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CN107677995B - OFDM waveform design method based on PMEPR-PSLR joint optimization - Google Patents

OFDM waveform design method based on PMEPR-PSLR joint optimization Download PDF

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CN107677995B
CN107677995B CN201710803313.4A CN201710803313A CN107677995B CN 107677995 B CN107677995 B CN 107677995B CN 201710803313 A CN201710803313 A CN 201710803313A CN 107677995 B CN107677995 B CN 107677995B
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崔国龙
李雯
李洋漾
熊丁丁
王祥丽
杨婧
孔令讲
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Abstract

The invention discloses an OFDM waveform design method based on PMEPR-PSLR joint optimization. The existing waveform design of the OFDM signal is optimized by considering a single parameter, that is, only optimizing a peak-to-average envelope ratio (PMEPR) or a peak side lobe level ratio (PSLR). Considering that modern electronic combat systems tend to be integrated comprehensively, namely, the research on radar communication integrated signal design is more and more mature, and not only the radar detection performance of the signals but also the application of the signals in communication are considered. Therefore, the optimization problem which takes PMEPR as an objective function and PSLR and energy as constraints is constructed by considering the convex optimization theory. First, the problem is simplified by using the SDP relaxation method, and the CVX toolbox is used for the relevant processing. And then, performing approximation processing on the optimal solution by using a randomization method. The feasibility of the design method can be further verified through simulation experiments, and the values corresponding to PMEPR and PSLR are correspondingly improved.

