CN-122017771-A - Quantization phase coding waveform design method based on alternate direction multiplier method

CN122017771ACN 122017771 ACN122017771 ACN 122017771ACN-122017771-A

Abstract

The invention discloses a quantized phase coding waveform design method based on an alternate direction multiplier method, which is used for constructing an optimization model aiming at minimizing integrated side lobe level and decomposing a complex non-convex optimization problem faced by the optimization model into two sub-problems of continuous waveform optimization and quantized phase projection, wherein the sub-problems can be solved efficiently by utilizing an ADMM frame. In the iterative process, an adjacent operator is innovatively introduced, and the obtained phase is precisely quantized into a preset quantized phase set, so that a constant-mode signal with low side lobe characteristics and high engineering realizability is generated.

Inventors

JIANG JUNZHENG
LU WEI
QUAN YINGHUI

Assignees

西安电子科技大学杭州研究院
西安电子科技大学

Dates

Publication Date: 20260512
Application Date: 20251230

Claims (10)

1. The quantized phase coding waveform design method based on the alternating direction multiplier method is characterized by comprising the following steps of: An optimization model of the quantized phase code waveform is established, wherein the optimization goal of the optimization model is to minimize the level of an integral side lobe related to the phase code waveform sequence, and constraint conditions comprise that each code element in the phase code waveform sequence meets a constant modulus condition and the phase of each code element belongs to a quantized phase set; introducing auxiliary variables and Lagrangian multipliers, and reconstructing an optimization model of the quantized phase encoding waveform with constraint conditions into an optimization model without constraint conditions; The method comprises the steps of obtaining an optimal phase coding waveform by solving an optimization model without constraint conditions, outputting the optimal phase coding waveform, determining an initial auxiliary variable and an initial Lagrangian multiplier, fixing the initial auxiliary variable and the initial Lagrangian multiplier, solving the optimization model without constraint conditions to obtain an intermediate phase coding waveform sequence, fixing the intermediate phase coding waveform sequence and the initial Lagrangian multiplier, quantizing the phases of the intermediate phase coding waveform sequence and the initial Lagrangian multiplier onto a quantized phase set through an adjacent operator and simultaneously meeting constant modulus conditions to obtain an intermediate auxiliary variable, judging whether the iteration stop condition is met according to the intermediate phase coding waveform sequence and the intermediate auxiliary variable, if the iteration stop condition is met, taking the intermediate phase coding waveform sequence of the current iteration as the optimal phase coding waveform sequence, and if the iteration stop condition is not met, calculating the intermediate Lagrangian multiplier according to the intermediate phase coding waveform sequence, the intermediate auxiliary variable and the initial Lagrangian multiplier, taking the intermediate auxiliary variable as the initial auxiliary variable and the intermediate Lagrangian multiplier as the initial Lagrangian multiplier, and returning the intermediate auxiliary variable and the initial Lagrangian multiplier to fix the phases of the intermediate phase coding waveform sequence and the initial Lagrangian multiplier until the iteration stop condition is met, and the optimal phase coding waveform sequence is obtained.
2. The method for designing a quantized phase encoded waveform based on the alternate direction multiplier method according to claim 1, wherein the constrained optimization model of the quantized phase encoded waveform is expressed as: ; Wherein, the A sequence of phase-encoded waveforms is represented, , Representing the first of a sequence of phase encoded waveforms A number of symbols of a symbol, Representing the number of symbols in the phase encoded waveform sequence, Representation of Is subjected to the conjugate-transpose operation, , , Representing the square of the modulus value, Representation of The constant modulus condition is satisfied, Representing the set of quantized phases, Representing the number of phase discretizations, The phase-finding operation is represented by the phase-finding operation, Representation of The phase of (2) belongs to 。
3. The method for designing a quantized phase encoded waveform based on the alternate direction multiplier method according to claim 1, wherein the unconstrained optimization model is formulated as: Wherein, the Respectively representing the phase encoding waveform sequence, the auxiliary variable and the Lagrangian multiplier, Representation of Is an unconstrained optimization model of the (c) model, Representing the number of symbols in the phase encoded waveform sequence, Representation of Is subjected to the conjugate-transpose operation, , , Representing the square of the modulus value, , Representing the set of quantized phases, Representing the number of quantization phases in the set of quantization phases, Representing the presentation to be Is projected on the phase of Is provided with a projection operator of the image processing system, , The phase-finding operation is represented by the phase-finding operation, Representing the first of the auxiliary variables The number of elements to be added to the composition, Representation of The phase of (2) belongs to , Representation of The phase of (2) is not of , Is a penalty parameter which is a function of the penalty parameter, Representing squaring the L2 norm.
