CN105050114A - High-frequency-band spectrum occupation Volterra prediction method - Google Patents

Abstract

The invention provides a high-frequency-band spectrum occupation Volterra prediction method, relates to the technical field of high-frequency-band spectrum monitoring, and realizes prediction of a dramatically changed non-stable high-frequency spectrum occupation factor sequence. State space reconstruction is performed on a high-frequency-band spectrum occupation factor sequence by utilizing the state space theory so that a spectrum occupation factor sequence state space reconstruction sequence is acquired; a Volterra prediction model of the high-frequency-band spectrum occupation factor sequence is established by utilizing the spectrum occupation factor sequence state space reconstruction sequence; and the nuclear coefficient of the Volterra prediction model is dynamically adjusted by adopting a recursive least square method so that Volterra prediction of high-frequency-band spectrum occupation is realized. The high-frequency-band spectrum occupation Volterra prediction method is suitable for prediction of the dramatically changed non-stable high-frequency spectrum occupation factor sequence.

Description

The Volterra Forecasting Methodology that high band frequency spectrum takies

Technical field

The present invention relates to high band spectrum monitoring technical field.

Background technology

High frequency radio frequency range between 3MHz-30MHz, because technology is simple and low cost and be widely used in the radio communication of long distance, radar detection and broadcast etc.But the frequency spectrum behavior of high-frequency band can be subject to time, season and sunspot cycle etc. affect and sharply change, and causes multipath effect, Doppler frequency shift and depth attenuation etc., limits the usable range of high frequency spectrum.In addition, the long range propagation characteristic of high frequency radio makes local frequency spectrum be subject to the interference of other high frequencies user of global range.Above factor causes this limited high frequency spectrum to become more crowded.Thus need to carry out monitoring and forecast to the situation that takies of high frequency spectrum, to selecting effective working channel for high-frequency apparatus.

The prediction that high frequency spectrum takies situation can carry out prediction processing as time series, comparatively conventional mould is autoregressive moving-average model (Auto-RegressiveandMovingAverageModel, ARMA) method, neural net method and SVMs (SupportVectorMachines, SVM) method etc.Arma modeling advantage is that model order is few, amount of calculation is little and convergence is strong.Deficiency is that ARMA is a kind of linear model, is difficult to the nonlinear characteristic describing high frequency spectrum dynamic behaviour; And along with the rising of exponent number, amount of calculation sharply increases.The advantage of neural net method is independent of model, can be used for non-linear and non-stationary process etc.; Shortcoming be excessive and its value of the number of free parameter often experience arrange, affect by training sample comparatively large, can not ensure to converge to optimal solution and training process amount of calculation is large.Similar with neural net method, SVM method also has independent of model, can be used for advantage that is non-linear and non-stationary process, in addition its advantage such as also have the few and forecasting process computation complexity of free parameter low; But also have the value experience setting often of free parameter, training process amount of calculation is large waits deficiency.

Summary of the invention

The present invention is the prediction in order to realize taking the violent non-stationary high frequency spectrum of change factor sequence, proposes the Volterra Forecasting Methodology that a kind of high band frequency spectrum takies.

The Volterra Forecasting Methodology that high band frequency spectrum of the present invention takies, the concrete steps of the method are:

Step one: utilization state Space Theory takies factor sequence to high band frequency spectrum and carries out state space reconstruction, obtains the reproducing sequence that frequency spectrum takies factor sequence state space;

Step 2: utilize frequency spectrum to take the reproducing sequence of factor sequence state space, sets up the Volterra forecast model that high band frequency spectrum takies factor sequence;

Step 3: adopt recursive least squares, carry out dynamic conditioning to the core coefficient of Volterra forecast model, realizes the Volterra prediction that high band frequency spectrum takies.