Description

OFDM waveform design method based on PMEPR-PSLR joint optimization
Technical Field
The invention belongs to the field of radar communication integrated waveform design, and particularly relates to the fields of OFDM (orthogonal frequency division multiplexing) signal modeling, optimization theory and radar detection.
Background
With the continuous development of modern scientific technology, the modern military war is moving towards the direction of system confrontation. This requires modern combat platforms to be equipped with numerous electronic combat equipment to enhance the survivability and the overall operational capabilities of the combat platform. That is, how to realize the horizontal integration of the system equipment develops a common concern for many researchers and scholars. The exploration and research of the related technology of the comprehensive integrated electronic combat system become one of the key problems to be solved in the modern war. The OFDM signal is a typical communication signal, and has the characteristics of good anti-interference capability, high-speed transmission capability and easy implementation, so that the OFDM signal is widely applied to integrated signal design. But the biggest defect is that the signal envelope fluctuates greatly, which causes the power amplifier to enter a saturation state in waveform transmission to cause signal distortion and possibly cause interference problems among subcarriers, so how to smooth the envelope of the OFDM signal is a major problem in research.
At present, the concept of radar communication integrated design has received wide attention and attention at home and abroad, the research on integrated waveforms based on OFDM is relatively complete, and in the literature, "OFDM wave design comprehensive estimation, side-band suppression and range resolution [ C ]. IEEE RadarConference, Cincinnati, USA,2014: 1424-. In the document "Low PMEPROMFradio wave shaped designing using the iterative least square signals, 22.11(2015): 1975-.
Disclosure of Invention
The invention aims to design an OFDM signal integrated with radar communication to realize the joint optimization of signal peak average envelope and peak side lobe, improve the radar target detection performance and ensure that the envelope of a smooth signal is easier to realize by hardware in consideration of the trend of a modern electronic combat system towards comprehensive integration, namely the research on the design of radar communication integrated signals is more and more mature.
The solution of the invention is as follows: first, a waveform optimization problem is designed. Considering the convex optimization theory, constructing an optimization problem which takes PMEPR as a target function and PSLR (peak side lobe level ratio) and energy as constraints; the problem is simplified by using a relaxation method of SDP (semi-positive definite programming), and relevant processing is carried out by using a convex optimization tool box; and performing approximation processing on the optimal solution by using a randomization method. Then, the target distance and velocity are measured using the designed waveform. The method effectively solves the problem of joint optimization of PSLR and PMEPR, and verifies the effectiveness of the algorithm through related simulation experiments.
The invention provides an OFDM waveform design method based on PMEPR-PSLR joint optimization, which comprises the following steps:
step 1, initializing system parameters
Initializing system parameters includes: bandwidth B, time width T, number of subcarriers N, subcarrier frequency interval delta f, and sampling rate f of OFDM signalsThe peak sidelobe constraint parameter is gamma, and the energy constraint parameter is P;
step 2, establishing a signal model
The corresponding OFDM signal is processed discretely, which can be expressed in the following form,
Figure BDA0001402078860000021
wherein: s [ l ]]L-th sample point, a, representing a sequence of discretized OFDM signalsnRepresenting the weight corresponding to the nth subcarrier; rewriting the discrete sequence into vector form, i.e. order
Figure BDA0001402078860000022
Therefore, the matrix expression form of the signal is
s＝Fa (2)
Wherein,
Figure BDA0001402078860000023
a fourier transform matrix is represented that is,
Figure BDA0001402078860000024
representing the weight vector/code word sequence corresponding to the OFDM signal; the design of the signal is directly converted into the calculation of a code word a;
step 3, PSLR matrixing
Since the expression of the discretized PSL (peak side lobe level) is,
Figure BDA0001402078860000025
wherein the discretized autocorrelation function R (m) is expressed as,
Figure BDA0001402078860000026
m represents a time delay unit;
in order to derive the discretized autocorrelation function, an operator of time delay is introduced, namely
Figure BDA0001402078860000027
The expression in the above formula is an expression obtained by delaying a vector x by m time delays; column blocking the fourier matrix according to equation (5) may result in F ═ F0,f1,…fN-1]The expression after the delay is:
Figure BDA0001402078860000031
wherein m is 0,1,2, 1, N-1; the discrete form of the autocorrelation function of the signal is further derived as,
Figure BDA0001402078860000032
order to
Figure BDA0001402078860000033
The final autocorrelation expression and PSLR are,
Figure BDA0001402078860000034
step 4, PMEPR matrixing
S [ l ] is]Is denoted by slThen the discretized PMEPR expression is,
Figure BDA0001402078860000035
El[|sl|2]represents | sl|2The mean value of (a); the matrix F rows are obtained by blocking,
Figure BDA0001402078860000036
wherein,
Figure BDA0001402078860000037
1,2, … N; therefore, it is possible to obtain,
Figure BDA0001402078860000038
and,
Figure BDA0001402078860000039
the expression for the PMEPR is found as,
Figure BDA0001402078860000041
step 5, establishing an optimization problem
Order to
Figure BDA0001402078860000042
So that an optimization problem with PMEPR as an objective function and PSLR as a constraint can be established,
Figure BDA0001402078860000043
wherein aoptExpressed is the optimal solution for the optimization problem, γ, P are given constants, m 1, 2.
Step 6, SDP optimization algorithm based on randomization
The relaxation method using SDP relaxes the above problem in that,
Figure BDA0001402078860000044
where tr (-) denotes the trace operation of the correspondence matrix,
let A be aaHIs a positive definite Hermitian matrix, which simplifies the above problem,
Figure BDA0001402078860000045
and solving through a convex optimization tool box to obtain a code word a.
Further, the specific method of step 6 is as follows:
step 6.1: generating a random vector of length W
Figure BDA0001402078860000051
Wherein
Figure BDA0001402078860000052
A covariance matrix representing the random variable;
step 6.2: order to
Figure BDA0001402078860000053
