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

High-frequency-band spectrum occupation Volterra prediction method Download PDF

Info

Publication number
CN105050114A
CN105050114A CN201510363063.8A CN201510363063A CN105050114A CN 105050114 A CN105050114 A CN 105050114A CN 201510363063 A CN201510363063 A CN 201510363063A CN 105050114 A CN105050114 A CN 105050114A
Authority
CN
China
Prior art keywords
mrow
msub
munderover
volterra
mtr
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201510363063.8A
Other languages
Chinese (zh)
Other versions
CN105050114B (en
Inventor
白杨
李宏博
张云
荆薇
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Harbin Institute of Technology
Original Assignee
Harbin Institute of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Harbin Institute of Technology filed Critical Harbin Institute of Technology
Priority to CN201510363063.8A priority Critical patent/CN105050114B/en
Publication of CN105050114A publication Critical patent/CN105050114A/en
Application granted granted Critical
Publication of CN105050114B publication Critical patent/CN105050114B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W16/00Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/02Resource partitioning among network components, e.g. reuse partitioning
    • H04W16/10Dynamic resource partitioning
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W24/00Supervisory, monitoring or testing arrangements
    • H04W24/02Arrangements for optimising operational condition

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

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

Volterra prediction method for high-frequency-band spectrum occupation
Technical Field
The invention relates to the technical field of high-band frequency spectrum monitoring.
Background
The high frequency radio band is between 3MHz and 30MHz, and is widely used for long distance radio communication, radar detection, broadcasting, etc. due to its simple technology and low cost. However, the spectrum behavior of the high frequency band may change sharply due to the influence of time, season, sun black sub-period, etc., resulting in multipath effect, doppler shift, depth attenuation, etc., limiting the usable range of the high frequency spectrum. In addition, the long-range transmission characteristics of high frequency radios cause the local spectrum to be interfered with by other high frequency users worldwide. The above factors cause the already limited high frequency spectrum to become more crowded. Therefore, monitoring and forecasting of the occupation of the high frequency spectrum is needed in order to select an effective working channel for the high frequency device.
The prediction of the occupation situation of the high frequency spectrum can be used as a time sequence for prediction processing, and the more commonly used models are an Auto-regressive moving average model (ARMA) method, a neural network method, a Support Vector Machine (SVM) method, and the like. The ARMA model has the advantages of less model order, small calculated amount and strong convergence. The ARMA is a linear model, and is difficult to describe the nonlinear characteristics of the dynamic behavior of the high-frequency spectrum; and as the order number increases, the amount of calculation increases sharply. The neural network method has the advantages that the method is independent of a model and can be used for nonlinear and non-stationary processes and the like; the disadvantages are that the number of free parameters is too large and the values are often set empirically, the impact of training samples is large, convergence to an optimal solution cannot be guaranteed, and the amount of calculation in the training process is large. Similar to the neural network method, the SVM method has the advantages of being independent of models, capable of being used for nonlinear and non-stationary processes, few in free parameters, low in calculation complexity of a prediction process and the like; however, the values of the free parameters are often set empirically, and the training process is computationally intensive.
Disclosure of Invention
The invention provides a Volterra prediction method for high-frequency band spectrum occupation, aiming at realizing prediction of a severely-changed non-stationary high-frequency spectrum occupation factor sequence.
The invention relates to a Volterra prediction method for high-band spectrum occupation, which comprises the following specific steps:
the method comprises the following steps: performing state space reconstruction on the high-frequency band frequency spectrum occupation factor sequence by using a state space theory to obtain a reconstruction sequence of the state space of the frequency spectrum occupation factor sequence;
step two: establishing a Volterra prediction model of the high-frequency band spectrum occupation factor sequence by utilizing a reconstruction sequence of the state space of the spectrum occupation factor sequence;
step three: and dynamically adjusting the nuclear coefficient of the Volterra prediction model by adopting a recursive least square algorithm, so as to realize the Volterra prediction of the high-frequency spectrum occupation.
The invention has the beneficial effects that:
1. the Volterra (Waltera) series model adopted by the invention can well characterize a nonlinear system and is suitable for predicting the nonlinear change of a high-frequency band spectrum occupation factor sequence;
2. the coefficient of the prediction model is dynamically adjusted by using the information in real time by using a Recursive Least Square (RLS) self-adaptive algorithm, so that the change process of the frequency spectrum occupation factor can be effectively tracked, and the adaptability of the prediction model is stronger than that of the traditional static prediction model;
3. the measured data processing result shows that: the prediction method provided by the invention has the advantages of high prediction accuracy, low calculation complexity in the training process and strong practical application value.
Drawings
FIG. 1 is a flow chart of a Volterra prediction method for high band spectrum occupancy in accordance with the present invention;
fig. 2 is a structural block diagram of the Volterra prediction method for the occupation situation of the high-frequency band spectrum according to the present invention (the order is 2, and the embedding dimension m is 4);
FIG. 3 is a diagram illustrating measurement of a spectrum occupancy factor Q on an ITU-allocated band;
FIG. 4 is a schematic diagram of a 24-hour variation curve simulation of occupancy factor measurement data over different ITU assigned frequency bands;
FIG. 5 is a schematic diagram showing the comparison of Root-Mean-square error (RMSE) between Volterra, Auto-regression (AR) and SVM predictions;
FIG. 6 is an enlarged view of a portion of FIG. 5;
FIG. 7 is a graph showing the comparison of training times (unit: ms, training sample 750 points) for Volterra, AR and SVM.
Detailed Description
In a first specific embodiment, the present embodiment is described with reference to fig. 1, where the Volterra prediction method for high-band spectrum occupancy in the present embodiment includes the specific steps of:
the method comprises the following steps: performing state space reconstruction on the high-frequency band frequency spectrum occupation factor sequence by using a state space theory to obtain a reconstruction sequence of the state space of the frequency spectrum occupation factor sequence;
step two: establishing a Volterra prediction model of the high-frequency band spectrum occupation factor sequence by utilizing a reconstruction sequence of the state space of the spectrum occupation factor sequence;
step three: and dynamically adjusting the nuclear coefficient of the Volterra prediction model by adopting a recursive least square algorithm, so as to realize the Volterra prediction of the high-frequency spectrum occupation.
The spectral occupancy factor is defined as: in a frequency band allocated by a given ITU (international telecommunications union), a ratio of the number of resolution units whose received signal power exceeds a given threshold to the total number of resolution units in the frequency band is referred to as a spectrum occupation factor and is denoted by Q; this definition was first proposed by lacycock and Gott and has been widely accepted and used internationally. As shown in fig. 3, when the given threshold is-77 dBm, 2 of the 100 resolution cells exceed the threshold, and the Q value is 0.02. The spectral occupancy factor reflects the degree to which the band is occupied at a given power threshold. When the Q value is 0, the frequency band is completely idle; when the Q value is 1, it indicates that the band is completely occupied.
In a second specific embodiment, the present embodiment is further described with respect to the Volterra prediction method for high-band spectrum occupancy described in the first specific embodiment, and the method for reconstructing state space of the high-band spectrum occupancy factor sequence described in the first step is as follows:
the time sequence of the spectrum occupation factor Q is Q ═ { Q (N), N ═ 1,2, …, N }, Q is reconstructed in a state space, and the reconstructed sequence of the spectrum occupation factor sequence in the state space is:
q(n)=[q(n),q(n-1),…,q(n-m+1)]
where Q (n) is the measurement of the spectrum occupancy factor Q at time n, Q (n-m +1) is the measurement of the spectrum occupancy factor Q at time n-m +1, and m is the embedding dimension.
In a third specific embodiment, the present embodiment is further described with respect to the Volterra prediction method for high-band spectrum occupancy described in the first specific embodiment, and the method for establishing the Volterra prediction model for the high-band spectrum occupancy factor sequence described in the second step is as follows:
expanding the Volterra series of the high-band spectrum of the nonlinear system:
<math> <mfenced open = '' close = ''> <mtable> <mtr> <mtd> <mrow> <msup> <mi>d</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>w</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <msub> <mi>w</mi> <msub> <mi>l</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <mn>...</mn> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mn>...</mn> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mn>...</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>
wherein, wc(n) represents the constant term Volterra kernel coefficient at time n,(n) (i ═ 0,1, …, infinity) denotes the ith order Volterra kernel coefficients of the prediction model at time n, x (n) is the input signal, d' (n) denotes the output of the unknown system in the absence of measurement noise in the system identification application; l1,l2,…,liIs a delay time;
second order truncated form of d' (n):
<math> <mrow> <msup> <mi>d</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>w</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>w</mi> <msub> <mi>l</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </math>
where m is the embedding dimension of the input signal x (n), e (n) is the truncation error, and d' (n) ═ q (n +1) and x (n) ═ q (n) are used to find the second order truncation Volterra series of q (n +1) using the reconstructed state vector q (n);
the Volterra prediction model of the high-frequency spectrum occupation factor sequence is a second-order truncated Volterra series of q (n +1), and the expression form is as follows:
<math> <mfenced open = '' close = ''> <mtable> <mtr> <mtd> <mrow> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>q</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>w</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>w</mi> <msub> <mi>l</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>
wherein, wc(n) represents the constant term Volterra kernel coefficient at time n,(n) represents the first order Volterra kernel coefficients at time n,(n) denotes the second order Volterra kernel coefficient at time n, with m being the embedding dimension.
In a fourth specific embodiment, the present embodiment is a further description of the Volterra prediction method for high-band spectrum occupancy described in the first specific embodiment, and the method for dynamically adjusting the kernel coefficients of the Volterra prediction model by using the recursive least squares algorithm described in the third step specifically includes:
the coefficient vector w (n) of the prediction model is:
W(n)=[wc(n),w0(n),w1(n),…,wm-1(n),w0,0(n),w0,1(n),…,wm-1,m-1(n)]T
the input signal vector u (n) is:
U(n)=[1,q(n),q(n-1),…,q(n-m+1),q2(n),q(n)q(n-1),…,q2(n-m+1)]Τ
then, the matrix representation of q (n +1) in the Volterra prediction model is of the form:
q(n+1)=UT(n)W(n)+e(n)
adjusting the coefficient vector W (n) of the Volterra series model in real time by using a recursive least square adaptive algorithm; recursive least squares adaptive algorithm recursion form:
<math> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <mover> <mi>q</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>U</mi> <msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mi>U</mi> <msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&psi;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>S</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>S</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>&lambda;</mi> </mfrac> <mo>&lsqb;</mo> <msub> <mi>S</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mrow> <mi>&psi;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msup> <mi>&psi;</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>&lambda;</mi> <mo>+</mo> <mi>&psi;</mi> <msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mi>S</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>
