CN101252560A - High-performance OFDM frame synchronization algorithm - Google Patents

Abstract

The invention belongs to wireless communication synchronization technical field, in particular to an OFDM frame alignment algorithm. The OFDM frame alignment algorithm includes the steps: LFM signals, as a training sequence, are added to data signals at the sending terminal of the OFDM system, and fractional Fourier transform (FRFT) is carried out to the received signals at the receiving terminal; the position of the peak point is detected, thus realizing frame alignment. The OFDM frame alignment algorithm makes use of the characteristic of energy convergence of the LFM signals through FRFT, greatly reducing computational complexity of frame alignment and obviously improving frame alignment precision. Simulation results show that the OFDM frame alignment algorithm is of low computational complexity and can effectively improve frame alignment precision.

Description

A kind of high-performance OFDM frame synchronization algorithm

Technical field

The invention belongs to radio communication simultaneous techniques field, be specifically related to a kind of high performance, OFDM frame synchronization algorithm fast.

Background technology

OFDM is a kind of multicarrier parallel transmission technology.Owing to can effectively resist frequency selective fading in the multi-path environment, and have advantages such as the high and system's implementation complexity of the availability of frequency spectrum is low, OFDM is considered to one of core technology of next generation wireless communication system.Because data are that unit handles with the piece in the ofdm system, for correct the recovery sends signal, receiving terminal is being made FFT (fast Fourier transform) before, needs to determine in advance the original position of each FFT window, i.e. frame synchronization ^[3]

Existing frame synchornization method mainly can be divided into two classes: based on the frame synchronization of Cyclic Prefix (CP) with based on the frame synchronization of training sequence.Document [1] has provided the frame synchornization method based on CP, and these class methods utilize the correlation between head and the tail two segment signals that bring owing to interpolation CP in each OFDM symbol synchronous with achieve frame.Document [2] has provided the frame synchornization method based on training sequence, and the training sequence (as periodic sequence or PN sequence) of these class methods by sending particular design is to finish frame synchronization.

Frame synchornization method based on CP or training sequence is searched for the original position of FFT window in certain is interval, each search all need be calculated correlation, have bigger operand and handle time-delay, and the transmission of training sequence has also reduced system's valid data transmission rate; In addition, under the low signal-to-noise ratio condition, the performance of these methods will seriously descend, and will be dispersed near the actual value the interval with very big probability such as, the estimated value of FFT window original position, and this also can have influence on follow-up Nonlinear Transformation in Frequency Offset Estimation.

Summary of the invention

At ofdm system, the objective of the invention is to propose a kind of high performance, frame synchronization algorithm fast.

The present invention utilizes the energy centralization characteristic of bilinearity frequency modulation (LFM) signal in the Fourier of particular fraction rank, the training sequence that transmitting terminal superposes and is made of the LFM signal on data-signal, receiving terminal is made Fourier Transform of Fractional Order (FRFT) to received signal, by the position of detection peak point, can achieve frame synchronous.Compare with document [1] [2], the present invention also can obtain higher frame synchronization precision when having low operand.In addition, because training sequence is being superimposed upon on the data-signal, the transmission of training sequence neither can reduce the valid data transmission rate of system, also can obviously not influence the performance of BER of system.

Particular content of the present invention is as follows:

1. system configuration

Consider ofdm system as shown in fig. 1, for purpose of brevity, omitted modules such as Frequency Synchronization and sampling clock be synchronous among the figure.Among Fig. 1, the time domain data signal that u (n) obtains after passing through inverse fast fourier transform (IFFT) and add CP for frequency domain data to be sent, c (n) is for being superimposed upon the training sequence that is made of the LFM signal on the data-signal, send signal s (n)=u (n)+c (n), n=0,1, ..., N-1, N=N _Subc+ N _g, N _SubcBe the OFDM sub-carrier number, N _gBe the length of CP.If T _sBe the sampling period of system, then the duration of an OFDM symbol is T=NT _s, wherein, the duration of useful data is T _u=N _SubcT _s, be spaced apart 1/T between each subcarrier _uBy Fig. 1, received signal r (n) can be expressed as:

