KR101012444B1 - Method of estimating frequency offset in an ofdm system using a pilot symbol - Google Patents

Abstract

The present invention relates to a method of estimating a frequency offset by making the sum of the pilot symbols zero in an OFDM system using pilot symbols. The frequency offset estimation method in an OFDM system includes receiving an OFDM signal including an OFDM symbol block having OFDM symbols and estimating a frequency offset from the received OFDM signal. Here, at least one of the OFDM symbols has a data symbol and a pilot symbol, and when the frequency offset is estimated, the sum of pilot symbols in the OFDM symbol block is zero.

OFDM, frequency offset, pilot symbol, CP

Description

A method of estimating frequency offset in an orthogonal frequency multiplexing system using pilot symbols {METHOD OF ESTIMATING FREQUENCY OFFSET IN AN OFDM SYSTEM USING A PILOT SYMBOL}

The present invention relates to a method for estimating a frequency offset in an OFDM system, and more particularly, to a method for estimating a frequency offset by making the sum of the pilot symbols equal to zero in an OFDM system using pilot symbols.

Orthogonal Frequency Division Multiplexing System (OFDM) is a system with high spectral efficiency because subcarriers are orthogonal to each other, such as IEEE 802.11a, Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), IEEE 802.16, and It is applied to the physical layer of various standards such as LTE equivalent.

However, when an error occurs in the frequencies between the oscillators of the transmitter and the receiver or a frequency offset occurs due to the Doppler effect due to mobility, interference between subcarriers is generated and the BER performance is sharply degraded.

Therefore, a technique for estimating frequency offset in an OFDM system is required, and as a result, various frequency offset estimation techniques have emerged.

A technique for estimating a frequency offset in an OFDM symbol including a data symbol and a pilot symbol for channel estimation is a representative technique. In this technique, since the channel response information for channel estimation is used in the frequency offset estimation, Channel estimation proceeds simultaneously. Specifically, the information used in the frequency offset estimation is used in the channel estimation, and then the channel response information in the channel estimation is again used for the frequency offset estimation. As described above, the frequency offset estimation and the channel estimation are simultaneously performed by repeating the process, that is, the frequency offset estimation and the channel estimation are simultaneously performed using an iterative algorithm.

However, when the iterative algorithm is used, the computational amount increases, that is, the complexity of the OFDM system is increased, and as a result, the processing speed of the OFDM system is slowed. Accordingly, there is a need for a method of independently estimating a frequency offset before channel estimation in order to improve the processing speed of the OFDM system.

An object of the present invention is to provide a frequency offset estimation method capable of independently estimating a frequency offset without channel response information by making the sum of pilot symbols zero to improve the processing speed of an OFDM system.

In order to achieve the above object, a frequency offset estimation method in an OFDM system according to an embodiment of the present invention comprises the steps of: receiving an OFDM signal including an OFDM symbol block having OFDM symbols; And estimating a frequency offset from the received OFDM signal. Here, at least one of the OFDM symbols has a data symbol and a pilot symbol, and when the frequency offset is estimated, the sum of pilot symbols in the OFDM symbol block is zero.

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In the OFDM system according to the present invention, the frequency offset estimation method uses an OFDM symbol including a pilot symbol used for channel estimation, and makes the sum of the pilot symbols to zero in the frequency offset estimation step through a decimation process. All. As a result, the channel response information used in the channel estimation is not used in the frequency offset estimation step, that is, the frequency offset estimation is completed independently before the channel estimation is performed, so that the complexity of the OFDM system is lowered so that the OFDM The processing speed of the system can be improved.

In addition, the frequency offset estimation method may use a polynomial rooting method and a decimation process to reduce complexity and polynomial order.

As the invention allows for various changes and numerous embodiments, particular embodiments will be illustrated in the drawings and described in detail in the written description. However, this is not intended to limit the present invention to specific embodiments, it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention. Like reference numerals are used for like elements in describing each drawing.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, the terms "comprise" or "have" are intended to indicate that there is a feature, number, step, operation, component, part, or combination thereof described in the specification, and one or more other features. It is to be understood that the present invention does not exclude the possibility of the presence or the addition of numbers, steps, operations, components, components, or a combination thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art, and are not construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

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

1 is a block diagram schematically illustrating a receiving end of an OFDM system according to an embodiment of the present invention.