wherein,for predicted values, q (n +1) is the true value, SDAnd (n) is an inverse matrix of the deterministic correlation matrix at the moment of n, psi (n +1) is an auxiliary vector for reducing the calculation load, and lambda is an exponential weighting factor and has the value range of 0-1.
Experiment of measured data
The prediction method proposed by the present invention was verified by selecting 18 sets of data of 9 high frequency bands of ITU, each band having two sets of measurement data, as shown in table 1. It can be seen that the selected frequency bands are evenly distributed over the entire high frequency band, and can basically represent the variation of the spectrum occupancy factor of the entire high frequency band. Fig. 4(a) - (r) sequentially correspond to the data sets 1-18 in table 1, and describe the 24-hour variation curve of the measured data of the spectrum occupancy factor of each set. Obviously, the high-band spectrum occupation factor has various changes and presents nonlinear and non-stationary characteristics.
TABLE 1 measurement data numbering table
The invention adopts a Volterra self-adaptive filter to train the nuclear coefficient through RLS, wherein the forgetting factor lambda is 0.982, and the embedding dimension is 4. Two comparative prediction methods are selected, which respectively comprise: the AR model calculates parameters by using a least square method, and the order is 4; the SVM selects the form of-SVR and performs 5 sets of cross validation by genetic algorithm to optimize parameters, and the embedding dimension is 4.
For 18 sets of measured data (see table 1 and fig. 4, panels (a) to (r)), each set had 1500 consecutive points and used the first 750 points as the training set and the last 750 points as the test set. The prediction method is evaluated here using Root-Mean-square error (RMSE) and the time taken for the training process for the same number of samples.
<math> <mrow> <mi>R</mi> <mi>M</mi> <mi>S</mi> <mi>E</mi> <mo>=</mo> <msqrt> <mrow> <mfrac> <mn>1</mn> <mi>l</mi> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msup> <mrow> <mo>(</mo> <mi>q</mi> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>-</mo> <mover> <mi>q</mi> <mo>^</mo> </mover> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </math>
Wherein l is the number of samples in the training set, Q (n +1) is the true value of the Q time sequence at the moment of n +1,and (4) predicting the Q time series at the n +1 moment. The experimental results are shown in fig. 5, fig. 6, fig. 7 and table 2, wherein fig. 5, fig. 6 and fig. 7 respectively show the comparison of the RMSE and the training time of the three algorithms for each set of data; table 2 gives the percentage RMSE improvement of the Volterra method over AR and SVM.
TABLE 2 percentage RMSE improvement for the Volterra method
As can be seen from the experimental results (see fig. 5, fig. 6, and table 2), the prediction accuracy of the Volterra model is greatly improved in most data. The RMSE of the Volterra prediction method and the AR model is close even in the data numbered 8, 14, 16 and 18, where the amplitude changes little over time. While SVMs perform the worst, data for numbers 4, 6, 7 and 17 have failed in the second half. This is because in the conventional prediction methods represented by AR and SVM, the prediction model is fixed, so it is difficult to perform long-term prediction on a severely varying non-stationary time series, and especially for SVM, it is generally performed with multi-group cross validation on training set data to achieve parameter optimization, so it takes a long training time (see fig. 7), and it is difficult to perform real-time adjustment on the model; the self-adaptive Volterra prediction method adjusts the model parameters in real time by adopting a recursive RLS algorithm, so that the method has stronger adaptability and accuracy.
The training times used by the three algorithms to predict each set of data are shown in fig. 7, and it can be seen that: (1) the training time used by the SVM is longest, and the calculation complexity is very high; (2) the AR model is simple, the used training time is minimum, and the calculation complexity is low; (3) the training time of the Volterra model is close to AR and much less than that of SVM. In addition, the training time and the prediction time of the Volterra model are approximately equal, because the Volterra filter adopts a successive recursion prediction mode, although a certain prediction time is relatively increased, the prediction precision is greatly improved.

