KR101023563B1 - A Method for Analysing OFDM Frequency Offset Estimation Accuracy Using a Repeated Training Symbol - Google Patents

Abstract

In the OFDM frequency offset estimation accuracy analysis method using repeated training symbols according to the present invention, for the method 1, the method 2, and the method 3, respectively, the method for analyzing the frequency offset estimation accuracy, the method, the frequency offset Generating an OFDM symbol for a simulation to estimate; Transmitting the generated OFDM symbols in an AWGN (additive white Gaussian noise) environment or a Rayleigh fading channel, respectively; Setting a normalized frequency offset; Comparing the frequency offset estimation accuracy of each technique with mean squear error (MSE) is performed to select the optimal technique.

Description

A method for analysing OFDM frequency offset estimation accuracy using a repeated training symbol}

The present invention relates to an OFDM frequency offset estimation accuracy analysis method using repeated training symbols. The present invention relates to an OFDM frequency offset estimation accuracy analysis method using training symbols.

Orthogonal frequency division multiplexing (OFDM) is a method of dividing an available frequency band into a plurality of subbands, and assigning and transmitting signals superimposed on respective subband carrier frequencies orthogonal to each other.

Compared to a single carrier system, it has a high performance, a high transmission speed, and a high frequency efficiency in a multipath fading channel environment.

However, OFDM systems have the disadvantage of being very sensitive to frequency offsets (see Ref. 2). When a frequency offset occurs, the orthogonality between subcarriers is broken, which causes intercarrier interference (ICI), resulting in a drastic drop in system performance. Therefore, the frequency offset estimation technique is one of the very important techniques in the OFDM system.

Many techniques have been studied to solve the disadvantage of the frequency offset estimation technique in the conventional OFDM system.

First, Cox proposed a technique for estimating frequency offset using training symbols with two repeated intervals (see Ref. 3). However, since two training symbols are used to estimate the integer frequency offset, data transmission efficiency is reduced, and one training symbol estimates only the frequency offset between [-1, 1), which is a normalized range of subcarrier intervals. Could.

Morelli proposed a technique for estimating the frequency offset using a single training symbol as a complement to the Cox technique (see Ref. 4). This technique allowed us to estimate the frequency offset over the full bandwidth of the signal with a single symbol.

Later, Song presented a technique for a multi-stage frequency offset estimator that can increase the offset estimation stepwise to make accurate offset estimation (see Ref. 5). Song's technique is relatively simple to estimate frequency offsets compared to the more complex systems of the Morelli technique.

However, these conventional techniques estimate the frequency offset of an orthogonal frequency division multiplexing signal through one technique using repetitive training symbols. In other words, the frequency offset could not be estimated efficiently because only one technique was used regardless of the situation.

references

[1] R. Van nee and R. Prasad, OFDM for Wreless Multimedia Communications. Norwood, MA: Artech House, 2000.

[2] PH Moose, "A technique for orthogonal frequency division multiplexing frequency offset correction," IEEE Trans. Commun. , vol. 42, pp. 2908-2914, Oct. 1994.

[3] TM Schmidl and DC Cox, "Robust frequency and timing synchronization for OFDM," IEEE Trans. Commun. , vol. 45, pp. 1613-1621, Dec. 1997.

[4] M. Morelli and U. Mengali, "An improved frequency offset estimator for OFDM applications," IEEE Commun. Lett. , vol. 3, pp. 75-77, mar. 1999.

[5] H.-K. Song et al., "Frequency-offset synchronization and channel estimation for OFDM-based transmission," IEEE Commun. Lett. , vol. 4, pp. 95-97, Mar. 2000.

The present invention has been made in view of the above, and compares and analyzes the results of using three different techniques using repeated training symbols in an existing orthogonal frequency division multiplexing system, and then selects an appropriate technique for the situation of the system. It is an object of the present invention to provide an OFDM frequency offset estimation accuracy analysis method using a repeated training symbol that can select and efficiently estimate a frequency offset.