4. The method for designing a quantized phase encoded waveform based on the alternate direction multiplier method according to claim 1, wherein the steps of fixing an initial auxiliary variable and an initial lagrangian multiplier, and solving an unconstrained optimization model to obtain an intermediate phase encoded waveform sequence include: fixing an initial auxiliary variable and an initial Lagrangian multiplier, and converting the optimization model without constraint conditions into a sub-optimization model without constraint conditions; Converting the sub-optimization model of the first unconstrained condition from complex-form solution to real-value-form solution to obtain a sub-optimization model of the second unconstrained condition; solving a sub-optimization model of the second unconstrained condition by using an NAG algorithm to obtain a real-value form of the phase coding waveform sequence; The real-valued form of the phase-encoded waveform sequence is converted to a complex form of the phase-encoded waveform sequence and serves as an intermediate phase-encoded waveform sequence.
5. The method for designing a quantized phase encoded waveform based on the alternate direction multiplier method according to claim 4, the method is characterized by comprising the following steps of a sub-optimization model without constraint conditions, wherein the formula is expressed as follows: ; Wherein, the Represent the first An intermediate phase encoded waveform sequence obtained by a plurality of iterations, Represent the first The initial auxiliary variable obtained from the number of iterations, Represent the first The initial lagrangian multiplier obtained from the multiple iterations, A sequence of phase-encoded waveforms is represented, Representing the number of symbols in the phase encoded waveform sequence, Representation of Is subjected to the conjugate-transpose operation, , , Is a penalty parameter which is a function of the penalty parameter, Representing squaring the L2 norm.
6. The method for designing a quantized phase encoded waveform based on the alternate direction multiplier method according to claim 4, the method is characterized by comprising the following steps of a second sub-optimization model without constraint conditions, wherein the formula is expressed as follows: ; Wherein, the Represent the first The real valued version of the intermediate phase encoded waveform sequence obtained from the multiple iterations, Representing a real valued version of the phase encoded waveform sequence, Representation of Is subjected to a transposition operation of (a), , , The representation takes the real part of the operation, Representing an operation of taking the imaginary part, , , Represent the first The real form of the initial auxiliary variable obtained from the multiple iterations, Represent the first The real form of the initial lagrangian multiplier obtained from the multiple iterations, Is a penalty parameter which is a function of the penalty parameter, Representing squaring the L2 norm.
7. The method for designing a quantized phase encoded waveform based on the alternating direction multiplier method according to claim 1, wherein fixing the intermediate phase encoded waveform sequence and the initial lagrangian multiplier, quantizing the phases of the intermediate phase encoded waveform sequence and the initial lagrangian multiplier onto the quantized phase set by the proximity operator while satisfying a constant modulus condition, and obtaining the intermediate auxiliary variable, comprises: fixing the intermediate phase code waveform sequence and the initial Lagrangian multiplier, and converting the optimization model of the unconstrained condition into a sub-optimization model of a third unconstrained condition; Solving a sub-optimization model of a third unconstrained condition by a proximity operator to map the phases of the intermediate phase-encoded waveform sequence and the initial Lagrangian multiplier to the nearest quantized phase; The intermediate auxiliary variable is solved according to the most recent quantized phase.
8. The method for designing a quantized phase encoded waveform based on the alternate direction multiplier method according to claim 7, the method is characterized by comprising the following steps of: ; Wherein, the Represent the first The first of the intermediate auxiliary variables obtained by the iteration The number of elements to be added to the composition, The value of (2) is 1-1 , Representing the number of symbols in the phase encoded waveform sequence, Representing the first of the auxiliary variables The number of elements to be added to the composition, Representation of The constant modulus condition is satisfied, Representing the set of quantized phases, Representing the number of quantization phases in the set of quantization phases, Representing the presentation to be Is projected on the phase of Is provided with a projection operator of the image processing system, Represent the first The first phase code waveform sequence obtained by iteration A number of symbols of a symbol, Represent the first The first iteration of the initial Lagrangian multiplier The number of elements to be added to the composition, Is a penalty parameter which is a function of the penalty parameter, Representing squaring the L2 norm.
9. The method of claim 7, wherein the mapped most recent quantization phase is formulated as: ; Wherein, the The sequence number representing the most recent quantized phase of the map, Represent the first The first phase code waveform sequence obtained by iteration A number of symbols of a symbol, Represent the first The first iteration of the initial Lagrangian multiplier The number of elements to be added to the composition, A sequence number representing the quantization phase in the set of quantization phases, , Representing the number of quantization phases in the set of quantization phases, Representing the most recent quantized phase The elements.
10. The method of claim 1, wherein the intermediate lagrangian multiplier is calculated by the formula: ; Wherein, the Represent the first Intermediate lagrangian multipliers obtained by the multiple iterations, Represent the first The initial lagrangian multiplier obtained from the multiple iterations, Represent the first An intermediate phase encoded waveform sequence obtained by a plurality of iterations, Represent the first Intermediate auxiliary variables obtained by the iteration.

