CN102413091B - Symmetrical-constant amplitude zero auto correlation (CAZAC)-sequence-based orthogonal frequency division multiplexing (OFDM) system synchronization method - Google Patents

Abstract

The invention relates to a symmetrical-constant amplitude zero auto correlation (CAZAC)-sequence-based orthogonal frequency division multiplexing (OFDM) system synchronization method, which comprises the following steps of: constructing a CAZAC sequence with a quadruple symmetrical structure in a time domain; correspondingly multiplying the first and third parts of the CAZAC sequence by using a complex pseudo-noise (PN) sequence to obtain a synchronization sequence; correspondingly multiplying the first and fourth parts of a received signal by using a known PN sequence to obtain a timing metric function; searching for a maximum value of the timing metric function to finish timing synchronization; obtaining decimal frequency offset by utilizing a phase difference between front and rear symmetrical sequences; and obtaining integral frequency offset by utilizing the shift of the CAZAC sequence in a frequency domain. By the method, the influence, caused by the existence of the symmetrical structure and cyclic prefix of the conventional sequence, of side peaks and a peak platform on timing is eliminated, so the timing is more accuracy. A frequency offset estimate has lower standard deviation, and simultaneously, the range of the frequency offset estimate is wider and can reach the whole system bandwidth.

Description

A kind of ofdm system synchronous method based on symmetrical CAZAC sequence

Technical field

The present invention relates to the synchronous method in OFDM technical field, particularly relate to a kind of ofdm system synchronous method based on symmetrical CAZAC sequence.

Background technology

Since the eighties in 20th century, OFDM (orthogonal frequency division multiplexi) is not only widely used in broadcast type digital audio and video field, and has become a part for WLAN standard.

OFDM (OFDM) technology, is a kind of multi-carrier modulation method, overcomes the frequency selective fading of channel by the impact reducing and eliminate intersymbol interference.Its basic principle is that data flow is resolved into some sub-bit streams, each sub data flow will have much lower bit rate like this, with the low rate multimode symbol that such low bit rate forms, remove again to modulate corresponding subcarrier, just formed the transmission system that a plurality of low rate symbol parallels send.Its advantage is effectively to reduce the intersymbol interference that the temporal dispersion due to wireless channel brings, overlapped by sub-channel spectra, reaches maximum spectrum utilance, and OFDM easily realizes, and is easy to be combined with other multiple cut-in methods.But OFDM exists impact and the too high problem of peak-to-average force ratio that is easily subject to frequency departure, had a strong impact on the performance of ofdm system.

In ofdm system, synchronously most important, because timing error meeting destroys the orthogonality between subcarrier, to introduce between subcarrier and disturb and intersymbol interference, many algorithms are used to timing and the frequency shift (FS) of estimating OFDM system.Whether by needing, data are auxiliary classifies, and synchronized algorithm can be divided into the auxiliary and auxiliary two large classes of non-data of data.Wherein non-data aided algorithm does not need additional designs synchronizing sequence, has saved system bandwidth, improved bandwidth availability ratio, but net synchronization capability is poorer than data aided algorithm.Data aided algorithm is to utilize some random sequences, completes Timing Synchronization, and then complete Frequency Synchronization by catching the peak value of timing metric function.Random sequence is mainly some auto-correlations, the good random sequences of cross-correlation performance such as PN sequence and CAZAC sequence.How designing more excellent synchronizing sequence, produce sharp-pointed timing metric functional dependence peak, avoid submaximum value that synchronizing sequence self structure and Cyclic Prefix introduce and the impact of peak value platform, improve synchronous accuracy rate, is the problem that this area researcher is relatively concerned about.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of ofdm system synchronous method based on symmetrical CAZAC sequence, in order to realize timing and the Frequency Synchronization of system higher accuracy.