In order to achieve the above object, the method of analyzing the accuracy of the OFM die frequency offset using repeated training symbols according to the present invention,

(여기서,

, r_1,n은 수신된 첫 번째 훈련심벌, N은 역 고속 푸리에 변환의 크기임)에 의해, 소수 주파수의 옵셋을 추정하고, 식

및

(여기서, R _1,k은 주파수 옵셋의 정수 부분을 추정하기 위해 채널을 통과하여 수신된 첫 번째 훈련 심벌의 고속 푸리에 변환된 신호, R _2,k는 두 번째 훈련 심벌의 고속 푸리에 변환된 신호,

는 훈련심벌의 상관값이고,

임)에 의해 정수 주파수 옵셋을 추정하는 기법 1과,expression

(here,

where r _{1, n} is the first training symbol received and N is the magnitude of the inverse fast Fourier transform).

And

Where R _{1, k} is the fast Fourier transformed signal of the first training symbol received through the channel to estimate the integer portion of the frequency offset, R _{2, k} is the fast Fourier transformed signal of the second training symbol,

Is the correlation of training symbols,

Technique 1 for estimating integer frequency offset by

(여기서,

, I는 훈련심벌이 반복되는 횟수임)에 의해 H개의 주파수 옵셋 후보군

을 이용하여 주파수 옵셋을 추정하는 기법 2 및,expression

(here,

, I is a training symbol repeated a number of times Im) H of frequency offset by the candidate that

A technique for estimating frequency offset using

(여기서,

는 소수 주파수 옵셋 추정치이고, q_i 는 식

와 같은 조건을 만족하는 정수, k는 OFDM 심벌의 부반송파 인덱스임)에 의해 순차적으로 주파수 옵셋을 추정하여 각 단계별로 정의된 주파수 옵셋 추정치의 후보 값을 산출하고, 최종 단계에서 하나의 주파수 옵셋 추정치

을 결정하여 주파수 옵셋을 추정하는 기법 3에 대해, 각각 주파수 옵셋 추정 정확도를 분석하는 방법에 있어서,expression

(here,

Is a fractional frequency offset estimate and q _i is

K is the subcarrier index of the OFDM symbol) to sequentially estimate the frequency offset to produce candidate values of the frequency offset estimates defined at each step, and at the final step, one frequency offset estimate.

In Method 3 for estimating the frequency offset by determining the frequency offset, respectively, the method for analyzing the frequency offset estimation accuracy,

This method,

Generating an OFDM symbol for a simulation to estimate the frequency offset;

Transmitting the generated OFDM symbols in an AWGN (additive white Gaussian noise) environment or a Rayleigh fading channel, respectively;

Setting a normalized frequency offset;

Comparing the frequency offset estimation accuracy of each technique by means of mean squear error (MSE) to select the optimal technique.

In the present invention, the OFDM symbol is characterized in that the sample interval is 0.2 ㎲, the number of subcarriers is 1024, the number of samples of the guard interval is 40.

(여기서, E는 신호의 파워, A_i는 다중경로 신호를 나타냄), 이동체의 속도 134km/h, 반송파 주파수 1GHz, 최대 도플러 주파수 125 Hz로 모델링되는 것을 특징으로 한다.In the present invention, the Rayleigh fading channel, the number of multipath 25, multipath delay length 24 samples, multipath signal power

(Where E is the power of the signal, A _i represents the multipath signal), the speed of the moving object is 134 km / h, the carrier frequency 1 GHz, the maximum Doppler frequency 125 Hz.

In the present invention, the normalized frequency offset is 0.3.

In addition, in the present invention, the simulation is made a plurality of times, characterized in that the number of times of the simulation is 10,000 times.

In addition, in the present invention, the frequency offset estimation accuracy for the techniques 1,2,3 is the MSE of each technique with respect to signal-to-noise ratio (SNR), the frequency offset estimation range of each technique, and It is characterized in that it is analyzed based on the implementation complexity of the technique.

Also, in the present invention, the frequency offset estimation range according to each of the above techniques is characterized in that technique 1 has [-1, 1), and techniques 2 and 3 have [-N / 2, N / 2). .

Also, in the present invention, the implementation complexity according to each of the above techniques is that the number of multipliers and adders in technique 1 is N / 2 + 1 and N / 2, respectively, and the number of multipliers and adders in technique 2 is H ( N-mM + 2) +3 and H (N-mM), where M represents the number of multipliers, and the number of multipliers and adders in technique 3 are N / 2 ⁱ + i + 2 and N / 2, respectively. ⁱ is characterized in that.

