CN108717180B - Networking radar power distribution method based on Stark-Berger game - Google Patents

Networking radar power distribution method based on Stark-Berger game Download PDF

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CN108717180B
CN108717180B CN201810727949.XA CN201810727949A CN108717180B CN 108717180 B CN108717180 B CN 108717180B CN 201810727949 A CN201810727949 A CN 201810727949A CN 108717180 B CN108717180 B CN 108717180B
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时晨光
汪飞
李海林
周建江
夏伟杰
孔莹莹
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/87—Combinations of radar systems, e.g. primary radar and secondary radar

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Abstract

The invention discloses a networking radar power distribution method based on a Starkelberg game, which comprises the following steps of: s1: acquiring path propagation loss between each radar and a target and between each radar and a communication system in a networking radar system; s2: establishing a networking radar power distribution model based on a non-cooperative game according to a preset target detection signal-to-interference-and-noise ratio threshold and each radar transmitting power upper limit; s3: calculating game income obtained by the communication system from a networking radar; s4: acquiring an iterative expression of the transmitting power of each radar in the networking radar system; s5: and the communication system increases the unit interference power price c, broadcasts to each radar, and continuously iteratively updates until the utility function of the communication system is converged, wherein the obtained emission power value of each radar meeting the constraint condition is obtained. The invention not only minimizes the transmitting power of each radar under the condition of meeting the detection performance of a given target, but also maximizes the game utility of the communication system.