Beneficial effect of the present invention is:

1. Volterra of the present invention (Wal Thailand draws) series model can carry out good sign to non linear system, and the nonlinear change being applicable to taking high band frequency spectrum factor sequence is predicted;

2. utilize recurrence least square (RecursiveLeastSquare, RLS) adaptive algorithm utilizes information to carry out dynamic conditioning to forecast model coefficient in real time, effectively can follow the tracks of the change procedure that frequency spectrum takies the factor, stronger than the adaptability of traditional static prediction model;

3. measured data result shows: the Forecasting Methodology prediction accuracy that the present invention proposes is high, and training process computation complexity is low, has very strong actual application value.

Accompanying drawing explanation

Fig. 1 is the flow chart of the Volterra Forecasting Methodology of the high band spectrum occupancy that the present invention relates to;

Fig. 2 is the structured flowchart (exponent number is 2, Embedded dimensions m=4) that the Volterra Forecasting Methodology of the high band spectrum occupancy that the present invention relates to realizes;

Fig. 3 is the measurement schematic diagram that in ITU distribution frequency range, frequency spectrum takies factor Q;

Fig. 4 is that different I TU distributes 24 hours change curve emulation schematic diagrames frequency range occupying factor metric data;

The root-mean-square error (Root-Mean-SquareError, RMSE) that Fig. 5 is Volterra, autoregression model (Auto-Regressive, AR) and SVM predict the outcome contrasts schematic diagram;

Fig. 6 is the partial enlarged drawing of Fig. 5;

Fig. 7 is training time contrast schematic diagram (unit: ms, training sample 750 point) of Volterra, AR and SVM.

Embodiment

Embodiment one, composition graphs 1 illustrate present embodiment, the Volterra Forecasting Methodology that the high band frequency spectrum described in present embodiment takies, and the concrete steps of the method are:

Step one: utilization state Space Theory takies factor sequence to high band frequency spectrum and carries out state space reconstruction, obtains the reproducing sequence that frequency spectrum takies factor sequence state space;

Step 2: utilize frequency spectrum to take the reproducing sequence of factor sequence state space, sets up the Volterra forecast model that high band frequency spectrum takies factor sequence;

Step 3: adopt recursive least squares, carry out dynamic conditioning to the core coefficient of Volterra forecast model, realizes the Volterra prediction that high band frequency spectrum takies.

Frequency spectrum takies the factor and is defined as: at a given ITU (InternationalTelecommunicationsUnion, International Telecommunications Union) in the frequency range of distributing, the ratio of the number and this frequency range resolution cell sum that claim the power of Received signal strength to exceed the resolution cell of given thresholding is that frequency spectrum takies the factor, represents with Q; First this definition is proposed by Laycock and Gott, is widely accepted and uses in the world.As shown in Figure 3, when given thresholding is-77dBm, have 2 resolution cell power to exceed thresholding in 100 resolution cells, then Q value is 0.02.Frequency spectrum takies the factor and reflects under given power threshold, the occupied degree of this frequency range.When Q value is 0, represent that this frequency range is completely idle; When Q value is 1, then represent that this frequency range is fully occupied.

Embodiment two, present embodiment are further illustrating the Volterra Forecasting Methodology that the high band frequency spectrum described in embodiment one takies, and the high band frequency spectrum described in step one takies the method that factor sequence carries out state space reconstruction and is:

The time series that frequency spectrum takies factor Q is Q={q (n), n=1,2 ..., N}, carries out state space reconstruction to Q, and the frequency spectrum after reconstruct takies the reproducing sequence of factor sequence state space:

q(n)＝[q(n),q(n-1),…,q(n-m+1)]

Wherein, q (n) is the measuring value taking factor Q at the frequency spectrum in n moment, and the frequency spectrum that q (n-m+1) is the n-m+1 moment takies the measuring value of factor Q, and m is Embedded dimensions.