According to the present invention, an efficient frequency offset estimation can be performed by comparing and analyzing the results of three different techniques using repeated training symbols in a conventional orthogonal frequency division multiplexing system to select an appropriate technique suitable for a system situation. Will be.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

In the time domain, the OFDM symbol model is represented by the inverse fast Fourier transform as in the following equation (a).

(a)

(a)

Here, c _k is a phase shift keying (PSK) or quadrature amplitude modulation (QAM) symbol of the k- th subcarrier, and N is the magnitude of an inverse fast Fourier transform. In order to prevent intersymbol interference (ISI), an OFDM symbol has a cyclic prefix (CP) longer than a maximum delay time of a multipath symbol. In a multipath channel environment, assuming that the time error is perfectly estimated, the received signal when there is a frequency offset is given by the following equation (b).

(b)

(b)

는 부반송파 간격으로 정규화된 주파수 옵셋으로, 정수 부분

과 소수 부분

으로 구성된다.

은 평균이 0이고, 분산이

인 덧셈꼴 백색 정규 잡음(additive white Gaussian noise : AWGN)이며,

은 다음의 식 (c)와 같이 정의된다.here,

Is the frequency offset normalized to the subcarrier interval, where the integer part

And fractional parts

It consists of.

Is 0 and the variance is

Additive white Gaussian noise (AWGN),

Is defined as in the following equation (c).

(c)

(c)

은 채널 계수이고, L은 다중 경로 개수이다. here,

Is the channel coefficient and L is the number of multipaths.

In the present invention, three frequency offset estimation techniques are compared and analyzed based on the received signal r _n .

First, the Cox technique (hereinafter referred to as technique 1) uses two training symbols in the time domain to estimate the frequency offset. The first training symbol in which two identical parts are repeated sends a pseudo noise signal to the even subcarrier and zeros to the odd subcarrier to repeat the same part twice. Subsequently, an inverse fast Fourier transform process results in a repeated signal in the time domain. The frequency offset can be estimated using this repeatability. First _, the fractional part of the frequency offset is estimated using the phase of the repeated part of the first received symbol r _{1, n} as shown in Equation (1) below.

(1)

(One)

이다. 식 (1)로부터, ∠의 범위는 [-π,π)이므로, 첫 번째 훈련 심벌을 이용한 기법 1의 소수 주파수 옵셋 추정 범위는

임을 알 수 있다.here,

to be. From Eq. (1), the range of ∠ is [-π, π), so the fractional frequency offset estimation range of technique 1 using the first training symbol is

It can be seen that.

을 생성한다. 상기 고속 푸리에 변환된 R _1,k, R _2,k와

를 이용하여 다음의 식 (2) 및 식 (3)과 같이 정수 주파수 옵셋을 추정한다.Next, the fast Fourier transformed signal of the first training symbol received through the channel to R _{1, k} and the Fast Fourier transformed signal of the second training symbol to R _{2, k} to estimate the integer portion of the frequency offset. Assume In addition, the correlation between the training symbols is generated by generating the first training symbol and the second training symbol without noise mixing at the receiving end.

. The fast Fourier transformed R _{1, k} , R _{2, k} and

Equation (2) and Eq. (3) are used to estimate the integer frequency offset.

(2)

(2)

(3)

(3)

이다.here,

to be.

The Morelli technique (hereinafter referred to as technique 2) estimates the frequency offset using one training symbol with I identical parts and has an estimation range of ± I / 2. The frequency offset estimation process of the above technique 2 is given by the following equation (4).

(4)

(4)

Where M = N / I and H is any value less than or equal to I -1.

Next, a candidate group of frequency offsets is estimated using the phase value of R _m as shown in Equation (5) below.

(5)

(5)

을 이용하여 최종 주파수 옵셋을 추정한다.Here, [·] _2π represents the remaining value obtained by dividing • by 2π. Finally, the H frequency offset candidates through the best linear unbiased estimation (BLUE) equation

We estimate the final frequency offset using

(6)

(6)

이다.here,

to be.

Song technique (hereinafter referred to as technique 3) estimates frequency offset using a multi-stage frequency offset estimator. Technique 3 can estimate a frequency offset in a wider range than technique 1 using one OFDM training symbol.

