CN103152313B - Based on data-aided QAM Signal-to-Noise evaluation method - Google Patents

Abstract

The invention provides a kind of based on data-aided QAM Signal-to-Noise evaluation method, concrete steps are: step one, determine the position of training sequence on planisphere; Step 2, adopt the circle of multiple different radii, planisphere is divided in lopping and circle exterior domain; And calculate matrix A; Step 3, to determine in planisphere optimum position of drawing a circle according to A; The signals and associated noises average power y of step 4, calculating received training sequence _swith the signals and associated noises average power y belonging to constellation point in optimal cycle _{in s}; Step 5, solve the average power signal P of received training sequence _swith noise power P _n; The signal to noise ratio of step 6, estimating received signal.The present invention utilizes the proportionate relationship of power between each constellation point, derives QAM Signal-to-Noise evaluation method, and signal-to-noise ratio (SNR) estimation is reduced to and solves linear equation in two unknowns group by the method, and algorithm is simple and easy to realize.

Description

Based on data-aided QAM Signal-to-Noise evaluation method

Technical field

The invention belongs to signal of communication processing technology field, be specifically related to a kind of based on data-aided quadrature amplitude modulation (QAM) Signal-to-Noise evaluation method.

Background technology

The flow processs such as catching to received signal, carrier synchronization, equilibrium, decoding all need the signal to noise ratio according to estimating to carry out the initialization of algorithm and the adjustment of iterative parameter.Signal-to-noise ratio (SNR) estimation can provide the information of channel quality, controls for dynamic assignment channel and power.M-ary Quadrature Amplitude modulation (Multiple quadratureamplitude modulation, MQAM) increases demodulation difficulty due to the constellation form of complexity, therefore needs accurately to estimate its signal to noise ratio, makes the performance that demodulating algorithm reaches optimum.

Under additive white Gaussian noise channel condition, conventional signal-to-noise ratio estimation algorithm is divided into two classes: a class is the estimation based on data auxiliary (Data-Aided, DA); Another kind of estimation does not need data to assist (Non-Data-Aided, NDA), is blind estimate.DA algorithm needs to insert known training sequence when sending data symbol, and estimated accuracy is high, the less requirement that can realize process in real time of operand.Maximum likelihood estimate and Minimum Mean Squared Error estimation method are two kinds of typical DA signal-noise ratio estimation methods, as maximum Likelihood utilizes training sequence to construct likelihood function.DA algorithm exchanges the raising of estimated accuracy for by reducing valid data transmission rate.NDA algorithm mainly contains two-order and four-order moments and the data fitting estimation technique etc. at present.The shortcoming of this type of algorithm calculates more complicated, and convergence rate is slow, performance degradation under low signal-to-noise ratio.

QAM is the signal that phase place and amplitude are modulated simultaneously, and traditional signal-noise ratio estimation method is general all for constant envelope signal, is not suitable for qam signal.Have article to the signal-to-noise ratio (SNR) estimation of QAM signal to be studied, comprise and utilize the blind estimate of signal autocorrelation matrix singular value decomposition realization to signal to noise ratio; Utilize the relation of fitting of a polynomial high-order statistic and signal to noise ratio; Signal to noise ratio parameter etc. is upgraded based on prior information successive ignition.But said method exists higher system complexity, when lacking hardware resource, often have larger estimated bias, even algorithm can not normally realize.

Summary of the invention

In view of this, the invention provides one based on data-aided QAM Signal-to-Noise evaluation method.The method is based on the minimum criterion of conditional number, to qam constellation diagram root region, utilize the proportionate relationship of power between each constellation point, derive QAM Signal-to-Noise evaluation method, and signal-to-noise ratio (snr) estimation is reduced to and solves linear equation in two unknowns group by the method, algorithm is simple and easy to realize, in the estimation range of-15 ~ 10dB, have higher estimated accuracy.

