CN109194422B - SNR estimation method based on subspace - Google Patents

SNR estimation method based on subspace Download PDF

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CN109194422B
CN109194422B CN201811024519.8A CN201811024519A CN109194422B CN 109194422 B CN109194422 B CN 109194422B CN 201811024519 A CN201811024519 A CN 201811024519A CN 109194422 B CN109194422 B CN 109194422B
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subspace
signal
covariance matrix
dimension
estimated value
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CN109194422A (en
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张小飞
孙泽洲
郑旺
王成华
朱秋明
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/336—Signal-to-interference ratio [SIR] or carrier-to-interference ratio [CIR]

Abstract

The invention discloses a subspace-based SNR estimation method, which comprises the following steps: step 1: solving an estimated value of a covariance matrix through a received signal obtained by communication equipment; step 2: solving the dimension of the signal subspace; and step 3: carrying out eigenvalue decomposition on the estimated value of the covariance matrix obtained in the step 1, and arranging the eigenvalues in a descending order according to the signal subspace dimension; and 4, step 4: and (4) solving the noise power and the signal power according to the characteristic value obtained in the step (3), thereby obtaining an estimated value of the SNR. The subspace-based SNR estimation method provided by the invention has the advantages that: the estimation method adopted by the application has the advantages of small calculation amount, higher processing speed and better estimation performance than other existing algorithms.