Embodiment three, present embodiment are further illustrating the Volterra Forecasting Methodology that the high band frequency spectrum described in embodiment one takies, and the method that high band frequency spectrum takies the Volterra forecast model of factor sequence of setting up described in step 2 is:

Volterra series expansion to non linear system high band frequency spectrum:

$\begin{array}{c}{d}^{\′}\left(n\right)=w_c\left(n\right)+\underset{l_1=0}{\overset{\mathrm{\∞}}{\Σ}}{w}_{l_1}\left(n\right)x(n-l_1)\\ +\underset{l_1=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{l_2=0}{\overset{\mathrm{\∞}}{\Σ}}{w}_{l_1,l_2}\left(n\right)x(n-I_1)x(n-I_1)x(n-l_2)\\ +\underset{l_1=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{l_2=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{l_3=0}{\overset{\mathrm{\∞}}{\Σ}}{w}_{l_1,l_2,l_3}\left(n\right)x(n-l_1)x(n-l_2)x(n-l_3)\\ +\underset{l_1=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{l_i=0}{\overset{\mathrm{\∞}}{\Σ}}\mathrm{...}\underset{l_i=0}{\overset{\mathrm{\∞}}{\Σ}}{w}_{l_1,l_2,\mathrm{...},l_3}\left(n\right)x(n-l_1)x(n-l_2)\mathrm{...}x(n-l_i)\\ +\mathrm{...}\end{array}$

Wherein, w _cn () represents the constant term Volterra core coefficient in the n moment, (n) (i=0,1 ..., ∞) represent at the forecast model i-th rank Volterra core coefficient in n moment, x (n) is input signal, d'(n) represent the output of unknown system when not having a measurement noises in System Discrimination application; l ₁, l ₂..., l _ifor time of delay;

D'(n) second order clipped form:

$d^{\′}\left(n\right)=w_c\left(n\right)+\underset{l_1=0}{\overset{m-1}{\Σ}}{w}_{l_1}\left(n\right)x(n-l_1)+\underset{l_1=0}{\overset{m-1}{\Σ}}\underset{l_2=0}{\overset{m-1}{\Σ}}{w}_{l_1,l_2}\left(n\right)x(n-l_1)x(n-l_2)+e\left(n\right)$

Wherein, m is the Embedded dimensions of input signal x (n), e (n) is truncated error, make d'(n)=q (n+1), x (n)=q (n), utilize the state vector q (n) after reconstruct, ask the second order of q (n+1) to block Volterra progression;

The Volterra forecast model that high band frequency spectrum takies factor sequence is that the second order of q (n+1) blocks Volterra progression, and representation is:

$\begin{array}{c}q(n+1)=F\left(q\right(n\left)\right)=w_c\left(n\right)+\underset{l_1=0}{\overset{m-1}{\Σ}}{w}_{l_1}\left(n\right)q(n-l_1)\\ +\underset{l_1=0}{\overset{n-1}{\Σ}}\underset{l_2=0}{\overset{m-1}{\Σ}}{w}_{l_1,l_2}\left(n\right)q(n-l_1)q(n-l_2)+e\left(n\right)\end{array}$

Wherein, w _cn () represents the constant term Volterra core coefficient in the n moment, n () represents the single order Volterra core coefficient in the n moment, n () represents the Second-Order Volterra core coefficient in the n moment, m is Embedded dimensions.

Embodiment four, present embodiment are further illustrating the Volterra Forecasting Methodology that the high band frequency spectrum described in embodiment one takies, and utilize recursive least squares to be specially the method that Volterra forecast model core coefficient carries out dynamic conditioning described in step 3:

Coefficient vector W (n) of forecast model is:

W(n)＝[w _c(n),w ₀(n),w ₁(n),…,w _m-1(n),w _0,0(n),w _0,1(n),…,w _m-1,m-1(n)] ^T，

Input signal vector U (n) is:

U(n)＝[1,q(n),q(n-1),…,q(n-m+1),q ²(n),q(n)q(n-1),…,q ²(n-m+1)] ^Τ，

So, in Volterra forecast model, the matrix representation forms of q (n+1) is:

q(n+1)＝U ^T(n)W(n)+e(n)

Recurrence least square adaptive algorithm is used to adjust coefficient vector W (n) of Volterra series model in real time; The recursive form of recurrence least square adaptive algorithm:

$\left\{\begin{array}{c}\hat{q}(n+1)=U{\left(n\right)}^{T}W\left(n\right)\\ e\left(n\right)=q(n+1)-U{\left(n\right)}^{T}W\left(n\right)\\ \mathrm{\ψ}(n+1)=S_D\left(n\right)U\left(n\right)\\ S_D(n+1)=\frac{1}{\mathrm{\λ}}\[S_D\left(n\right)-\frac{\mathrm{\ψ}(n+1){\mathrm{\ψ}}^T(n+1)}{\mathrm{\λ}+\mathrm{\ψ}{(n+1)}^{T}U\left(n\right)}\]\\ W(n+1)=W\left(n\right)+e\left(n\right)S_D(n+1)U\left(n\right)\end{array}\right.$

Wherein, for predicted value, q (n+1) is actual value, S _dn () is the inverse matrix of the certainty correlation matrix in the n moment, ψ (n+1) is the auxiliary vector for reducing computation burden, and λ is exponential weighting factor, and span is 0≤λ≤1.

Measured data is tested

The 18 groups of data selecting 9 of ITU high frequencies to distribute frequency range are verified the Forecasting Methodology that the present invention proposes, and each frequency range has two groups of metric data, as shown in table 1.Can find out that selected frequency range is evenly distributed in whole high band, the frequency spectrum that substantially can represent whole high band takies the situation of change of the factor.Fig. 4 (a)-(r) is corresponding in turn to the 1-18 group data in table 1, describes 24 hours change curves that each group of frequency spectrum takies factor metric data.Obviously, the version that high band frequency spectrum takies the factor is various, presents feature that is non-linear, non-stationary.

Table 1 metric data number table

The present invention adopts Volterra sef-adapting filter, is trained core coefficient by RLS, wherein forgetting factor λ=0.982, and Embedded dimensions is 4.Select two kinds to contrast Forecasting Methodology, be respectively: AR model least square method carrys out calculating parameter, exponent number is 4; SVM selects ε-SVR form and carries out 5 groups of cross validations by genetic algorithm and carrys out Optimal Parameters, and Embedded dimensions is 4.

To 18 groups of measured datas (see the figure (a) in table 1 and Fig. 4 to figure (r)), often group gets wherein continuous print 1500 point, and makes training set with first 750, makes test set at latter 750.Here the training process of root-mean-square error (Root-Mean-SquareError, RMSE) and the same sample number time used is used to evaluate Forecasting Methodology.

$RMSE=\sqrt{\frac{1}{l}\underset{i=1}{\overset{l}{\Σ}}{\left(q\right(n+1)-\hat{q}(n+1\left)\right)}^2}$

Wherein, l is training set sample number, q (n+1) for Q time series is at the actual value in n+1 moment, for Q time series is in the predicted value in n+1 moment.Experimental result is as shown in Fig. 5, Fig. 6, Fig. 7 and table 2, and wherein Fig. 5, Fig. 6, Fig. 7 sets forth three kinds of algorithm RMSE to each group of data and the comparison of training time; Table 2 gives and improves percentage relative to the RMSE of AR and SVM, Volterra method.