를 산출한다.Figure 2 is a view of the training symbol structure for a multi-stage frequency offset estimation scheme of the third, also group the single training symbol according to the value of the method 3 is i, as shown in a 2 ⁱ of the same block. Then, i fractional frequency offset estimates are obtained using the phase difference between the groups as shown in Equation (7) below.

Calculate

(7)

(7)

를 이용하여 아래의 과정을 통해 최종 주파수 옵셋 추정치를 얻는다. I dogs calculated from the above formula (7)

By using the following process to obtain the final frequency offset estimate.

FIG. 3 is a diagram illustrating a multi-stage frequency offset estimation process of Technique 3. First, Technique 3 estimates frequency offset sequentially as shown in FIG. 3, wherein candidate values of the frequency offset estimates defined for each stage are as follows. It is defined as Equation (8).

(8)

(8)

In said formula (8), q _i is an integer which satisfy | fills the conditions similar to following formula (9).

(9)

(9)

은 q _i 에 따라 다양한 값을 가지게 된다. 이때 추정 단계가 한 단계 증가하면, 식 (9)에 의해 옵셋 후보의 개수는 1/2만큼 줄어들게 된다.As in Eq. (8), Eq. (9),

Has various values depending on q _i . At this time, if the estimating step is increased by one step, the number of offset candidates is reduced by 1/2 according to equation (9).

과 다양한 정수 주파수 옵셋 후보 q ₁이 결정된다.In the first step, since the fractional frequency offset is estimated using the largest number of samples, an accurate fractional frequency offset estimate in the range of [-1, 1) is obtained.

And various integer frequency offset candidates q ₁ are determined.

을 포함한 다양한 주파수 옵셋 후보들이 순차적으로 다음 단계의 주파수 옵셋 후보들과 비교되면서, 첫 번째 단계의 주파수 옵셋 후보들 중, 각 단계에서 추정된 주파수 옵셋에 가까운 후보들이 선택된다. 결국, 각 단계를 거치면서 선택되는 주파수 옵셋의 후보가 줄어들게 되고, 결국 최종 단계에서 하나의 주파수 옵셋 추정치

이 결정된다. 여기서, 각 단계별 주파수 옵셋 추정 범위는

이다.First step

The various frequency offset candidates including are sequentially compared with the frequency offset candidates of the next stage, and candidates close to the frequency offset estimated in each stage are selected among the frequency offset candidates of the first stage. As a result, candidates for the frequency offset selected during each step are reduced, resulting in one frequency offset estimate at the end.

This is determined. Here, the frequency offset estimation range for each step is

to be.

The proposed multistage frequency offset estimation technique can estimate the exact frequency offset with a relatively simple implementation through continuous comparison and selection.

1 is a schematic diagram for performing an OFDM frequency offset estimation accuracy analysis method using repetitive training symbols according to the present invention. The performance of each of the three techniques is compared and analyzed, and the results of the comparison and analysis Based on this, it is possible to select the optimal technique for the situation of the system.

That is, an OFDM symbol for a simulation for estimating a frequency offset is generated, and the generated OFDM symbol is transmitted in an AWGN environment or a Rayleigh fading channel, respectively. Then, to set the normalized frequency offset, to compare the frequency offset estimation accuracy of each technique by means of mean squear error (MSE) to select the optimal technique.

In order to compare the three frequency offset estimation techniques, the present invention provides three methods for frequency offset estimation range, implementation complexity, and additive white Gaussian noise (AWGN) and Rayleigh fading channel environment. The mean squear error (MSE) of the techniques can be used to compare the frequency offset estimation accuracy of each technique.

The simulation environment for comparing the frequency offset estimation accuracy of each technique is shown in Table 1 below.

In other words, we estimate the accuracy of frequency offset estimation for each technique through mean squear error (MSE) of the three techniques in additive white Gaussian noise (AWGN) and Rayleigh fading channel environments. The comparison process is as follows.

, 이동체의 속도 134km/h, 반송파 주파수 1GHz, 최대 도플러 주파수 125Hz로 모델링 한다.First, in order to estimate the frequency offset, an OFDM symbol suitable for the simulation environment is generated. An OFDM symbol with a sample spacing of 0.2 ms, a number of subcarriers of 1024, and a number of samples of a guard interval is generated. The OFDM symbol thus generated is transmitted in the AWGN environment and the Rayleigh fading channel. Here, the Rayleigh fading channel has 25 multipaths, 24 multipath delay lengths, and multipath signal power.