The technical solution adopted for the present invention to solve the technical problems is: a kind of ofdm system synchronous method based on symmetrical CAZAC sequence is provided, comprises the following steps:

(1) structure has the CAZAC sequence of quadruple symmetrical structure;

(2) use the first of multiple PN sequence and CAZAC sequence and third part is corresponding multiplies each other, obtain synchronous required sequence, wherein, the length of answering PN sequence is 1/4 of CAZAC sequence length;

(3) utilize known multiple PN sequence and receive signal first and the 4th part is corresponding multiplies each other, obtaining timing metric function;

(4) search timing metric function maximum, completes Timing Synchronization;

(5) utilize the phase difference of former and later two symmetric sequences to obtain fraction frequency offset estimation;

(6) utilize the displacement of CAZAC sequence on frequency domain to obtain integer-times frequency offset estimation;

(7) complete Frequency Synchronization.

Described step (1) comprises the following steps: in a length of frequency domain structure, be first N ₁the CAZAC sequence of=N/4, the length that wherein N is synchronizing sequence, this sequence can be expressed as

wherein, j is imaginary unit, r and N ₁relatively prime, k=0,1 ..., N ₁-1; Then c (k) is carried out to zero insertion processing, at frequency domain, obtains the sequence μ that new length is N (k), $\mathrm{\&mu;}\left(k\right)=\left\{\begin{array}{cc}c(k/4),& {\mathrm{<figure-callout\; id="4"\; label="k\; mod"\; filenames="HDA0000107608750000022.png,HDA0000107608750000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_{\mathrm{mod}}=0\\ 0,& {\mathrm{<figure-callout\; id="4"\; label="k\; mod"\; filenames="HDA0000107608750000022.png,HDA0000107608750000031.png"\; state="\{\{state\}\}">k</figure-callout>}}_{\mathrm{mod}}\&NotEqual;0\end{array}\right.,$ Wherein, k=0,1 ..., N-1; Finally sequence μ (k) is carried out to N point IFFT conversion, can obtain having the CAZAC sequence T of quadruple symmetrical structure, T=[A A A A].

Described step (2) comprises the following steps: first constructing length is N ₁multiple PN sequence, multiple PN sequence pn (i), i=0,1 ..., N ₁-1, by the first of pn (i) and CAZAC sequence T with third part is corresponding multiplies each other, obtain synchronous required sequence T _syn, T _syn=[B A B A].

The timing metric function obtaining in described step (3)

wherein, $P\left(d\right)=\underset{k=0}{\overset{N_1-1}{\mathrm{\&Sigma;}}}\mathrm{pn}\left(k\right)\&CenterDot;r^{*}(d+k)\&CenterDot;r(d+k+3N/4),$ $R\left(d\right)=\frac{1}{4}\&CenterDot;\underset{l=0}{\overset{3}{\mathrm{\&Sigma;}}}\underset{k=0}{\overset{N_1-1}{\mathrm{\&Sigma;}}}{\left|r(d+k+l\&CenterDot;N/4)\right|}^2,$ () ^*for getting conjugation; Wherein, r () represents to receive signal, and d is sampled point, k, and l is function P (d), the intermediate variable of R (d).

In described step (4), by the maximum of search timing metric function M (d), complete Timing Synchronization, d when M (d) gets maximum is denoted as

In described step (5) by calculating receive in signal by former and later two length of determining are respectively the phase difference of the sequence of N/2, obtain fraction frequency offset estimated value ε _f.

In described step (6) first to received signal in by

definite length is that the sequence of N is carried out fractional part of frequency offset compensation, the sequence that is then N by multiple PN sequence with this length first, third part is corresponding multiplies each other, and then utilizes the character of CAZAC sequence frequency domain displacement, obtains integer-times frequency offset estimated value ε _i.

Described step (7) is specially utilizes fraction frequency offset estimated value and integer-times frequency offset estimated value, completes Frequency Synchronization, and Frequency offset estimation value is fraction frequency offset estimated value and integer-times frequency offset estimated value sum.

