Extremely precise frequency estimation apparatus and method for single receiver

Abstract

A frequency estimation apparatus and method for a single receiver. The frequency estimation apparatus for the single receiver includes: a coarse frequency estimation unit estimating a coarse frequency by calculating an average of frequency estimation values for each single pulse; a direct current domain transformation unit transforming a reception signal into a direct current domain based on the coarse frequency; a fine frequency estimation unit estimating a fine frequency by applying regression analysis to a pulse train in the direct current domain of the coarse frequency; and an extremely fine frequency estimation unit estimating an extremely fine frequency by compensating an error of the coarse frequency with the fine frequency.

Claims

1. An extremely fine frequency estimation apparatus for a single receiver, the apparatus comprising: a coarse frequency estimation unit estimating a coarse frequency by calculating an average of frequency estimation values for each single pulse; a direct current domain transformation unit transforming a reception signal into a direct current domain based on the coarse frequency; a fine frequency estimation unit estimating a fine frequency by applying regression analysis to a pulse train in the direct current domain of the coarse frequency; and an extremely fine frequency estimation unit estimating an extremely fine frequency by compensating an error of the coarse frequency with the fine frequency.

2. The apparatus of claim 1, wherein the frequency estimation value of each single pulse is an inclination in linear regression analysis where vectors indicating a phase shift value and an acquisition time of the pulse are used.

3. The apparatus of claim 1, wherein the fine frequency is an inclination in linear regression analysis where vectors indicating a phase shift value and an acquisition time of the pulse train are used.

4. The apparatus of claim 1, wherein a frequency error between the coarse frequency and the reception signal has a negative or positive correlation with an inclination of a pulse train signal transformed into the direct current domain based on the coarse frequency.

5. The apparatus of claim 1, wherein the extremely fine frequency estimation unit estimates the extremely fine frequency by adding the coarse frequency and the fine frequency.

6. The apparatus of claim 2, wherein the inclination is a frequency value indicated as an angle.

7. An extremely fine frequency estimation method for a single receiver, the method comprising: estimating a coarse frequency by calculating an average of frequency estimation values for each single pulse; transforming a reception signal into a direct current domain based on the coarse frequency; estimating a fine frequency by applying regression analysis to a pulse train in the direct current domain of the coarse frequency; and estimating an extremely fine frequency by compensating an error of the coarse frequency with the fine frequency.

8. The method of claim 7, wherein the frequency estimation value of each single pulse is an inclination in linear regression analysis where vectors indicating a phase shift value and an acquisition time of the pulse are used.

9. The method of claim 7, wherein the fine frequency is an inclination in linear regression analysis where vectors indicating a phase shift value and an acquisition time of the pulse train are used.

10. The method of claim 7, wherein a frequency error between the coarse frequency and the reception signal has a negative or positive correlation with an inclination of the signal transformed into the direct current domain based on the coarse frequency.

11. The method of claim 8, wherein the inclination is a frequency value indicated as an angle.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above and other objects, features and advantages of the present invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which:

(2) FIGS. 1A and 1B is a view showing the Fourier transform of a pulse-type signal;

(3) FIG. 2 is a view showing a measurement phase of a reception signal according to an acquisition time;

(4) FIG. 3 is a view showing the result of unwrapping the reception signal of FIG. 2;

(5) FIG. 4 is a view showing a comparison between unwrapping results of a continuous wave signal and a pulse signal;

(6) FIG. 5 is a view showing an extremely precise frequency estimation apparatus for a single receiver according to an embodiment of the present invention; and

(7) FIG. 6 is a view showing signal characteristics depending on an estimation error when a reception signal is transformed into a direct current domain region based on a coarse frequency.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

(8) The present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the embodiment of the present invention may be changed to a variety of embodiments and the scope and spirit of the present invention are not limited to the embodiment described hereinbelow. The embodiment of the present invention described hereinbelow is provided for allowing those skilled in the art to more clearly comprehend the present invention, Therefore, it should be understood that the shape and size of the elements shown in the drawings may be exaggeratedly drawn to provide an easily understood description of the structure of the present invention. The same reference numerals will be used throughout the drawings and the description to refer to the same or like elements or parts. In the following description, it is to be noted that, when the functions of conventional elements and the detailed description of elements related with the present invention may make the gist of the present invention unclear, a detailed description of those elements will be omitted.