Be achieved by the following technical solution based on data-aided QAM Signal-to-Noise evaluation method:

Step one, for each data of training sequence received, determine its position on planisphere, then add up each data on training sequence and drop on the quantity on planisphere in each constellation point;

Step 2, with the center of planisphere for initial point, adopt the circle of multiple different radii, planisphere to be divided in lopping and circle exterior domain; Be directed to each dividing condition, calculate matrix $A=\left[\begin{array}{cc}1& 1\\ k& 1\end{array}\right],$ Wherein variable k represents the average power signal P of constellation in circle _{in s}with the average power signal P of all constellations _sratio;

In step 3, exhaustive matrix A, institute's likely value of variable k, minimum for principle with the conditional number cond of matrix A (A), determines the value of optimum variable k, and determine optimum position of drawing a circle in planisphere according to optimum variable k;

The signals and associated noises average power y of step 4, calculating received training sequence _swith the signals and associated noises average power y belonging to constellation point in optimal cycle _{in s};

Step 5, solve the average power signal P of received training sequence according to linear equation Ax=y _swith noise power P _n, wherein vector $x=\left[\begin{array}{c}{P}_s\\ P_n\end{array}\right],$ Vector

The signal to noise ratio of step 6, estimation Received signal strength

Further, the present invention adopts the circle of K-1 different radii to be divided by planisphere in lopping and circle exterior domain, and wherein K is total number of signal amplitude on planisphere; A described K-1 radius of a circle is between two constellation point of adjacent amplitude on planisphere respectively.

Beneficial effect

First, the QAM Signal-to-Noise evaluation method auxiliary based on training sequence proposed by the invention, by qam constellation diagram root circle and circle exterior domain, the proportionate relationship according to zones of different constellation signals average power solves signal to noise ratio.In order to ensure that the constellation point of constant power all belongs to an identical region, therefore adopt circle to carry out Region dividing, the method is not limited to the exponent number of QAM modulation.

Secondly, the present invention is minimum for principle with the conditional number cond of matrix A (A), can make like this one of received signal vector y very microvariations only cause the disturbance that solution vector x is very little, thus ensure that to the signal power of received training sequence and noise power estimation more accurate, make the precision of signal-to-noise ratio (SNR) estimation higher.

Again, the present invention adopts the mode solving linear equation, estimate signal power and the noise power of received training sequence, then accurately estimate the signal to noise ratio of QAM signal, avoid complicated formulae discovery and derivation, computing is simple, be adapted at fpga logic hardware realizes, effectively reduce system implementation complexity, within the scope of the signal-to-noise ratio (SNR) estimation of-15 ~ 10dB, reach good estimated accuracy.

Accompanying drawing explanation

Fig. 1 is the mode sending training sequence in embodiment.

Fig. 2 is the planisphere of 16QAM in embodiment.

Fig. 3 is at different E in embodiment _b/ N ₀under, 16QAM planisphere affected by noise.

Fig. 4 is at different E in embodiment _b/ N ₀under, the simulation comparison figure of the 16QAM Signal-to-Noise evaluated error curve that different training sequence length is corresponding.

Fig. 5 is at different E in embodiment _b/ N ₀under, the simulation comparison figure of the normalization standard root-mean-square error curve that mode that what 16QAM was different draw a circle is corresponding.

Embodiment

To develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

The principle of the present invention's design: consider the QAM system in multiple additive white Gaussian noise channel, assuming that when receiver is in completely balanced and Complete Synchronization, then the training sequence for signal-to-noise ratio (SNR) estimation received can be expressed as following form:

r _k＝ha _k+n _k，k＝1，2，...，L

Wherein, h is channel fading coefficient, is unknown fixing constant within observing time.A _k∈ C is the independent identically distributed QAM training sequence of known transmission, C={s ₁, s ₂..., s _mit is the signal constellation (in digital modulation) space of M point.N _kbe the white complex gaussian noise of zero-mean, the variance of its real part and imaginary part is all σ ²/ 2, training sequence and noise are uncorrelated each other.L is the length of the training sequence for estimated snr.

