d) | d point corresponding while getting maximum is as thick synchronous point wherein, C ^*(n) be local Zadoff-Chu sequence C _ncomplex conjugate; R (d+n) is the sampled value that d+n baseband equivalence receives signal;

Step S2: according to the thick synchronous point in step S1 system is carried out to frequency deviation estimation, obtains frequency departure ε, and according to r ' (n)=r (n) e ^{-j2 π ε}baseband equivalence is received to signal and carry out compensate of frequency deviation;

Step S3: according to calculate the timing metric functional value at d baseband equivalence reception signal place after compensate of frequency deviation;

Step S4: in scope, select to meet | M'(d) | V ' _tand minimum d is as best Timing Synchronization point n _gfor the length of Cyclic Prefix, V ' _tfor judging threshold.

In order to realize adaptive threshold judgement, above-mentioned decision threshold V ' _t=V _t+ Δ V, wherein:

$V_T=\sqrt{P_{\mathrm{fa}}^{-1/J}-1\underset{d=1}{\overset{J}{\mathrm{\Σ}}}{\left|M\left(d\right)\right|}^2};$

$\mathrm{\ΔV}=\frac{1}{N_p}\left|e^{-\mathrm{j\π}/N_p}\frac{1-e^{\mathrm{j\π}{\mathrm{\Δ\ϵ}}_{\max }}}{1-e^{-\mathrm{j\π}(2-{\mathrm{\Δ\ϵ}}_{\max })/N_p}}\right|*\left|M{\hat{d}}_{\mathrm{coarse}}\right|;$

Δ ε _maxfor the maximum residual frequency departure of system, in practical application, can be taken as maximum doppler frequency, the number that J is energy sampled point, arranges J=N conventionally _g, P _fafor the false alarm probability of system.

In order further to understand operation principle of the present invention and technique effect, further said method is set forth below.

Under multipath channel condition, it is the time of advent of energy maximum diameter, and in practical communication environment, energy maximum diameter might not be the first footpath, as shown in Figure 3, in the time that the second footpath is energy maximum diameter, FFT window can fix on the data division of the first footpath signal and cause intersymbol interference (Inter-Symbol Interference, ISI) and inter-carrier interference (Inter-Carrier Interference, ICI).

Can judge according to following process the time of advent in the first footpath: from Timing Synchronization point lv sampling point starts to search for backward before, timing metric M (d) compared with threshold value, if certain moment M (d) exceedes thresholding, using this moment as final timing position.These class methods require timing metric function M (d) can correctly reflect channel impulse response feature, otherwise choosing of threshold value will be very difficult.

Ignoring under the condition of the propagation delay time between transmitted from transmitter to receiver, timing metric function is opened and can be obtained:

$\begin{array}{c}M\left(d\right)=\frac{1}{N}\underset{n=0}{\overset{N_p-1}{\mathrm{\Σ}}}r(d+n)C^{*}\left(n\right)\\ =\frac{1}{N}\underset{n=0}{\overset{N_p-1}{\mathrm{\Σ}}}\underset{l=0}{\overset{v-1}{\mathrm{\Σ}}}h\left(l\right)C(d+n-l)C^{*}\left(n\right)+\frac{1}{N_p}\underset{n=0}{\overset{N_p-1}{\mathrm{\Σ}}}w(d+n)C^{*}\left(n\right)\\ =\underset{l=0}{\overset{v-1}{\mathrm{\Σ}}}h\left(l\right)\mathrm{\δ}(d-l)+w^{\′}\left(d\right)\\ =h\left(d\right)+w^{\′}\left(d\right)\end{array}$

Wherein, h (l) represents channel impulse response, δ representation unit impulse function, and w (n) is that average is 0, variance is δ ²additive white Gaussian noise, according to central-limit theorem, work as N _pwhen fully large, w ' (d)～CN (0, σ ²/ N _p).The conditional probability density function that can obtain M (d) according to the relation between M in formula (d) and channel impulse response h (d) is:

$p\left(M\left(d\right)\right|h\left(d\right))=\frac{1}{\sqrt{2\mathrm{\π}/N_p}\mathrm{\σ}}\exp \{-\frac{N_p}{2{\mathrm{\σ}}^2}{[M\left(d\right)-h\left(d\right)]}^2\};$

By maximal possibility estimation equation:

$\frac{\∂\ln p(M/h)}{\∂h}={\frac{N_p[M\left(d\right)-h\left(d\right)]}{{\mathrm{\σ}}^2}|}_{h\left(d\right)={\hat{h}}_{\mathrm{ML}}\left(d\right)}=0;$

Known, M (d) is the maximal possibility estimation of channel impulse response,

Fig. 4 is the mean square error (Mean Squared Error, MSE) that SUI-3 channel lower channel impulse response is estimated.As seen from the figure, MSE declines rapidly along with the increase of signal to noise ratio.In the time that signal to noise ratio is greater than 3dB, mSE approach very much zero.

