KR20050053844A - Method for joint estimation of frequency and phase offsets in wireless digital communications system - Google Patents

Abstract

The present invention relates to a method for simultaneously interpolating and estimating a frequency offset caused by a transmission / reception frequency difference and a Doppler frequency on a channel and a phase offset occurring while passing through a wireless channel in digital wireless communication.

In the wireless digital communication system of the present invention, a method for simultaneously estimating a frequency offset and a phase includes periodically sampling a received signal to obtain a received data string; Obtaining a predetermined frequency correlation value for obtaining a main lobe sample of the frequency spectrum of the sampled signal; Obtaining a predetermined phase correlation value for obtaining a main lobe sample of the phase spectrum of the sampled signal; The method includes estimating a frequency offset using the frequency correlation value and the frequency interpolation method and estimating a phase offset using the estimated frequency offset, the phase correlation value and the phase interpolation method.

Therefore, in the wireless digital communication system of the present invention, the simultaneous estimation of frequency offset and phase can simultaneously estimate the frequency and phase offset in a burst mode digital transmission system such as a satellite communication system. There is an effect that the complexity can be significantly reduced, and the interpolation scheme proposed in the present invention can be used for both data-assisted estimation and non-assisted estimation.

Description

Method for joint estimation of frequency and phase offsets in wireless digital communications system

The present invention relates to a method of simultaneously estimating a frequency and a phase offset in a wireless digital communication system. More particularly, the present invention relates to a radio frequency (RF) signal in a transceiver in a wireless digital communication system. The present invention relates to a method for interpolating and estimating a frequency offset caused by a transmission / reception frequency difference of an oscillator and a Doppler frequency on a channel and a phase offset occurring while passing through a wireless channel.

In systems using Burst Mode Digital Transmission, such as in Digital Satellite Communications Systems, simultaneous estimation of frequency and phase offset is very important in modem design. There are already many prior art techniques for independently estimating system parameters such as frequency and phase offset.

These techniques can be largely divided into a time domain approach and a frequency domain approach. First, in the time domain, the average of the received sample string is used for estimating the system parameters. Typically, there is an efficient blind algorithm for estimating the phase offset of the M-ary phase shift keying (PSK) signal. . In contrast, in the frequency domain, a Discrete Fourier Transform (DFT) algorithm is used to estimate system parameters.

There is also a method for estimating the frequency and phase offset into blinds simultaneously based on the least square (LS) technique. However, according to the above method, only coarse estimation of frequency and phase offsets can be performed, and the proposed coarse estimation method alone does not provide a desired estimation performance, and a good performance can be obtained only when an additional fine estimation technique is added. have. This is because the resolution capability of the Discrete Fourier Transform algorithm is limited by the DFT size.

Another solution is to use a non-data-assisted system parameter estimation algorithm (NDA) or oversampling. However, this method is not a good solution because the size of the DFT increases hardware complexity.

There is also a method using interpolation in the frequency domain for fine estimation of system parameters. As described above, the interpolation method by the secant method has been conventionally introduced for fine estimation, but the method is not only complicated but also has a problem that the phase cannot be interpolated by the method. Therefore, there is a need for a new and simple interpolation method that can simultaneously estimate not only fine frequency offsets but also phase offsets.

The training symbol determination method and the frequency offset estimation method and apparatus in the orthogonal frequency division multiplexing system of the prior art Korea Patent Publication No. 10-2001-0035579 are transmitted from a transmitter of an orthogonal frequency division multiplexing system using N subcarriers In the method and apparatus for newly determining the training symbol structure used for symbol synchronization and frequency synchronization in order to easily estimate the frequency offset, and using the training symbol to estimate the frequency offset of the baseband orthogonal frequency division multiplexing system signal It is about.

However, the above method can be used only in an orthogonal frequency division multiplexing system, and there is a problem in that the process for estimating frequency offset is complicated and the frequency and phase offset cannot be estimated simultaneously.

The sampling frequency offset estimation method of the asynchronous OFDM system of the Republic of Korea Republic of Korea Patent No. 10-0330191 of the prior art is sampled in the time domain of the receiver after transmitting one or two OFDM training symbols containing only a specific sub-channel data in the frequency domain of the transmitter The present invention relates to a method for estimating a sampling frequency offset by obtaining a phase difference between two different samples.

However, the above method can be used only in an asynchronous OFDM system and there is a problem in that the frequency and phase offset cannot be estimated simultaneously.