Description

Networking radar power distribution method based on Stark-Berger game
Technical Field
The invention relates to the field of radar signal processing, in particular to a networking radar power distribution method.
Background
The spectrum sharing technology can improve the spectrum utilization rate, and becomes a research hotspot in the field of spectrum resource management in recent years. The power control technology is adopted in the networking radar-communication system frequency spectrum coexistence environment, so that the interference of the networking radar to the communication system can be reduced, the radio frequency stealth performance of the networking radar can be improved, and the mutual interference among the radars can be reduced, thereby realizing the frequency spectrum sharing of the networking radar and the communication system.
The existing method provides a networking radar power control idea based on a non-cooperative game in a frequency spectrum coexistence environment, improves the radio frequency stealth performance of a networking radar system in the frequency spectrum coexistence environment, but does not fully mobilize the positivity of a communication system, and does not consider the game income of the communication system.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects in the prior art, the invention provides a networking radar power distribution method based on a Starkelberg game by considering the coexistence of a networking radar and a communication system frequency spectrum.
The technical scheme is as follows: the invention relates to a networking radar power distribution method based on a Stark-Berger game, which comprises the following steps of:
s1: acquiring path propagation loss between each radar and a target and between each radar and a communication system in a networking radar system;
s2: establishing a networking radar power distribution model based on a non-cooperative game according to a preset target detection signal-to-interference-and-noise ratio threshold and each radar transmitting power upper limit;
s3: calculating game income obtained by the communication system from a networking radar;
s4: acquiring an iterative expression of the transmitting power of each radar in the networking radar system;
s5: and the communication system increases the unit interference power price c, broadcasts to each radar, and continuously iteratively updates until the utility function of the communication system is converged, wherein the obtained emission power value of each radar meeting the constraint condition is obtained.
Further, in step S1, path propagation losses between each radar and the target and between each radar and the communication system in the networking radar system are obtained according to equation (1):
Figure BDA0001720160510000021
in the formula (1), the reaction mixture is,
Figure BDA0001720160510000022
for the path propagation loss from radar i to the target and then to radar i,
Figure BDA0001720160510000023
for the path propagation loss from radar i to target to radar j,
Figure BDA0001720160510000024
for the direct wave path propagation loss from radar i to radar j,
Figure BDA0001720160510000025
for the direct path propagation loss, G, of radar i to the communication systemtFor the transmitting antenna gain of each radar, GrIs receive antenna gain, G ', of each radar'tAntenna gain, G ', is transmitted for each radar sidelobe'rFor each radar side lobe receiving antenna gain,
Figure BDA0001720160510000026
is the radar cross section of the target relative to radar i,
Figure BDA0001720160510000027
is the radar cross section of the target relative to radar i and radar j, lambda is the radar emission signal wavelength, RiDistance between radar i and target, RjDistance between radar j and target, di,jDistance between radar i and radar j, diIs the distance between radar i and the communication system.
Further, in step S2, a networking radar power distribution model based on a non-cooperative game is established according to equation (2):
Figure BDA0001720160510000028
in the formula (2), PiIs the transmission power of radar i, NTFor the total number of radars in a networked radar system, Ui(Pi,P-i) For the game utility function of the radar i,
Figure BDA0001720160510000029
for a predetermined signal-to-noise threshold, gamma, of radar iiFor radar iSignal to noise ratio of aiA target detection performance weight coefficient of a radar i, n is the number of times of iteration, biAs a penalty factor for the radar i,
Figure BDA00017201605100000210
propagation loss of path from radar i to target and then to radar i, Pi maxDenotes the upper limit of the transmission power, P, of radar ii dRepresenting the transmit power of radar i at the d-th iteration.
Further, the signal-to-noise ratio γ of the radar iiCalculated according to equation (3):
Figure BDA0001720160510000031
in the formula (3), ci,jRepresenting the cross-correlation coefficient, P, between radar i and radar jCIn order to transmit power for the communication system,
Figure BDA0001720160510000032
in order for the noise power of the radar receiver to be,
Figure BDA0001720160510000033
for the path propagation loss from radar i to target to radar j,
Figure BDA0001720160510000034
for the direct wave path propagation loss from radar i to radar j,
Figure BDA0001720160510000035
for the propagation loss of the radar i to the direct path of the communication system, PjIs the transmit power of radar j.
Further, in step S3, the game profit is calculated according to equation (4):
Figure BDA0001720160510000036
in the formula (4), UCFor gaming benefits of communication systems, NTC is given as the total number of radars in the networked radar system, P is the price per unit interference poweri *For the transmit power at which radar i reaches nash equilibrium,
Figure BDA0001720160510000037
for the direct path propagation loss, Q, of radar i to the communication systemthA maximum interference threshold is set for the communication system.
Further, in step S4, the transmission power iterative expression of each radar is calculated according to equation (5):
Figure BDA0001720160510000038
in the formula (5), Pi (ite+1)Is the transmission power, P, of radar i at the ite +1 iterationi (ite)For the transmission power of radar i at the ite iteration,
Figure BDA0001720160510000039
for the signal-to-noise ratio of radar i at the ite iteration,
Figure BDA00017201605100000310
the penalty factor for radar i at the ite iteration,
Figure BDA00017201605100000311
the weight coefficient of the target detection performance of the radar i during the iteration of the second time, n is the number of times of iteration,
Figure BDA00017201605100000312
propagation loss of path from radar i to target and then to radar i, Pi maxDenotes the upper limit of the transmission power, P, of radar ii dRepresenting the transmit power of radar i at the d-th iteration,
Figure BDA00017201605100000313
for a predetermined signal-to-noise ratio threshold of radar i。