Referring to FIG. 1, the receiving end of the OFDM system according to the present embodiment includes a CP remover 100, a decimator 102, a serial / parallel converter 104, a synchronizer 106, and a channel estimator 108. do.

The CP removing unit 100 removes the cyclic prefix from the OFDM signal received from the transmitting end of the OFDM system. Here, each OFDM symbol of the OFDM signal includes a data symbol and a pilot symbol used for channel estimation.

A decimator 102 decimates the CP-removed OFDM signal, i.e., down-samples the sum of pilot symbols to zero. Here, the decimator 102 is essentially used in an additive white Gaussian noise (AWGN) environment in which channel estimation is not required, while selectively used in a frequency selective environment. Detailed description thereof will be described later.

A serial / parallel converter (S / P) 104 converts the decimated OFDM signal in parallel.

The synchronizer 106 performs frame synchronization, integer error compensation, symbol timing synchronization, and frequency offset estimation on the OFDM signal output from the S / P 104. Here, unlike the prior art, the channel response information used in the channel estimation is not used when estimating the frequency offset of this embodiment.

The channel estimator 108 estimates a channel using the pilot symbols after the frequency offset estimation is completed.

In short, the receiving end of the OFDM system of this embodiment independently estimates the frequency offset without using channel response information before the channel estimation. To this end, the receiver controls the sum of pilot symbols to be zero through the decimation process. As a result, the frequency offset estimation of the present embodiment is performed independently before the channel estimation, as compared with the conventional technique in which the frequency offset estimation and the channel estimation are performed simultaneously through an iterative algorithm. Therefore, the complexity for the estimations is lowered, and as a result, the processing speed of the OFDM system of the present embodiment can be improved than that of the conventional OFDM system.

Hereinafter, the frequency offset estimation method of this embodiment will be described in detail by dividing into two environments.

First, a frequency offset estimation method in an AWGN environment in which channel estimation is not required will be described in detail.

2 is a flowchart illustrating a frequency offset estimation process according to an embodiment of the present invention, Figure 3 is a block diagram showing the flow of an OFDM signal for frequency offset estimation in an AWGN environment according to an embodiment of the present invention .

2 and 3, the transmitting end of the OFDM system of the present embodiment generates an OFDM symbol having a data symbol and a pilot symbol for channel estimation (S200). Here, the i-th OFDM symbol X _i consists of a data symbol X _i ^d and a pilot symbol X _i ^p .

Subsequently, the transmitter outputs an OFDM signal including the OFDM symbols (S202). In detail, as illustrated in FIG. 3, CPs are added to the OFDM symbols, and then serially converted, and then converted into a time function through a Fourier transform (DFT).

Subsequently, the receiving end of the OFDM system receives the output OFDM signal (S204), and then removes the CP from the OFDM signal (S206). In this case, the OFDM signal y _i from which the CP is removed is represented by Equation 1 below.

X _i = X _i ^d + X _i ^p

Where F _N is an N × N DFT matrix, Φ (ε) is a frequency offset representation matrix, and N _S is the sum of N (number of subcarriers) and N _CP and represents the length of one OFDM symbol with CP. , Z _i is the noise component.

Subsequently, the receiving end decimates the OFDM signal y _i , and for example, down-samples the OFDM signal y _{i at} a ratio of M (an integer of 2 or more), and then converts them in parallel (S208 and S210). As a result, the decimated OFDM signal W _i is given by Equation 2 below.

Where F _{N / M} is an N / M × N / M DFT matrix, and X _i ′ is Is a decimated OFDM symbol (frequency domain), and Z _{i '} is a decimated noise component.