Method and apparatus for estimating a frequency offset of US Patent US6104767, which relates to an apparatus and method for estimating a frequency offset between a carrier frequency of a transmitter and a local frequency reference of a receiver in a communication system, is described in detail. Successively collected phase differences are calculated until N sums of phase differences are dumped, the phase differences are summed to the cumulative phase difference, and the N sums of M phase differences are each weighted and the weighted N sums are This adds up to an estimated frequency offset.

However, the above method has a problem in that the process for estimating the frequency offset is complicated and the frequency and phase offset cannot be estimated simultaneously.

Accordingly, the present invention is to solve the problems of the prior art as described above, by using the correlation value of the main lobe of the frequency / phase spectrum, the frequency offset is first estimated by interpolating the frequency / phase offset based on the end point SUMMARY OF THE INVENTION An object of the present invention is to provide a method of simultaneously estimating frequency offset and phase so that the frequency offset is simultaneously estimated using the phase offset estimation.

The object of the present invention is to periodically sample a received signal to obtain a received data string; Obtaining a predetermined frequency correlation value for obtaining a main lobe sample of the frequency spectrum of the sampled signal; Obtaining a predetermined phase correlation value for obtaining a main lobe sample of the phase spectrum of the sampled signal; Estimating a frequency offset using the frequency correlation value and the frequency interpolation method, and estimating a phase offset using the estimated frequency offset and the phase correlation value and phase interpolation method. And a simultaneous estimation method of phase offsets.

Assuming perfect symbol timing, the samples in the M-ary PSK burst can be modeled as in Equation (1).

here silver Phase of the transmission sample with the value of. Is the frequency offset, Is the symbol period, Denotes a phase offset. Is additive white Gaussian noise (AWGN), Represents the length of the burst.

The data unaided frequency and phase offset estimates are given by Equations 2 and 3.

Where approximate integer frequency offset estimate Phase offset estimate multiplied by M times Can be obtained by solving the least-squares optimization problem of equation (4).

Solution to minimize LS error To satisfy Equation 5 Given by value.

And the sun Is given by Equation 6.

At this time, Is obtained as shown in equation (7).

The first equation (7-1) above can be interpreted as taking the DFT of the received sample and the second equation (7-2) can be seen as the spectrum of the received signal. In this case, frequency offset ( )silver Is the same as Equation (7-2), that is, the result of the DFT is not a sinc function. This results in the same result as the above expression (7-2) because the DFT is limited in size and distortion occurs in the frequency domain. if Let us assume that can be derived by including the sinc function as shown in (7-3).

The estimation method of the present invention provides two consecutive sized samples in the main leaf as described above. It is based on finding the end point of, and preferably the end point can be summarized by Equation (8).

Again from the definition of the sinc function,

The end point X in Equation 8 is a fine frequency offset from the relationship between Equation 9 and Eq. It can be seen that the same as).

Phase offset estimate ( ) May be estimated using the end point X. Using the linearity of the phase in the sinc function, the interpolation for the phase can be obtained as shown in Equation (11).

Equations 10 and 11 may be arranged as in Equation 12.

From the definition of the sinc function can be obtained as shown in equation (13).

As demonstrated above, the simultaneous estimation method of the present invention can be referred to as asymptotic unbiased estimation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Details of the above objects and technical configurations of the present invention and the effects thereof will be more clearly understood by the following detailed description with reference to the drawings showing preferred embodiments of the present invention.

First, FIG. 1 relates to a schematic diagram sequentially illustrating a method for simultaneously estimating frequency and phase offset of the present invention. Referring to FIG. 1, a method for simultaneously estimating frequency and phase offset may be performed by sampling a received signal to obtain a received data sequence (S101), and then obtaining a frequency correlation value (S102) to obtain a sample of the main lobe of the sampled frequency and phase spectrum. ) And a phase correlation value (S103), a frequency offset is estimated using the obtained frequency correlation value and frequency interpolation scheme (S104), and then the phase is obtained using the estimated frequency offset, the phase correlation value, and the phase interpolation scheme. Estimating an offset (105).

Next, FIG. 2 is a flowchart of a first simultaneous estimation method of frequency and phase offsets according to an embodiment of the present invention, and FIG. 5 is a diagram illustrating a variety of received sample sequences of an unmodulated ternary PSK in the absence of noise and interference. The present invention relates to a spectrum of a main lobe and a correlation value of a frequency spectrum according to a frequency offset and a frequency estimation method using a first simultaneous estimation method. 2 and 5 together, three frequency correlation values in the sampled signal after periodically sampling the received signal to obtain a received data stream And three phase correlations Obtain The three frequency correlation values and The frequency offset can be estimated by dividing into two ranges of (d) and (e) in FIG. ) Has a positive value and the range of correlation values Where (a) and (b) show that the frequency offset has a negative value and the correlation range If is a graph. (C) is a graph when the frequency offset is zero.