$r\left(n\right)=s\left(n\right)*h\left(n\right)+v\left(n\right)=\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{h}_{l}s(n-{\mathrm{\τ}}_l)+v\left(n\right),0\≤n\≤N-1---\left(1\right)$

In the formula (1), ^*The expression convolution, v (n) is that average is zero, variance is σ _v ²Additive white Gaussian noise, h (n) is that length is the channel impulse response of L, is expressed as:

$h\left(n\right)=\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{h}_l\mathrm{\δ}(n-{\mathrm{\τ}}_l)---\left(2\right)$

In the formula (2), h _lBe the complex gain in l footpath, τ _lIt is the time-delay (being assumed to be an integer sampling interval here) in l footpath.Be without loss of generality, suppose that channel remains unchanged in the duration of an OFDM symbol, and the time-delay τ in first footpath ₀=0.

Long for the training sequence c (n) of N be by to continuous LFM signal c (t) in interval [π, π], with T _cFor the cycle samples and gets.C (t) is provided by following formula:

$c\left(t\right)={\mathrm{\σe}}^{{\mathrm{j\π\μt}}^2}---\left(3\right)$

In the formula (3), σ and μ are respectively average power and the frequency modulation rate of c (t).

2. frame synchronization algorithm

As shown in Figure 2, r _M-1(n), r _m(n) and r _M+1(n) respectively expression to receive (m-1) of signal r (n) individual, m and (m+1) individual OFDM symbol, wherein, θ represents the deviation of m OFDM symbol original position, and dash area represents because the hangover of the previous OFDM symbol that the channel delay expansion causes.In order to determine the original position of m OFDM symbol, intercepting length is designated as y (n) for one section of N from received signal.Y (n) is by r _M-1(n) back θ sampled point and r _m(n) the individual sampled point of preceding (N-θ) is formed.For the purpose of convenient, suppose θ＞0.Same analysis can be applied to the situation of θ＜0 o'clock, and y this moment (n) is by r _m(n) back (N-θ) individual sampled value and r _M+1(n) preceding θ sampled value formed.

Y (n) can be expressed as:

y(n)＝r′ _m-1(n)+r′ _m(n) 0≤n≤N-1 (4)

In the following formula, $r_{m-1}^{\&prime;}\left(n\right)=\begin{array}{c}\left\{\begin{array}{cc}{r}_{m-1}(N-\mathrm{\&theta;}+n)& 0\&le;n<\mathrm{\&theta;}\\ r_{\mathrm{tail}}(n-\mathrm{\&theta;})& \mathrm{\&theta;}\&le;n<\mathrm{\&theta;}+L\\ 0& \mathrm{\&theta;}+L\&le;n\&le;N-1\end{array}\right.,\end{array}$ $r_m^{\&prime;}\left(n\right)=\left\{\begin{array}{cc}0& 0\&le;n<\mathrm{\&theta;}\\ r_m(n-\mathrm{\&theta;})& \mathrm{\&theta;}\&le;n\&le;N-1\end{array}\right.,$

r _Tail(n) be because the hangover of (m-1) individual OFDM symbol that the time delay expansion of channel causes.

Is the N point FRFT of p=2/ π atan (1/ μ) to y (n) as exponent number, can get:

F ^p[y(n)]＝F ^p[r′ _m-1(n)+r′ _m(n)]

＝F ^p[r′ _m(n)]+F ^p[r′ _m-1(n)]

＝F ^p[r _m(n-θ)]+F ^p[r′ _m-1(n)] (5)

＝F ^p[c _m(n-θ)*h _m(n-θ)]

+F ^p[u _m(n-θ)*h _m(n-θ)]+F ^p[r′ _m-1(n)]

In the following formula, u _m(n), c _m(n) and h _m(n) be data-signal, training sequence and channel impulse response respectively corresponding to m OFDM symbol.First in the formula (5) is: c _m(n) and h _m(n) FRFT after the convolution can be expressed as:

$F^p[c_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]$

$=F^p\left[\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{c}_m(n-\mathrm{\&theta;}-{\mathrm{\&tau;}}_{m,l})\right]$

$=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{F}^p\left[c_m(n-\mathrm{\&theta;}-{\mathrm{\&tau;}}_{m,l})\right]---\left(6\right)$

