KR20170043718A - Signal detection apparatus using compressive sensing and method thereof - Google Patents

Signal detection apparatus using compressive sensing and method thereof Download PDF

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KR20170043718A
KR20170043718A KR1020150142912A KR20150142912A KR20170043718A KR 20170043718 A KR20170043718 A KR 20170043718A KR 1020150142912 A KR1020150142912 A KR 1020150142912A KR 20150142912 A KR20150142912 A KR 20150142912A KR 20170043718 A KR20170043718 A KR 20170043718A
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signal
linear measurement
denotes
detecting
original signal
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KR101755240B1 (en
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신요안
정홍규
김광열
응웬뚜랑녹
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숭실대학교산학협력단
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/16—Spectrum analysis; Fourier analysis
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R23/00—Arrangements for measuring frequencies; Arrangements for analysing frequency spectra
    • G01R23/02—Arrangements for measuring frequency, e.g. pulse repetition rate; Arrangements for measuring period of current or voltage
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/28—Testing of electronic circuits, e.g. by signal tracer
    • G01R31/317—Testing of digital circuits
    • G01R31/3181—Functional testing
    • G01R31/3183—Generation of test inputs, e.g. test vectors, patterns or sequences

Abstract

The present invention relates to a signal detection apparatus based on compressive sensing and a method thereof. According to the present invention, the signal detection apparatus comprises: a reception unit which receives a reception signal from a reception end; a signal compression unit which compresses the reception signal by using a pre-saved linear measurement matrix and generates a linear measurement vector; and a detection unit which calculates a probability density function of the linear measurement vector and detects the source signal in the linear measurement vector by using the probability density function and a likelihood ratio test. Accordingly, the present invention can remarkably reduce the complexity of the signal detection apparatus and the calculation procedure of a system by using fewer samples than those for conventional signal detection methods and greatly improve energy efficiency.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a signal detection apparatus based on compression sensing,

More particularly, the present invention relates to a compression-sensing-based signal detection apparatus and method for detecting a source signal transmitted from a transmission terminal from a reception signal using a compression sensing technique .

Spectrum Sensing is a technology that measures the spectrum and identifies channel users or channel users. Spectral sensing is classified into cooperative sensing and non-cooperative sensing. Non-cooperative sensing includes energy detection, matched filter method, and cyclostationary detection. .

However, such spectrum sensing requires a large amount of data to be processed because a wide frequency band is searched to identify whether the channel is used or not. In particular, in order to process a digital signal, an ADC (Analog to Digital Convert) process, which samples an analog signal and converts it into digital data, is necessary. In order to sample a signal and restore it to its original signal without loss, (Nyquist's sampling theory) In order to process a signal of the corresponding frequency, an ADC (Analog to Digital Converter) having a sampling rate of twice or more of the frequency is required, .

As a result, the configuration of the equipment becomes complicated in the spectrum sensing, and the data processing takes a long time.

The technology of the background of the present invention is disclosed in Korean Patent Publication No. 10-2013-0065458 (published on June 19, 2013).

According to an aspect of the present invention, there is provided a compression-sensing-based signal detection apparatus and method for detecting a source signal transmitted from a transmission signal from a reception signal using a compression sensing technique.

According to an aspect of the present invention, there is provided a signal detecting apparatus including a receiver for receiving a received signal from a transmitter, a signal compressor for compressing the received signal using the stored linear measurement matrix to generate a linear measurement vector, And a detector for calculating a probability density function of the linear measurement vector and detecting the original signal among the linear measurement vectors using the probability density function and the likelihood ratio test.

The detecting unit may calculate the probability density function f (y) of the linear measurement vector through the following equation.

Figure pat00001

Here, y denotes the linear measurement vector,

Figure pat00002
Denotes a case where the received signal is composed of a noise signal,
Figure pat00003
Wherein A denotes a linear measurement matrix, m denotes a number of rows of the linear measurement matrix, and sigma denotes a standard deviation of the linear measurement vector , And s denotes the original signal.

The detection unit may detect the original signal among the linear measurement vectors using the likelihood ratio test expressed by the following equation.

Figure pat00004

Here, L (y) denotes the likelihood ratio test function, and τ denotes the likelihood ratio test constant.

The detection unit can detect the original signal among the linear measurement vectors through the following equation.

Figure pat00005

here,

Figure pat00006
Means a sufficient statistic,
Figure pat00007
The
Figure pat00008
, And s denotes the original signal.

A signal detection method according to another embodiment of the present invention is a signal detection method using a signal detection apparatus, comprising: receiving a reception signal from a transmission terminal; compressing the reception signal using a pre- Calculating a probability density function of the linear measurement vector, and detecting the original signal among the linear measurement vectors using the probability density function and the likelihood ratio test.

As described above, according to the present invention, the complexity of the signal detection apparatus and the operation procedure of the system can be significantly lowered by utilizing fewer samples compared to the conventional signal detection technique at the time of signal detection, and energy efficiency can be greatly improved.