Beneficial effect

Owing to having adopted above-mentioned technical scheme, the present invention compared with prior art, there is following advantage and good effect: the present invention has eliminated the timing metric peak of function platform that Cyclic Prefix is introduced, and eliminated the submaximum value of the timing metric function of introducing due to the symmetrical structure of Cyclic Prefix and synchronizing sequence self, above two advantages make Timing Synchronization more accurate.Utilize the phase difference of the sequence that two length are N/2 to carry out fraction frequency offset estimation, estimated accuracy is higher, at frequency domain, utilize the displacement of CAZAC sequence to estimate integer-times frequency offset, good autocorrelation due to CAZAC sequence, improved estimation accuracy rate, estimation range can reach whole system bandwidth simultaneously.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention;

Fig. 2 is the comparison diagram of the present invention and algorithm 1 and algorithm 2 Frequency offset estimation value scope under Gaussian channel when signal to noise ratio is 20dB;

Fig. 3 A is the comparison diagram of the present invention and algorithm 1 and the Frequency offset estimation value standard deviation of algorithm 2 under Gaussian channel, wherein N _g=32;

Fig. 3 B is the comparison diagram of the present invention and algorithm 1 and the Frequency offset estimation value standard deviation of algorithm 2 under Gaussian channel, wherein N _g=64;

Fig. 4 A is the present invention and algorithm 1 and the timing slip estimated value expectation comparison diagram of algorithm 2 under multidiameter fading channel;

Fig. 4 B is the comparison diagram of the present invention and algorithm 1 and the timing slip estimated value standard deviation of algorithm 2 under multidiameter fading channel;

Fig. 5 A is the present invention and algorithm 1 and the Frequency offset estimation value expectation comparison diagram of algorithm 2 under multidiameter fading channel;

Fig. 5 B is the comparison diagram of the present invention and algorithm 1 and the comment bias estimation value standard deviation of algorithm 2 under multidiameter fading channel.

Embodiment

Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiment are only not used in and limit the scope of the invention for the present invention is described.In addition should be understood that those skilled in the art can make various changes or modifications the present invention after having read the content of the present invention's instruction, these equivalent form of values fall within the application's appended claims limited range equally.

Embodiments of the present invention relate to a kind of ofdm system synchronous method based on symmetrical CAZAC sequence, as shown in Figure 1, specifically comprise the following steps:

(1) in a length of frequency domain structure, be N ₁the CAZAC sequence of=N/4, the length that wherein N is synchronizing sequence.

This sequence can be expressed as:

wherein j is imaginary unit, r and N ₁relatively prime, k=0,1 ..., N ₁-1.

Next c (k) is carried out to zero insertion processing, at frequency domain, obtains the sequence μ that new length is N (k),

$\mathrm{\&mu;}\left(k\right)=\left\{\begin{array}{cc}c(k/4),& k_{\mathrm{<figure-callout\; id="4"\; label="mod"\; filenames="HDA0000107608750000022.png,HDA0000107608750000031.png"\; state="\{\{state\}\}">mod</figure-callout>}4}=0\\ 0,& k_{\mathrm{<figure-callout\; id="4"\; label="mod"\; filenames="HDA0000107608750000022.png,HDA0000107608750000031.png"\; state="\{\{state\}\}">mod</figure-callout>}4}\&NotEqual;0\end{array}\right.,$ K=0 wherein, 1 ..., N-1.

Sequence μ (k) is carried out to N point IFFT conversion, can obtain having the CAZAC sequence T of quadruple symmetrical structure, T=[A A A A].

(2) structure length is N ₁multiple PN sequence, multiple PN sequence pn (i), i=0,1 ..., N ₁-1, by the first of pn (i) and sequence T with third part is corresponding multiplies each other, obtain synchronous required sequence T _syn, T _syn=[B A B A], T _synstill symmetrical structure before and after having.

