CN110224769A - Combine the estimation method of amplitude and noise variance in a kind of communication system - Google Patents

Combine the estimation method of amplitude and noise variance in a kind of communication system Download PDF

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CN110224769A
CN110224769A CN201910461002.3A CN201910461002A CN110224769A CN 110224769 A CN110224769 A CN 110224769A CN 201910461002 A CN201910461002 A CN 201910461002A CN 110224769 A CN110224769 A CN 110224769A
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estimation
amplitude
noise variance
model
value
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CN110224769B (en
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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
Zhejiang University of Science and Technology ZUST
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Zhejiang Lover Health Science and Technology Development Co Ltd
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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
    • H04B17/318—Received signal strength

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  • Quality & Reliability (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Computer Networks & Wireless Communication (AREA)
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  • Noise Elimination (AREA)

Abstract

The invention discloses the estimation methods for combining amplitude and noise variance in a kind of communication system, the reception signal of the communication system is available complex representation, the signal comprising multiple additive white Gaussian noise, method includes the following steps: in (1) collection communicating system signal receiving end sampled point signal intensity samples collection；(2) amplitude and Noise Variance Estimation model 1 and model 2 in communication system are established；(3) amplitude that step (2) are established is combined solution with Noise Variance Estimation model 1 with model 2 to estimate, available amplitude estimation value or Noise Variance Estimation value.The present invention is not necessarily to Frequency Estimation, phase estimation without detection noise variance in advance, is not necessarily to phase unwrapping, and flexible in application, performance is better than traditional method for parameter estimation.

