CN109194422A - A kind of SNR estimation method based on subspace - Google Patents

Abstract

The invention discloses a subspace-based SNR estimation method, comprising the following steps: Step 1: obtain an estimated value of a covariance matrix through a received signal obtained by a communication device; Step 2: solve the dimension of the signal subspace; Step 3: Perform eigenvalue decomposition on the estimated value of the covariance matrix obtained in step 1, and arrange the eigenvalues in descending order according to the dimension of the signal subspace; step 4: solve the noise power and signal power according to the eigenvalues obtained in step 3, thereby obtaining the estimation of SNR value. The advantages of the subspace-based SNR estimation method provided by the present invention are that the estimation method adopted in the present application has less calculation amount, faster processing speed, and better estimation performance than other existing algorithms.

Description

A Subspace-Based SNR Estimation Method

technical field

The present invention relates to the technical field of signal processing, and in particular, to a subspace-based SNR estimation method.

Background technique

Mars is the most explored planet in the solar system. Due to the long distance between Mars and the Earth, the signal transmission time is prolonged and the signal attenuation is large. At the same time, the relative distance changes rapidly, and the detector load and power consumption are also very limited. All these realities have caused great trouble to the ground fire communication. A short communication arc will lead to less effective communication time, so a higher effective data transmission rate is required. Furthermore, the real-time change of the relative distance and relative attitude between the devices will also cause the signal-to-noise ratio (SNR) of the signal received by the receiver to change in real time. This requires real-time adjustment of the code rate to make it as high as possible. SNR estimation uses parameter estimation theory to calculate the signal-to-noise power ratio and provides the required channel quality information through modulation mode switching, rate adjustment, power control and channel allocation methods. Furthermore, many parameter estimation algorithms require SNR as a precondition to optimize performance.

SNR estimation methods include time domain method and frequency domain method. Time-domain methods are classified into data aided (DA) methods and non-data aided (NDA) methods. The DA method has higher estimation accuracy than the NDA method, but it needs to insert a periodic preamble sequence, which will reduce the transmission efficiency. In the time domain method, DA-based SNR estimation methods include minimum mean square error (MMSE), maximum likelihood (ML), and separating character matrix es- timing, SSME) and high-order cumulant signal-to-noise separation method, etc. The NDA-based SNR estimation methods include the second-order and fourth-order matrix estimation method (M2M4), the signal variance ratio estimation method (Signal-to-Variation Ratio, SVR), the squared signal-to-noise variance ratio estimation (Squared signal-to-NoiseVariance, SNV) and data fitting estimation method (Data Fitting, DF) and so on. The classical frequency domain method is based on the flat characteristic of the power spectrum of white noise, and is suitable for SNR estimation of additive white Gaussian Noise (AWGN) channel, but is not applicable in chromatic noise environment.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a subspace-based SNR estimation method with better performance.

The present invention solves the above-mentioned technical problems through the following technical solutions:

A subspace-based SNR estimation method, comprising the following steps:

Step 1: Calculate the estimated value of the covariance matrix through the received signal obtained by the communication device;

Step 2: Solve the dimension of the signal subspace;

Step 3: perform eigenvalue decomposition on the estimated value of the covariance matrix obtained in step 1, and arrange the eigenvalues in descending order according to the dimension of the signal subspace;

Step 4: Calculate the noise power and the signal power according to the eigenvalues obtained in Step 3, so as to obtain the estimated value of SNR.

Preferably, the method for solving the estimated value of the covariance matrix described in step 1 is:

Taking L received signals from time t forward to form the received signal vector r(t) at time t, then

r(t)=[r _t ,r _t-1 ,...,r _t - _L+1 ] ^T

The covariance matrix can be obtained as

R _rr =E[r(t)r ^H (t)]

Assuming there are K constant observation vectors, the estimated covariance matrix is

where k∈{0,1,…,L-1}.

Preferably, in step 2, the minimum description length criterion MDL is used to estimate the dimension p of the signal subspace ,

k and the subspace dimension p satisfy the following relationship

p=arg _k min MDL(k).