The RMSE of table 2Volterra method improves percentage

As can be seen from experimental result (see Fig. 5, Fig. 6, table 2), in most data, the precision of prediction of Volterra model has and significantly improves.Even if change little data in time being numbered 8,14,16 and 18 this amplitudes, the RMSE of Volterra Forecasting Methodology and AR model is also close.And SVM performance is the poorest, the data being numbered 4,6,7 and 17 were lost efficacy in the second half.This is because the traditional prediction method being representative with AR and SVM, forecast model is fixing, thus be difficult to carry out long-term forecast to the nonstationary time series of acute variation, particularly concerning SVM, general leading to carries out organizing cross validation to training set data more, to realize parameter optimization, so need the training time (see Fig. 7) grown very much, be difficult to adjust in real time model; And Adaptive Volterra Forecasting Methodology, adopt the RLS algorithm adjustment model parameter in real time of recursive form, thus there is stronger adaptability and accuracy.

Training time used when three kinds of algorithm predicts respectively organize data as shown in Figure 7, can be found out: (1) SVM training time used is the longest, and computation complexity is very high; (2) AR model is because fairly simple, and the training time used is minimum, and computation complexity is less; (3) training time of Volterra model and AR close to and much smaller than training time of SVM.In addition, the training time of Volterra model and predicted time approximately equal, this is because Volterra filter have employed successively the mode of stepwise predict, although relatively add certain predicted time, precision of prediction has and significantly promotes.

Claims (4)

1. the Volterra Forecasting Methodology that takies of high band frequency spectrum, it is characterized in that, the concrete steps of the method are:

Step one: utilization state Space Theory takies factor sequence to high band frequency spectrum and carries out state space reconstruction, obtains the reproducing sequence that frequency spectrum takies factor sequence state space;

Step 2: utilize frequency spectrum to take the reproducing sequence of factor sequence state space, sets up the Volterra forecast model that high band frequency spectrum takies factor sequence;

Step 3: adopt recursive least squares, carry out dynamic conditioning to the core coefficient of Volterra forecast model, realizes the Volterra prediction that high band frequency spectrum takies.

2. the Volterra Forecasting Methodology that takies of high band frequency spectrum according to claim 1, is characterized in that, the high band frequency spectrum described in step one takies the method that factor sequence carries out state space reconstruction and is:

The time series that frequency spectrum takies factor Q is Q={q (n), n=1,2 ..., N}, carries out state space reconstruction to Q, and the frequency spectrum after reconstruct takies the reproducing sequence of factor sequence state space:

q(n)＝[q(n),q(n-1),…,q(n-m+1)]

Wherein, q (n) is the measuring value taking factor Q at the frequency spectrum in n moment, and the frequency spectrum that q (n-m+1) is the n-m+1 moment takies the measuring value of factor Q, and m is Embedded dimensions.

3. the Volterra Forecasting Methodology that takies of high band frequency spectrum according to claim 1, is characterized in that, the method that high band frequency spectrum takies the Volterra forecast model of factor sequence of setting up described in step 2 is:

Volterra series expansion to non linear system high band frequency spectrum:

$\begin{array}{c}{d}^{\′}\left(n\right)=w_c\left(n\right)+\underset{l_1=0}{\overset{\mathrm{\∞}}{\Σ}}{w}_{l_1}\left(n\right)x(n-l_1)\\ +\underset{l_1=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{l_2=0}{\overset{\mathrm{\∞}}{\Σ}}{w}_{l_1,l_2}\left(n\right)x(n-l_1)x(n-l_2)\\ +\underset{l_1=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{l_2=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{l_3=0}{\overset{\mathrm{\∞}}{\Σ}}{w}_{l_1,l_2,l_3}\left(n\right)x(n-l_1)x(n-l_2)x(n-l_3)\\ +\underset{l_1=0}{\overset{\mathrm{\∞}}{\Σ}}\underset{l_2=0}{\overset{\mathrm{\∞}}{\Σ}}\mathrm{...}\underset{l_i=0}{\overset{\mathrm{\∞}}{\Σ}}{w}_{l_1,l_2,\mathrm{...},l_i}\left(n\right)x(n-l_1)x(n-l_2)\mathrm{...}x(n-l_i)\\ +\mathrm{...}\end{array}$