The model is modeled with a moving speed of 134 km / h, a carrier frequency of 1 GHz, and a maximum Doppler frequency of 125 Hz.

Then, the frequency offset of the normalized 0.3 is set, and the frequency offset of the transmitted OFDM symbols is estimated using the above three techniques. The closer to the normalized frequency offset of 0.3, the more accurate the estimation. Here, the accuracy of the estimation is determined by MSE indicating the difference between the normalized frequency offset and the frequency offset value estimated using the actual technique. For more accurate experiments, increase the number of simulations to 10000 to test the accuracy of the estimate.

Frequency offset estimation accuracy of the three techniques can be compared as shown in FIG. 4 and FIG.

FIG. 4 is a graph showing MSE of three techniques for SNR implemented according to the method of the present invention in an AWGN environment. From FIG. 4, MSEs of Technique 3 and Technique 1 are identical to each other. It can be seen that is the lowest over the entire SNR range. Here, the performance of technique 3 and technique 2 is the same because the process of estimating the fractional frequency offset of technique 1 is the same as the process of estimating frequency offset when i = 1 in technique 3.

In addition, since technique 2 calculates an optimal frequency offset using the estimation theory of BLUE rather than simply selecting one frequency offset among frequency offset candidates, it shows better performance than the other two techniques.

5 is a graph showing the MSE of the three techniques for the SNR implemented according to the method of the present invention in a Rayleigh fading channel environment, it can be observed that the MSE of the technique 1 and 3 is the same as in FIG. It can be seen that technique 2 has the lowest MSE. However, unlike the AWGN channel environment, as the SNR increases, the MSE of the three schemes is the same.

FIG. 6 shows the frequency offset estimation ranges of the three schemes, and the frequency offset estimation ranges of the three schemes can be compared as shown in FIG. 6. When one training symbol was used, the estimated range of each technique is shown.

Technique 1 has a frequency offset estimation range of [-1, 1) using one training symbol. Technique 1 can be estimated over the full bandwidth of the signal using two training symbols, but in this case, there is a disadvantage in that data efficiency is lower than that of the other two techniques.

In both techniques 2 and 3, a single training symbol can be used to estimate the frequency offset over the entire bandwidth, that is, from -N / 2 to N / 2. Therefore, since one training symbol is used, data efficiency is better than that of Technique 1.

Finally, the implementation complexity of the three techniques can be compared. The implementation complexity of the three techniques is shown in Table 2.

                   Table 2 Implementation Complexity of Techniques 1,2,3

Multiplier Count (M) Adder count (A) Cox (Technique 1) N / 2 + 1 N / 2 Morelli (Technique 2) H (N-mM + 2) +3 H (N-mM) Song (Technique 3) N / 2 ⁱ + i + 2 N / 2 ⁱ

The number of multipliers (M) and the number of adders (A) are determined based on equation (1) in technique 1, equation (6) in technique 2, and equation (7) in technique 3, In the equations (1), (6) and (7), the number of additions and the number of multiplications of the above equations are shown based on how many times are added or multiplied.

That is, the number of multipliers M determined from equation (1) of technique 1 is N / 2 + 1, and the number A of adders is N / 2. Further, the number of multipliers M determined from equation (6) of technique 2 is H (N-mM + 2) +3, and the number A of adders is H (N-mM). Further, the number of multipliers M determined from equation (7) of technique 3 is N / 2 ⁱ + i + 2, and the number A of adders is N / 2 ⁱ .

According to this, it can be seen that technique 3 is the simplest to implement among the three techniques, and the implementation of technique 2 is the most complicated.

By comparing the MSE of each technique with respect to the above three items, the frequency offset estimation range of each technique, and the complexity of implementation of each technique, technique 2 has the highest frequency offset estimation accuracy and one training. The symbol can be used to estimate the frequency offset over the full bandwidth of the signal, but the implementation is more complex than the other two techniques. On the other hand, technique 3 has the same frequency offset estimation range as technique 2, and can be implemented most simply with the same estimation accuracy as technique 1.