Description

Combine the estimation method of amplitude and noise variance in a kind of communication system
Technical field
The present invention relates to the estimations for combining amplitude and noise variance in field of communication technology more particularly to a kind of communication system Method.
Background technique
In communication system, amplitude is estimated from a series of noise-containing signals and noise variance is Signal parameter estimation Important research problem, the estimation method of the few joint amplitudes and noise variance of conventional estimated method.Generally firstly the need of detection Then noise variance parameter recycles the Fast Fourier Transform (FFT) (FFT) based on Frequency Domain Solution to go estimation signal frequency, phase ginseng Amplitude parameter could be estimated after number.Alternatively, estimating amplitude parameter after Combined estimator signal frequency, phase parameter.It is most common Solution be using maximum likelihood (ML) estimation theory.ML estimation based on the assumption that: unknown parameter does not have priori knowledge, i.e., Amplitude may be arbitrary nonnegative value, frequency and phase may be section [- π, π) between any value；It is constant when channel is Multiple additive white Gaussian noise channel.
Traditional ML estimation method is firstly the need of detection noise variance parameter in advanceAnd in calculated rate estimated value And phase estimationAfterwards, the estimated value of amplitude can just be obtainedThe estimation performance for improving signal amplitude depends on Accuracy.It is well known that detection noise variance parameter, the frequency of estimation signal and phase need to face many FAQs, Such as computation complexity and phase unwrapping.These problems bring difficulty to the estimation of amplitude, reduce the estimation performance of amplitude.
Summary of the invention
It is an object of the invention to overcome above-mentioned estimation signal amplitude to need detection noise variance, dependent Frequency, phase in advance The problem of position estimated value accuracy, proposes the estimation method for combining amplitude and noise variance in a kind of communication system.This method base In maximum likelihood principle, adopted without carrying out Frequency Estimation, phase estimation by signal strength without detection noise variance in advance One stepization of sample realizes the parameter Estimation of estimation amplitude or noise variance.
The purpose of the present invention is what is be achieved through the following technical solutions: combining amplitude and noise variance in a kind of communication system Estimation method, method includes the following steps:
(1) in collection communicating system signal receiving end sampled point signal intensity samples collectionWherein, | r (k) | indicate the sample value of k-th of sampled point,Indicate that sampled point quantity is the sample set of N；
(2) amplitude and Noise Variance Estimation model 1 and model 2 in communication system are established, as follows respectively:
Model 1:
Model 2:
Wherein,For amplitude estimation value,For multiple additive white Gaussian noise real part or the estimate of variance of imaginary part, For sample average,For mean-square value, calculation formula is as follows:
Sample average:
Sample mean-square value:
(3) amplitude that step (2) are established is combined with Noise Variance Estimation model 1 with model 2 to solve and is estimated, it can be with Obtain amplitude estimation valueOr Noise Variance Estimation value
(3.1) estimation method according to step (3), which is characterized in that amplitude and Noise Variance Estimation model 1 and mould The joint of type 2 solves, and can solve amplitude estimation valueCalculation formula is as follows:
Wherein,Expression takes the real part of its numerical value；
(3.2) estimation method according to step (3), which is characterized in that step amplitude and Noise Variance Estimation model 1 with The joint of model 2 solves, and can solve Noise Variance Estimation valueCalculation formula is as follows:
Compared with prior art, the present invention having the advantage that
(1) the case where being directed to without knowledge of noise covariance proposes estimation method, without measuring or estimating noise variance, step in advance Simply, it can be realized and be estimated with a stepization, improve efficiency.
(2) signal amplitude parameter is directly restored from signal sampling value size information, therefore not by the shadow of Doppler frequency shift It rings, estimates accuracy of the performance independent of Frequency Estimation or phase estimation.
(3) approximate evaluation method has done reasonable approximate calculation, therefore substantially reduces computation complexity.
(4) performance of this amplitude estimation method is better than conventional vibration amplitude estimation method.
Detailed description of the invention
Fig. 1 is the geometric representation for receiving signal；
Fig. 2 is the method for the present invention example signal amplitude estimation method, conventional vibration amplitude estimation method and amplitude estimation method gram The mean square error performance comparison of Latin America's sieve lower bound (CRLB)；
Fig. 3 is the mean square error performance of the method for the present invention example noise variance parameter.
Specific embodiment
Amplitude of the present invention is derived from Noise Variance Estimation model 1 and model 2 based on maximum likelihood principle, under Face elaborates to derivation process of the invention in conjunction with attached drawing.
The reception signal of communication system is available complex representation, the signal r (k) comprising multiple additive white Gaussian noise, signal Model is as follows:
R (k)=Aej(ωk+θ)+ n (k), k=0,1,2 ... (1)
Wherein, A indicates to send the actual amplitude of signal, and ω and θ respectively indicate the frequency and phase of signal, and n (k) is indicated Mean value is zero, variance is 2 σ2Multiple additive white Gaussian noise, real part and imaginary part variance are σ2.Receive the geometry phasor of signal Representation method is as described in Figure 1, and n (k), which is broken down into, is parallel to Aej(ωk+θ)In-phase component nI(k) and perpendicular to Aej(ωk+θ)Just Hand over component nQ(k), therefore signal model can be write as r (k)=A+nI(k)+nQ(k).Its modulus value is calculated, formula is as follows:
| r (k) | for obey L-S distribution stochastic variable, conditional probability density function p (| r (k) | | A, σ2) following institute Show:
Wherein, I0() and I1() is respectively the first kind modified Bessel function of zeroth order, single order.
Thus conditional probability density function can derive the combination condition probability density function for receiving signal modulus value, calculation formula It is as follows:
Its likelihood function is as follows:
Amplitude and 1 specific derivation process of Noise Variance Estimation model are as follows:
Using maximum likelihood principle to Λ (A, σ2) local derviation about A is sought, it enables as a result 0, can obtain:
By first kind modified Bessel function propertyFurther abbreviation substitutes into formula (6) can be obtained about A andBinary function:
The expansion of first kind modified Bessel function is specific as follows:
When variable x tends to infinity, I0It is substantially equal toI1It is substantially equal to
Therefore, the ratio of first-order bessel function and zero Bessel function can be write
When variable x tends to infinity, the ratio of first-order bessel function and zero Bessel function is substantially equal toI.e.
Formula (10) are substituted into formula (7), abbreviation can obtain amplitude and Noise Variance Estimation model 1, and following is not:
Wherein,For amplitude estimation value,For Noise Variance Estimation value,For sample average, specific formula for calculation is such as Under:
Amplitude and 2 specific derivation process of Noise Variance Estimation model are as follows:
Using maximum likelihood principle to Λ (A, σ2) ask about σ2Local derviation, enable as a result 0, can obtain:
Formula (7) are substituted into formula (13), abbreviation can obtain amplitude and Noise Variance Estimation model 2:
Wherein,For sample mean-square value, specific formula for calculation is as follows:
Amplitude and 2 simultaneous solution of Noise Variance Estimation model 1 and model, specific solution procedure are as follows:
It is σ by 2 abbreviation of model2Calculation formula about A:
The above results are substituted into 1 formula of model (11), abbreviation can obtain:
Above-mentioned quadratic equation with one unknown is solved, can be obtained:
Through simulating, verifying, the solution of "+", final amplitude estimation value are takenCalculation formula is as follows:
Wherein,Expression takes the real part of its numerical value.
Formula (19) is substituting in 2 formula of model (14), abbreviation can similarly obtain Noise Variance Estimation valueCalculation formula is such as Under:
The scheme in the embodiment of the present invention work is clearly and completely described with reference to the accompanying drawing.This example with It is lower premised on technical solution of the present invention to carry out embodiment, give detailed embodiment and performance evaluation, but guarantor of the invention Shield range is not limited to the following embodiments 1.
Embodiment 1:
The reception signal of communication system is available complex representation, the signal comprising multiple additive white Gaussian noise in this example, Without knowledge of noise covariance, amplitude parameter may be any nonnegative number.For the order of accuarcy for verifying this example amplitude estimation result, letter is sent Number amplitude be set as A=7.9527, if noise variance be σ2=1.
(1) in collection communicating system N=50 sampled point of signal receiving end signal intensity samples set It is as shown in the table to acquire specific sample set:
7.24184115 6.91531413 7.61029472 9.47743658 6.82542039
8.05596987 8.09149243 8.70531613 8.26985753 8.05824876
6.75697043 8.65203282 7.78524821 8.16689649 8.67553135
7.15413666 9.09781655 8.84214583 9.54734366 10.55048659
7.96898892 9.62863441 7.20189339 7.15230592 7.31111287
9.48881583 8.04511774 6.56326146 8.64976159 8.39895912
7.22803032 6.46600366 6.61789003 8.80057407 7.88737630
8.32423388 7.88655721 8.50817831 7.85702423 6.17675044
7.93290026 7.15133362 7.96692309 8.22136860 7.52596624
9.11576737 10.30747251 7.84951552 6.84402395 6.24620566
(2) amplitude and Noise Variance Estimation model 1 and model 2 in communication system are established, as follows respectively:
Model 1:
Model 2:
Wherein,For amplitude estimation value,For multiple additive white Gaussian noise real part or the estimate of variance of imaginary part, For sample average,For mean-square value, calculation formula is as follows:
Sample average:
Sample mean-square value:
(3) amplitude that step (2) is established is combined solution with Noise Variance Estimation model 1 with model 2 to estimate, it can To obtain amplitude estimation valueOr Noise Variance Estimation valueWherein,Expression takes it The real part of numerical value.
Amplitude estimation value both can be used alone with Noise Variance Estimation value, can also obtain simultaneously.
This example calculated result shows real amplitude A=7.9527, the noise variance σ with transmission signal2=1 compares, connection Close amplitude and Noise Variance Estimation resultσ2=0.97575180 is reliable effective.
In order to further prove the performance advantage of this method, the present invention will be measured using the mean square error based on signal-to-noise ratio The order of accuarcy of method estimation, and compare in traditional estimation method.As shown in figure 3, in the feelings Jing Guo same communication system Under condition, noise variance is constant, and sampled point quantity is respectively N=10, N=50, N=100, and signal-to-noise ratio γ takes 0 to 20dB, wherein Signal-to-noise ratio γ is defined as follows:
Each signal-to-noise ratio γ, can correspondingly be calculated a square mean error amount, and mean square error MSE calculates public Formula is as follows:
Wherein, M indicates sampling number, takes 1,000,000 time in this example；For amplitude estimation result；A is corresponding Send the actual amplitude of signal；For Noise Variance Estimation result；σ2For the corresponding actual noise variance for sending signal.
The result shows that present example mean square error with the increase of signal-to-noise ratio monotone decreasing, better than traditional estimation side Method；Tend to a carat Metro lower bound (CRLB) under high s/n ratio.
The above, the present invention provides the estimation method for combining amplitude and noise variance in a kind of communication system, the party Method computational complexity is small, and calculating step is simple, and a stepization is realized, accuracy of estimation is high.Containing largely adopting in communication system The accuracy of the inventive method and terms of the computation complexity have a clear superiority in the case where all, greatly improve communication system The economy and efficiency for amplitude estimation of uniting.

