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Prolate spherical wave pulse generating method based on normalized Legendre polynomial

A generation method and normalization technology, applied in baseband system components, shaping network in transmitter/receiver, electrical components, etc., can solve the problems that affect the performance of communication systems, without accurate and reliable data transmission, without fast and efficient Pulse generation method and other issues

Active Publication Date: 2010-11-10
中国人民解放军海军航空大学航空作战勤务学院
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Problems solved by technology

The performance of the PSWF pulse generation method directly affects the performance of the communication system. Without a fast and efficient pulse generation method, there will be no accurate and reliable data transmission.

Method used

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  • Prolate spherical wave pulse generating method based on normalized Legendre polynomial
  • Prolate spherical wave pulse generating method based on normalized Legendre polynomial
  • Prolate spherical wave pulse generating method based on normalized Legendre polynomial

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Embodiment

[0052] Design requirements: Design duration T = 2s, with the first 10 PSWF pulses limited to [-5Hz, 5Hz].

[0053] Design analysis: according to design requirements, time bandwidth product c=15.708, adopt the present invention, concrete realization process is as follows:

[0054] ① Determine the highest order of the normalized Legendre polynomial

[0055] Under the condition that the time-bandwidth product c=15.708, the highest order of the normalized Legendre polynomial is determined according to formula (6) as

[0056] ② Create a lookup table

[0057] According to c=15.708 and formulas (1), (2), and (3), calculate the 2N-dimensional characteristic matrix A, and divide it into two N-dimensional triangular symmetric matrices A even and A odd . It is necessary to generate the first 10-order PSWF pulses, so the eigenvectors corresponding to the first 5 smallest eigenvalues ​​in each matrix are respectively obtained, and these eigenvectors form a coefficient lookup table an...

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Abstract

The invention discloses a PSWF (Prolate Spheroidal Wave Function) pulse generating method in a communication system, and relates to a pulse generating method based on a normalized Legendre polynomial, which comprises the following steps of: computing the coefficient of the normalized Legendre polynomial according to the duration T and the bandwidth B of a pulse to be designed, and establishing a coefficient lookup table on the basis; when the pulse is generated, obtaining the coefficient of the normalized Legendre polynomial from the coefficient lookup table according to a design parameter, and generating a required PSWF pulse through the mode of the weighted sum of the Legendre polynomial. The coefficient of the normalized Legendre polynomial is only stored in the coefficient lookup table, so that fewer storage spaces are needed, and the hardware complexity is reduced. The PSWF pulse can be generated in real time in the invention according to the requirements of system frequency spectra. The PSWF pulse generated by the invention can be dynamically adapted to the requirements of the system frequency spectra.

Description

technical field [0001] The invention relates to a pulse generation method in a communication system, in particular to a frequency controllable ellipsoid spherical wave pulse generation method. Background technique [0002] Prolate Spheroidal Wave Functions (PSWF for short) was first proposed by D. Slepian et al. of Bell Laboratories in the early 1960s. The function is concentrated in the time domain and band-limited in the frequency domain. It has very good energy aggregation and has been widely used in electromagnetic field theory, communication, image processing and other fields. The application of PSWF in communication system mainly focuses on the aspect of pulse waveform design. As a pulse waveform, PSWF has flexible spectrum controllability and bi-orthogonal characteristics, and has been applied in ultra-wideband systems and CDMA systems, especially in non-sinusoidal time-domain orthogonal communication systems (see patent: Wang Hongxing, Zhao Zhiyong, Liu Xiguo, Mao ...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H04L25/02H04L25/03H04B1/69
Inventor 王红星陈昭男赵志勇刘锡国康家方
Owner 中国人民解放军海军航空大学航空作战勤务学院
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