In the case of FIG. 5D under the assumption that there is no noise Is located in the side lobe, so Than the size of Will always be larger. In addition, in the case of FIG. Is located in the side lobe and is not shown in the figure. Than the size of Will always be larger. Using this property, the frequency offset in the first simultaneous estimation method can be calculated by Equation 14.

The estimation method is asymptotically unbiased estimation Since we have only the complexity of complex multiplication of, its complexity is very small.

The frequency offset estimated by the frequency offset estimation method proposed above may be used to estimate the phase offset. First, estimate the frequency offset The phase correlation value from the received sample sequence After obtaining, the phase offset may be estimated using Equation 15 using the estimated frequency offset value and the phase correlation value.

The bias characteristics of the first estimation method are as follows. 5C illustrates a correlation between the main lobe of the frequency spectrum and the frequency offset when the frequency offset occurs near 0. FIG. The spectrum of is shown. In this case, according to the first estimation method and The magnitudes must be compared, but even with a little noise, the probability of error is very high. This error results in a significant reduction in estimation performance regardless of the magnitude of the noise, which is a magnitude comparison process, so this bias should be reduced to near zero frequency offset. It is said to have a high search bias regardless of the size of. However, in the case of (c), the difference between the sinc function (7-3) and the actual frequency spectrum (7-2) becomes very small, thereby reducing the interpolation bias generated during interpolation. Thus, the interpolation bias is very small.

5 (b) and 5 (d) show a correlation with the main lobe of the frequency spectrum when a frequency offset of a fractional multiple occurs. The spectrum of is shown. In this case and The comparison bias that occurs when comparing the sizes of is not very large. However, the louder the noise, the larger the magnitude comparison error. In addition, since the difference between the sinc function 7-3 and the actual frequency spectrum 7-2 becomes very large, the interpolation bias generated during interpolation becomes large. This bias is low at prime frequency offset. With high comparison bias It is said to have a high interpolation bias, which is not desirable.

In FIGS. 5A and 5E, when the intermediate frequency offset between integer offsets occurs, the principal lobe and the correlation value of the frequency spectrum are generated. The spectrum of is shown. Here and There is little comparison bias that occurs when comparing the magnitudes of, and there is no interpolation bias even in interpolation using two selected correlation values. The performance in this case is close to the CBR (Cramer-Rao Bound), which is the limit of the estimation performance as shown in FIG. This bias is highly desirable because there is no comparison bias and interpolation bias at the intermediate frequency offset.

As mentioned in the bias analysis of the first simultaneous estimation method, one of the fundamental causes of bias is comparative bias, and the biggest way to solve the comparison bias is to eliminate the comparison operation.

3 is a flow chart of a second simultaneous estimation method of frequency and phase offset according to an embodiment of the present invention, and FIG. 6 is a frequency / phase of a received sample sequence of an unmodulated ternary PSK in the absence of noise and interference. The frequency / phase estimation method using the spectrum of the main lobe and the correlation value of the spectrum and the second simultaneous estimation method is shown. 3 and 6 together, the second simultaneous estimation method intentionally makes the frequency offset positive and unintentionally removes the intermediate frequency offset to the received signal in order to eliminate the comparison operation. After adding, we convert to the frequency axis. Therefore, the comparison operation is not necessary in the second simultaneous estimation method.

In the second method of frequency estimation, the frequency correlation value of the sampled signal after periodically sampling the received signal as shown in FIG. And phase correlation Next, the frequency offset is estimated using Equation 16, which is a frequency interpolation method, and the frequency correlation value.

The principle of the second simultaneous estimation method can be explained as follows. First term of denominator Is the received sample shifted in the frequency axis ( ) Means the magnitude of the zero frequency component of the second term of the denominator Is the received sample shifted in the frequency axis ( Means the magnitude of the first integer frequency component. Thus, the principle of the second estimation method is based on interpolation between two correlation values in which the received signal is moved along the frequency axis. In order to correct the frequency value finally shifted on the frequency axis, Will be subtracted.

The phase offset may be estimated using the estimated frequency offset, the phase correlation value, and a phase interpolation scheme as shown in Equation 17.