$=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{A}_p{A}_l\mathrm{\&delta;}[u-(\mathrm{\&theta;}+{\mathrm{\&tau;}}_{m,l})\cos \mathrm{\&alpha;}]$

In the following formula, $A_l=e^{j\frac{{\left[(\mathrm{\&theta;}+{\mathrm{\&tau;}}_{m,l}){\mathrm{\&omega;}}_1\right]}^2}{2}\sin \mathrm{\&alpha;}\cos \mathrm{\&alpha;}-\mathrm{ju}(\mathrm{\&theta;}+{\mathrm{\&tau;}}_{m,l}){\mathrm{\&omega;}}_1^2\sin \mathrm{\&alpha;}},$ ω ₁=T _cCos α, h _{M, l}And τ _{M, l}Be the complex gain and the time delay in l footpath, α=p/2 π.A _pThe same A of expression formula ₁, second in the formula (5) is u _m(n) and h _m(n) FRFT after the convolution, the 3rd is r ' _M-1(n) FRFT.This energy of two all can not converge in the fractional number order Fourier of p rank, is considered as distracter.

Here, provide about θ and τ _{M, l}Two preconditions:

i)θ＞＞τ _m，l，l＝0，1，...，L-1。This condition can be met by the original position of suitably adjusting y (n) when intercepting y (n).

Ii) in the formula (6), the absolute value of cos α is enough little, thereby $({\mathrm{\&tau;}}_{m,l}\&CenterDot;\cos \mathrm{\&alpha;})<<1.$ This condition can be met as training sequence by the LFM signal of selecting to have suitable frequency modulation rate.Promptly this frequency modulation rate makes the FRFT angle that can correspondingly produce power converges approach pi/2 or be pi/2.

As condition i) and when ii) being met, formula (6) can be approximated to be:

$F^p[c_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]$

$=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{A}_p{A}_l\mathrm{\&delta;}[u-\mathrm{\&theta;}\cos \mathrm{\&alpha;}-{\mathrm{\&tau;}}_{m,l}\cos \mathrm{\&alpha;}]---\left(7\right)$

$\&ap;\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{A}_p{A}_l\mathrm{\&delta;}[u-\mathrm{\&theta;}\cos \mathrm{\&alpha;}]$

By formula (7), formula (5) can be expressed as:

$F^p\left[y\left(n\right)\right]=F^p[c_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]$

$+F^p[u_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]+F^p\left[r_{m-1}^{\&prime;}\left(n\right)\right]$

$\&ap;\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{A}_p{A}_l\mathrm{\&delta;}[u-\mathrm{\&theta;}\cos \mathrm{\&alpha;}]---\left(8\right)$

$+F^p[u_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]+F^p\left[r_{m-1}^{\&prime;}\left(n\right)\right]$

Search F ^pThe amplitude maximum of [y (n)], its position can be expressed as:

$u_1=\arg \underset{u}{\max }\left\{\right|F^p\left[y\left(n\right)\right]\left|\right\}=\mathrm{\&theta;}\cos \mathrm{\&alpha;}---\left(9\right)$

Therefore, original position deviation θ can estimate with following formula:

$\widehat{\mathrm{\&theta;}}=\mathrm{round}\left[\frac{u_1}{\cos \mathrm{\&alpha;}}\right]---\left(10\right)$

In the following formula, symbol round[x] expression gets the integer nearest apart from x.

According to above-mentioned introduction, the concrete steps of frame synchronization algorithm of the present invention are as follows:

1. at the ofdm system transmitting terminal, the LFM signal c (n) that selects to have suitable frequency modulation rate μ is superimposed upon on the data-signal u (n) 1 as training sequence; As sending signal S (n): S (n)=u (n)+c (n);

2. at the ofdm system receiving terminal, as shown in Figure 2, intercepting is long from received signal r (n) is the segment signal of N, obtains y (n);

3. y (n) is carried out the N point FRFT that exponent number is p, obtain F ^p[y (n)];

4. search | F ^pThe maximum of points of [y (n)] remembers that its position is u1;

5. by u1,, can obtain the estimated value of OFDM symbol original position deviation, thereby achieve frame is synchronous according to formula (10).