Judging whether the vector meets the constraint in the step 6; if the inequality is satisfied, then a(w)Recording and storing the data in an empty matrix B; if not, jumping out of the cycle;
step 6.3: let the column vector of matrix B be denoted B(q)Where Q is 1,2, … Q, Q represents the number of column vectors included in matrix B, and B represents(q)Get by bringing into the objective function
Figure BDA0001402078860000054
Step 6.4: calculating the optimal q*，
Figure BDA0001402078860000055
Step 6.5: can obtain the optimal vector
Figure BDA0001402078860000056
The method solves the problem of joint optimization of signal peak average envelope and peak side lobe, improves the radar target detection performance, and smoothes the envelope of the signal. And solving the optimization problem about PSLR and PMEPR by using a randomized SDP algorithm so as to obtain the optimal weight of the corresponding OFDM waveform. The method has the advantages that the optimization of two performance indexes is considered jointly, the realization is easy, and the feasibility of the algorithm for radar target detection is verified through simulation.
Drawings
Fig. 1 is a time-frequency domain diagram of a basic OFDM pulse signal.
Wherein the abscissa represents the time dimension and the ordinate represents the frequency dimension.
Figure 2 compares the extent of envelope fluctuation of a signal generated from a random phase encoded sequence with a sequence optimized based on a randomized SDP algorithm.
Fig. 3 shows the improvement of PSL compared to the signal autocorrelation in different optimization algorithms.
Fig. 4 shows a ranging result based on the time-domain correlation process of the OFDM signal.
Fig. 5 shows the velocity measurement result based on moving target detection.
Detailed Description
The invention mainly adopts a computer simulation method to verify, and all steps and conclusions are verified to be correct on MATLAB-R2014 a. The specific implementation steps are as follows:
step 1, initializing system parameters
Let bandwidth B of OFDM signal 100MHZ, time width T2.075 μ s, subcarrier number N128, subcarrier frequency interval Δ f B/N, number of sampling points K128, sampling rate fsN/T, the number of pulse accumulations is 104The number of corresponding randomized vectors is 105. Suppose that the range-velocity information of two targets is (100m,3m/s), (200m,4 m/s) respectively) Signal to noise ratio
Figure BDA0001402078860000061
Is 20 dB.
Step 2, signal model establishment
Discrete processing the corresponding OFDM signal and obtaining a matrix expression s-Fa thereof, wherein a represents the weight vector to be optimized,
Figure BDA0001402078860000062
a fourier transform matrix is represented.
Step 3, optimization problem construction
From the above, it is possible to further obtain discrete expressions for PSLR and PMEPR, respectively
Figure BDA0001402078860000063
Wherein R ism，R0And αlAre all known. And establishing an optimization problem by taking PMEPR as a target function and PSLR as constraint, and solving by using a randomized SDP algorithm.
Step 4, solving optimization problem
According to the PMEPR-PSLR combined optimization problem designed in the step 3, firstly, the problem is relaxed into a convex optimization problem by using an SDP algorithm, and an optimal matrix is solved by using a CVX optimization tool box. Then, the matrix is subjected to rank-one decomposition by using a randomization method, and an optimal weight vector meeting the constraint condition is constructed and solved
Figure BDA0001402078860000064
Further, the optimal OFDM sequence can be solved.
And 5, analyzing, researching and optimizing the peak side lobe and peak-to-average envelope ratio of the signal autocorrelation function.
And 6, transmitting the optimized signal through a Gaussian white noise channel for moving target detection.
The optimal matrix can be solved according to the algorithm, and whether the matrix meets the rank-one constraint or not is analyzed. If it is solved to obtain
Figure BDA0001402078860000065
Is 1, then it can be represented by the equation
Figure BDA0001402078860000066
Direct solution of optimal weight vector
Figure BDA0001402078860000067
Where λ is the corresponding eigenvalue, which is a constant. If solved for
Figure BDA0001402078860000068
Is greater than 1, then rank one decomposition is not applicable at this time. Therefore, the solution is approximated by using a randomized method, and because the constraint in the problem is considered in the solution approximation process, the specific steps are as follows:
step 7, radar performance analysis
In a radar receiving part, the autocorrelation characteristic of the signal is researched by utilizing the principle of matched filtering, and the peak side lobe level of the signal and the envelope fluctuation of the signal are further verified; the initial position and the moving speed of the moving object are detected by time domain correlation processing and MTD (moving object detection).
The three curves in fig. 2 respectively represent the PMEPR-based optimization, PMEPR-PSLR-based joint optimization, and the random phase coding sequence. The corresponding PMEPR values are respectively: 3.7672,4.9584,6.6496. It can be seen that although the level of smoothness of the envelope decreases after the autocorrelation constraint is added, the effectiveness of the optimization algorithm in suppressing the envelope fluctuations can be obtained by comparison with the random phase encoded sequence.
In fig. 3, comparing two different optimization cases, it can be clearly seen that the peak sidelobe of the signal autocorrelation under the joint optimization is improved compared with the former one, which is reduced by about 4dB, and the effectiveness of the algorithm is further verified.
Fig. 4 and 5 mainly show the radar detection performance of the OFDM waveform. Only the influence of white noise on radar detection is considered, and distance and speed can be accurately measured by analyzing the distance and speed measuring principle of the OFDM signal, wherein the target distance measuring errors are respectively 4.5% and 2.75%, and the target speed measuring errors are both 3.1%. Through the verification, the effectiveness of the PMEPR-PSLR joint optimization-based OFDM signal in the aspect of radar detection is verified, and a certain foundation is laid for further research of a radar communication integrated system.
Through the specific implementation of the invention, the invention realizes the joint optimization of the signal peak-to-average envelope and the peak sidelobe by designing the OFDM signal integrating radar communication, improves the radar target detection performance, smoothes the signal envelope, inhibits the signal distortion and the interference among subcarriers, and ensures the strict orthogonal relation among the subcarriers. The implementation of the invention also provides a possibility for designing the radar communication integrated signal.