The principle of the second phase estimation method can be explained as follows. First term of the molecule Is the difference between the estimated frequency offset and zero frequency, the second term of the numerator is the phase of the zero frequency component shifted along the frequency axis, and the third term of the numerator Is the estimated frequency offset and phase of the first integer frequency component. Thus, the second phase estimation method is based on interpolation between two phase correlation values shifted on the frequency axis of the received signal. Also, because phase is frequency independent No subtraction is necessary. The second simultaneous estimation method Because only complex multiplication of is required, it is suitable for systems requiring simple hardware.

However, the second simultaneous estimation method is an estimation method for overcoming the comparison bias and still does not overcome the interpolation bias. Therefore, a new method is needed to overcome interpolation bias. The third simultaneous estimation method is shown in FIG. 4 in a mixture of the first and second estimation methods.

4 is a flowchart illustrating a third simultaneous estimation method of frequency and phase offset according to an embodiment of the present invention. Referring to FIG. 4, the third simultaneous estimation method periodically samples a received signal to obtain a received data string, and then uses a frequency correlation value in the sampled signal. And phase correlation Obtain The frequency correlation value is divided into a range of the following equations S ₄₁ , S ₄₂ , and S ₄₃ .

S ₄₁ :

S ₄₂ :

S ₄₃ :

Frequency and phase interpolation schemes according to respective ranges may be represented by Equations 18 and 19.

The third simultaneous estimation method is based on the following principle. In the case of the first simultaneous estimation method, a large bias is generated at the zero frequency offset (Fig. 5 (c)), which causes a lot of deterioration in the estimation performance.In contrast, at the intermediate frequency offset (Figs. 5 (b) and (d)), the bias is almost Performance is close to the CRB. This result can also be confirmed in the result of FIG. 7. Therefore, when the offset around the intermediate frequency occurs, it is advantageous to use the first simultaneous estimation method.

In the case of the second simultaneous estimation method, the performance approaches the CRB because the bias rarely occurs at the zero frequency offset, whereas the bias occurs at the intermediate frequency offset, resulting in deterioration of the performance. This result can also be confirmed in the result of FIG. 7. Therefore, when an offset around zero frequency occurs, it is advantageous to use the second estimation method.

Therefore, by combining the first and second simultaneous estimation methods, the second simultaneous estimation method around the zero frequency and the first simultaneous estimation method around the intermediate frequency offset can be used to construct a good estimator. However, the last problem to be solved is whether a frequency offset occurs near zero frequency (in this case, the second estimation method), or whether a frequency offset occurs near the intermediate frequency offset (in this case the second estimation method). How to judge). This is done by using the magnitude of the two correlation values included in the main lobe. In other words, the difference between two correlation values of the main lobe obtained for the first simultaneous estimation method or If is less than the difference between the two correlation values of the main lobe shifted on the frequency axis obtained for the second simultaneous estimation method, then the first multiple estimation method is used. If the value is larger, the offset occurs around the zero frequency. This is evidence of the use of a second simultaneous estimation method. It immediately S ₄₁ showing the above-mentioned conditions by the following formula, S _42, S ₄₃ becomes. The third estimation method can also be viewed as a form of obtaining diversity gain between the above two estimation methods.

7 is a graph illustrating data auxiliary frequency offset estimation performance by three simultaneous estimation methods of the present invention. Referring to FIG. 7, it can be seen that the performance of the first estimation method is very degraded at zero frequency offset. This is due to the bias characteristics of the first estimation method described above. On the contrary, the performance of the second estimation method has no performance deterioration at zero frequency offset and severe performance deterioration at intermediate frequency offset. On the other hand, the performance of the third estimation method follows the performance of the second estimation method when zero frequency offset occurs and the performance of the first estimation method when the intermediate frequency offset occurs. Can be.

The modulation method in the embodiment of FIG. 7 is QPSK and the length of the burst Is set to 128 and the ideal CBR for frequency offset estimation error is indicated as the reference performance.

Although the present invention has been shown and described with reference to preferred embodiments as described above, it is not limited to the above-described embodiments and those skilled in the art without departing from the spirit of the present invention. Various changes and modifications will be possible.

Therefore, in the wireless digital communication system of the present invention, a method of simultaneously estimating frequency offset and phase is a system for performing burst mode digital transmission such as a satellite communication system by interpolating and estimating frequency and phase using end points in correlation values of magnitude and spectrum. We can estimate the frequency and phase offset at the same time and reduce the complexity of the hardware in the implementation of the practical estimator. In addition, the interpolation scheme proposed in the present invention has an advantage that it can be used for both data-assisted estimation and non-assisted estimation.