(9) FIG. 5 is a view showing an extremely precise frequency estimation apparatus for a single receiver according to an embodiment of the present invention, and FIG. 6 is a view showing signal characteristics depending on an estimation error when a reception signal is transformed into a direct current domain region based on a coarse frequency.

(10) As shown in FIG. 5, according to the embodiment of the present invention, the extremely precise frequency estimation apparatus (hereinafter, referred to as a frequency estimation apparatus 100) of the single receiver may provide an extremely fine frequency estimation technique that reduces RMS error of scores Hz to several kHz, which occur with conventional frequency estimation techniques, to precisely estimate a frequency of a signal source in the single receiver, whereby it is possible to analyze and process the frequency.

(11) To this end, a frequency estimation method having three steps is applied to the frequency estimation apparatus 100. That is, the first step is estimating a coarse frequency of a reception signal, and the second step is estimating a fine frequency of a signal transformed into a direct current domain of the coarse frequency, and the third step is estimating an extremely fine frequency by compensating the coarse frequency with the fine frequency.

(12) In comparison with a conventional frequency estimation method, the frequency estimation apparatus 100 provides extremely fine frequency estimation accuracy. That is, the frequency estimation apparatus 100 has RMS error equal to or less than several Hz. In addition, the frequency estimation apparatus 100 provides a process that is faster and simpler than Fourier transform. Particularly, different from Fourier transform requiring an input value as an input variable for a section where a signal does not exist, the frequency estimation apparatus 100 requires an input value only for a section where a signal exists, and thus the frequency estimation apparatus requires reduced computation and memory requirements.

(13) Specifically, the frequency estimation apparatus 100 includes a coarse frequency estimation unit 110, a direct current domain transformation unit 120, a fine frequency estimation unit 130, and an extremely fine frequency estimation unit 140. Here, it is desirable that the frequency estimation apparatus 100 is included in the single receiver.

(14) First, the coarse frequency estimation unit 110 estimates a coarse frequency from pulse trains received during a predetermined time. Here, the coarse frequency may be a frequency where an error still exists without considering error correction.

(15) The coarse frequency estimation unit 110 may estimate the coarse frequency as shown in formula 1.

(16) $\begin{array}{cc}\mathrm{CoarseFRQ}=\frac{1}{N}\underset{j=1}{\overset{N}{.Math.}}{b}_1^j& \left[\mathrm{formula}1\right]\end{array}$

(17) Here, the coarse frequency is designated as CoarseFRQ, the number of pulse trains is designated as N, a frequency estimation value by regression analysis on the j-th pulse is designated as b.sub.1.sup.j. Through formula 1, the coarse frequency of N pulse trains may be calculated from an average of frequency estimation values where regression analysis on each single pulse is used.

(18) In the meantime, the frequency estimation value of each single pulse on which regression analysis is performed may be calculated through linear regression analysis such as formulas 2 and 3.
Y=XB[formula 2]

(19) Here, a vector indicating a phase shift value of a pulse is designated as Y, a vector indicating an acquisition time of the pulse is designated as X, a vector indicating a parameter for inclination (slope) and intercept in linear regression analysis is designated as B meaning a frequency value (angle, degree) and an initial phase value.

(20) Y is indicated as Y=[y.sub.1, y.sub.2, . . . , y.sub.].sup.T, X is indicated as X=[x.sub.1, x.sub.2, . . . , x.sub.,].sup.T. B is indicated as B=[b.sub.1, b.sub.2].sup.T that respectively means parameters for inclination and intercept in linear regression analysis. Accordingly, formula 2 may be indicated as formula 3.

(21) $\begin{array}{cc}\left[\begin{array}{c}{y}_1\\ y_2\\ y_3\\ \mathrm{.Math.}\\ \mathrm{.Math.}\\ y_{-2}\\ y_{-1}\\ y_{}\end{array}\right]=\left[\begin{array}{cc}{x}_1& 1\\ x_2& 1\\ x_3& 1\\ \mathrm{.Math.}& \mathrm{.Math.}\\ \mathrm{.Math.}& \mathrm{.Math.}\\ x_{-2}& 1\\ x_{-1}& 1\\ x_{}& 1\end{array}\right]\left[\begin{array}{c}{b}_1\\ b_2\end{array}\right]& \left[\mathrm{formula}3\right]\end{array}$

(22) Accordingly, B may be calculated by using linear algebra as shown in formula 4.
B=(X.sup.TX).sup.1X.sup.TY[formula 4]

(23) Here, a transform matrix for the vector X is designated as X.sup.T, and an inverse matrix for the vector X is designated as X.sup.1. In B=[b.sub.1, b.sub.2].sup.T calculated through formula 4, b.sub.1 is a frequency estimation value of each single pulse.

