CN113297724B - Distributed MIMO radar power and bandwidth joint optimization method based on target positioning - Google Patents
Distributed MIMO radar power and bandwidth joint optimization method based on target positioning Download PDFInfo
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Abstract
The invention discloses a distributed MIMO radar power and bandwidth joint optimization method based on target positioning, which comprises the steps of firstly, constructing a scene of target positioning of a distributed MIMO radar system; secondly, CRLB of target position estimation is adopted as a target positioning performance index; then, taking the minimum total transmitting power of the distributed MIMO radar system as an optimization target, taking the target positioning performance and the distributed MIMO radar system resources as constraint conditions, and establishing a distributed MIMO radar power and bandwidth joint optimization model based on target positioning; and finally, solving the constructed optimization model by using an alternate multiplier method. The method not only meets the requirement of the distributed MIMO radar system on the target positioning precision, but also can minimize the total transmitting power of the distributed MIMO radar system under the condition of any system resource constraint.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly provides a distributed MIMO radar power and bandwidth joint optimization method based on target positioning.
Background
A distributed Multiple-Input Multiple-Output (MIMO) radar system transmits a specific waveform signal by using Multiple radar transmitting antennas, and processes echoes through Multiple radar receiving antennas to estimate the state of a target. Compared with the traditional radar system, the system has the advantages of beam diversity and space diversity, and has become one of the hot spots for the research of new system radar in the last decade. Theoretically, the larger the transmission power and the effective bandwidth of the distributed MIMO radar system, the higher the accuracy of parameter estimation on the target. However, in practical application, the total transmitting power of the distributed MIMO radar system needs to be reduced by means of power and bandwidth optimization allocation.
For the problem of power optimization allocation in target positioning of a distributed MIMO radar system, scholars have already made a lot of research. Foremost, foreign scholars have adopted the Lower cricket-Rao Lower Bound (CRLB) as an optimization index, using constraint relaxation and region decomposition algorithms to optimize power distribution. Subsequently, in order to evaluate the influence of the speed estimation accuracy on the power distribution, domestic researchers derive equivalent fischer information matrices (Equivalent Fisher Information Matrix, EFIM) containing both the position and speed information of the target, and use this as an optimization index, and then solve the power distribution problem by using a Semi-definite programming (Semi-Definite Programming, SDP) algorithm.
However, careful study has found that current scholars only give allocation algorithms in cases where the power and bandwidth are greater than zero, but in other cases, such as: when the power and the bandwidth have upper and lower limits, whether the proposed optimization algorithm is still effective or not is worth deeply thinking and exploring.
In view of this, the patent proposes a distributed MIMO radar power and bandwidth joint optimization method based on target positioning, and optimizes the power and bandwidth of each radar transmitter at the same time, so as to achieve the purpose of minimizing the system radiation power, aiming at the power and bandwidth optimization problem of bilateral constraint which has not been considered in the prior art.
Disclosure of Invention
The invention aims to: the invention provides a distributed MIMO radar power and bandwidth joint optimization method based on target positioning, which not only meets the requirement of a distributed MIMO radar system on target positioning precision, but also can minimize the total transmitting power of the distributed MIMO radar system under the condition of any system resource constraint.
The technical scheme is as follows: the invention discloses a distributed MIMO radar power and bandwidth joint optimization method based on target positioning, which comprises the following steps:
(1) Constructing a target positioning scene of a distributed MIMO radar system;
(2) CRLB of target position estimation is adopted as a target positioning performance index;
(3) Taking the minimum total transmitting power of the distributed MIMO radar system as an optimization target, taking the meeting of target positioning performance and distributed MIMO radar system resources as constraint conditions, and establishing a distributed MIMO radar power and bandwidth joint optimization model based on target positioning;
(4) And (3) solving the optimization model constructed in the step (3) by using an alternate multiplier method.
Further, the distributed MIMO radar system in step (1) is composed of M radar transmitters and N radar receivers; the radar transmitter transmits incoherent orthogonal signals, and the radar receiver receives signals transmitted by M radar transmitters reflected by the target at the same time and processes the signals to obtain the position information of the target.
Further, the trace of CRLB of the target location in the step (2) is:
Where tr (·) represents the trace of the matrix; (. Cndot.) T represents a matrix transpose; the product of Hadamard; p= [ P 1,p2,…pM]T and b= [ B 1,B2,…BM]T are transmission power and bandwidth vectors, respectively, where P i, i=1, … 2, M and B i, i=1, 2, …, M represent power and bandwidth ; H＝a+b,A＝abT-ccT;a＝[a1,a2,…aM]T、b＝[b1,b2,…bM]T and c= [ c 1,c2,…cM]T, respectively, of the i-th radar transmitter transmission signal; position coordinates of an mth radar transmitter; /(I) Position coordinates of the nth radar receiver; (x, y) is the position coordinates of the target; q is the cumulative number of pulses; g n is the signal processing gain of the nth radar receiver; xi mn is the radar reflection section on the signal propagation path received by the nth radar receiver after the mth radar transmitter transmits the signal reflected by the target; c is the speed of light; /(I)Is zero-mean gaussian white noise.