1 is a flow chart of a method for the simultaneous estimation of frequency and phase offset according to the present invention.

2 is a flow chart of a first simultaneous estimation method of frequency and phase offset according to an embodiment of the present invention.

3 is a process flow diagram of a second simultaneous estimation method of frequency and phase offset according to an embodiment of the present invention.

4 is a flow chart of a third simultaneous estimation method of frequency and phase offset according to an embodiment of the present invention.

5 is a method of estimating frequency using the spectrum and the first simultaneous estimation method of the main lobe and the correlation value of the frequency spectrum according to various frequency offsets.

6 is a method of estimating frequency / phase using a spectrum of a main lobe and a correlation value of a frequency / phase spectrum of a received sample sequence and a second simultaneous estimation method;

7 is a graph illustrating data auxiliary frequency offset estimation performance by three simultaneous estimation methods of the present invention.

<Description of the symbols for the main parts of the drawings>

101: sampling the received signal 102: calculating the frequency correlation value

103: calculating phase correlation value 104: frequency offset estimation step

105: phase offset estimation step

Claims (11)

In the simultaneous estimation method of frequency and phase offset in a wireless digital communication system, Sampling the received signal periodically to obtain a received data string; Obtaining a predetermined frequency correlation value for obtaining a main lobe sample of the frequency spectrum of the sampled signal; Obtaining a predetermined phase correlation value for obtaining a main lobe sample of the phase spectrum of the sampled signal; Estimating a frequency offset using the frequency correlation value and the frequency interpolation scheme; And Estimating a phase offset using the estimated frequency offset, the phase correlation value, and a phase interpolation scheme Simultaneous estimation method of frequency and phase offset, characterized in that comprises a. The method of claim 1, The frequency correlation value is the following equation (S ₂₁ ), the phase correlation value is the following equation (S ₂₂ ), the frequency interpolation method is the following equation (S ₂₃ , S ₂₄ ), and the phase interpolation method is the following equation Simultaneous estimation of frequency and phase offset characterized by having (S ₂₅ , S ₂₆ ). S ₂₁ : S ₂₂ : S ₂₃ : S ₂₄ : S ₂₅ : S ₂₆ : The method of claim 2, The frequency correlation value is divided into the following equations (S ₂₇ ), (S ₂₈ ) characterized in that the simultaneous estimation of the frequency and phase offset. S ₂₇ : S ₂₈ : The method of claim 3, wherein And the frequency interpolation method is equation (S ₂₃ ) and the phase interpolation method is equation (S ₂₅ ) when the correlation value range is equation (S ₂₇ ). The method of claim 3, wherein And the frequency interpolation method is equation (S ₂₄ ) and the phase interpolation method is equation (S ₂₆ ) when the correlation value range is equation (S ₂₈ ). The method of claim 1, The frequency correlation value is the following equation (S ₃₁ ), the phase correlation value is the following equation (S ₃₂ ), the frequency interpolation method is the following equation (S ₃₃ ), and the phase interpolation method is the following equation (S _34). A method of simultaneous estimation of frequency and phase offset, characterized in that S ₃₁ : S ₃₂ : S ₃₃ : S ₃₄ : The method of claim 1, The frequency correlation value is the following equation (S ₂₁ ), the phase correlation value is the following equation (S ₂₂ ), the frequency interpolation method is the following equation (S ₂₃ , S ₂₄ , S ₃₃ ), and the phase interpolation method is A method of simultaneously estimating frequency and phase offsets, characterized by the following equations (S ₂₅ , S ₂₆ , S ₃₄ ): S ₂₁ : S ₂₂ : S ₂₃ : S ₂₄ : S ₃₃ : S ₂₅ : S ₂₆ : S ₃₄ : The method of claim 7, wherein The frequency correlation value is divided into the following equations (S ₄₁ ), (S ₄₂ ), (S ₄₃ ) characterized in that the simultaneous estimation method of frequency and phase offset. S ₄₁ : S ₄₂ : S ₄₃ : The method of claim 8, And the frequency interpolation method is equation (S ₂₃ ) and the phase interpolation method is equation (S ₂₅ ) when the correlation value range is equation (S ₄₁ ). The method of claim 8, And the frequency interpolation method is equation (S ₂₄ ) and the phase interpolation method is equation (S ₂₆ ) when the correlation value range is equation (S ₄₂ ). The method of claim 8, And the frequency interpolation method is equation (S ₃₃ ) and the phase interpolation method is equation (S ₃₄ ) when the correlation value range is equation (S ₄₃ ).