The signal to noise ratio of Received signal strength wherein, P _sfor the average power signal of received training sequence, P _nfor channel noise power, for sending the signal averaging amplitude of training sequence, || be the operation that takes absolute value.

Corresponding K the signal amplitude D of M constellation point of MQAM _i(i=1,2 ..., K), namely all constellation point are made up of K amplitude.Constellation signals amplitude meets D ₁< D ₂< ... < D _k, the constellation point of same magnitude has identical average power.The present invention estimates that the method for signal to noise ratio is by planisphere zoning (namely " drawing a circle "), is namely radius of a circle (D with D _i< D < D _i+1, i=1,2 ..., K-1) draw a circle on qam constellation figure, planisphere is divided into outer two regions of circle inner ring.Vector operation is done to planisphere, tries to achieve the average power signal P being positioned at circle constellation _{in s}with the average power signal P of all constellations _s.Received training sequence is added up, tries to achieve the signals and associated noises average power y belonging to constellation point in optimal cycle _{in s}with the signals and associated noises total mean power y received _s, linear equation in two unknowns group can be derived

Above-mentioned suitable fixed linear equation in two unknowns group can be equivalent to Ax=y.Wherein, 2 × 2 matrixes $A=\left[\begin{array}{cc}1& 1\\ k& 1\end{array}\right]$ Be an element be the coefficient matrix of datum, according to the vector correlation of each constellation point, variable k represents the average power signal P of constellation in circle _{in s}with the average power signal P of all constellations _sratio, namely 2 × 1 vectors calculate the known vector of trying to achieve by the signals and associated noises received.2 × 1 vectors $x=\left[\begin{array}{c}{P}_s\\ P_n\end{array}\right]$ It is a unknown parameter vector to be solved.

Minimum for principle with the conditional number of matrix A to the Region dividing of qam constellation figure, wish when one of received signal vector y very microvariations only cause the disturbance that solution vector x is very little.Conditional number weighs an important indicator of linear equation numerical stability, is specifically reflected as when solving linear equation, and error expands as the degree of the error of solution vector x through the propagation of matrix A.The conditional number of matrix A be defined as cond (A)=|| A ^-1|| || A||, wherein, || A|| is the second order norm of matrix A.The conditional number of matrix A is less, shows that the impact of error on solution vector x is less, to the signal power of received training sequence and noise power estimation more accurate, then the precision of signal-to-noise ratio (SNR) estimation is higher.

For the ease of signal-to-noise ratio (SNR) estimation in the present embodiment, the training sequence of certain length is inserted at the frame head of transmitting terminal Frame, training sequence can be circulated transmission by traveling through the mode of each constellation point, the present invention advises the send mode of training sequence as shown in Figure 1, first send the QAM signal on the little constellation of amplitude, then it is large to send amplitude.In order to not affect message transmission rate, the length of training sequence is limited; Meanwhile, the length of training sequence can not be very few because training sequence is very few just do not possess statistical property, use in this example length be 10000 training sequence.

Based on above-mentioned theory analysis, below estimation procedure of the present invention is described in detail:

Step one, for each data on the training sequence received, determine its position on planisphere, then add up each data on training sequence and drop on the quantity on planisphere in each constellation point.

Because training sequence is known, therefore can determine according to known training sequence which constellation point is each data be positioned in, then statistics drops on the quantity of data in each constellation point, ensures M constellation point to receive the length L that auxiliary QAM data count equals training sequence.

For the planisphere of 16QAM and bit mapping shown in accompanying drawing 2.Under the condition of SNR=-5dB, 0dB, 5dB, 10dB, the received training sequence of 16QAM modulation distinguishes situation as shown in Figure 3 on planisphere.When high s/n ratio, the training sequence major part next-door neighbour ideal constellation point position of reception, its concentration range is less; When noise power increase makes SNR decline, the scattered band of training sequence around constellation point expands.Because training sequence is known, receiver accurately can judge the constellation of Received signal strength, not by the constraint of signal to noise ratio size.