(3) utilize local multiple PN sequence and reception signal r (n) to construct new timing metric function M (d), wherein, $P\left(d\right)=\underset{k=0}{\overset{N_1-1}{\mathrm{\&Sigma;}}}\mathrm{pn}\left(k\right)\&CenterDot;r^{*}(d+k)\&CenterDot;r(d+k+3N/4),$ $R\left(d\right)=\frac{1}{4}\&CenterDot;\underset{l=0}{\overset{3}{\mathrm{\&Sigma;}}}\underset{k=0}{\overset{N_1-1}{\mathrm{\&Sigma;}}}{\left|r(d+k+l\&CenterDot;N/4)\right|}^2,$ () ^*for getting conjugation, r () represents to receive signal, and d is sampled point, k, and l is function P (d), the intermediate variable of R (d).

(4) by the maximum of search timing metric function M (d), complete Timing Synchronization, obtain

(5) by calculating receive in signal by former and later two length of determining are respectively the phase difference of the sequence of N/2, obtain fraction frequency offset estimated value ε _f, ${\mathrm{\&epsiv;}}_f=-\mathrm{angle}\{\underset{k=0}{\overset{N/2-1}{\mathrm{\&Sigma;}}}r(\hat{d}+k)\&CenterDot;r^{*}(\hat{d}+k+N/2)\}/\mathrm{\&pi;}.$

(6) first to received signal in by

definite length is that the sequence of N is carried out fractional part of frequency offset compensation, the sequence that is then N by multiple PN sequence with this length first, third part is corresponding multiplies each other, and then utilizes the character of CAZAC sequence frequency domain displacement, obtains integer-times frequency offset estimated value ε _i.

Receive in signal by

definite length is that the sequence of N is

it is carried out to fraction frequency offset compensation, and then uses PN sequence to multiply each other with the first, third part is corresponding, obtain length and be the sequence r ' of N (k),

$r^{\&prime;}\left(k\right)=\left\{\begin{array}{cc}{\mathrm{pn}}^{*}\left(k\right)\&CenterDot;r(\hat{d}+k),& k=\mathrm{0,1},...,N/4-1\\ {\mathrm{pn}}^{*}(k-N/2)\&CenterDot;r(\hat{d}+k),& k=N/2,N/2+1,...,3N/4-1\\ r(\hat{d}+k),& \mathrm{others}\end{array}\right.$

R ' (k) is done to N point FFT conversion and obtain sequence z (k), utilize the character of CAZAC sequence, define a detection function F (g), g=0,1 ..., N-1, $F\left(g\right)=\frac{{|\underset{k=0}{\overset{N/4-1}{\mathrm{\&Sigma;}}}\mathrm{\&mu;}\left(4k\right)\&CenterDot;z^{*}(4k+g)|}^2}{{\left(\underset{k=0}{\overset{N/4-1}{\mathrm{\&Sigma;}}}{\left|z\left(4k\right)\right|}^2\right)}^2},$ By searching for its maximum, obtain integer-times frequency offset estimated value ε _i,

μ () is the sequence that described in step (1), length is N, z () converts for r ' (k) being done to N point FFT in this step the sequence obtaining, k is the intermediate variable in function F () calculating formula, and g is the independent variable of function F (), and scope is 0 to N-1.

(7) utilize fraction frequency offset value and the integer-times frequency offset value of estimating, complete Frequency Synchronization.Frequency offset estimation value ε, ε=ε _i+ ε _f.

Below by emulation, test net synchronization capability of the present invention, simulation parameter arranges as follows:

Number of sub carrier wave N=512, circulating prefix-length in two kinds of situation, N _g=32 and N _g=64.The r value that produces CAZAC sequence is set to N ₁-1.Channel is divided into two kinds of Gaussian channel and multidiameter fading channels, and wherein in multidiameter fading channel, multipath number is 5, and each footpath postpones, for [0 357 11], to gain as [1 0.8913 0.3548 0.3162 0.1], and frequency shift (FS) is 0.3.The net synchronization capability that compares algorithm of the present invention and algorithm 1 (algorithm described in document 1), algorithm 2 (algorithm described in document 2).