Obtaining the estimated value of channel impulse response afterwards, suitable thresholding need to be set and detect the first footpath.Fairly simple method is to adopt fixed threshold to detect, but fixed threshold can not adaptation signal decline, the dynamic change of the channel circumstance such as noise jamming, cause in system synchronization process that false alarm probability is high or false dismissal probability is high.The process of searching for the first footpath is equal to the process that adopts the method for matched filtering to carry out peak value detection in noise circumstance in itself, and therefore, as preferred, the present invention has adopted the adaptive threshold detecting method based on noise power, and its adaptive threshold can be set to: $V_T=\sqrt{(P_{\mathrm{fa}}^{-1/J}-1)\underset{d=1}{\overset{J}{\mathrm{\Σ}}}{u}_d\left(t\right)};$

Wherein under Low SNR, noise is the main cause that affects timing accuracy, can make the synchronous detection probability of system reach maximum according to the detection threshold based on noise power in above formula, and it is constant that false alarm probability keeps.But under the higher condition of signal to noise ratio, the impact of noise can be ignored, the principal element that now affects timing accuracy is the residual frequency departure in system.In the time there is residual frequency departure in system, ignore the impact of channel fading and noise, the correlation function that receives signal and local sequence can be expressed as:

$\begin{array}{c}{R}_{\mathrm{\Δ\ϵ}}\left(m\right)=\underset{n=0}{\overset{N_p-1}{\mathrm{\Σ}}}{e}^{j\frac{{\mathrm{\πn}}^2}{N_p}}\·e^{j\frac{2\mathrm{\π}{\mathrm{\Δ\ϵ}}_{\max }n}{N}}\·e^{-j\frac{\mathrm{\π}{(n+m)}^2}{N_p}}\\ =e^{-\mathrm{j\π}{m}^2/N_p}\frac{1-e^{\mathrm{j\π}{\mathrm{\Δ\ϵ}}_{\max }}}{1-e^{\mathrm{j\π}({\mathrm{\Δ\ϵ}}_{\max }-2m)/N_p}}\\ =\left\{\begin{array}{c}{N}_p\frac{1-e^{-\mathrm{j\π}{\mathrm{\Δ\ϵ}}_{\max }}}{1-e^{\mathrm{j\π}{\mathrm{\Δ\ϵ}}_{\max }/N_p}},m=0\\ e^{-\mathrm{j\π}{m}^2/N_p}\frac{1-e^{\mathrm{j\π}{\mathrm{\Δ\ϵ}}_{\max }}}{1-e^{\mathrm{j\π}({\mathrm{\Δ\ϵ}}_{\max }-2m)/N_p}},m\≠0\end{array}\right.\end{array};$

Wherein m is the number of samples that receives signal and the unjustified phase difference of local sequence, Δ ε _maxto the maximum residual frequency departure of the system after subcarrier spacing normalization, conventionally be made as system maximum doppler frequency, because residual frequency departure can destroy the periodic correlation property of Zadoff-Chu sequence, in the time of m ≠ 0, residual frequency departure can make timing metric produce submaximum value, this will cause the synchronous false alarm probability detecting to raise, for effectively suppressing false-alarm, and can be at original adaptive threshold V _tbasis on add a small fixed amount Δ V and form new thresholding V ' _t, the therefore decision threshold V ' in step S4 _t=V _t+ Δ V.

In formula, the secondary peak amplitude maximum that m=1 is corresponding, therefore can establish and Δ V is normalized energy maximum diameter amplitude, to obtain final product:

$\mathrm{\ΔV}=\frac{1}{N_p}\left|e^{-\mathrm{j\π}/N_p}\frac{1-e^{\mathrm{j\π}{\mathrm{\Δ\ϵ}}_{\max }}}{1-e^{-\mathrm{j\π}(2-{\mathrm{\Δ\ϵ}}_{\max })/N_p}}\right|*\left|M{\hat{d}}_{\mathrm{coarse}}\right|;$

From analyzing above, if energy maximum diameter is not the first footpath, exist in scope, at least exist a bit, make M (d) > V ' _t.The in the situation that of channel maximum delay expansion v the unknown, can select L=N _g, because being typically designed as, the length of Cyclic Prefix is greater than channel maximum delay expansion, therefore, and can be in scope, select | M'(d) | > V ' _tpoint as best Timing Synchronization point

For checking this method validity, by the method the performance in high-speed mobile fading channel carry out simulating, verifying.Simulation parameter arranges as follows: OFDM frame number is 10000, FFT points N=1024, circulating prefix-length N _g=128, sampling clock f _s=80MHz, system false alarm probability P _fa=0.0001.In time, becomes fading channel and adopts SUI model, and number of path is 3, and the second footpath is most powerful path, and Doppler factor is 500Hz and 1000Hz, can support that in 900MHz frequency range channel parameter is in table 1 up to the translational speed of 600km/h and 1200km/h.