Claims (3)

1. combining the estimation method of amplitude and noise variance in a kind of communication system, the reception signal of the communication system is available Complex representation, the signal comprising multiple additive white Gaussian noise, which is characterized in that method includes the following steps:
(1) in collection communicating system signal receiving end sampled point signal intensity samples collectionWherein, | r (k) | table Show the sample value of k-th of sampled point,Indicate that sampled point quantity is the sample set of N；
(2) amplitude and Noise Variance Estimation model 1 and model 2 in communication system are established, as follows respectively:
Model 1:
Model 2:
Wherein,For amplitude estimation value,For multiple additive white Gaussian noise real part or the estimate of variance of imaginary part,For sample This mean value,For mean-square value, calculation formula is as follows:
Sample average:
Sample mean-square value:
(3) amplitude that step (2) are established is combined solution with Noise Variance Estimation model 1 with model 2 to estimate, it is available Amplitude estimation valueOr Noise Variance Estimation value
2. estimation method according to claim 1, which is characterized in that joint solves in step (3), can solve amplitude estimation ValueCalculation formula is as follows:
Wherein,Expression takes the real part of its numerical value.
3. estimation method according to claim 1, which is characterized in that joint solves in step (3), can solve noise variance Estimated valueCalculation formula is as follows:
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Citations (4)

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Publication number Priority date Publication date Assignee Title
US6680983B2 (en) * 1999-07-27 2004-01-20 Nokia Corporation Method for noise energy estimation
CN101444022A (en) * 2006-05-15 2009-05-27 高通股份有限公司 System and method of calculating noise variance
CN105785324A (en) * 2016-03-11 2016-07-20 西安电子科技大学 MGCSTFT-based chirp signal parameter estimation method
CN107332632A (en) * 2017-06-24 2017-11-07 西安电子科技大学 The method of estimation of Alpha Stable distritations noise parameter under MSK modulation systems

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6680983B2 (en) * 1999-07-27 2004-01-20 Nokia Corporation Method for noise energy estimation
CN101444022A (en) * 2006-05-15 2009-05-27 高通股份有限公司 System and method of calculating noise variance
CN105785324A (en) * 2016-03-11 2016-07-20 西安电子科技大学 MGCSTFT-based chirp signal parameter estimation method
CN107332632A (en) * 2017-06-24 2017-11-07 西安电子科技大学 The method of estimation of Alpha Stable distritations noise parameter under MSK modulation systems

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
JAMES HICKS: "Fast, Blind, and Joint Maximum Likelihood Estimation of MPSK Signal Parameters", 《IEEE ICC 2012 - SIGNAL PROCESSING FOR COMMUNICATIONS SYMPOSIUM》 *
V. RAMON等: "EM ALGORITHM-BASED ESTIMATION OF CARRIER PHASE, AMPLITUDE AND NOISE VARIANCE IN MULTIUSER TURBO RECEIVERS", 《ISSSTA2004》 *

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