Through the performance analysis of the OFDM frequency offset estimation techniques using the repeated training symbols, a frequency offset can be efficiently estimated by selecting a method satisfying the data transmission efficiency, the frequency offset estimation range, and the implementation complexity according to the system situation. Will be.

In addition, this invention is not limited to the said Example, It can variously deform and implement within the range which does not deviate from the summary of this invention.

1 is a schematic diagram for performing a method of analyzing the accuracy of the OFM die frequency offset estimation using repeated training symbols, according to the present invention,

2 is a diagram showing a training symbol structure for multi-stage frequency offset estimation of Technique 3;

3 is a diagram illustrating a multi-stage frequency offset estimation process of Technique 3;

4 is a graph showing the MSE of three techniques for SNR implemented according to the method of the present invention in an AWGN environment,

5 is a graph showing the MSE of three techniques for SNR implemented according to the method of the present invention in a Rayleigh fading channel environment,

6 shows a frequency offset estimation range of three techniques.

Claims (8)

expression

(here,

where r _{1, n} is the first training symbol received and N is the magnitude of the inverse fast Fourier transform).

And

Where R _{1, k} is the fast Fourier transformed signal of the first training symbol received through the channel to estimate the integer portion of the frequency offset, R _{2, k} is the fast Fourier transformed signal of the second training symbol,

Is the correlation of training symbols,

Technique 1 for estimating integer frequency offset by expression

(here,

, I is a training symbol repeated a number of times Im) H of frequency offset by the candidate that

A technique for estimating frequency offset using expression

(here,

Is a fractional frequency offset estimate and q _i is

K is the subcarrier index of the OFDM symbol) to sequentially estimate the frequency offset to produce candidate values of the frequency offset estimates defined at each step, and at the final step, one frequency offset estimate.

In Method 3 for estimating the frequency offset by determining the frequency offset, respectively, the method for analyzing the frequency offset estimation accuracy, This method, Generating an OFDM symbol for a simulation to estimate the frequency offset; Transmitting the generated OFDM symbols in an AWGN (additive white Gaussian noise) environment or a Rayleigh fading channel, respectively; Setting a normalized frequency offset; Comparing the frequency offset estimation accuracy of each technique using mean squear error (MSE) to select the optimal technique, OFDM frequency offset estimation accuracy analysis using repeated training symbols Way. The method of claim 1, wherein the OFDM symbol has a sample spacing of 0.2 ms, a number of subcarriers of 1024, and a number of samples of a guard interval of 40. 2. The method of claim 1, wherein the Rayleigh fading channel has a multipath number of 25, a multipath delay length of 24 samples, and a multipath signal power.

(Where E is the signal power, A _i is the multipath signal), the speed of the moving object is 134 km / h, the carrier frequency is 1 GHz, the maximum Doppler frequency is modeled at an OFDM frequency with repeated training symbols Offset estimation accuracy analysis method. The method of claim 1, wherein the normalized frequency offset is 0.3. The method of claim 1, wherein the simulation is performed a plurality of times, and the number of simulations is 10,000 times. 2. The method of claim 1, wherein the frequency offset estimation accuracy for the techniques 1,2,3 is determined by the MSE of each technique with respect to signal-to-noise ratio (SNR), the frequency offset estimation range of each technique, and Accuracy analysis method for OFDM frequency offset estimation using repeated training symbols characterized in that the analysis based on the implementation complexity of the technique. 7. The method of claim 6, wherein the frequency offset estimation range according to each technique is that technique 1 has [-1, 1) and techniques 2 and 3 have [-N / 2, N / 2). Accuracy Analysis Method for OFDM Frequency Offset Estimation Using Repeated Training Symbols. 7. The method of claim 6, wherein the implementation complexity of each technique is that the number of multipliers and adders in technique 1 is N / 2 + 1 and N / 2, respectively, and the number of multipliers and adders in technique 2 is H ( N-mM + 2) +3 and H (N-mM), where M represents the number of multipliers, and the number of multipliers and adders in technique 3 are N / 2 ⁱ + i + 2 and N / 2, respectively. OFDM frequency offset estimation accuracy analysis method using a repeated training symbol, characterized in that ⁱ .

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