Document 1 is Guo Y, Liu G, Ge J, A new time and frequency synchronization scheme for OFDMsystems, IEEE Transactions on Consumer Electronics, 54 (2): 321-325,2008.

Document 2 is Jingbo Meng, Guihua Kang, A novel OFDM synchronization algorithm based on CAZAC sequence, International Conference on Computer Application and System Modeling, 14:634-637,2010.

Fig. 2 provides algorithm of the present invention and algorithm 1 and the algorithm 2 Frequency offset estimation value scope under Gaussian channel when signal to noise ratio is 20dB, can find out, under different circulating prefix-lengths, the Frequency offset estimation value scope of algorithm of the present invention and algorithm 1 is all greater than algorithm 2.

Fig. 3 provides algorithm of the present invention and algorithm 1 and the algorithm 2 Frequency offset estimation value standard deviation under Gaussian channel, and that wherein Fig. 3 A represents is N _gthat=32 situation and Fig. 3 B represent is N _g=64 situation, can find out, the standard deviation of algorithm of the present invention and algorithm 2 is more approaching, is all less than algorithm 1, in the situation that especially circulating prefix-length is less.

Fig. 4 provides algorithm of the present invention and algorithm 1 and algorithm 2 expectation of timing slip estimated value and the standard deviation under multidiameter fading channel, wherein, what Fig. 4 A represented is the expectation of timing slip estimated value, what Fig. 4 B represented is that in timing slip estimated value standard deviation figure, algorithm of the present invention only has a point, its residual value is infinitely great, can find out, the timing slip estimated value expectation of algorithm of the present invention is minimum, standard deviation is also minimum, is better than algorithm 1 and algorithm 2.

Fig. 5 provides algorithm of the present invention and algorithm 1 and algorithm 2 expectation of Frequency offset estimation value and the standard deviation under multidiameter fading channel, wherein, what Fig. 5 A represented is the Frequency offset estimation value expectation under multidiameter fading channel, what Fig. 5 B represented is the Frequency offset estimation value standard deviation under multidiameter fading channel, can find out now Frequency offset estimation value mistake of algorithm 2, algorithm of the present invention and algorithm 1 relatively approach ideal value, and the Frequency offset estimation value standard deviation of algorithm of the present invention is minimum, thereby performance is also optimum.

Therefore,, under Gaussian channel and multidiameter fading channel, the performance of algorithm of the present invention is all better than algorithm 1 and algorithm 2.

Claims (6)

1. the ofdm system synchronous method based on symmetrical CAZAC sequence, is characterized in that, comprises the following steps: (1) structure has the CAZAC sequence of quadruple symmetrical structure, comprising: in a length of frequency domain structure, be first N ₁the CAZAC sequence of=N/4, the length that wherein N is synchronizing sequence, this sequence can be expressed as

wherein, j is imaginary unit, r and N ₁relatively prime, k=0,1 ..., N ₁-1; Then c (k) is carried out to zero insertion processing, at frequency domain, obtains the sequence μ that new length is N (k), $\mathrm{\&mu;}\left(k\right)=\left\{\begin{array}{cc}c(k/4),& k_{\mathrm{mod}4}=0\\ 0,& k_{\mathrm{mod}4}\&NotEqual;0\end{array}\right.,$ Wherein, k=0,1 ..., N-1; Finally sequence μ (k) is carried out to N point IFFT conversion, can obtain having the CAZAC sequence T of quadruple symmetrical structure, T=[A A A A];

(2) use the first of multiple PN sequence and CAZAC sequence and third part is corresponding multiplies each other, obtain synchronous required sequence, wherein, the length of answering PN sequence is 1/4 of CAZAC sequence length;