Wherein, w _cn () represents the constant term Volterra core coefficient in the n moment, (i=0,1 ..., ∞) and represent that x (n) is input signal, d'(n at the forecast model i-th rank Volterra core coefficient in n moment) represent the output of unknown system when not have measurement noises in System Discrimination application; l ₁, l ₂..., l _ifor time of delay;

D'(n) second order clipped form:

$d^{\′}\left(n\right)=w_c\left(n\right)+\underset{l_1=0}{\overset{m-1}{\Σ}}{w}_{l_1}\left(n\right)x(n-l_1)+\underset{l_1=0}{\overset{m-1}{\Σ}}\underset{l_2=0}{\overset{m-1}{\Σ}}{w}_{l_1,l_2}\left(n\right)x(n-l_1)x(n-l_2)+e\left(n\right)$

Wherein, m is the Embedded dimensions of input signal x (n), e (n) is truncated error, make d'(n)=q (n+1), x (n)=q (n), utilize the state vector q (n) after reconstruct, ask the second order of q (n+1) to block Volterra progression;

The Volterra forecast model that high band frequency spectrum takies factor sequence is that the second order of q (n+1) blocks Volterra progression, and representation is:

$\begin{array}{c}q(n+1)=F\left(q\left(n\right)\right)=w_c\left(n\right)+\underset{l_1=0}{\overset{m-1}{\Σ}}{w}_{l_1}\left(n\right)q(n-l_1)\\ +\underset{l_1=0}{\overset{m-1}{\Σ}}\underset{l_2=0}{\overset{m-1}{\Σ}}{w}_{l_1,l_2}\left(n\right)q(n-l_1)q(n-l_2)+e\left(n\right)\end{array}$

Wherein, w _cn () represents the constant term Volterra core coefficient in the n moment, represent the single order Volterra core coefficient in the n moment, represent the Second-Order Volterra core coefficient in the n moment, m is Embedded dimensions.

4. the Volterra Forecasting Methodology that takies of high band frequency spectrum according to claim 1, is characterized in that, utilize recursive least squares to be specially the method that Volterra forecast model core coefficient carries out dynamic conditioning described in step 3:

Coefficient vector W (n) of forecast model is:

W(n)＝[w _c(n),w ₀(n),w ₁(n),…,w _m-1(n),w _0,0(n),w _0,1(n),…,w _m-1,m-1(n)] ^T，

Input signal vector U (n) is:

U(n)＝[1,q(n),q(n-1),…,q(n-m+1),q ²(n),q(n)q(n-1),…,q ²(n-m+1)] ^Τ，

So, in Volterra forecast model, the matrix representation forms of q (n+1) is:

q(n+1)＝U ^T(n)W(n)+e(n)

Recurrence least square adaptive algorithm is used to adjust coefficient vector W (n) of Volterra series model in real time; The recursive form of recurrence least square adaptive algorithm:

$\left\{\begin{array}{c}\hat{q}(n+1)=U{\left(n\right)}^{T}W\left(n\right)\\ e\left(n\right)=q(n+1)-U{\left(n\right)}^{T}W\left(n\right)\\ \mathrm{\ψ}(n+1)=S_D\left(n\right)U\left(n\right)\\ S_D(n+1)=\frac{1}{\mathrm{\λ}}\[S_D\left(n\right)-\frac{\mathrm{\ψ}(n+1){\mathrm{\ψ}}^T(n+1)}{\mathrm{\λ}+\mathrm{\ψ}{(n+1)}^{T}U\left(n\right)}\]\\ W(n+1)=W\left(n\right)+e\left(n\right)S_D(n+1)U\left(n\right)\end{array}\right.$

Wherein, for predicted value, q (n+1) is actual value, S _dn () is the inverse matrix of the certainty correlation matrix in the n moment, ψ (n+1) is the auxiliary vector for reducing computation burden, and λ is exponential weighting factor, and span is 0≤λ≤1.