Amount of calculation is analyzed:

Frame synchronization algorithm among the present invention need calculate the FRFT that N is ordered.If adopt the fast discrete algorithm that proposes in the document [3], the complexity of frame synchronization algorithm is O (Nlog among the present invention ₂N).For in the document [1] based in the frame synchornization method of CP and the document [2] based on the frame synchornization method of training sequence, the hunting zone of supposing OFDM symbol original position is N _Subc/ 2, then the computation complexity of these two kinds of methods is respectively O (N _Subc/ 2N _g) and O (N _Subc/ 2N _Subc).As subcarrier number N _SubcWith circulating prefix-length N _gWhen getting different values, three kinds of method amounts of calculation more as shown in table 1.As can be seen, the method in document [1] and the document [2], the computation complexity of method greatly reduces among the present invention.

Table 1. computation complexity relatively

	Method among the present invention	Method in the document [4]	Method in the document [5]
				N subc＝1024，N g＝128	O(1152·log 21152)	O(512·128)	O(1024·512)
N subc＝1024，N g＝256	O(1280·log 21280)	O(512·256)	O(1024·512)
				N subc＝2048，N g＝128	O(2176·log 22176)	O(1024·128)	O(2048·1024)
N subc＝2048，N g＝256	O(2304·log 22304)	O(1024·256)	O(2048·1024)

Technique effect

The present invention proposes a kind of high performance, OFDM frame synchronization algorithm fast.It utilizes the energy centralization characteristic of LFM signal in fractional number order Fourier, has effectively reduced the computation complexity of frame synchronization, has improved the precision of frame synchronization simultaneously.

Description of drawings

Fig. 1 is the system model diagram.

Fig. 2 is the received signal diagram.

Fig. 3 is the average diagram of frame synchronization error.

Fig. 4 is the variance diagram of frame synchronization error.

Fig. 5 is the bit error rate diagram.

Embodiment

(1), carry out sequence c (n) that uniform sampling obtains in [π, π] interval as training sequence, on the data-signal u (n) that is added to, as sending signal s (n) from LFM signal c (t) at the ofdm system transmitting terminal:

s(n)＝u(n)+c(n)，n＝0，1，...，N-1，

Here N=N _Subc+ N _g, N _SubcBe the OFDM sub-carrier number, N _gBe the length of CP, u (n) is for the contrary fast Fourier transformation (being designated as IFFT) of frequency domain data warp to be sent and add the time domain data signal that CP obtains, $c\left(t\right)={\mathrm{\&sigma;e}}^{{\mathrm{j\&pi;\&mu;<figure-callout\; id="2"\; label="t"\; filenames="A20071004770500113.png,A20071004770500121.png"\; state="\{\{state\}\}">t</figure-callout>}}^2},$ Here σ is the average power of c (t), and μ is the frequency modulation rate of c (t);

(2) at the receiving terminal of ofdm system, received signal r (n) is:

$r\left(n\right)=s\left(n\right)*h\left(n\right)+v\left(n\right)=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{l}s(n-{\mathrm{\&tau;}}_l)+v\left(n\right),0\&le;n\&le;N-1---\left(1\right)$

In the formula (1), ^*The expression convolution, v (n) is that average is zero, variance is σ _v ²Additive white Gaussian noise, h (n) is that length is the channel impulse response of L, is expressed as:

$h\left(n\right)=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_l\mathrm{\&delta;}(n-{\mathrm{\&tau;}}_l)---\left(2\right)$

In the formula (2), h _lBe the complex gain in l footpath, τ _lIt is the time-delay in l footpath;

Intercepted length is the segment signal of N from r (n), is designated as y (n):

y(n)＝r′ _m-1(n)+r′ _m(n) 0≤n≤N-1 (4)