Description

Quantization phase coding waveform design method based on alternate direction multiplier method Technical Field The invention belongs to the technical field of radar signal processing, and particularly relates to a quantized phase encoding waveform design method based on an alternate direction multiplier method. Background With the increasing electronic challenge, frequency modulated (Frequency Modulation, FM) signals present challenges in maintaining performance in electronic warfare environments due to the high real-time complexity. In contrast, phase modulation techniques have significant advantages, including greater noise immunity, higher bandwidth efficiency, robustness to multipath effects, lower power consumption, and simpler hardware complexity. These characteristics make phase modulation techniques particularly suitable for digital communication systems, enabling efficient data transmission within a limited bandwidth while maintaining immunity to noise and multipath interference. However, during radar signal pulse compression, high side lobes inevitably reduce the ability to detect weak targets. In addition, some radar systems use quantized phase values to simplify the signal generation and processing. Therefore, designing a low sidelobe phase encoded waveform having a phase quantization characteristic has become a key research focus. There has been a great deal of correlation research directed at the design of low sidelobe phase-encoding sequences. Numerical optimization algorithms generally follow a set of general flows by first constructing a mathematical model with the goal of minimizing the integrated sidelobe level (INTEGRATED SIDELOBE LEVEL, ISL) or peak sidelobe level (Peak Sidelobe Level, PSL), and then solving the model using various optimization methods such as gradient descent, alternate direction multiplier (ALTERNATING DIRECTION METHOD OF MULTIPLIERS, ADMM), etc. With the continuous development of science and technology, the deep learning method shows excellent performance in terms of operation efficiency, namely, firstly generating a training data set containing a random initialization waveform and performance indexes thereof, secondly designing a neural network, training the neural network by minimizing a preset cost function (such as an expected ISL value), and finally generating the waveform by using a trained model, and verifying the performance of the waveform by simulation. However, the application of deep learning is often limited by the quality of the training data, and furthermore, training complex deep learning models requires a large amount of computational resources, including high performance hardware support. Nevertheless, most existing algorithms focus on the design of continuous phase waveforms, i.e., the phase can take arbitrary values in the range of 0, 2 pi. Although continuous phase encoded waveforms have a large degree of freedom in theoretical design, their implementation is complex-not only requiring high resolution digital-to-analog converters and sophisticated analog circuitry, but also being prone to distortion due to noise and component imperfections. Quantized phase-coded waveforms are effective in alleviating these drawbacks and are therefore widely used in practical radar and communication systems. While heuristic algorithms can be used to design quantized phase encoded waveforms, their high computational complexity makes them less effective in coping with increasingly complex environments. The methods such as simulated annealing (Simulated Annealing, SA), genetic algorithm (Genetic Algorithm, GA) and the like can realize phase quantization, but have the problem of high computational complexity, while the algorithms such as Majorization-Minimization (MM), extreme point tracking (Extremal Point Pursuit, EXPP) and the like can reduce the computational complexity, but can not realize phase quantization. Disclosure of Invention In order to solve the problems in the prior art, the invention provides a quantization phase coding waveform design method based on an alternate direction multiplier method. The technical problems to be solved by the invention are realized by the following technical scheme: The embodiment of the invention provides a quantized phase coding waveform design method based on an alternate direction multiplier method, which comprises the following steps: An optimization model of the quantized phase code waveform is established, wherein the optimization goal of the optimization model is to minimize the level of an integral side lobe related to the phase code waveform sequence, and constraint conditions comprise that each code element in the phase code waveform sequence meets a constant modulus condition and the phase of each code element belongs to a quantized phase set; introducing auxiliary variables and Lagrangian multipliers, and reconstructing an optimization model of the quantized phase encoding waveform with constraint conditions into