The present embodiment supposes the signal constellation (in digital modulation) space { s of in known 16QAM planisphere 16 ₁, s ₂..., s ₁₆∈ C, wherein C={ ± 1A ± Aj, ± 1A ± 3Aj, ± 3A ± Aj, ± 3A ± 3Aj}.There is the constellation point of three kinds of amplitudes, amplitude is respectively with the training sequence of the 16QAM modulation that statistics receives, obtains signal and is positioned at radius and is circumferentially count as l, signal is positioned at radius and is constellation point on count as m, signal is positioned at radius and is constellation point on count as n.When signal is when the prior probability of each constellation point is equal, have l: m: n=1: 2: 1.

Step 2, with the center of planisphere for initial point, adopt the circle of different radii, planisphere divided in lopping and outer two regions of circle; Be directed to each dividing condition (i.e. the circle of each zoning), calculate matrix $A=\left[\begin{array}{cc}1& 1\\ k& 1\end{array}\right],$ Wherein variable k represents the average power signal P of constellation in circle _{in s}with the average power signal P of all constellations _sratio;

The present invention adopts the circle of K-1 different radii to be divided by planisphere in lopping and circle exterior domain, and wherein K is total number of signal amplitude on planisphere; (namely there are not any two circles to be between two constellation point of same adjacent amplitude) between two constellation point that a described K-1 radius of a circle is in adjacent amplitude on planisphere respectively.

Such as, M corresponding K the signal amplitude D of constellation on planisphere _i(i=1,2 ..., K), namely all constellation point are made up of K amplitude, and constellation signals amplitude meets D ₁< D ₂< ... < D _k, the constellation point of same magnitude has identical average power, take D as radius of a circle (D _j< D < D _j+1, j=1,2 ..., K-1) draw a circle on qam constellation figure, then there is K-1 kind and draw circle situation, this step solves matrix A in each stroke of circle situation.

In step 3, exhaustive matrix A, institute's likely value of variable k, minimum for principle with the conditional number cond of matrix A (A), determines the value of optimum variable k, and determine optimum position of drawing a circle in planisphere according to optimum variable k.

Such as, corresponding K the signal amplitude D of M the constellation of known MQAM _i(i=1,2 ..., K), therefore there is the mode of drawing a circle in K-1 and planisphere is divided into 2 regions, the variable k namely in matrix A has the possibility of K-1 value.Along with signal amplitude D _iincrease, in circle, constellation point quantity is also more, and the value of variable k is more close to 1.

As shown in Figure 1, the corresponding two kinds of modes of drawing a circle of the constellation point of three kinds of amplitudes in 16QAM planisphere.Comprise 4 constellation point in the first mode centre circle of drawing a circle, the radius D that draws a circle meets the average power signal of constellation and the average power signal ratio of all constellations in corresponding circle $k=\frac{{\left(\sqrt{2}A\right)}^2}{[{\left(\sqrt{2}A\right)}^{2}l+{\left(\sqrt{10}A\right)}^{2}m+{\left(3\sqrt{2}A\right)}^{2}n]/(l+m+n)};$ The second is drawn a circle in mode circle and is comprised 12 constellation point, and the radius D that draws a circle meets the average power signal of constellation and the average power signal ratio of all constellations in corresponding circle $k=\frac{[{\left(\sqrt{2}A\right)}^{2}l+{\left(\sqrt{10}A\right)}^{2}m]/(l+m)}{[{\left(\sqrt{2}A\right)}^{2}l+{\left(\sqrt{10}A\right)}^{2}m+{\left(3\sqrt{2}A\right)}^{2}n]/(l+m+n)}.$

The conditional number of matrix A in 16QAM under the prerequisite that the sending probability of each constellation point is identical, the first mode of drawing a circle is corresponding it is corresponding that the conditional number 10.05 of the matrix A drawn is less than the second mode of drawing a circle the conditional number 47.86 of the matrix A drawn.Therefore, the matrix that the first mode of drawing a circle is corresponding is selected $A=\left[\begin{array}{cc}1& 1\\ \frac{1}{5}& 1\end{array}\right]$ As the coefficient matrix solving linear equation Ax=y.