Description

SNR estimation method based on subspace
Technical Field
The invention relates to the technical field of signal processing, in particular to an SNR estimation method based on subspace.
Background
Mars are the planets in the solar system that are most detected by humans. Due to the fact that the distance between the mars and the earth is far, signal transmission time is prolonged, and signal attenuation is large. Meanwhile, the relative distance changes rapidly, and the load and power consumption of the detector are also very limited. These real situations all cause great trouble to the ground fire communication. A short communication arc results in less effective communication time and therefore a higher effective data rate. Moreover, real-time changes of the relative distance and the relative attitude between the devices can also cause real-time changes of the signal-to-noise ratio (SNR) of the signals received by the receiving end. This requires real-time adjustment of the code rate to increase it as much as possible. SNR estimation uses parameter estimation theory to calculate the noise-to-power ratio of a signal and provides the required channel quality information through modulation mode switching, rate adaptation, power control and channel allocation methods. Furthermore, many parameter estimation algorithms require SNR as a precondition to optimize performance.
The SNR estimation method includes a time domain method and a frequency domain method. The time domain method is classified into a Data Aided (DA) method and a non-data aided (NDA) method. The DA method has higher estimation accuracy than the NDA method, but it requires insertion of a periodic preamble sequence, which reduces transmission efficiency. In the time domain method, the DA-based SNR estimation method includes a Minimum Mean Square Error (MMSE), a maximum likelihood estimation (ML), a discrete symbol matrix estimation (SSME), a signal-to-noise separation of high-order cumulants, and the like. The NDA-based SNR estimation method includes a second-order fourth-order matrix estimation method (M2M4), a Signal-to-Variance Ratio estimation (SVR), a Squared Signal-to-Noise Variance Ratio estimation (SNV), a Data Fitting estimation (DF), and the like. The classical frequency domain method is based on the flat characteristic of a White Noise power spectrum, is suitable for the SNR estimation of an Additive White Gaussian Noise (AWGN) channel, and is not suitable for the color Noise environment.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a subspace-based SNR estimation method with better performance.
The invention solves the technical problems through the following technical scheme:
a subspace-based SNR estimation method, comprising the steps of:
step 1: solving an estimated value of a covariance matrix through a received signal obtained by communication equipment;
step 2: solving the dimension of the signal subspace;
and step 3: carrying out eigenvalue decomposition on the estimated value of the covariance matrix obtained in the step 1, and arranging the eigenvalues in a descending order according to the signal subspace dimension;
and 4, step 4: and (4) solving the noise power and the signal power according to the characteristic value obtained in the step (3) so as to obtain an estimated value of the SNR.
Preferably, the method for solving the estimated value of the covariance matrix in step 1 is:
taking L receiving signals from t time forward to form a receiving signal vector r (t) at t time, and then
r(t)＝[rt,rt-1,…,rt-L+1]T
The covariance matrix can be obtained as
Rrr＝E[r(t)rH(t)]
Assuming K invariant observation vectors, the estimated value of the covariance matrix is
Figure BDA0001788151090000031
Where k is {0,1, …, L-1 }.
Preferably, the dimension p of the signal subspace is estimated in step 2 using a minimum description length criterion MDL,
Figure BDA0001788151090000032
k and the subspace dimension p satisfy the following relationship
p＝argk min MDL(k)。
Preferably, the eigenvalue decomposition method of step 3 is:
assuming that the signal power and the noise power are uncorrelated, the covariance matrix estimate can be expressed as:
Rrr＝Rxx+Rnn
according to the eigenvalue decomposition theory, RrrCan be decomposed into
Rrr＝AΣAH
Wherein A is composed of orthogonal feature vectors; diagonal matrix Σ ═ diag (b)i) From the characteristic values b of the matrixiIs formed therein
b1≥b2≥…bL
The autocorrelation matrix of white noise satisfies
Figure BDA0001788151090000041
Wherein the content of the first and second substances,
Figure BDA0001788151090000042
is the variance of the noise power;
the eigenvalue of the covariance matrix obtained by descending order is
Figure BDA0001788151090000043
Wherein the content of the first and second substances,
Figure BDA0001788151090000044
representing the signal power of the ith eigenvector, p representing the dimension of the signal subspace, the first p eigenvectors constituting the signal subspace, and the last L-p eigenvectors constituting the noise subspace.
Using the estimated value of the covariance matrix obtained in step 1
Figure BDA0001788151090000045
The above decomposition is carried out to obtain the characteristic value RrrIs estimated from the maximum likelihood.
Preferably, the SNR estimate is
ρ＝10lg(Ps/Pn)
Wherein the content of the first and second substances,
Figure BDA0001788151090000046
Pnas noise power, PsIs the signal power.
The subspace-based SNR estimation method provided by the invention has the advantages that: the estimation method adopted by the application has the advantages of small calculation amount, higher processing speed and better estimation performance than other existing algorithms.
Drawings
FIG. 1 is a diagram illustrating the performance of a subspace-based SNR estimation method provided by an embodiment of the present invention for different SNR cases;
FIG. 2 is a diagram illustrating SNR estimation performance of a subspace-based SNR estimation method under different snapshot conditions according to an embodiment of the present invention;
fig. 3 is a comparison of estimated performance of different algorithms.
Detailed Description
In order that the objects, aspects and advantages of the present invention will become more apparent, the present invention will be further described in detail with reference to the accompanying drawings in which specific embodiments are shown.
In a complex AWGN channel, the received signal may be represented as
rk＝xk+nk
Wherein nk is complex white Gaussian noise with zero mean value under sequential sampling, and its variance is
Figure BDA0001788151090000051
The noise column vector consisting of L times of sampling data before t time can be expressed as
n(t)＝[nt,nt-1,…,nt-L+1]T
Wherein (C)TRepresenting transpose, the second moment of the noise vector can be represented as
Figure BDA0001788151090000052
Where E [ ] represents the mathematical expectation, the superscript H represents the conjugate transpose, and I is an L identity matrix.
Figure BDA0001788151090000053
xkAt a carrier frequency fcThe lower band pass signal is represented as
Figure BDA0001788151090000054
Where θ represents the initial phase, fsRepresenting the sampling frequency.
Figure BDA0001788151090000061
Is a complex equivalent baseband signal that, for a Multiple Phase Shift Keying (MPSK) signal,
Figure BDA0001788151090000062
wherein A ∈ R+Representing the amplitude of the signal.
In performing a Multiple Quadrature Amplitude Modulation (MQAM) signal,
Figure BDA0001788151090000063
wherein A islAnd e C represents the amplitude corresponding to the l-th phase.
Let PsAnd PnRepresenting signal power and noise power, respectively, the SNR can be expressed as
ρ＝10lg(Ps/Pn)
Based on the above analysis, the emphasis of SNR estimation is to find the signal power PsSum noise power PnThe subspace-based SNR method provided by the invention comprises the following steps:
step 1: solving an estimated value of a covariance matrix through a received signal obtained by communication equipment;
taking L receiving signals from t time forward to form a receiving signal vector r (t) at t time, and then
r(t)＝[rt,rt-1,…,rt-L+1]T
The covariance matrix can be obtained as
Rrr＝E[r(t)rH(t)]
In practice, a covariance matrix R is obtainedrrIs very difficult and therefore we can only estimate with a finite length of the received signal.
Assuming K invariant observation vectors, the estimated value of the covariance matrix is
Figure BDA0001788151090000064
Where k is {0,1, …, L-1 }.
Step 2: solving the dimension of the signal subspace;
the minimum description length criterion MDL is heard in the preferred embodiment to estimate the number of dimensions p of the signal subspace,
Figure BDA0001788151090000071
k and the subspace dimension p satisfy the following relationship
p＝argk min MDL(k)。
And step 3: carrying out eigenvalue decomposition on the estimated value of the covariance matrix obtained in the step 1, and arranging the eigenvalues in a descending order according to the signal subspace dimension;
assuming that the signal power and the noise power are uncorrelated, the covariance matrix estimate can be expressed as:
Rrr＝Rxx+Rnn
according to the eigenvalue decomposition theory, RrrCan be decomposed into
Rrr＝AΣAH
Wherein A is composed of orthogonal feature vectors; diagonal matrix Σ ═ diag (b)i) From the characteristic values b of the matrixiIs formed therein
b1≥b2≥…bL
The autocorrelation matrix R of white noisennSatisfy the requirement of
Figure BDA0001788151090000072
Wherein the content of the first and second substances,
Figure BDA0001788151090000073
is the variance of the noise power;
the eigenvalue of the covariance matrix obtained by descending order is
Figure BDA0001788151090000081
Wherein the content of the first and second substances,
Figure BDA0001788151090000082
representing the signal power of the ith eigenvector, P representing the dimension of the signal subspace, the first P eigenvectors constituting the signal subspace, the last L-P eigenvectors constituting the noise subspace, the noise power P of whichnFrom L to p
Figure BDA0001788151090000083
When the dimension p of the signal subspace is constant, the SNR estimation can be passed
Figure BDA0001788151090000084
And PnTo obtain an estimate of (c).
Using the estimated value of the covariance matrix obtained in step 1
Figure BDA0001788151090000085
By performing the decomposition, the characteristic value R can be obtainedrrIs estimated from the maximum likelihood.
And 4, step 4: and (4) solving the noise power and the signal power according to the characteristic value obtained in the step (3) so as to obtain an estimated value of the SNR.
It can be known from the previous analysis
ρ＝10lg(Ps/Pn)
Wherein the content of the first and second substances,
Figure BDA0001788151090000086
Pnas noise power, PsIs the signal power.
The calculated quantity of the above algorithm is O (L)2N+L3) A sub-multiplication, where N is the number of symbols.
The performance of the algorithm provided by the embodiment of the invention is analyzed by using MATLAB simulation, and the result is as follows:
FIG. 1 is an estimation performance of a subspace-based SNR estimation method under different SNR cases; it can be seen from fig. 1 that the subspace approach has better SNR estimation performance. As the SNR increases, the estimate of the SNR can approach the true value.
FIG. 2 is a diagram of SNR estimation performance for different snapshot scenarios for a subspace-based SNR estimation method; it can be seen that the estimation of SNR gets better and better as the number of snapshots increases.
Fig. 3 is a comparison of the estimated performance of the different algorithms (N-300); comparison was made with DF, M2M4, SVR and SNV algorithms. It can be seen from the figure that the estimation performance of the subspace approach is better than other algorithms.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only examples of the present invention, and are not intended to limit the present invention, and any modifications, equivalent substitutions, improvements, etc. made by those skilled in the art without departing from the spirit and principles of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims (2)