(24) Next, the direct current domain transformation unit 120 transforms the reception signal into a direct current domain region based on the coarse frequency. This is indicated as shown in formula 5.
DC_Sig=Sige.sup.j2XCoarseFRQ[formula 5]

(25) Here, a signal transformed into the direct current domain region is designated as DC_Sig, and an actual reception signal is designated as Sig. In addition, an acquisition time is designated as X.

(26) When a coarse frequency and an original frequency of an original signal are the same without error, inclination of the signal transformed into the direct current domain region based on the coarse frequency has a value close to zero. That is, in an ideal case without noise, the inclination converges on zero. In contrast, when the error is large, the inclination of the signal is large. FIG. 6 shows such characteristics. Here, the coarse frequency error means an error between the coarse frequency and the original frequency. As described above, the error between the coarse frequency and the reception signal frequency has a negative or positive correlation with the inclination of the signal transformed into the direct current domain based on the coarse frequency.

(27) Next, the fine frequency estimation unit 130 estimates a fine frequency of the signal transformed by the direct current domain transformation unit 120. This may be indicated as shown in formula 6.
y.sup.1N=X.sup.1NB[formula 6]

(28) Here, a vector indicating phase shift values of the first pulse to the n-th pulse is designated as y.sup.1N, and a vector indicating an acquisition time of the first pulse to the n-the pulse is designated as X.sup.1N, namely, y.sup.1N=[y.sub.1.sup.1, y.sub.2.sup.1, . . . , y.sub..sup.1, y.sub.1.sup.2, y.sub.2.sup.2, . . . , y.sub..sub.2.sup.2, . . . y.sub.1.sup.N, y.sub.2.sup.N, . . . , y.sub..sub.N.sup.N].sup.T and X.sup.1N=[x.sub.1.sup.1, x.sub.2.sup.1, . . . , x.sub..sup.1, x.sub.1.sup.2, x.sub.2.sup.2, . . . , x.sub..sub.2.sup.2, . . . x.sub.1.sup.N, x.sub.2.sup.N, . . . , x.sub..sub.N.sup.N].sup.T.

(29) As described above, B is indicated as B=[b.sub.1, b.sub.2].sup.T. In B=[b.sub.1, b.sub.2].sup.T, b.sub.1 and b.sub.2 are vectors respectively indicating parameters for inclination and intercept in linear regression analysis, namely, a frequency value and an initial phase value.

(30) Accordingly, B=[b.sub.1, b.sub.2].sup.T may be calculated through formula 4. Here, b.sub.1 is a fine frequency value estimated in the direct current domain of the coarse frequency. Here, FineFRQ is a fine frequency estimated in the direct current domain, and may be indicated as shown in formula 7.
FineFRQ=b.sub.1[formula 7]

(31) Finally, the extremely fine frequency estimation unit 140 estimates an extremely fine frequency. This is indicated as shown in formula 8.
ExtFineFRQ=FineFRQ+CoarseFRQ[formula 8]

(32) Here, ExtFineFRQ means an extremely fine frequency, FineFRQ means a fine frequency, and CoarseFRQ means a coarse frequency. The extremely fine frequency estimation unit 140 estimates an extremely fine frequency by adding the coarse frequency and the fine frequency. The extremely fine frequency is finally estimated as shown in formula 7 by compensating the error of the roughly measured coarse frequency with the fine frequency precisely estimated in the direct current domain.

(33) Although the embodiment of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed in the accompanying claims. It is thus well known to those skilled in that art that the present invention is not limited to the embodiment disclosed in the detailed description, and the patent right of the present invention should be defined by the scope and spirit of the invention as disclosed in the accompanying claims. Accordingly, it should be understood that the present invention includes various modifications, additions and substitutions without departing from the scope and spirit of the invention as disclosed in the accompanying claims.