Claims (2)

1. An OFDM waveform design method based on PMEPR-PSLR joint optimization comprises the following steps:
step 1, initializing system parameters
Initializing system parameters includes: bandwidth B, time width T, number of subcarriers N, subcarrier frequency interval delta f, and sampling rate f of OFDM signalsThe peak sidelobe constraint parameter is gamma, and the energy constraint parameter is P;
step 2, establishing a signal model
The corresponding OFDM signal is processed discretely, which can be expressed in the following form,
Figure FDA0002263300680000011
wherein: s [ l ]]L-th sample point, a, representing a sequence of discretized OFDM signalsnRepresenting the weight corresponding to the nth subcarrier; rewriting the discrete sequence into vector form, i.e. order
Figure FDA0002263300680000012
Therefore, the matrix expression form of the signal is
s＝Fa (2)
Wherein,
Figure FDA0002263300680000013
a fourier transform matrix is represented that is,
Figure FDA0002263300680000014
representing a code word sequence corresponding to the OFDM signal; directly converting the design of the signal into the calculation of a code word sequence a;
step 3, PSLR matrixing
Since the expression of the discretized PSL is,
Figure FDA0002263300680000015
wherein the discretized autocorrelation function R (m) is expressed as,
Figure FDA0002263300680000016
m represents a time delay unit;
in order to derive the discretized autocorrelation function, an operator of time delay is introduced, namely
Figure FDA0002263300680000017
The expression in the above formula is an expression obtained by delaying a vector x by m time delays; column blocking the fourier matrix according to equation (5) may result in F ═ F0,f1,…fN-1]The expression after the delay is:
Figure FDA0002263300680000018
wherein m is 0,1,2, …, N-1; the discrete form of the autocorrelation function of the signal is further derived as,
Figure FDA0002263300680000021
order to
Figure FDA0002263300680000022
The final autocorrelation expression and PSLR are,
Figure FDA0002263300680000023
step 4, PMEPR matrixing
S [ l ] is]Is denoted by slThen the discretized PMEPR expression is,
Figure FDA0002263300680000024
El[|sl|2]represents | sl|2The mean value of (a); the matrix F rows are obtained by blocking,
Figure FDA0002263300680000025
wherein,
Figure FDA0002263300680000026
therefore, it is possible to obtain,
Figure FDA0002263300680000027
and,
Figure FDA0002263300680000028
the expression for the PMEPR is found as,
Figure FDA0002263300680000031
step 5, establishing an optimization problem
Order to
Figure FDA0002263300680000032
So that an optimization problem with PMEPR as an objective function and PSLR as a constraint can be established,
Figure FDA0002263300680000033
wherein a isoptExpressed is the optimal solution for the optimization problem, γ, P are given constants, m is 1,2, …, N-1;
step 6, SDP optimization algorithm based on randomization
The relaxation method using SDP relaxes the above problem in that,
Figure FDA0002263300680000034
where tr (-) denotes the trace operation of the correspondence matrix,
let A be aaHIs a positive definite Hermitian matrix, which simplifies the above problem,
Figure FDA0002263300680000035
and solving through a convex optimization tool box to obtain a codeword sequence a.
2. The method for designing an OFDM waveform based on PMEPR-PSLR joint optimization according to claim 1, wherein the specific method in step 6 is:
step 6.1: generating a random vector of length W
Figure FDA0002263300680000041
Wherein
Figure FDA0002263300680000042
A covariance matrix representing the random variable;
step 6.2: order to
Figure FDA0002263300680000043
Judging whether the vector meets the constraint in the step 6; if the inequality is satisfied, then a(w)Recording and storing the data in an empty matrix B; if not, jumping out of the cycle;
step 6.3: let the column vector of matrix B be denoted B(q)Where Q is 1,2, … Q, Q represents the number of column vectors included in matrix B, and B represents(q)Get by bringing into the objective function
Figure FDA0002263300680000044
Step 6.4: calculating the optimal q*，
Figure FDA0002263300680000045
Step 6.5: can obtain the optimal vector
Figure FDA0002263300680000046
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CN108512797B (en) * 2018-03-21 2020-10-23 电子科技大学 Radar communication integrated signal design method based on orthogonal frequency division multiplexing
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