CN110224769B - Estimation method for joint amplitude and noise variance in communication system - Google Patents

Estimation method for joint amplitude and noise variance in communication system Download PDF

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CN110224769B
CN110224769B CN201910461002.3A CN201910461002A CN110224769B CN 110224769 B CN110224769 B CN 110224769B CN 201910461002 A CN201910461002 A CN 201910461002A CN 110224769 B CN110224769 B CN 110224769B
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estimation
amplitude
noise variance
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communication system
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吴茗蔚
甘培润
金艳
孟婷
周武杰
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Zhejiang Lover Health Science and Technology Development Co Ltd
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Abstract

The invention discloses a method for estimating joint amplitude and noise variance in a communication system, wherein a received signal of the communication system can be represented by a complex number and comprises a signal of complex Gaussian white noise, and the method comprises the following steps: (1) collecting a signal strength sample set of a signal receiving end sampling point in a communication system; (2) establishing an amplitude and noise variance estimation model 1 and a model 2 in a communication system; (3) and (3) jointly solving the amplitude and noise variance estimation model 1 and the noise variance estimation model 2 established in the step (2) for estimation, so as to obtain an amplitude estimation value or a noise variance estimation value. The invention does not need to detect the noise variance in advance, does not need frequency estimation, phase estimation and phase expansion, is flexible to apply and has better performance than the traditional parameter estimation method.