In the following formula, $r_{m-1}^{\&prime;}\left(n\right)=\begin{array}{c}\left\{\begin{array}{cc}{r}_{m-1}(N-\mathrm{\&theta;}+n)& 0\&le;n<\mathrm{\&theta;}\\ r_{\mathrm{tail}}(n-\mathrm{\&theta;})& \mathrm{\&theta;}\&le;n<\mathrm{\&theta;}+L\\ 0& \mathrm{\&theta;}+L\&le;n\&le;N-1\end{array}\right.,\end{array}$ $r_m^{\&prime;}\left(n\right)=\left\{\begin{array}{cc}0& 0\&le;n<\mathrm{\&theta;}\\ r_m(n-\mathrm{\&theta;})& 0\&le;n\&le;N-1\end{array}\right.,$ r _tail(n)

Be because the hangover of (m-1) individual OFDM symbol that the time delay expansion of channel causes.

r _M-1(n), r _m(n) and r _M+1(n) respectively expression to receive (m-1) of signal r (n) individual, m and (m+1) individual OFDM symbol, wherein, θ represents the deviation of m OFDM symbol original position;

(3) y (n) is carried out the N point FRFT that exponent number is p=2/ π atan (1/ μ):

$F^p\left[y\left(n\right)\right]=F^p[c_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]$

$+F^p[u_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]+F^p\left[r_{m-1}^{\&prime;}\left(n\right)\right]$

$\&ap;\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{A}_p{A}_l\mathrm{\&delta;}[u-\mathrm{\&theta;}\cos \mathrm{\&alpha;}]---\left(8\right)$

$+F^p[u_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]+F^p\left[r_{m-1}^{\&prime;}\left(n\right)\right]$

In the following formula, u _m(n), c _m(n) and h _m(n) be data-signal, training sequence and channel impulse response respectively corresponding to m OFDM symbol.First in the formula (5) is: c _m(n) and h _m(n) FRFT after the convolution can be expressed as:

$F^p[c_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]$

$=F^p\left[\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{c}_m(n-\mathrm{\&theta;}-{\mathrm{\&tau;}}_{m,l})\right]$

$=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{F}^p\left[c_m(n-\mathrm{\&theta;}-{\mathrm{\&tau;}}_{m,l})\right]---\left(6\right)$

$=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{A}_p{A}_l\mathrm{\&delta;}[u-(\mathrm{\&theta;}+{\mathrm{\&tau;}}_{m,l})\cos \mathrm{\&alpha;}]$

In the following formula, $A_l=e^{j\frac{{\left[(\mathrm{\&theta;}+{\mathrm{\&tau;}}_{m,l}){\mathrm{\&omega;}}_1\right]}^2}{2}\sin \mathrm{\&alpha;}\cos \mathrm{\&alpha;}-\mathrm{ju}(\mathrm{\&theta;}+{\mathrm{\&tau;}}_{m,l}){\mathrm{\&omega;}}_1^2\sin \mathrm{\&alpha;}},$ ω ₁=T _cCos α, h _{M, l}And τ _{M, l}Be the complex gain and the time delay in l footpath, α=p/2 π.A _pThe same A of expression formula ₁, second in the formula (5) is u _m(n) and h _m(n) FRFT after the convolution, the 3rd is r ' _M-1(n) FRFT.This energy of two all can not converge in the fractional number order Fourier of p rank, is considered as distracter.

(4) search F ^pThe amplitude maximum of [y (n)], its position can be expressed as:

${\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="A20071004770500112.png,A20071004770500113.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=\arg \underset{u}{\max }\left\{\right|F^p\left[y\left(n\right)\right]\left|\right\}=\mathrm{\&theta;}\cos \mathrm{\&alpha;}---\left(9\right)$

(5) promptly get the estimated value of OFDM symbol original position deviation θ by following formula Thereby, implement frame synchronization:

$\widehat{\mathrm{\&theta;}}=\mathrm{round}\left[\frac{{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="A20071004770500112.png,A20071004770500113.png"\; state="\{\{state\}\}">u</figure-callout>}}_1}{\cos \mathrm{\&alpha;}}\right]---\left(10\right)$

In the following formula, symbol round[x] expression gets the integer nearest apart from x.

Simulated conditions:

OFDM sub-carrier number N _Subc=2048, the CP length N _g=256, the frequency domain data symbol adopts the QPSK modulation.The systematic sampling period T _s=1e-7s.Power ratio between data-signal and the training sequence is 10: 1.Other parameter of training sequence is elected T as _c=0.0027, μ=2.5.The time delay power spectrum of multipath channel [4] as shown in table 2.The fast discrete algorithm of FRFT is provided by document [3].