Has the advantages that: the invention discloses a networking radar power distribution method based on a Stackelberg game, which comprises the steps of taking a communication system as a game leader, taking a networking radar as a game follower, setting unit interference price for each radar by the communication system, optimally distributing the own transmitting power among the networking radars through a non-cooperative game on the basis, minimizing the transmitting power of each radar in the networking radar system under the condition of meeting the target detection performance constraint, the networking radar total interference power constraint and the radar transmitting power constraint, and achieving the purpose of improving the radio frequency stealth performance of the networking radar in the spectrum coexistence environment. The invention not only minimizes the transmitting power of each radar under the condition of meeting the detection performance of a given target, but also maximizes the game utility of the communication system as much as possible, ensures the normal communication of the communication system and improves the participation enthusiasm of the communication system.
Drawings
Fig. 1 is a starkeberg game model under the coexistence environment of the networking radar and the communication system frequency spectrum in the embodiment of the present invention;
fig. 2 is a flow chart of the networking radar power distribution of the starkeberg game model in the embodiment of the present invention.
Detailed Description
The specific embodiment discloses a networking radar power distribution method based on a Starkelberg game, wherein the Starkelberg game is called a Stackelberg game in English, and fig. 1 shows the structure of the Stackelberg game. As shown in fig. 2, the method comprises the following steps:
s1: acquiring path propagation loss between each radar and a target and between each radar and a communication system in a networking radar system;
s2: establishing a networking radar power distribution model based on a non-cooperative game according to a preset target detection signal-to-interference-and-noise ratio threshold and each radar transmitting power upper limit;
s3: calculating game income obtained by the communication system from a networking radar;
s4: acquiring an iterative expression of the transmitting power of each radar in the networking radar system;
s5: and the communication system increases the unit interference power price c, broadcasts to each radar, and continuously iteratively updates until the utility function of the communication system is converged, wherein the obtained emission power value of each radar meeting the constraint condition is obtained.
In step S1, path propagation loss between each radar and the target and between each radar and the communication system in the networking radar system is obtained according to formula (1):
Figure BDA0001720160510000051
in the formula (1), the reaction mixture is,
Figure BDA0001720160510000052
for the path propagation loss from radar i to the target and then to radar i,
Figure BDA0001720160510000053
for the path propagation loss from radar i to target to radar j,
Figure BDA0001720160510000054
for the direct wave path propagation loss from radar i to radar j,
Figure BDA0001720160510000055
for the direct path propagation loss, G, of radar i to the communication systemtFor the transmitting antenna gain of each radar, GrIs receive antenna gain, G ', of each radar'tAntenna gain, G ', is transmitted for each radar sidelobe'rFor each radar side lobe receiving antenna gain,
Figure BDA0001720160510000056
is the radar cross section of the target relative to radar i,
Figure BDA0001720160510000057
is the radar cross section of the target relative to radar i and radar j, lambda is the radar emission signal wavelength, RiBetween radar i and targetDistance, RjDistance between radar j and target, di,jDistance between radar i and radar j, diIs the distance between radar i and the communication system.
In step S2, a networking radar power distribution model based on a non-cooperative game is established according to equation (2):
Figure BDA0001720160510000058
in the formula (2), PiIs the transmission power of radar i, NTFor the total number of radars in a networked radar system, Ui(Pi,P-i) For the game utility function of the radar i,
Figure BDA0001720160510000059
for a predetermined signal-to-noise threshold, gamma, of radar iiIs the signal-to-noise ratio of radar i, aiA target detection performance weight coefficient of a radar i, n is the number of times of iteration, biAs a penalty factor for the radar i,
Figure BDA00017201605100000510
propagation loss of path from radar i to target and then to radar i, Pi maxDenotes the upper limit of the transmission power, P, of radar ii dRepresenting the transmit power of radar i at the d-th iteration.
Signal-to-noise ratio gamma of radar iiCalculated according to equation (3):
Figure BDA0001720160510000061
in the formula (3), ci,jRepresenting the cross-correlation coefficient, P, between radar i and radar jCIn order to transmit power for the communication system,
Figure BDA0001720160510000062
in order for the noise power of the radar receiver to be,
Figure BDA0001720160510000063
for the path propagation loss from radar i to target to radar j,
Figure BDA0001720160510000064
for the direct wave path propagation loss from radar i to radar j,
Figure BDA0001720160510000065
for the propagation loss of the radar i to the direct path of the communication system, PjIs the transmit power of radar j.
In step S3, the game yield is calculated according to equation (4):
Figure BDA0001720160510000066
in the formula (4), UCFor gaming benefits of communication systems, NTC is given as the total number of radars in the networked radar system, P is the price per unit interference poweri *For the transmit power at which radar i reaches nash equilibrium,
Figure BDA0001720160510000067
for the direct path propagation loss, Q, of radar i to the communication systemthA maximum interference threshold is set for the communication system.
In step S4, the transmission power iterative expression of each radar is calculated according to equation (5):
Figure BDA0001720160510000068
in the formula (5), Pi (ite+1)Is the transmission power, P, of radar i at the ite +1 iterationi (ite)For the transmission power of radar i at the ite iteration,
Figure BDA0001720160510000069
for the signal-to-noise ratio of radar i at the ite iteration,
Figure BDA00017201605100000610
the penalty factor for radar i at the ite iteration,
Figure BDA00017201605100000611
the weight coefficient of the target detection performance of the radar i during the iteration of the second time, n is the number of times of iteration,
Figure BDA00017201605100000612
propagation loss of path from radar i to target and then to radar i, Pi maxDenotes the upper limit of the transmission power, P, of radar ii dRepresenting the transmit power of radar i at the d-th iteration,
Figure BDA00017201605100000613
is a preset signal-to-noise ratio threshold of the radar i.