Subsequently, the receiving end estimates the frequency offset (S212). Here, it is assumed that the number N of subcarriers and the number N _P of pilot symbols are integer multiples of M, respectively, and the pilot symbols cancel each other as the frequency region of the OFDM signal is extended by M times by the decimation. That is, the sum of the pilot symbols becomes 0 through the decimation process, as shown in Equation 3 below.

Here, I _P ′ means a set of exponents representing pilot subcarriers from 0 to (N / M−1).

가 0이 된다. As mentioned above, since the pilot symbols are set to cancel each other,

Becomes 0.

Hereinafter, the probability density functions of the I consecutive W's for ε will be expressed by Equation 4 below.

Using maximum likelihood (ML) estimation, the probability density function of Equation 4 above must be maximized, which results in a problem of minimizing the cost function shown in Equation 5 below. Can be.

Here, U _{N / M} ^H is a sub-matrix obtained by extracting only a column corresponding to a data subcarrier from F _{N / M} ^H.

로 표현되어질 수 있다. In order to maximize the probability density function of Equation 4, the value of the exponent of Equation 4 should be minimized. Therefore, the cost function of Equation 5 representing the exponent obtained by using the natural log should be minimized. In addition, since the sum of pilot symbols in the decimated OFDM symbol X _i ′ is 0, X _i ′ in Equation 5 is

It can be expressed as

를 구하면, 아래의 수학식 6과 같다. In order to find the minimum value of the cost function of Equation 5, the derivative is differentiated to zero.

Is obtained from Equation 6 below.

를 수학식 5에 대입하면, 아래의 수학식 7과 같이 표현된다. As shown in Equation 6 above

Is substituted into Equation 5, it is expressed as Equation 7 below.

Here, V _{N / M} ^H is a sub-matrix in which only a column corresponding to a pilot subcarrier is extracted from F _{N / M} ^H.

Since the cost function of equation (7) must be minimized as mentioned above, [epsilon] is determined as a value that minimizes the cost function, and is expressed as equation (8) below.

If Equation 8 is replaced with a correlation function on the time axis, it may be expressed as Equation 9 below.

The above method is a frequency offset estimation method similar to the well-known MUSIC. Since the range of values that epsilon can have when observing the frequency offset must be observed, it may take a long time to estimate the frequency offset. Therefore, the frequency offset estimation method of the present embodiment may use the Polynomial Rooting method.

In detail, since Equation 9 should be minimized, the equation 9 is differentiated into ε, and z = e ^{j2πεM / N} is substituted into Equation 10 below.

Solving in Equation 10 above will yield a large number of z's.

은

로 추정된다. Subsequently, substituting the obtained z's into Equation 9 finds z to make the minimum value, and z is found as z _rt .

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Is estimated.

In short, the frequency offset estimation method of the present embodiment independently performs the frequency offset estimation without using any channel response information used for channel estimation as described above. That is, unlike the prior art in which frequency offset estimation and channel estimation are performed simultaneously through an iterative algorithm, the channel estimation is performed after the frequency offset estimation is independently performed (S214). As a result, the complexity for the above estimations of the OFDM system of the present embodiment is lowered, so that the processing speed of the OFDM system of the present embodiment can be improved than that of the conventional OFDM system.

In addition, the frequency offset estimation method of the present embodiment can reduce the complexity of the system by minimizing the calculation process using the Polynomial Rooting method.

Next, a frequency offset estimation method in a frequency selective environment will be described in detail.

4 is a block diagram illustrating an OFDM signal flow for frequency offset estimation in a frequency selective environment according to an embodiment of the present invention.

Hereinafter, before estimating the frequency offset, the time-varying model of the channel assumes that the channel is constant for N _h (≧ 2) OFDM symbol intervals as slow fading. X _i means a symbol in the i th OFDM symbol block indicated in the frequency domain, and one symbol block is composed of N _h OFDM symbols. In addition, X _{i, k} consists of X _{i, k} ^P and X _{i, k} ^d . Here, X _{i, k} ^P denotes the k-th pilot symbol in the i-th OFDM symbol block, and X _{i, k} ^d denotes the k-th data symbol in the i-th OFDM symbol block.

In addition, when the pilot symbols up to the N _h index are summed in one OFDM symbol block, the sum of the pilot symbols is set to 0 as shown in Equation 11 below.

That is, the frequency offset estimation method of the present embodiment uses an OFDM symbol block and sets the sum of pilot symbols in the OFDM symbol block to be zero. As a result, the frequency offset can be estimated independently without channel response information used in channel estimation, as described below.

Hereinafter, the frequency offset estimation process will be described in detail.

The receiving end of the OFDM system receives the OFDM signal output from the transmitting end (S204), and then removes the CP from the OFDM signal (S206). Here, the OFDM signal y _i from which the CP has been removed is represented by Equation 12 below.

x _{i, k} = H _i X _{i, k}

Here, H _i denotes a channel response experienced by the i th symbol block.

라고 하면, OFDM 신호(y_i′)는 아래의 수학식 13과 같이 표현된다. 여기서, 본 실시예의 주파수 오프셋 추정 방법에서는 상기 OFDM 심볼 블록 내의 파일롯 심볼들의 합이 0이 되도록 설정되었으므로 데시메이팅 과정(S208)은 선택 사항이다. In Equation 12 above

In this case, the OFDM signal y _i ′ is expressed by Equation 13 below. Here, in the frequency offset estimation method of this embodiment, since the sum of pilot symbols in the OFDM symbol block is set to 0, the decimating process (S208) is optional.

Here, H _i ^d is a vector representing the channel response experienced by the data subcarriers in the i-th OFDM symbol block in the form of a diagonal matrix, and U _N ^H means a sub-matrix in which only a column corresponding to a data symbol is extracted from F _N ^H.

Hereinafter, the probability density functions of adjacent I y _i ′ will be expressed as Equation 14 below.

Using the maximum likelihood (ML) estimation, since the probability density function of Equation 14 should be maximized, the frequency offset estimation can result in a problem of minimizing the Cost function shown in Equation 15 below.

Here, U _N ^H is a sub-matrix in which only a column corresponding to a data symbol is extracted from F _N ^H.

Since the value of the exponent of Equation 14 should be minimized in order to maximize the probability density function of Equation 14, the cost function of Equation 15 representing the exponent obtained by using the natural logarithm should be minimized. When x _{i, k} in this case is detected, it is expressed by the following expression (16).

Substituting the value shown in Equation 16 into Equation 15, it is expressed as Equation 17 below.

Here, V _N ^H is a sub-matrix in which only a column corresponding to a pilot symbol is extracted from F _N ^H.

Since the cost function of equation (17) should be minimized, [epsilon] is determined as a value that minimizes the cost function, and is expressed as equation (18) below.

If Equation 18 is replaced with a correlation function on the time axis, it may be expressed as Equation 19 below.

The above method is a frequency offset estimation method similar to the well-known MUSIC. Since the frequency offset has to observe all the ranges of values that ε can have, it may take a long time to estimate the frequency offset. Therefore, the frequency offset estimation method of the present embodiment may use the Polynomial Rooting method.

In detail, since the above equation (19) should be minimized, the equation (9) is differentiated into [epsilon], and z = e ^{j2 [pi] M / N} is substituted.

=0

= 0

Solving in Equation 20 above will yield a large number of z's.

은

로 추정된다. 예를 들어, N_h를 2라고 하면, 수학식 19는 아래의 수학식 21로 표현될 수 있다. Subsequently, substituting the obtained z's into Equation 19 finds z to make the minimum value, and z is found as z _rt .

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Is estimated. For example, if N _h is 2, Equation 19 may be represented by Equation 21 below.

In short, the frequency offset estimation method in the frequency selective environment independently estimates the frequency offset without using any channel response information at the time of channel estimation as described above. As a result, frequency offset estimation in the OFDM system of the present embodiment. For this reason, the complexity of the scheme is lowered, and thus the processing speed of the OFDM system of the present embodiment can be improved than that of the conventional OFDM system.