Table 2. multidiameter delay power spectrum

Time delay (us)	0	0.2	0.5	1.6	2.3	5.0
							Power (dB)	-3.0	0.0	-2.0	-6.0	-8.0	-10.0

Simulation result:

Conveniently relatively, provide the frame synchronization performance simulation curve of method in the method among the present invention that corresponds respectively to, the middle method of document [1] and the document [2] here simultaneously.Fig. 3 has provided the average of frame synchronization error and the relation curve between the signal to noise ratio, and as can be seen, the average of the frame synchronization error of three kinds of methods fluctuates near different values respectively, and the average of the frame synchronization error of method more approaches 0 among the present invention.Fig. 4 has provided the variance of frame synchronization error and the relation curve between the signal to noise ratio.As can be seen, in three kinds of methods, the variance of the frame synchronization error of method is significantly less than other two kinds of methods among the present invention, and significant change does not take place along with the variation of signal to noise ratio, and the variance of the frame synchronization error of method then all is progressively to descend along with the increase of signal to noise ratio in document [1] and the document [2].By Fig. 3 and Fig. 4 as can be known, the method in document [1] and the document [2], the method among the present invention has also improved the precision of frame synchronization when reducing the frame synchronization computation complexity.

Fig. 5 has provided in awgn channel and multipath channel, and the bit error rate (BER) of the system model that adopts and the relation curve between the signal to noise ratio snr among the present invention suppose that receiving terminal can know channel information accurately.As a comparison, provided the bit error rate (is example with the system in the document [1]) that does not adopt the system of overlying training sequence among the figure simultaneously.As can be seen, in two kinds of channels, the stack of training sequence can be ignored fully to all almost not influences of bit error rate of system.Adopting the benefit of overlying training sequence then is to reduce the valid data transmission rate of system.

List of references (References)

[1]Meng-Han Hsieh，Che-Ho Wei.A low-complexity frame synchronization and frequencyoffset compensation scheme for OFDM systems over fading channels.IEEE Transactions onVehicular Technology，1999，48(5)：1596-1609.

[2]Minn H，Zeng M，Bhargava V K.On timing offset estimation for OFDM systems.IEEECommunications Letters，2000，4(7)：242-244.

[3]Ozaktas H M，Arikan O，Kutay M A，etal.Digital computation of the fractional Fouriertransform[J].IEEE Transactions on Signal Processing，1996，44(9)：2141-2150.

[4]Digital cellular telecommunication system：Radio transmission and reception[S].ETSI TS100 910 V5.12.0，2001

Claims (1)

1. high-performance OFDM frame synchronization algorithm is characterized in that concrete steps are as follows:

(1), carry out sequence c (n) that uniform sampling obtains in [π, π] interval as training sequence, on the data-signal u (n) that is added to, as sending signal s (n) from LFM signal c (t) at the ofdm system transmitting terminal:

s(n)＝u(n)+c(n)，n＝0，1，...，N-1，

Here N=N _Subc+ N _g, N _SubcBe the OFDM sub-carrier number, N _gBe the length of CP, u (n) is the contrary fast Fourier transformation of frequency domain data warp to be sent, be designated as IFFT, and add the time domain data signal that CP obtains, $c\left(t\right)={\mathrm{\&sigma;e}}^{{\mathrm{j\&pi;\&mu;t}}^2},$ Here σ is the average power of c (t), and μ is the frequency modulation rate of c (t); OFDM is that OFDM is multiplexing, and CP is a Cyclic Prefix, and LEM is a bilinearity frequency modulation;

(2) at the receiving terminal of ofdm system, received signal r (n) is:

$r\left(n\right)=s\left(n\right)*h\left(n\right)+v\left(n\right)=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{l}s(n-{\mathrm{\&tau;}}_l)+v\left(n\right),0\&le;n\&le;N-1---\left(1\right)$

In the formula (1), * represents convolution, and v (n) is that average is zero, variance is σ _v ²Additive white Gaussian noise, h (n) is that length is the channel impulse response of L, is expressed as:

$h\left(n\right)=\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_l\mathrm{\&delta;}(n-{\mathrm{\&tau;}}_l)---\left(2\right)$

In the formula (2), h _lThe complex gain in l footpath, τ _lIt is the time-delay in l footpath;

Intercepted length is the segment signal of N from r (n), is designated as y (n):

$y\left(n\right)=r_{m-1}^{\&prime;}\left(n\right)+r_m^{\&prime;}\left(n\right),0\&le;n\&le;N-1---\left(4\right)$

In the following formula, $r_{m-1}^{\&prime;}\left(n\right)=\left\{\begin{array}{cc}{r}_{m-1}(N-\mathrm{\&theta;}+n)& 0\&le;n<\mathrm{\&theta;}\\ r_{\mathrm{tail}}(n-\mathrm{\&theta;})& \mathrm{\&theta;}\&le;n<\mathrm{\&theta;}+L\\ 0& \mathrm{\&theta;}+L\&le;n\&le;N-1\end{array}\right.,$ $r_m^{\&prime;}\left(n\right)=\left\{\begin{array}{cc}0& 0\&le;n<\mathrm{\&theta;}\\ r_m(n-\mathrm{\&theta;})& \mathrm{\&theta;}\&le;n\&le;N-1\end{array}\right.,$

r _Tail(n) be because the hangover of (m-1) individual OFDM symbol that the time delay expansion of channel causes;

r _M-1(n), r _m(n) and r _M+1(n) respectively expression to receive (m-1) of signal r (n) individual, m and (m+1) individual OFDM symbol, wherein, θ represents the deviation of m OFDM symbol original position;

(3) y (n) is carried out the N point FRFT that exponent number is p=2/ π atan (1/ μ):

$F^p\left[y\left(n\right)\right]=F^p[c_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]$

$+F^p[u_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]+F^p\left[r_{m-1}^{\&prime;}\left(n\right)\right]$

$\&ap;\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{h}_{m,l}{A}_p{A}_l\mathrm{\&delta;}[u-\mathrm{\&theta;}\cos \mathrm{\&alpha;}]---\left(8\right)$

$+F^p[u_m(n-\mathrm{\&theta;})*h_m(n-\mathrm{\&theta;})]+F^p\left[r_{m-1}^{\&prime;}\left(n\right)\right]$

In the following formula, u _m(n), c _m(n) and h _m(n) be data-signal, training sequence and channel impulse response respectively corresponding to m OFDM symbol, $A_l=e^{j\frac{{\left[(\mathrm{\&theta;}+{\mathrm{\&tau;}}_{m,l}){\mathrm{\&omega;}}_1\right]}^2}{2}-\sin \mathrm{\&alpha;}\cos \mathrm{\&alpha;}-\mathrm{ju}(\mathrm{\&theta;}+{\mathrm{\&tau;}}_{m,l}){\mathrm{\&omega;}}_1^2\sin \mathrm{\&alpha;}},$ ω ₁=T _cCos α, h _{M, l}And τ _{M, l}Be the complex gain and the time delay in l footpath, α=p/2 π, A _pThe same A of expression-form ₁, first in the formula (5) is: c _m(n) and h _m(n) FRFT after the convolution, second is u _m(n) and h _m(n) FRFT after the convolution, the 3rd is r ' _M-1(n) FRFT, this energy of two all can not converge in the fractional number order Fourier of p rank, is considered as distracter; Here FRFT is the fractional order fourier transform;

(4) search F ^pThe amplitude maximum of [y (n)], its position is expressed as:

$u_1=\arg \underset{u}{\max }\left\{\right|F^p\left[y\left(n\right)\right]\left|\right\}=\mathrm{\&theta;}\cos \mathrm{\&alpha;}---\left(9\right)$

(5) promptly get the estimated value of OFDM symbol original position deviation θ by following formula

Thereby achieve frame is synchronous:

$\widehat{\mathrm{\&theta;}}=\mathrm{round}\left[\frac{u_1}{\cos \mathrm{\&alpha;}}\right]---\left(10\right)$

In the following formula, symbol round[x] expression gets the integer nearest apart from x.

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