Description

Estimation method for joint amplitude and noise variance in communication system
Technical Field
The invention relates to the technical field of communication, in particular to an estimation method for joint amplitude and noise variance in a communication system.
Background
In a communication system, the estimation of amplitude and noise variance from a series of signals containing noise is an important research problem for signal parameter estimation, and the traditional estimation method has few estimation methods for combining the amplitude and the noise variance. Generally, the noise variance parameter needs to be detected first, and then the amplitude parameter can be estimated only after the frequency and phase parameters of the signal are estimated by using a Fast Fourier Transform (FFT) based on a frequency domain solution. Alternatively, the amplitude parameter is estimated after jointly estimating the signal frequency and phase parameters. The most common solution is to use Maximum Likelihood (ML) estimation theory. ML estimation is based on the assumption: the unknown parameters have no prior knowledge, namely the amplitude can be any non-negative value, and the frequency and the phase can be any values between intervals of [ -pi, pi); the channel is a time invariant additive white gaussian noise channel.
The traditional ML estimation method firstly needs to detect the noise variance parameter in advance
Figure GDA0002976899730000011
And obtaining the frequency estimation value
Figure GDA0002976899730000012
And phase estimation
Figure GDA0002976899730000013
Thereafter, an estimate of the amplitude can be obtained
Figure GDA0002976899730000014
Improving the estimation performance of the signal amplitude depends on
Figure GDA0002976899730000015
To the accuracy of (2). It is known that detecting the noise variance parameter, estimating the frequency and phase of the signal, and so on, face many common problems, such as computational complexity and phase unwrapping. These problems cause difficulty in amplitude estimation and degrade the amplitude estimation performance.
Disclosure of Invention
The invention aims to overcome the problem that the estimation of the signal amplitude needs to detect the noise variance in advance and depends on the accuracy of frequency and phase estimation values, and provides an estimation method for combining the amplitude and the noise variance in a communication system. The method is based on the maximum likelihood principle, does not need to detect the noise variance in advance, does not need to carry out frequency estimation and phase estimation, and realizes parameter estimation for estimating the amplitude or the noise variance through signal intensity sampling in one step.
The purpose of the invention is realized by the following technical scheme: a method for estimating a combined amplitude and noise variance in a communication system, the method comprising the steps of:
(1) collecting signal strength sample set of signal receiving end sampling point in communication system
Figure GDA0002976899730000021
Where | r (k) | denotes a sample value of a kth sampling point,
Figure GDA0002976899730000022
a sample set representing the number of sampling points N;
(2) establishing an amplitude and noise variance estimation model 1 and a model 2 in a communication system, which are respectively as follows:
model 1:
Figure GDA0002976899730000023
model 2:
Figure GDA0002976899730000024
wherein the content of the first and second substances,
Figure GDA0002976899730000025
for the purpose of an amplitude estimation,
Figure GDA0002976899730000026
is the variance estimation value of the real part or the imaginary part of the complex additive white gaussian noise,
Figure GDA0002976899730000027
is the average value of the samples and is,
Figure GDA0002976899730000028
for the mean square value, the calculation formula is as follows:
sample mean value:
Figure GDA0002976899730000029
mean square value of the sample:
Figure GDA00029768997300000210
(3) jointly solving the amplitude and noise variance estimation model 1 and the noise variance estimation model 2 established in the step (2) for estimation to obtain an amplitude estimation value
Figure GDA00029768997300000211
Or noise variance estimate
Figure GDA00029768997300000212
(3.1) the estimation method according to the step (3), wherein the amplitude and noise variance estimation model 1 and the model 2 are jointly solved to obtain the amplitude estimation value
Figure GDA00029768997300000213
The calculation formula is as follows:
Figure GDA00029768997300000214
wherein the content of the first and second substances,
Figure GDA00029768997300000215
representing the real part of the value taken;
(3.2) the estimation method according to the step (3), wherein the step amplitude and noise variance estimation model 1 and the model 2 are jointly solved to obtain the noise variance estimation value
Figure GDA00029768997300000216
The calculation formula is as follows:
Figure GDA00029768997300000217
compared with the prior art, the invention has the following advantages:
(1) the estimation method is provided for the case that the noise variance is unknown, the noise variance does not need to be measured or estimated in advance, the steps are simple, the estimation can be realized in one step, and the efficiency is improved.
(2) The signal amplitude parameter is directly recovered from the size information of the signal sampling value, so that the signal amplitude parameter is not influenced by Doppler frequency shift, and the estimation performance does not depend on the accuracy of frequency estimation or phase estimation.
(3) The approximate estimation method carries out reasonable approximate calculation, thereby greatly reducing the calculation complexity.
(4) The performance of the local oscillation amplitude estimation method is superior to that of the traditional amplitude estimation method.
Drawings
FIG. 1 is a geometric representation of a received signal;
FIG. 2 is a comparison of the mean square error performance of the Clalmelo lower bound (CRLB) of the method example of the present invention;
figure 3 is the mean square error performance of the noise variance parameter of an example of the method of the present invention.
Detailed Description
The amplitude and noise variance estimation models 1 and 2 are derived based on the maximum likelihood principle, and the derivation process of the invention is described in detail below with reference to the accompanying drawings.
The received signal of the communication system is a signal r (k) which can be represented by a complex number and comprises complex white gaussian noise, and a signal model is as follows:
r(k)＝Aej(ωk+θ)+n(k)，k＝0,1,2,... (1)
where A represents the actual amplitude of the transmitted signal, ω and θ represent the frequency and phase of the signal, respectively, and n (k) represents a mean of zero and a variance of 2 σ2The variance of the real part and the imaginary part of the complex additive white Gaussian noise is sigma2. The geometric phasor representation of the received signal is illustrated in FIG. 1, where n (k) is decomposed parallel to Aej(ωk+θ)In-phase component n ofI(k) And perpendicular to Aej(ωk+θ)Of (2) orthogonal component nQ(k) Thus, the signal model can be written as r (k) ═ a + nI(k)+nQ(k) In that respect The modulus is calculated, and the formula is as follows:
Figure GDA0002976899730000031
the conditional probability density function p (| r (k) | A, σ) of | r (k) | is a random variable obeying the Rice distribution2) As follows:
Figure GDA0002976899730000032
wherein, I0(g) And I1(g) The first modified Bessel function is zero order and first order respectively.
From this conditional probability density function, a joint conditional probability density function of the received signal modulus can be derived, the calculation formula is as follows:
Figure GDA0002976899730000041
the likelihood function is as follows:
Figure GDA0002976899730000042
the specific derivation process of the amplitude and noise variance estimation model 1 is as follows:
using maximum likelihood principle to Λ (A, σ)2) Obtaining the partial derivative for A, and making the result 0, can obtain:
Figure GDA0002976899730000043
modifying Bessel function properties by a first kind
Figure GDA0002976899730000044
Further simplification, substituting formula (6) can result in the values for A and
Figure GDA0002976899730000045
the binary function of (c):
Figure GDA0002976899730000046
the expansion of the first modified bessel function is specifically as follows:
Figure GDA0002976899730000047
when the variable x tends to infinity, I0Is infinitely close to
Figure GDA0002976899730000048
I1Is infinitely close to
Figure GDA0002976899730000049
Thus, the ratio of a first order Bessel function to a zeroth order Bessel function can be written as
Figure GDA0002976899730000051
When the variable x tends to infinity, the ratio of the first order bessel function to the zero order bessel function approaches infinity
Figure GDA0002976899730000052
Namely, it is
Figure GDA0002976899730000053
By substituting equation (10) into equation (7), the amplitude and noise variance estimation model 1 can be simplified as follows:
Figure GDA0002976899730000054
wherein the content of the first and second substances,
Figure GDA0002976899730000055
for the purpose of an amplitude estimation,
Figure GDA0002976899730000056
in order to be an estimate of the variance of the noise,
Figure GDA0002976899730000057
the specific calculation formula for the sample mean is as follows:
Figure GDA0002976899730000058
the specific derivation process of the amplitude and noise variance estimation model 2 is as follows:
using maximum likelihood principle to Λ (A, σ)2) To find a relation2The partial derivatives of (1) are set to 0, and thus:
Figure GDA0002976899730000059
the amplitude and noise variance estimation model 2 is simplified by substituting equation (7) for equation (13):
Figure GDA00029768997300000510
wherein the content of the first and second substances,
Figure GDA00029768997300000511
the specific calculation formula is as follows:
Figure GDA00029768997300000512
the amplitude and noise variance estimation model 1 and the model 2 are solved simultaneously, and the specific solving process is as follows:
reduction of model 2 to σ2The formula for A:
Figure GDA0002976899730000061
substituting the above result into model 1, formula (11), and simplifying to obtain:
Figure GDA0002976899730000062
solving the above quadratic equation of one unit can obtain:
Figure GDA0002976899730000063
after simulation verification, the solution of plus is taken, and the final amplitude estimation value
Figure GDA0002976899730000064
The calculation formula is as follows:
Figure GDA0002976899730000065
wherein the content of the first and second substances,
Figure GDA0002976899730000066
representing the real part of its value.
Substituting the formula (19) into the formula (14) of the model 2, simplifying the process, and obtaining the noise variance estimation value in the same way
Figure GDA0002976899730000067
The calculation formula is as follows:
Figure GDA0002976899730000068
the embodiments of the present invention will be described more fully hereinafter with reference to the accompanying drawings. In this example, detailed embodiments and performance analysis are given by performing examples on the premise of the technical solution of the present invention, but the scope of the present invention is not limited to the following example 1.
Example 1:
the received signal of the communication system in this example is a complex representable signal containing complex white gaussian noise, whose noise variance is unknown, and the amplitude parameter may be any non-negative number. To verify the accuracy of the amplitude estimation result of this example, the amplitude of the transmitted signal is set toLet a be 7.9527 and let the variance of the noise be σ2＝1。
(1) Collecting signal strength sample set of signal receiving end N-50 sampling points in communication system
Figure GDA0002976899730000069
The specific sample sets collected are shown in the following table:
Figure GDA00029768997300000610
Figure GDA0002976899730000071
(2) establishing an amplitude and noise variance estimation model 1 and a model 2 in a communication system, which are respectively as follows:
model 1:
Figure GDA0002976899730000072
model 2:
Figure GDA0002976899730000073
wherein the content of the first and second substances,
Figure GDA0002976899730000074
for the purpose of an amplitude estimation,
Figure GDA0002976899730000075
is the variance estimation value of the real part or the imaginary part of the complex additive white gaussian noise,
Figure GDA0002976899730000076
is the average value of the samples and is,
Figure GDA0002976899730000077
for the mean square value, the calculation formula is as follows:
sample mean value:
Figure GDA0002976899730000078
mean square value of the sample:
Figure GDA0002976899730000079
(3) jointly solving the amplitude and noise variance estimation model 1 and the noise variance estimation model 2 established in the step (2) for estimation to obtain an amplitude estimation value
Figure GDA00029768997300000710
Or noise variance estimate
Figure GDA00029768997300000711
Wherein the content of the first and second substances,
Figure GDA00029768997300000712
representing the real part of its value.
The amplitude estimation value and the noise variance estimation value can be used independently or can be obtained simultaneously.
The calculation result shows that the true amplitude a of the transmission signal is 7.9527, and the noise variance σ is2Joint amplitude and noise variance estimation results by comparison with 1
Figure GDA00029768997300000713
σ20.97575180 is reliable and effective.
In order to further prove the performance superiority of the method, the accuracy of the estimation of the method is measured by adopting the mean square error based on the signal-to-noise ratio and compared with the traditional estimation method. As shown in fig. 3, in the case of passing through the same communication system, the noise variance is not changed, the number of sampling points is N10, N50, and N100, respectively, and the signal-to-noise ratio γ is 0 to 20dB, where the signal-to-noise ratio γ is defined as follows:
Figure GDA0002976899730000081
each signal-to-noise ratio γ can be correspondingly calculated to obtain a mean square error value, and the mean square error MSE calculation formula is as follows:
Figure GDA0002976899730000082
Figure GDA0002976899730000083
wherein M represents the number of samplings, in this example 1,000,000;
Figure GDA0002976899730000084
is the amplitude estimation result; a is the actual amplitude of the corresponding transmitted signal;
Figure GDA0002976899730000085
estimating a result for the noise variance; sigma2Is the actual noise variance of the corresponding transmitted signal.
The result shows that the mean square error of the embodiment of the invention is monotonically decreased along with the increase of the signal-to-noise ratio, and the method is superior to the traditional estimation method; tending towards the cramer leno lower bound (CRLB) at high signal-to-noise ratios.
The invention provides the estimation method for the combined amplitude and the noise variance in the communication system, which has the advantages of small calculation complexity, simple calculation steps, one-step implementation and high estimation accuracy. The method has obvious advantages in the aspects of accuracy and computational complexity under the condition that a large number of sampling samples are contained in the communication system, and the economy and the efficiency of amplitude estimation of the communication system are greatly improved.