1 is a configuration diagram of a signal detecting apparatus according to an embodiment of the present invention.
2 is a flowchart illustrating a signal detection method according to an embodiment of the present invention.
3 is a graph illustrating signal detection probability according to the false alarm probability according to the embodiment of the present invention.
4 is a graph illustrating signal detection probability according to the compression ratio according to the embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the present invention. The present invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. In order to clearly illustrate the present invention, parts not related to the description are omitted, and similar parts are denoted by like reference characters throughout the specification.

Throughout the specification, when an element is referred to as "comprising ", it means that it can include other elements as well, without excluding other elements unless specifically stated otherwise.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily carry out the present invention.

First, a signal detecting apparatus 100 according to an embodiment of the present invention will be described with reference to FIG. 1 is a configuration diagram of a signal detecting apparatus according to an embodiment of the present invention.

As shown in FIG. 1, the signal detecting apparatus 100 includes a receiving unit 110, a signal compressing unit 120, and a detecting unit 130.

First, the reception unit 110 receives a reception signal from a transmission terminal. In this case, the received signal may be a k-sparse signal, and may be composed of only a noise signal, or may be composed of an original signal and a noise signal. Then, the receiving unit 110 transmits the received signal to the signal compressing unit 120.

The signal compressing unit 120 compresses the received signal received from the transmitting end to generate a linear measurement vector. At this time, the signal compressing unit 120 compresses the received signal using a predetermined linear measurement matrix, and the linear measurement matrix satisfies the RIP (Restricted Isometry Property). Then, the signal compressing unit 120 transmits the result of compressing the received signal, that is, the linear measurement vector, to the detecting unit 130.

Next, the detection unit 130 detects the original signal among the linear measurement vectors. Specifically, the detecting unit 130 calculates a probability density function of the linear measurement vector, and detects the original signal among the linear measurement vectors using the probability density function and the likelihood ratio test of the calculated linear measurement vector.

Hereinafter, a signal detection method using the signal detection apparatus 100 according to an embodiment of the present invention will be described with reference to FIG. 2 is a flowchart illustrating a signal detection method according to an embodiment of the present invention.

First, the signal detection apparatus 100 receives a reception signal from a transmission terminal (S210). Here, the received signal may be composed of the original signal and the noise signal because the original signal transmitted by the transmitting terminal is included in the process of being transmitted to the receiving end. Also, the received signal may be composed of only the noise signal due to the fact that the original signal is lost during transmission or the transmitter does not transmit the original signal.

Therefore, the received signal can be expressed by Equation (1) below.

Figure pat00009

Here, x denotes a received signal, s denotes an original signal, and w denotes a noise signal.

Here, the received signal may be a k-sparse signal, where a k-sparse signal is a signal in which the majority of a component of a signal is zero and only a few fractional components, Is a signal having a non-zero component.

Then, the signal detecting apparatus 100 generates a linear measurement vector by compressing the received signal using the previously stored linear measurement matrix (S220). Specifically, the signal detecting apparatus 100 compresses the received signal using Equation (2) below.

Figure pat00010

Here, y denotes a linear measurement vector, A denotes a linear measurement matrix (

Figure pat00011
), X denotes the received signal (
Figure pat00012
).

At this time, the linear measurement matrix must satisfy the RIP (Restricted Isometry Property) when m << n.

Next, the signal detecting apparatus 100 calculates a probability density function of the linear measurement vector (S230).

Specifically, the signal detecting apparatus 100 calculates a probability density function of a linear measurement vector for each of the case where the received signal is composed of only noise signals and the case where the received signal is composed of a noise signal and an original signal.

At this time, the signal detecting apparatus 100 can define a hypothesis for the case where the received signal is composed of only the noise signal and the case where the received signal is composed of the noise signal and the original signal as shown in Equation (3).

Figure pat00013

here,

Figure pat00014
Denotes a case where the received signal is composed of a noise signal,
Figure pat00015
Means a case where the received signal is composed of a noise signal and an original signal.

Then, the signal detecting apparatus 100 calculates the following equation (4)

Figure pat00016
Wow
Figure pat00017
(F (y)).

Figure pat00018

Here, y denotes a linear measurement vector,

Figure pat00019
Denotes a case where the received signal is composed of a noise signal,
Figure pat00020
A denotes a linear measurement matrix, m denotes the number of rows of the linear measurement matrix, σ denotes a standard deviation of the linear measurement vector, s means the original signal.

Then, the signal detection apparatus 100 detects the original signal among the linear measurement vectors using the probability density function of the linear measurement vector and the likelihood ratio test (S240).

Here, the Likelihood Ratio Test is a method of comparing the likelihood ratios of the two cases by comparing the likelihood ratios of the two cases, and the likelihood ratio test function according to the present invention (5) &quot; (5) &quot;

Figure pat00021

Here, L (y) denotes the likelihood ratio test function, and τ denotes the likelihood ratio test constant.

At this time, the likelihood ratio test value τ is stored in the signal detecting apparatus 100 and satisfies the following equation (6).

Figure pat00022

Here, P FA denotes a false alarm probability, and α denotes a false alarm probability value. At this time, the false alarm probability means a probability that the original signal is included in the received signal even though the original signal is not included, and can be set arbitrarily.

Equation (4) is applied to Equation (5), and a log function is applied to each term, the following Equation (7) is obtained.