Claims (5)

1. A networking radar power distribution method based on a Stark-Berger game is characterized in that: the method comprises the following steps:
s1: acquiring path propagation loss between each radar and a target and between each radar and a communication system in a networking radar system according to the formula (1):
Figure FDA0003038836800000011
in the formula (1), the reaction mixture is,
Figure FDA0003038836800000012
for the path propagation loss from radar i to the target and then to radar i,
Figure FDA0003038836800000013
for the path propagation loss from radar i to target to radar j,
Figure FDA0003038836800000014
for radar i to radar jThe propagation loss of the arriving wave path is reduced,
Figure FDA0003038836800000015
for the direct path propagation loss, G, of radar i to the communication systemtFor the transmitting antenna gain of each radar, GrGain of receiving antenna for each radar, Gt'gain of each radar sidelobe transmitting antenna, G'rFor each radar side lobe receiving antenna gain,
Figure FDA0003038836800000016
is the radar cross section of the target relative to radar i,
Figure FDA0003038836800000017
is the radar cross section of the target relative to radar i and radar j, lambda is the radar emission signal wavelength, RiDistance between radar i and target, RjDistance between radar j and target, di,jDistance between radar i and radar j, diDistance between radar i and the communication system;
s2: establishing a networking radar power distribution model based on a non-cooperative game according to a preset target detection signal-to-interference-and-noise ratio threshold and each radar transmitting power upper limit;
s3: calculating game income obtained by the communication system from a networking radar;
s4: acquiring an iterative expression of the transmitting power of each radar in the networking radar system;
s5: and the communication system increases the unit interference power price c, broadcasts to each radar, and continuously iteratively updates until the utility function of the communication system is converged, wherein the obtained emission power value of each radar meeting the constraint condition is obtained.
2. The networking radar power distribution method based on the Starkelberg game of claim 1, wherein: in the step S2, a networking radar power distribution model based on a non-cooperative game is established according to the formula (2):
Figure FDA0003038836800000021
in the formula (2), PiIs the transmission power of radar i, NTFor the total number of radars in a networked radar system, Ui(Pi,P-i) For the game utility function of the radar i,
Figure FDA0003038836800000022
for a predetermined signal-to-noise threshold, gamma, of radar iiIs the signal-to-noise ratio of radar i, aiA target detection performance weight coefficient of a radar i, n is the number of times of iteration, biAs a penalty factor for the radar i,
Figure FDA0003038836800000023
propagation loss of path from radar i to target and then to radar i, Pi maxDenotes the upper limit of the transmission power, P, of radar ii dRepresenting the transmit power of radar i at the d-th iteration.
3. The networking radar power distribution method based on the Starkelberg game of claim 2, wherein: signal-to-noise ratio gamma of the radar iiCalculated according to equation (3):
Figure FDA0003038836800000024
in the formula (3), ci,jRepresenting the cross-correlation coefficient, P, between radar i and radar jCIn order to transmit power for the communication system,
Figure FDA0003038836800000025
in order for the noise power of the radar receiver to be,
Figure FDA0003038836800000026
for the path from radar i to target to radar jThe loss of the radial propagation is reduced,
Figure FDA0003038836800000027
for the direct wave path propagation loss from radar i to radar j,
Figure FDA0003038836800000028
for the propagation loss of the radar i to the direct path of the communication system, PjIs the transmit power of radar j.
4. The networking radar power distribution method based on the Starkelberg game of claim 1, wherein: in the step S3, the game profit is calculated according to equation (4):
Figure FDA0003038836800000029
in the formula (4), UCFor gaming benefits of communication systems, NTC is given as the total number of radars in the networked radar system, P is the price per unit interference poweri *For the transmit power at which radar i reaches nash equilibrium,
Figure FDA00030388368000000210
propagation loss i, Q of direct wave path from radar i to communication systemthA maximum interference threshold is set for the communication system.
5. The networking radar power distribution method based on the Starkelberg game of claim 1, wherein: in step S4, the transmission power iterative expression of each radar is calculated according to equation (5):
Figure FDA0003038836800000031
in the formula (5), Pi (ite+1)Is the radar at the time of the ite +1 iterationi transmission power, Pi (ite)For the transmission power of radar i at the ite iteration,
Figure FDA0003038836800000032
for the signal-to-noise ratio of radar i at the ite iteration,
Figure FDA0003038836800000033
the penalty factor for radar i at the ite iteration,
Figure FDA0003038836800000034
the weight coefficient of the target detection performance of the radar i during the iteration of the second time, n is the number of times of iteration,
Figure FDA0003038836800000035
propagation loss of path from radar i to target and then to radar i, Pi maxDenotes the upper limit of the transmission power, P, of radar ii dRepresenting the transmit power of radar i at the d-th iteration,
Figure FDA0003038836800000036
is a preset signal-to-noise ratio threshold of the radar i.
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