Claims (3)

1. A method for estimating a joint amplitude and noise variance in a communication system having a received signal that is complex representable and that includes complex gaussian white noise, the method comprising the steps of:
(1) collecting signal strength sample set of signal receiving end sampling point in communication system
Figure FDA0002976899720000011
Where | r (k) | denotes a sample value of a kth sampling point,
Figure FDA0002976899720000012
a sample set representing the number of sampling points N;
(2) establishing an amplitude and noise variance estimation model 1 and a model 2 in a communication system, which are respectively as follows:
model 1:
Figure FDA0002976899720000013
model 2:
Figure FDA0002976899720000014
wherein the content of the first and second substances,
Figure FDA0002976899720000015
for the purpose of an amplitude estimation,
Figure FDA0002976899720000016
is the variance estimation value of the real part or the imaginary part of the complex additive white gaussian noise,
Figure FDA0002976899720000017
is the average value of the samples and is,
Figure FDA0002976899720000018
for the mean square value, the calculation formula is as follows:
sample mean value:
Figure FDA0002976899720000019
mean square value of the sample:
Figure FDA00029768997200000110
(3) combining the amplitude and noise variance estimation models 1 and 2 established in the step (2)Solving and estimating to obtain amplitude estimation value
Figure FDA00029768997200000111
Or noise variance estimate
Figure FDA00029768997200000112
The complex Gaussian white noise satisfies that the mean value is zero and the variance is 2 sigma2。
2. The estimation method according to claim 1, wherein the joint solution in step (3) is used to obtain the amplitude estimation value
Figure FDA00029768997200000113
The calculation formula is as follows:
Figure FDA00029768997200000114
wherein the content of the first and second substances,
Figure FDA00029768997200000115
representing the real part of its value.
3. The estimation method according to claim 1, wherein the joint solution in step (3) is used to obtain the noise variance estimation value
Figure FDA00029768997200000116
The calculation formula is as follows:
Figure FDA0002976899720000021
wherein the content of the first and second substances,
Figure FDA0002976899720000022
show to take itThe real part of the value.
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