Figure pat00023

Equation (7) is summarized as Equation (8), and the signal detecting apparatus (100) detects an original signal from a linear measurement vector through Equation (8).

Figure pat00024

here,

Figure pat00025
Is a sufficient statistic,
Figure pat00026
The
Figure pat00027
.

In addition, the signal detecting apparatus 100 can calculate the detection probability and the false alarm probability of the original signal through Equation (8) using the Q-function.

At this time, the detection probability P D is calculated by the following equation (9).

Figure pat00028

Then, the false alarm probability (P FA ) is calculated through Equation (10).

Figure pat00029

If P FA is defined as?, Equation (10) can be expressed as Equation (11), and the mathematical expression for ROC (Receiver Operating Characteristic) can be summarized.

Figure pat00030

And E (AA T ) can be approximated to I m if the linear measurement matrix A is an orthogonal matrix satisfying AA T = I m and is an isotropic measurement matrix, and finally, the detection probability Can be calculated.

Figure pat00031

here,

Figure pat00032
Denotes a signal-to-noise ratio of a linear measurement vector,
Figure pat00033
.

Hereinafter, simulation results according to an embodiment of the present invention will be described with reference to FIGS. 3 and 4. FIG. FIG. 3 is a graph illustrating a signal detection probability according to a false alarm probability according to an embodiment of the present invention, and FIG. 4 is a graph illustrating signal detection probability according to a compression ratio according to an embodiment of the present invention.

3 shows ROC (Receiver Operating Characteristic) performance according to various compression ratios (m / n) when the SNR is 25 dB based on Equation (12). As shown in FIG. 3, it can be seen that the detection probability of the signal detection algorithm using compression sensing is improved as the compression ratio is lower.

Next, FIG. 4 shows signal detection performance for various SNRs when the probability of false alarm is 0.1. As shown in FIG. 4, the detection probability increases as the SNR increases.

As a result, it can be seen that the probability of signal detection increases as the compression ratio is lowered and the SNR is increased.

As described above, according to the embodiment of the present invention, when the signal is detected, the complexity of the signal detecting apparatus and the calculation procedure of the system can be significantly lowered by using fewer samples compared to the conventional signal detecting technique, and energy efficiency can be greatly improved.

While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

100: signal detecting device 110:
120: signal compressing unit 130: detecting unit

Claims (8)

A receiving unit for receiving a receiving signal from a transmitting terminal,
A signal compression unit for compressing the received signal using a pre-stored linear measurement matrix to generate a linear measurement vector, and
And a detector for calculating a probability density function of the linear measurement vector and detecting the original signal among the linear measurement vectors using the probability density function and the likelihood ratio test. The method according to claim 1,
Wherein:
A signal detecting apparatus for calculating a probability density function (f (y)) of the linear measurement vector by the following equation:
Figure pat00034

Here, y denotes the linear measurement vector,
Figure pat00035
Denotes a case where the received signal is composed of a noise signal,
Figure pat00036
Wherein A denotes a linear measurement matrix, m denotes a number of rows of the linear measurement matrix, and sigma denotes a standard deviation of the linear measurement vector , And s denotes the original signal. 3. The method of claim 2,
Wherein:
A signal detecting apparatus for detecting an original signal among the linear specified vectors using the likelihood ratio test expressed by the following equation:
Figure pat00037

Here, L (y) denotes the likelihood ratio test function, and τ denotes the likelihood ratio test constant. The method of claim 3,
Wherein:
A signal detecting apparatus for detecting an original signal among linear measurement vectors using the following equation:
Figure pat00038

here,
Figure pat00039
Means a sufficient statistic,
Figure pat00040
The
Figure pat00041
, And s denotes the original signal. A signal detecting method using a signal detecting apparatus,
Receiving a received signal from a transmitting end,
Compressing the received signal using a pre-stored linear measurement matrix to generate a linear measurement vector, and
Calculating a probability density function of the linear measurement vector, and detecting the original signal among the linear measurement vectors using the probability density function and the likelihood ratio test. 6. The method of claim 5,
Wherein the step of detecting the original signal comprises:
Calculating a probability density function f (y) of the linear measurement vector using the following equation:
Figure pat00042

Here, y denotes the linear measurement vector,
Figure pat00043
Denotes a case where the received signal is composed of a noise signal,
Figure pat00044
Wherein A denotes a linear measurement matrix, m denotes a number of rows of the linear measurement matrix, and sigma denotes a standard deviation of the linear measurement vector , And s denotes the original signal. The method according to claim 6,
Wherein the step of detecting the original signal comprises:
A signal detection method for detecting an original signal among linear measurement vectors using the likelihood ratio test expressed by the following equation:
Figure pat00045

Here, L (y) denotes the likelihood ratio test function, and τ denotes the likelihood ratio test constant. 8. The method of claim 7,
Wherein the step of detecting the original signal comprises:
A signal detecting method for detecting an original signal among linear measurement vectors using the following equation:
Figure pat00046

here,
Figure pat00047
Means a sufficient statistic,
Figure pat00048
The
Figure pat00049
, And s denotes the original signal.
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