1. A subspace-based SNR estimation method, characterized in that: the method comprises the following steps:
step 1: solving an estimated value of a covariance matrix through a received signal obtained by communication equipment;
step 2: solving the dimension of the signal subspace;
and step 3: carrying out eigenvalue decomposition on the estimated value of the covariance matrix obtained in the step 1, and arranging the eigenvalues in a descending order according to the signal subspace dimension;
and 4, step 4: solving the noise power and the signal power according to the characteristic value obtained in the step 3, thereby obtaining an estimated value of the SNR; the method for solving the estimation value of the covariance matrix in the step 1 comprises the following steps:
taking L received signals from time t to form received signal vector r (t) at time t, then r (t) ═ rt,rt-1,…,rt-L+1]T
The covariance matrix can be obtained as
Rrr＝E[r(t)rH(t)]
Assuming K invariant observation vectors, the estimated value of the covariance matrix is
Figure FDA0003012684550000011
Wherein k belongs to {0,1, …, L-1 };
the dimension p of the signal subspace is estimated in step 2 using the minimum description length criterion MDL,
Figure FDA0003012684550000012
k and the subspace dimension p satisfy the following relationship
p＝argkmin MDL(k)；
The eigenvalue decomposition method in step 3 comprises the following steps:
assuming that the signal power and the noise power are uncorrelated, the covariance matrix can be expressed as:
Rrr＝Rxx+Rnn
according to the eigenvalue decomposition theory, RrrCan be decomposed into
Rrr＝AΣAH
Wherein A is composed of orthogonal feature vectors; diagonal matrix Σ ═ diag (b)i) From the eigenvalues b of the matrixiIs formed therein
b1≥b2≥…bL
The autocorrelation matrix of white noise satisfies
Figure FDA0003012684550000021
Wherein the content of the first and second substances,
Figure FDA0003012684550000022
is the variance of the noise power;
the eigenvalue of the covariance matrix obtained by descending order is
Figure FDA0003012684550000023
Wherein the content of the first and second substances,
Figure FDA0003012684550000024
representing the signal power of the ith eigenvector, p representing the dimension of a signal subspace, wherein the first p eigenvectors form the signal subspace, and the last L-p eigenvectors form a noise subspace;
using the estimated value of the covariance matrix obtained in step 1
Figure FDA0003012684550000025
Performing the decomposition to obtain a characteristic value RrrMaximum likelihood estimation of (1).
2. The subspace-based SNR estimation method according to claim 1, wherein: SNR estimation value of
ρ＝10lg(Ps/Pn)
Wherein the content of the first and second substances,
Figure FDA0003012684550000031
Pnas noise power, PsIs the signal power.
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