Further, in the step (3), the distributed MIMO radar power and bandwidth joint optimization model based on target positioning is:
Wherein epsilon p is a preset target position estimation accuracy threshold; b total is the total bandwidth of the distributed MIMO radar system; b max and B min are the upper and lower bounds of the transmit signal bandwidth of each radar transmit antenna, respectively; p max and p min are the upper and lower bounds, respectively, of the transmit signal power of each radar transmit antenna.
Further, the implementation process of the step (4) is as follows:
Using the lagrangian multiplier method, writing (2) as follows:
L2(P,B,η,μ)＝f(P)+η(g(P,B)-εp)+μ(h(B)-Btotal) (7)
Where f (P) = TP;h(B)＝1T B, Η and μ are lagrange multipliers;
using the alternate multiplier algorithm, the variables of (3) are updated as follows:
In the method, in the process of the invention, Representing minimizing an objective function by optimizing power; /(I)Representing minimizing an objective function by optimizing bandwidth; p k、Bk、ηk and μ k are power, bandwidth, and multiplier values after k updates; p k+1、Bk+1、ηk+1 and μ k+1 are power, bandwidth and multiplier values after k+1 updates; ρ 1 and ρ 2 are update steps of the multipliers η and μ, respectively.
The beneficial effects are that: compared with the prior art, the invention has the beneficial effects that: the invention not only meets the requirement of the distributed MIMO radar system on the target positioning precision, but also can minimize the total transmitting power of the distributed MIMO radar system under the condition of any system resource constraint by adopting the alternative multiplier rule.
Drawings
FIG. 1 is a flow chart of the present invention;
Fig. 2 is a graph of the distribution results of the transmission power and the transmission bandwidth according to the present invention compared with the prior art, wherein (a) the distribution results of the power are compared with each other; (b) bandwidth allocation results versus graph.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The invention provides a distributed MIMO radar power and bandwidth joint optimization method based on target positioning, which is shown in fig. 1 and specifically comprises the following steps:
step 1: and constructing a target positioning scene of the distributed MIMO radar system.
Considering a distributed MIMO radar system consisting of M radar transmitters and N radar receivers, the radar transmitters transmit incoherent orthogonal signals, and the radar receivers can simultaneously receive the signals transmitted by the M radar transmitters reflected by the target and process the signals to obtain the position information of the target.
Step 2: the CRLB trace of the target position estimate is used as a measure of target positioning performance.
The trace of CRLB for target location can be expressed as:
Where tr (·) represents the trace of the matrix; (. Cndot.) T represents a matrix transpose; the product of Hadamard; p= [ P 1,p2,…pM]T and b= [ B 1,B2,…BM]T are transmission power and bandwidth vectors, respectively, where P i, i=1, 2, M and B i, i=1, 2, …, M represents power and bandwidth ; H＝a+b,A＝abT-ccT;a＝[a1,a2,…aM]T、b＝[b1,b2,…bM]T and c= [ c 1,c2,…cM]T, respectively, of the i-th radar transmitter transmission signal; position coordinates of an mth radar transmitter; /(I) Position coordinates of the nth radar receiver; (x, y) is the position coordinates of the target; q is the cumulative number of pulses; g n is the signal processing gain of the nth radar receiver; xi mn is the radar reflection section (RCS) on the signal propagation path that the mth radar transmitter transmits, after reflection by the target, received by the nth radar receiver; c is the speed of light; /(I)Is zero-mean gaussian white noise.
Step 3: and establishing a distributed MIMO radar power and bandwidth joint optimization model based on target positioning.
Taking the minimum total transmitting power of the distributed MIMO radar system as an optimization target, taking the meeting of target positioning performance and distributed MIMO system resources as constraint conditions, and establishing a distributed MIMO radar power and bandwidth joint optimization model based on target positioning, wherein the model is expressed as:
Wherein epsilon p is a preset target position estimation accuracy threshold; b total is the total bandwidth of the distributed MIMO radar system; b max and B min are the upper and lower bounds of the transmit signal bandwidth of each radar transmit antenna, respectively; p max and p min are the upper and lower bounds, respectively, of the transmit signal power of each radar transmit antenna.
Step 4: and solving the distributed MIMO radar power and bandwidth joint optimization model based on target positioning by using an alternate multiplier method.