Claims (4)

1. The Volterra prediction method for the high-frequency spectrum occupation is characterized by comprising the following specific steps:
the method comprises the following steps: performing state space reconstruction on the high-frequency band frequency spectrum occupation factor sequence by using a state space theory to obtain a reconstruction sequence of the state space of the frequency spectrum occupation factor sequence;
step two: establishing a Volterra prediction model of the high-frequency band spectrum occupation factor sequence by utilizing a reconstruction sequence of the state space of the spectrum occupation factor sequence;
step three: and dynamically adjusting the nuclear coefficient of the Volterra prediction model by adopting a recursive least square algorithm, so as to realize the Volterra prediction of the high-frequency spectrum occupation.
2. The Volterra prediction method of high band spectrum occupancy according to claim 1, wherein the method for reconstructing the state space of the high band spectrum occupancy factor sequence in the first step is:
the time sequence of the spectrum occupation factor Q is Q ═ { Q (N), N ═ 1,2, …, N }, Q is reconstructed in a state space, and the reconstructed sequence of the spectrum occupation factor sequence in the state space is:
q(n)=[q(n),q(n-1),…,q(n-m+1)]
where Q (n) is the measurement of the spectrum occupancy factor Q at time n, Q (n-m +1) is the measurement of the spectrum occupancy factor Q at time n-m +1, and m is the embedding dimension.
3. The method for predicting Volterra occupied by the high-band spectrum according to claim 1, wherein the method for establishing the Volterra prediction model of the high-band spectrum occupancy factor sequence in the second step comprises the following steps:
expanding the Volterra series of the high-band spectrum of the nonlinear system:
<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mrow> <msup> <mi>d</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>w</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <msub> <mi>w</mi> <msub> <mi>l</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>3</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <mn>...</mn> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mi>&infin;</mi> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msub> <mi>l</mi> <mi>i</mi> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mn>...</mn> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mn>...</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>
wherein, wc(n) represents the constant term Volterra kernel coefficient at time n,(i ═ 0,1, …, ∞) denotes the Volterra kernel coefficients of the i-th order of the prediction model at time n, x (n) is the input signal, d' (n) denotes the output of the unknown system without measurement noise in the system identification application; l1,l2,…,liIs a delay time;
second order truncated form of d' (n):
<math> <mrow> <msup> <mi>d</mi> <mo>&prime;</mo> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>w</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>w</mi> <msub> <mi>l</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </math>
where m is the embedding dimension of the input signal x (n), e (n) is the truncation error, and d' (n) ═ q (n +1) and x (n) ═ q (n) are used to find the second order truncation Volterra series of q (n +1) using the reconstructed state vector q (n);
the Volterra prediction model of the high-frequency spectrum occupation factor sequence is a second-order truncated Volterra series of q (n +1), and the expression form is as follows:
<math> <mfenced open='' close=''> <mtable> <mtr> <mtd> <mrow> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>F</mi> <mrow> <mo>(</mo> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>w</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>w</mi> <msub> <mi>l</mi> <mn>1</mn> </msub> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>w</mi> <mrow> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>
wherein, wc(n) represents the constant term Volterra kernel coefficient at time n,representing the first order Volterra kernel coefficients at time instant n,representing the second order Volterra kernel coefficients at time n, with m being the embedding dimension.
4. The Volterra prediction method for high-band spectrum occupation according to claim 1, wherein the method for dynamically adjusting the kernel coefficients of the Volterra prediction model by using the recursive least square algorithm in the third step specifically comprises:
the coefficient vector w (n) of the prediction model is:
W(n)=[wc(n),w0(n),w1(n),…,wm-1(n),w0,0(n),w0,1(n),…,wm-1,m-1(n)]T
the input signal vector u (n) is:
U(n)=[1,q(n),q(n-1),…,q(n-m+1),q2(n),q(n)q(n-1),…,q2(n-m+1)]Τ
then, the matrix representation of q (n +1) in the Volterra prediction model is of the form:
q(n+1)=UT(n)W(n)+e(n)
adjusting the coefficient vector W (n) of the Volterra series model in real time by using a recursive least square adaptive algorithm; recursive least squares adaptive algorithm recursion form:
<math> <mfenced open='{' close=''> <mtable> <mtr> <mtd> <mrow> <mover> <mi>q</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>U</mi> <msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>q</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mi>U</mi> <msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&psi;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>S</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>S</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>&lambda;</mi> </mfrac> <mo>&lsqb;</mo> <msub> <mi>S</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mrow> <mi>&psi;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <msup> <mi>&psi;</mi> <mi>T</mi> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>&lambda;</mi> <mo>+</mo> <mi>&psi;</mi> <msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>T</mi> </msup> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mi>W</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>e</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <msub> <mi>S</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>U</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </math>
wherein,for predicted values, q (n +1) is the true value, SDAnd (n) is an inverse matrix of the deterministic correlation matrix at the moment of n, psi (n +1) is an auxiliary vector for reducing the calculation load, and lambda is an exponential weighting factor and has the value range of 0-1.
CN201510363063.8A 2015-06-26 2015-06-26 The Volterra prediction techniques that high band frequency spectrum occupies Active CN105050114B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201510363063.8A CN105050114B (en) 2015-06-26 2015-06-26 The Volterra prediction techniques that high band frequency spectrum occupies