Table 1 multipath channel parameter

Fig. 5 and Fig. 6 have compared respectively this method synchronizes detection probability with Yang algorithm in Kishore & Reddy algorithm and document [4] in document [3] in SUI-3 and SUI-5 channel.In two kinds of channel circumstances, the detection probability of this method under low signal-to-noise ratio environment is all apparently higher than Kishore & Reddy algorithm.Because noise intensity is the principal element that impact detects performance in low signal-to-noise ratio environment, adopt the adaptive threshold based on noise power effectively to solve this problem herein.Under high s/n ratio environment, the performance of the algorithm of carrying is also better than Kishore & Reddy algorithm herein.Although Yang algorithm has also adopted Zadoff-Chu sequence, it has ignored the impact of frequency deviation on sequence dependent features, causes the detection poor-performing of this algorithm in mobile environment.

Comparison diagram 5 and Fig. 6 are visible, and the performance of this method in SUI-5 channel has 1%～2% decline than the performance in SUI-3 channel.Because the Doppler frequency shift of SUI-5 channel is more remarkable, the residual frequency departure in system can be larger, and therefore algorithm performance is affected.By adaptive threshold is revised, reduce to a certain extent the impact of residual frequency departure, make algorithm in high s/n ratio environment, keep higher detection probability.

Fig. 7 and Fig. 8 have compared respectively the MSE of this method and other two kinds of algorithms timing points in different channels environment, the MSE in figure be actual timing point and desirable timing point difference square expectation.As seen from the figure, the MSE of this method and Yang algorithm is starkly lower than Kishore & Reddy algorithm.Kishore & Reddy algorithm utilizes least square (Least Square, LS) criterion to estimate channel impulse response, does not consider the impact of noise power, therefore this algorithm mean square error under low signal-to-noise ratio environment is very large.Analysis according to frequency deviation on detector timing properties b impact, system residual frequency departure can cause false-alarm submaximum, and these false-alarm submaximums are close to correct Timing Synchronization point, although therefore Yang algorithm detection probability is low, mean square error is less.This method makes its impact that can resist residual frequency departure by revising adaptive threshold, ensures that algorithm has good performance, and from upper figure, this method MSE in the time that signal to noise ratio is 3dB just approximates 0, has extremely low mean square error.

Finally it should be noted that, above detailed description is only preferred embodiment of the present invention.Should be appreciated that those of ordinary skill in the art just can design according to the present invention make many modifications and variations without creative work.Therefore, all technical staff in the art, all should be in by the determined protection range of claims under this invention's idea on the basis of existing technology by the available technical scheme of logical analysis, reasoning, or a limited experiment.

Claims (4)

1. the OFDM accurate timing synchronous method based on Zadoff-Chu sequence, is characterized in that carrying out according to following steps:

Step S1, according to calculate the timing metric functional value that d baseband equivalence receives signal place, and using | M (d) | d point corresponding while getting maximum is as thick synchronous point wherein:

N _pfor the cycle of Zadoff-Chu sequence, and N _p=N/2 is also even number, and N is system subcarrier number; Local Zadoff-Chu sequence definition is j is imaginary unit, and r is positive integer, and r and N _prelatively prime; C ^*(n) be local Zadoff-Chu sequence C _ncomplex conjugate; R (d+n) is the sampled value that d+n baseband equivalence receives signal;

Step S2: according to the thick synchronous point in step S1 system is carried out to frequency deviation estimation, obtains frequency departure ε, and according to r ' (n)=r (n) e ^{-j2 π ε}baseband equivalence is received to signal and carry out compensate of frequency deviation;

Step S3: according to calculate the timing metric functional value at d baseband equivalence reception signal place after compensate of frequency deviation;

Step S4: in scope, select to meet | M'(d) | > V ' _tand minimum d is as best Timing Synchronization point n _gfor the length of Cyclic Prefix, V ' _tfor judging threshold.

2. a kind of OFDM accurate timing synchronous method based on Zadoff-Chu sequence according to claim 1, is characterized in that: decision threshold V ' _t=V _t+ Δ V, wherein:

$V_T=\sqrt{P_{\mathrm{fa}}^{-1/J}-1\underset{d=1}{\overset{J}{\mathrm{\Σ}}}{\left|M\left(d\right)\right|}^2};$

$\mathrm{\ΔV}=\frac{1}{N_p}\left|e^{-\mathrm{j\π}/N_p}\frac{1-e^{\mathrm{j\π}{\mathrm{\Δ\ϵ}}_{\max }}}{1-e^{-\mathrm{j\π}(2-{\mathrm{\Δ\ϵ}}_{\max })/N_p}}\right|*\left|M{\hat{d}}_{\mathrm{coarse}}\right|;$

Δ ε _maxfor the maximum residual frequency departure of system, the number that J is energy sampled point, P _fafor the false alarm probability of system.

3. a kind of OFDM accurate timing synchronous method based on Zadoff-Chu sequence according to claim 2, is characterized in that: the number J=N of described energy sampled point _g.

4. according to a kind of OFDM accurate timing synchronous method based on Zadoff-Chu sequence described in claim 1-3 any one, it is characterized in that: local Zadoff-Chu sequence middle r is made as 1.