The invention solves the optimization model by adopting an alternate multiplier method. Firstly, fixing a bandwidth B and optimizing power P; secondly, fixing the power P, optimizing the bandwidth B, and alternately optimizing the power P and the bandwidth B in a reciprocating manner; finally, until the power P and the bandwidth B are converged to a certain constant value, an optimal solution is obtained by taking the transmission power P and the transmission signal bandwidth B with the lowest total radiation power of the system as a model under the condition that the constraint conditions are met, and the specific process is as follows:
First, (6) is written as follows using the lagrange multiplier method:
L2(P,B,η,μ)＝f(P)+η(g(P,B)-εp)+μ(h(B)-Btotal) (3)
Where f (P) = TP;h(B)＝1T B, Η and μ are Lagrangian multipliers.
Next, using the alternate multiplier algorithm, the variables of equation (7) are updated as follows:
In the method, in the process of the invention, Representing minimizing an objective function by optimizing power; /(I)Representing minimizing an objective function by optimizing bandwidth; p k、Bk、ηk and μ k are power, bandwidth, and multiplier values after k updates; p k+1、Bk+1、ηk+1 and μ k+1 are power, bandwidth and multiplier values after k+1 updates; ρ 1 and ρ 2 are multipliers, respectively.
FIG. 2 is a graph comparing the output results of two algorithms when 0.1.ltoreq.p m≤5,1≤Bm.ltoreq.4 with the existing algorithm of the present invention: wherein fig. 2 (a) is a comparison of power allocation results; fig. 2 (b) is a comparison graph of bandwidth allocation results. It can be seen from fig. 2 that the method of the present patent has significant advantages over the prior art in terms of minimizing the total power of the system for the power and bandwidth joint optimization problem with bilateral constraints.
Claims (4)
1. The distributed MIMO radar power and bandwidth joint optimization method based on target positioning is characterized by comprising the following steps of:
(1) Constructing a target positioning scene of a distributed MIMO radar system;
(2) CRLB of target position estimation is adopted as a target positioning performance index;
(3) Taking the minimum total transmitting power of the distributed MIMO radar system as an optimization target, taking the meeting of target positioning performance and distributed MIMO radar system resources as constraint conditions, and establishing a distributed MIMO radar power and bandwidth joint optimization model based on target positioning;
(4) Solving the optimization model constructed in the step (3) by using an alternate multiplier method;
The trace of CRLB for the target location described in step (2) is:
Where tr (·) represents the trace of the matrix; (. Cndot.) T represents a matrix transpose; the product of Hadamard; p= [ P 1,p2,…pM]T and b= [ B 1,B2,…BM]T are transmission power and bandwidth vectors, respectively, where P i, i=1, 2, …, M and B i, i=1, 2, …, M represents the power and bandwidth ;H＝a+b,A＝abT-ccT;a＝[a1,a2,…aM]T、b＝[b1,b2,…bM]T and c= [ c 1,c2,…cM]T, respectively, of the i-th radar transmitter transmission signal; position coordinates of an mth radar transmitter; /(I) Position coordinates of the nth radar receiver; (x, y) is the position coordinates of the target; q is the cumulative number of pulses; g n is the signal processing gain of the nth radar receiver; xi mn is the radar reflection section on the signal propagation path received by the nth radar receiver after the mth radar transmitter transmits the signal reflected by the target; c is the speed of light; /(I)Is zero-mean gaussian white noise.
2. The target positioning-based distributed MIMO radar power and bandwidth joint optimization method of claim 1, wherein the distributed MIMO radar system of step (1) is composed of M radar transmitters and N radar receivers; the radar transmitter transmits incoherent orthogonal signals, and the radar receiver receives signals transmitted by M radar transmitters reflected by the target at the same time and processes the signals to obtain the position information of the target.
3. The target positioning-based distributed MIMO radar power and bandwidth joint optimization method of claim 1, wherein the target positioning-based distributed MIMO radar power and bandwidth joint optimization model in step (3) is:
Wherein epsilon p is a preset target position estimation accuracy threshold; b total is the total bandwidth of the distributed MIMO radar system; b max and B min are the upper and lower bounds of the transmit signal bandwidth of each radar transmit antenna, respectively; p max and p min are the upper and lower bounds, respectively, of the transmit signal power of each radar transmit antenna.
4. The method for jointly optimizing power and bandwidth of a distributed MIMO radar based on target positioning according to claim 1, wherein the implementation process of step (4) is as follows:
Using the lagrangian multiplier method, writing (2) as follows:
L2(P,B,η,μ)＝f(P)+η(g(P,B)-εp)+μ(h(B)-Btotal) (3)
Where f (P) = TP;h(B)＝1T B, Η and μ are lagrange multipliers;
using the alternate multiplier algorithm, the variables of (3) are updated as follows:
In the method, in the process of the invention, Representing minimizing an objective function by optimizing power; /(I)Representing minimizing an objective function by optimizing bandwidth; p k、Bk、ηk and μ k are power, bandwidth, and multiplier values after k updates; p k+1、Bk+1、ηk+1 and μ k+1 are power, bandwidth and multiplier values after k+1 updates; ρ 1 and ρ 2 are update steps of the multipliers η and μ, respectively.
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