Preferably, the eigenvalue decomposition method described in step 3 is:

Assuming that the signal power and noise power are not correlated, the estimated covariance matrix can be expressed as:

R _rr =R _xx +R _nn

According to the eigenvalue decomposition theory, R _rr can be decomposed into

R _rr =AΣA ^H

Among them, A consists of orthogonal eigenvectors; the diagonal matrix Σ=diag(b _i ) consists of the eigenvalues b _i of the matrix, where

b ₁ ≥b ₂ ≥…b _L

Then the autocorrelation matrix of white noise satisfies

in, is the variance of the noise power;

The eigenvalues of the covariance matrix obtained in descending order are

in, Represents the signal power of the ith eigenvector, p represents the dimension of the signal subspace, the first p eigenvectors constitute the signal subspace, and the last Lp eigenvectors constitute the noise subspace.

Use the estimate of the covariance matrix obtained in step 1 The above decomposition is carried out to obtain the maximum likelihood estimate of the eigenvalue R _rr .

Preferably, the SNR estimate is

ρ=10lg(P _s /P _n )

in,

P _n is the noise power, and P _s is the signal power.

The advantages of the subspace-based SNR estimation method provided by the present invention are that the estimation method adopted in the present application has less computation amount, faster processing speed and better estimation performance than other existing algorithms.

Description of drawings

Fig. 1 is the estimation performance of the SNR estimation method based on subspace provided by the embodiment of the present invention under different SNR situations;

Fig. 2 is the SNR estimation performance of the subspace-based SNR estimation method provided by the embodiment of the present invention under different snapshot situations;

Figure 3 is a comparison of the estimated performance of different algorithms.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

In a complex AWGN channel, the received signal can be expressed as

r _k =x _k +n _k

Among them, nk is the complex Gaussian white noise with zero mean under sequential sampling, and its variance is The noise column vector composed of L sampled data before time t can be expressed as

n(t)=[n _t ,n _t-1 ,...,n _t - _L+1 ] ^T

Among them, () ^T represents the transposition, and the second-order moment of the noise vector can be expressed as

where E[] represents the mathematical expectation, the superscript H represents the conjugate transpose, and I is an L×L identity matrix.

x _k is the band-pass signal at the carrier frequency f _c , denoted as

where θ is the initial phase and _fs is the sampling frequency.

is a complex equivalent baseband signal. As far as the Multiple Phase Shift Keying (MPSK) signal is concerned,

where A∈R ⁺ represents the amplitude of the signal.

In performing multiple quadrature amplitude modulation (Multiple Quadrature Amplitude Modulation, MQAM) signals,

Among them, A _l ∈ C represents the amplitude corresponding to the l-th phase.

Let P _s and P _n denote signal power and noise power, respectively, then SNR can be expressed as

ρ=10lg(P _s /P _n )

Based on the above analysis, the key point of SNR estimation is to obtain the signal power P _s and the noise power P _n . The subspace-based SNR method provided by the present invention includes the following steps:

Step 1: Calculate the estimated value of the covariance matrix through the received signal obtained by the communication device;

Taking L received signals from time t forward to form the received signal vector r(t) at time t, then

r(t)=[r _t ,r _t-1 ,...,r _t - _L+1 ] ^T

The covariance matrix can be obtained as

R _rr =E[r(t)r ^H (t)]

In practice, it is very difficult to get the true value of the covariance matrix R _rr , so we can only estimate it through a finite length of the received signal.

Assuming there are K constant observation vectors, the estimated covariance matrix is

where k∈{0,1,…,L-1}.

Step 2: Solve the dimension of the signal subspace;

In the preferred embodiment, the minimum description length criterion MDL estimates the dimension p of the signal subspace,

k and the subspace dimension p satisfy the following relationship

p=arg _k min MDL(k).