Step 4, accumulation calculate the vectorial y in linear equation, namely calculate the signals and associated noises average power y of received training sequence _swith the signals and associated noises average power y belonging to constellation point in optimal cycle _{in s};

Receive the total mean power y of signals and associated noises _scalculating is the mould square from the mould square statistic of training sequence the 1st data to L data, and the value be averaged.

$y_s=\frac{1}{L}\underset{k=1}{\overset{L}{\mathrm{\&Sigma;}}}{\left|r_k\right|}^2,$

The signals and associated noises average power y of constellation point in circle _{in s}be the data of L data meta constellation in optimal cycle on training sequence, and add up the mean value of its power.

The present embodiment accounts for total number of constellation points due to number of constellation points in the circle of the first mode of drawing a circle r _ithe signals and associated noises of constellation point in the circle that expression receives, then the signals and associated noises average power belonging to constellation in 16QAM optimal cycle is

Step 5, solve the average power signal P of received training sequence (namely at all constellations) according to linear equation Ax=y _swith noise power P _n;

The signal to noise ratio of step 6, estimation Received signal strength

This embodiment is at different E _b/ N ₀under, the simulation comparison figure of the 16QAM Signal-to-Noise evaluated error curve that different training sequence length is corresponding is as shown in Figure 4.Can find out, in the SNR ranges of whole estimation, the signal to noise ratio average of 16QAM signal estimation and actual value all closely, prove that the method is unbiased esti-mator.Along with the increase of training sequence length, estimated performance progressively improves, and so can determine according to the requirement of practical application to estimated accuracy and information transmission real-time the length sending training sequence.Normalization standard root-mean-square error curve simulation comparison figure corresponding to mode that what 16QAM was different draw a circle as shown in Figure 5.Accompanying drawing 5 illustrates, at actual E _b/ N ₀in the gamut of-15dB to 10dB, normalization standard root-mean-square error is drawn a circle by qam constellation figure the impact of mode, should select the mode of drawing a circle that matrix A conditional number is minimum.

The present invention, by using conditional number as the foundation of drawing a circle to qam constellation figure, adds up the constellation signals average power of training sequence, solves system of linear equations estimating received signal power and noise power, and then the signal to noise ratio of estimation QAM signal.This invention avoids complicated formulae discovery and derivation, is easy to realize, and is adapted at fpga logic hardware realizes.In the estimation range of-15 ~ 10dB, have higher signal-to-noise ratio (SNR) estimation precision, be a kind of method accurately can estimating QAM Signal-to-Noise.

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1., based on data-aided QAM Signal-to-Noise evaluation method, it is characterized in that, concrete steps are:

Step one, for each data of training sequence received, determine its position on planisphere, then add up each data in training sequence and drop on the quantity on planisphere in each constellation point;

Step 2, with the center of planisphere for initial point, adopt the circle of multiple different radii, planisphere to be divided in lopping and circle exterior domain; Be directed to each dividing condition, calculate matrix wherein variable k represents the average power signal P of constellation in circle _{in s}with the average power signal P of all constellations _sratio;

Wherein, adopt the circle of K-1 different radii to be divided by planisphere in lopping and circle exterior domain, wherein K is total number of signal amplitude on planisphere; A described K-1 radius of a circle is between two constellation point of adjacent amplitude on planisphere respectively;

In step 3, exhaustive matrix A, institute's likely value of variable k, minimum for principle with the conditional number cond of matrix A (A), determines the value of optimum variable k, and determine optimum position of drawing a circle in planisphere according to optimum variable k;

The signals and associated noises average power y of step 4, calculating received training sequence _swith the signals and associated noises average power y belonging to constellation point in optimal cycle _{in s};

Step 5, solve the average power signal P of received training sequence according to linear equation Ax=y _swith noise power P _n, wherein vector vector

The signal to noise ratio of step 6, estimation Received signal strength