Hereinafter, a method of further reducing complexity in the frequency offset estimation process of the present embodiment will be described.

In the above-described embodiment, the degree of polynomial is 2 ((N _h -1) N _S + (N-1)). In other words, it is necessary to reduce the polynomial order because the order of the polynomial is high. For this purpose, a method of reducing the polynomial order is proposed by using the same spacing of pilot subcarriers. Hereinafter, assuming that the distance between adjacent pilot subcarriers is the same and N _S / M is an integer, the number of pilot subcarriers becomes N / N _P and N _P becomes an integer multiple of M. Therefore, N _P = M ^Q is satisfied. Where M and Q are integers.

When a decimation function having a ratio of _M is called D _M (x), W _i is expressed by Equation 22 below.

Here, I _P 'means a set of exponents from 0 to (N / M-1) pilot subcarriers, and U _{N / M} ^H represents a column of exponents corresponding to the data subcarriers remaining after day meshing among F _N ^Hs . Indicates.

Next, a cost function is obtained, as shown in Equation 23 below.

Since the cost function of Equation 23 should be minimized, [epsilon] is determined as a value that minimizes the cost function and is expressed as Equation 24 below.

Here, y _{i, l} 'is a decimated received signal corresponding to the k-th subcarrier vector of the i-th OFDM symbol block.

Substituting z = e ^{j2πεM / N} is represented by Equation 25 below.

Solving for Equation 25 above will yield a large number of z's.

은

로 추정된다. 이 경우, 수학식 25에서의 다항식 차수를 살펴보면 아래의 수학식 26으로 표현된다. Subsequently, substituting the obtained z's into Equation 24 finds z to make a minimum value, and z is found as z _rt .

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Is estimated. In this case, the order of polynomials in Equation 25 is expressed by Equation 26 below.

As shown in Equation 26 above, it is confirmed that the polynomial order is significantly reduced.

The embodiments of the present invention described above are disclosed for purposes of illustration, and those skilled in the art having ordinary knowledge of the present invention may make various modifications, changes, and additions within the spirit and scope of the present invention. Should be considered to be within the scope of the following claims.

1 is a block diagram schematically illustrating a receiving end of an OFDM system according to an embodiment of the present invention.

2 is a flowchart illustrating a frequency offset estimation process according to an embodiment of the present invention.

3 is a block diagram illustrating a flow of an OFDM signal for frequency offset estimation in an AWGN environment according to an embodiment of the present invention.

4 is a block diagram illustrating an OFDM signal flow for frequency offset estimation in a frequency selective environment according to an embodiment of the present invention.

Claims (13)

delete delete delete delete delete delete Receiving an OFDM signal comprising an OFDM symbol block having OFDM symbols; And Estimating a frequency offset from the received OFDM signal, At least one of the OFDM symbols has a data symbol and a pilot symbol, and the sum of the pilot symbols in the OFDM symbol block is zero when the frequency offset is estimated. 8. The method of claim 7, wherein the information at the time of channel estimation is not used in the frequency offset estimation. 8. The method of claim 7, wherein the frequency offset estimation is performed independently before channel estimation is performed. 8. The method of claim 7, wherein estimating the frequency offset comprises: Removing a cyclic prefix (CP) from the received OFDM signal; Obtaining a probability density function of the OFDM signal from which the cyclic prefix has been removed; Obtaining a cost function of the probability density function using a maximum likelihood estimate; And Estimating a frequency offset [epsilon] that minimizes the cost function. 8. The method of claim 7, wherein estimating the frequency offset comprises: Removing a cyclic prefix (CP) from the received OFDM signal; Decimating an OFDM signal from which the periodic prefix code (CP) has been removed; Obtaining a probability density function of the decimated OFDM signal; Obtaining a cost function of the probability density function using a maximum likelihood estimate; And Estimating a frequency offset [epsilon] that minimizes the cost function. 12. The method of claim 10 or 11, wherein a polynomial rooting method is used to estimate the frequency offset [epsilon]. 8. The method of claim 7, wherein the frequency offset estimation is performed in a frequency selective environment.

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