(3) utilize known multiple PN sequence and receive signal first and the 4th part is corresponding multiplies each other, obtaining timing metric function;

(4) search timing metric function maximum, completes Timing Synchronization;

(5) utilize the phase difference of former and later two symmetric sequences to obtain fraction frequency offset estimation, wherein former and later two symmetric sequences refer to first half sequence and the latter half sequence in CAZAC sequence;

(6) utilize the displacement of CAZAC sequence on frequency domain to obtain integer-times frequency offset estimation, comprising: receive in signal by timing metric function

definite length is that the sequence of N is it is carried out to fraction frequency offset compensation, and then uses PN sequence to multiply each other with the first, third part is corresponding, obtain the sequence r'(k that length is N),

$r^{\&prime;}\left(k\right)=\left\{\begin{array}{c}{\mathrm{pn}}^{*}\left(k\right)\&CenterDot;r(\hat{d}+k),k=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,N/4-1\\ {\mathrm{pn}}^{*}(k-N/2)\&CenterDot;r(\hat{d}+k),k=N/2,N/2+1,\&CenterDot;\&CenterDot;\&CenterDot;,3N/4-1\\ r(\hat{d}+k),\mathrm{others}\end{array}\right.$

To r'(k) do N point FFT conversion and obtain sequence z (k), utilize the character of CAZAC sequence, define a detection function F (g), g=0,1 ..., N-1,

by searching for its maximum, obtain integer-times frequency offset estimated value ε _i,

μ () is the sequence that described in step (1), length is N, z () in this step to r'(k) be N point FFT and convert the sequence obtaining, k is the intermediate variable in function F () calculating formula, and g is the independent variable of function F (), and scope is 0 to N-1;

(7) complete Frequency Synchronization.

2. the ofdm system synchronous method based on symmetrical CAZAC sequence according to claim 1, is characterized in that, described step (2) comprises the following steps: first constructing length is N ₁multiple PN sequence, multiple PN sequence pn (i), i=0,1 ..., N ₁-1, by the first of pn (i) and CAZAC sequence T with third part is corresponding multiplies each other, obtain synchronous required sequence T _syn, T _syn=[B A B A].

3. the ofdm system synchronous method based on symmetrical CAZAC sequence according to claim 1, is characterized in that, the timing metric function obtaining in described step (3)

wherein, $P\left(d\right)=\underset{k=0}{\overset{N_1-1}{\mathrm{\&Sigma;}}}\mathrm{pn}\left(k\right)\&CenterDot;r^{*}(d+k)\&CenterDot;r(d+k+3N/4),R\left(d\right)=\frac{1}{4}\&CenterDot;\underset{l=0}{\overset{3}{\mathrm{\&Sigma;}}}\underset{k=0}{\overset{N_1-1}{\mathrm{\&Sigma;}}}{\left|r(d+k+l\&CenterDot;N/4)\right|}^2,$ () ^*for getting conjugation; Wherein, r () represents to receive signal, and d is sampled point, k, and l is function P (d), the intermediate variable of R (d).

4. the ofdm system synchronous method based on symmetrical CAZAC sequence according to claim 1, it is characterized in that, in described step (4), by the maximum of search timing metric function M (d), complete Timing Synchronization, d when M (d) gets maximum is denoted as

.

5. the ofdm system synchronous method based on symmetrical CAZAC sequence according to claim 4, is characterized in that, in described step (5) by calculating receive in signal by

former and later two length of determining are respectively the phase difference of the sequence of N/2, obtain fraction frequency offset estimated value ε _f.

6. a kind of ofdm system synchronous method based on symmetrical CAZAC sequence according to claim 1, it is characterized in that, described step (7) is specially utilizes fraction frequency offset estimated value and integer-times frequency offset estimated value, complete Frequency Synchronization, Frequency offset estimation value is fraction frequency offset estimated value and integer-times frequency offset estimated value sum.

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