Step 3: perform eigenvalue decomposition on the estimated value of the covariance matrix obtained in step 1, and arrange the eigenvalues in descending order according to the dimension of the signal subspace;

Assuming that the signal power and noise power are not correlated, the estimated covariance matrix can be expressed as:

R _rr =R _xx +R _nn

According to the eigenvalue decomposition theory, R _rr can be decomposed into

R _rr =AΣA ^H

Among them, A consists of orthogonal eigenvectors; the diagonal matrix Σ=diag(b _i ) consists of the eigenvalues b _i of the matrix, where

b ₁ ≥b ₂ ≥…b _L

Then the autocorrelation matrix R _nn of white noise satisfies

in, is the variance of the noise power;

The eigenvalues of the covariance matrix obtained in descending order are

in, represents the signal power of the ith eigenvector, p represents the dimension of the signal subspace, the first p eigenvectors constitute the signal subspace, and the last Lp eigenvectors constitute the noise subspace, and the noise power P _n consists of Lp composition, when the dimension p of the signal subspace is constant, the SNR estimation can be obtained by and the estimated value of P _n .

Use the estimate of the covariance matrix obtained in step 1 By performing the above decomposition, the maximum likelihood estimation of the eigenvalue R _rr can be obtained.

Step 4: Calculate the noise power and the signal power according to the eigenvalues obtained in Step 3, so as to obtain the estimated value of SNR.

It can be known from the previous analysis that

ρ=10lg(P _s /P _n )

in,

P _n is the noise power, and P _s is the signal power.

The calculation amount of the above algorithm is O(L ² N+L ³ ) multiplications, where N is the number of symbols.

Utilize MATLAB simulation to analyze the algorithm performance that the embodiment of the present invention provides, the result is as follows:

Figure 1 shows the estimation performance of the subspace-based SNR estimation method under different SNR conditions; it can be seen from Figure 1 that the subspace method has better SNR estimation performance. As the SNR increases, the estimate of the SNR can be approximated to the true value.

Figure 2 shows the SNR estimation performance of the subspace-based SNR estimation method in different snapshot situations; it can be seen that as the number of snapshots increases, the SNR estimation is getting better and better.

Figure 3 is a comparison of the estimated performance of various algorithms (N=300); compared with DF, M2M4, SVR and SNV algorithms. It can be seen from the figure that the estimation performance of the subspace method is better than other algorithms.

The specific embodiments described above further describe the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention, and are not intended to limit the present invention. Without departing from the spirit and principle of the present invention, any modification, equivalent replacement, improvement, etc. made by those of ordinary skill in the art to the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims (5)

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: 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.

2. The subspace-based SNR estimation method according to claim 1, wherein: the method for solving the estimation value of the covariance matrix in the step 1 comprises the following steps:

taking L receiving signals from t time forward to form a receiving signal vector r (t) at t time, and then

r(t)＝[r_t,r_t-1,…,r_t-L+1]^T

The covariance matrix can be obtained as

R_rr＝E[r(t)r^H(t)]

Assuming K invariant observation vectors, the estimated value of the covariance matrix is

Where k is {0,1, …, L-1 }.

3. A subspace-based SNR estimation method according to claim 2, characterized in that: the dimension p of the signal subspace is estimated in step 2 using the minimum description length criterion MDL,

k and the subspace dimension p satisfy the following relationship

p＝arg_kmin MDL(k)。

4. A subspace-based SNR estimation method according to claim 3, characterized in that: 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 estimate can be expressed as:

R_rr＝R_xx+R_nn

decomposition according to eigenvaluesTheory, R_rrCan be decomposed into

R_rr＝AΣA^H

Wherein A is composed of orthogonal feature vectors; diagonal matrix Σ ═ diag (b)_i) From the eigenvalues b of the matrix_iIs formed therein

b₁≥b₂≥…b_L

The autocorrelation matrix of white noise satisfies

Wherein,is the variance of the noise power;

the eigenvalue of the covariance matrix obtained by descending order is

Wherein,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 1Performing the decomposition to obtain a characteristic value R_rrIs estimated from the maximum likelihood.

5. The subspace-based SNR estimation method according to claim 4, wherein: SNR estimation value of

ρ＝10lg(P_s/P_n)

Wherein,

P_nas noise power, P_sIs the signal power.