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201510363063.8A CN105050114B (en) 2015-06-26 2015-06-26 The Volterra prediction techniques that high band frequency spectrum occupies

Publications (2)

Publication Number Publication Date
CN105050114A true CN105050114A (en) 2015-11-11
CN105050114B CN105050114B (en) 2018-10-02

Family

ID=54456214

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201510363063.8A Active CN105050114B (en) 2015-06-26 2015-06-26 The Volterra prediction techniques that high band frequency spectrum occupies

Country Status (1)

Country Link
CN (1) CN105050114B (en)

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5706402A (en) * 1994-11-29 1998-01-06 The Salk Institute For Biological Studies Blind signal processing system employing information maximization to recover unknown signals through unsupervised minimization of output redundancy
US6091361A (en) * 1998-05-12 2000-07-18 Davis; Dennis W. Method and apparatus for joint space-time array signal processing

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5706402A (en) * 1994-11-29 1998-01-06 The Salk Institute For Biological Studies Blind signal processing system employing information maximization to recover unknown signals through unsupervised minimization of output redundancy
US6091361A (en) * 1998-05-12 2000-07-18 Davis; Dennis W. Method and apparatus for joint space-time array signal processing

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
S. A. MAAS: "Volterra Analysis of Spectral Regrowth", 《IEEE MICROWAVE AND GUIDED WAVE LETTERS》 *
张玉梅 曲仕茹: "基于混沌的交通流量Volterra自适应预测模型", 《计算机应用研究》 *
张茜 刘光斌 郭金库 余志勇: "基于混沌时间序列建模的频谱状态持续时长预测", 《电子与信息学报》 *

Also Published As

Publication number Publication date
CN105050114B (en) 2018-10-02

Similar Documents

Publication Publication Date Title
CN107135041B (en) RBF neural network channel prediction method based on phase space reconstruction
CN113011581B (en) Neural network model compression method and device, electronic equipment and readable storage medium
CN102959625B9 (en) Method and apparatus for adaptively detecting voice activity in input audio signal
CN1354873A (en) Signal noise reduction by time-domain spectral subtraction using fixed filters
CN113221781B (en) Carrier signal detection method based on multitask deep convolutional neural network
CN113497771A (en) Supervised learning based doppler spread estimation
CN107947761B (en) Variable threshold value proportion updating self-adaptive filtering method based on fourth order of least mean square
CN103995950A (en) Wavelet coefficient partial discharge signal noise elimination method based on related space domain correction threshold values
KR20210124897A (en) Method and system of channel esimiaion for precoded channel
Gosse et al. Perfect reconstruction versus MMSE filter banks in source coding
CN1905383B (en) Shared frequency cell channel estimating apparatus and method
Zhao et al. Wavelet transform-based network traffic prediction: a fast on-line approach
Delamou et al. Deep learning-based estimation for multitarget radar detection
AU688228B1 (en) A system and method of estimating CIR
CN111796253B (en) Radar target constant false alarm detection method based on sparse signal processing
CN105050114B (en) The Volterra prediction techniques that high band frequency spectrum occupies
CN116155319A (en) Electromagnetic situation monitoring and analyzing system and method
CN103782520B (en) Channel estimation method, channel estimation apparatus and communication device for CDMA systems
CN116055261A (en) OTFS channel estimation method based on model-driven deep learning
EP3712626B1 (en) High-rate dft-based data manipulator and data manipulation method for high performance and robust signal processing
CN101741776B (en) Method and device for eliminating interference signals
Strelkovskaya et al. Comparative analysis of the methods of wavelet-and spline-extrapolation in problems of predicting self-similar traffic
RU2461874C2 (en) Adaptive two-dimensional method of multiplying estimates and apparatus for realising said method
CN1485798A (en) Optimizing training method of neural network equalizer
Sadough et al. A wavelet packet based model for and ultra-wide band indoor propagation channel

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant