CN114928375A - Frequency hopping system optimization method with frequency error robustness - Google Patents

Frequency hopping system optimization method with frequency error robustness Download PDF

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CN114928375A
CN114928375A CN202210539058.8A CN202210539058A CN114928375A CN 114928375 A CN114928375 A CN 114928375A CN 202210539058 A CN202210539058 A CN 202210539058A CN 114928375 A CN114928375 A CN 114928375A
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frequency
signal
frequency hopping
transmitting
artificial noise
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CN114928375B (en
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宋长庆
秦俪之
赵宏志
邵士海
唐友喜
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/713—Spread spectrum techniques using frequency hopping
    • H04B1/7136—Arrangements for generation of hop frequencies, e.g. using a bank of frequency sources, using continuous tuning or using a transform
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/713—Spread spectrum techniques using frequency hopping
    • H04B1/7156—Arrangements for sequence synchronisation
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/336—Signal-to-interference ratio [SIR] or carrier-to-interference ratio [CIR]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/382—Monitoring; Testing of propagation channels for resource allocation, admission control or handover
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K3/00—Jamming of communication; Counter-measures
    • H04K3/40—Jamming having variable characteristics
    • H04K3/42—Jamming having variable characteristics characterized by the control of the jamming frequency or wavelength
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a frequency hopping system optimization method with frequency error robustness, which comprises the following steps: s1, a frequency hopping transmitting device transmits a sum signal of an information sequence and an artificial noise sequence after aliasing with a frequency hopping carrier; s2, calculating a mathematical expression of the signal-to-noise ratio at legal receiving equipment under the scene of transmitting and receiving frequency deviation; s3, legal receiving equipment respectively calculatesNA mathematical expression of the signal-to-noise ratio at the illegal eavesdropping device; s4, under a multi-eavesdropping scene with transmitting and receiving frequency offset, designing a frequency hopping system transmitting power distribution scheme with frequency error robustness; and S5.The legal receiving equipment feeds back the power distribution scheme to the frequency hopping transmitting equipment, and the frequency hopping transmitting equipment adjusts the transmission power distribution strategy. The invention can effectively improve the robustness of the system to the frequency synchronization error and improve the existence of the frequency synchronization error by adjusting the transmitting power ratio of the information sequence and the artificial noise in the frequency hopping transmitting equipmentNThe privacy capability of the frequency hopping system when an unauthorized eavesdropping is placed on the device.

Description

Frequency hopping system optimization method with frequency error robustness
Technical Field
The invention relates to the field of secure communication, in particular to a frequency hopping system optimization method with frequency error robustness under a multi-eavesdropping scene.
Background
The frequency hopping communication system under the assistance of artificial noise can effectively resist malicious interference and illegal eavesdropping, and strong safety communication is realized. However, the artificial noise consumes the power budget of the transmitting device and reduces the transmission power of the secret signal, so that the artificial noise needs to be optimized to the transmission power ratio of the secret signal while introducing the artificial noise. Moreover, under the dual effects of complex propagation environment and device engineering errors, frequency offset inevitably exists between transceivers, and the artificial noise suppression effect at the receiver of the own party can be reduced. In addition, a plurality of illegal eavesdropping devices generally exist in the communication environment, and mathematical modeling and optimization need to be performed on the communication environment in a strong eavesdropping scene. In summary, when optimizing the transmission power, the influence of the transceiving frequency offset and the environment of the multi-eavesdropping device needs to be considered, and the artificial noise suppression effect of the own receiving device is optimized.
In view of this, the present patent considers the communication environment in which multiple eavesdropping devices exist, and proposes a frequency hopping system optimization method with frequency error robustness, which can effectively improve the robustness of the system to the frequency synchronization error and improve the secrecy capacity performance of the system in the scene in which multiple illegal eavesdropping devices exist by adjusting the transmission power ratio of the information sequence and the artificial noise.
Disclosure of Invention
The invention aims to overcome the defects of the existing scheme, considers the communication environment with a plurality of eavesdropping devices, and provides a frequency hopping system optimization method with frequency error robustness.
The purpose of the invention is realized by the following technical scheme: a frequency hopping system optimization method with frequency error robustness comprises the following steps:
s1, a frequency hopping transmitting device transmits a sum signal of an information sequence and an artificial noise sequence after aliasing with a frequency hopping carrier;
the step S1 includes the following sub-steps:
s101, frequency hopping transmitting equipment generates an information sequence s (l), wherein the information sequence s (l) is not related to an artificial noise sequence p (l);
superposing the information sequence s (l) and the artificial noise sequence p (l) to obtain a sum signal, carrying out aliasing operation on the sum signal and a frequency hopping carrier wave, and then transmitting an m-th hop transmission signal
Figure BDA0003647549000000011
Expressed as:
Figure BDA0003647549000000021
where l and m are integers and m is 0, s (t) and p (t) are continuous time versions of information sequence s (l) and artificial noise sequence p (l), psi (t) represents the impulse response of the root-raised cosine roll-off filter,' indicates convolution operation, f m Is the carrier frequency of the m-th hop signal,
Figure BDA0003647549000000022
transmitting a signal for the mth hop
Figure BDA0003647549000000023
The initial phase of (a). T ═ L.T b Representing the period of each signal hop, L representing the number of bits per signal hop, T b Representing the duration of the signal per bit. g (T) a rectangular window function representing the start and end times of each hop signal when T e (0, T)]The value is 1 when the value is exceeded, or 0 when the value is not exceeded.
S2, under the scene of receiving and sending frequency offset, firstly, carrying out frequency hopping artificial noise cancellation on legal receiving equipment, then carrying out mathematical modeling on residual artificial noise caused by the frequency offset, and finally calculating a mathematical expression of a signal-to-noise ratio at the legal receiving equipment;
the step S2 includes the following sub-steps:
s201, a radio frequency receiving signal at a legal receiving device may be represented as:
Figure BDA0003647549000000024
wherein
Figure BDA0003647549000000025
τ r And f r Respectively representing the channel gain, propagation delay and frequency offset between a transmitting device and a legitimate receiving device, w r (t) is additive white gaussian noise from the transmitting device to the legitimate receiving device.
After frequency hopping synchronization and matched filtering are performed on the received signal r (t), the obtained baseband received signal r (n) can be represented as:
r(n)＝r s (n)+r p (n)+w r (n),
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003647549000000026
Figure BDA0003647549000000027
respectively representing an information component and an artificial noise component. h is r 、D r And F r Respectively representing equivalent channel gain, normalized propagation delay and normalized frequency offset, w, at a transmitting device to a legitimate receiving device r (n) is w r The discrete form of (t), Ψ (t), is the combination of the raised cosine impulse response function of the transmitting device and the legitimate receiving device, equivalent to the impulse response of the raised cosine roll-off filter.
And S202, the legal receiving equipment executes the reference artificial noise reconstruction operation. It is assumed that the channel gain and propagation delay have been accurately estimated. Performing frequency offset estimation on the baseband signal, and recording the frequency offset estimation error as
Figure BDA0003647549000000028
Wherein
Figure BDA0003647549000000029
Is the frequency offset estimate. Reconstruction of reference artificial noise sequence by using channel gain, propagation delay and frequency offset estimation value
Figure BDA0003647549000000031
The resulting reference sequence can be expressed as:
Figure BDA0003647549000000032
s203, the legal receiving equipment executes artificial noise cancellation operation. Subtracting the reconstructed reference artificial noise sequence from the baseband received signal r (n)
Figure BDA0003647549000000033
It is possible to obtain:
Figure BDA0003647549000000034
wherein
Figure BDA0003647549000000035
The residual artificial noise after the artificial noise cancellation is shown to reduce the signal-to-noise ratio performance of the frequency hopping communication system.
And S204, assuming that the receiver updates the frequency estimation value once every time the receiver receives one-hop signals, namely the frequency compensation period is L symbols. Note r p (n) and
Figure BDA0003647549000000036
respectively, of the fast Fourier transformIs R p (k) And
Figure BDA0003647549000000037
both satisfy:
Figure BDA0003647549000000038
wherein the content of the first and second substances,
Figure BDA0003647549000000039
is an inter-frequency interference component caused by a frequency error. Let P {. be said to calculate the power of {. The
Figure BDA00036475490000000310
Wherein P is p Representing the transmit power of the artificial noise signal p (t).
After the artificial noise cancellation, the frequency domain expression of the residual artificial noise can be expressed as:
Figure BDA00036475490000000311
the power of the residual artifacts may be expressed as:
P{ΔR p (k)}＝[2-2sinc(L·ΔF r )]|h r | 2 P p .
after the legal receiving equipment completes the artificial noise cancellation operation, the signal-to-noise ratio of the obtained signal is recorded as gamma r The expression is:
Figure BDA00036475490000000312
wherein, P s Representing the transmit power of the security signal s (t),
Figure BDA0003647549000000041
representing the normalized transmit power budget at the legitimate receiving device,
Figure BDA0003647549000000042
representing the transmission power allocation factor of the artificial noise sequence and the information sequence at the transmitting device.
S3, the legal receiving equipment respectively performs mathematical modeling on the received signals of the N illegal eavesdropping equipment and respectively calculates mathematical expressions of signal-to-noise ratios of the N illegal eavesdropping equipment;
the step S3 includes the following sub-steps:
s301, suppose that there are N illegal eavesdropping devices in the system. The radio frequency signal received by the ith illegal eavesdropping device is:
Figure BDA0003647549000000043
wherein i is more than or equal to 1 and less than or equal to N,
Figure BDA0003647549000000044
and
Figure BDA0003647549000000045
respectively representing the channel gain, propagation delay and frequency offset between the transmitting device to the i-th illegal eavesdropping device,
Figure BDA0003647549000000046
is additive white gaussian noise at the ith eavesdropping device.
In a strong eavesdropping scene, the illegal eavesdropping equipment can accurately detect and acquire frequency hopping signal parameters, so that the operations of frequency hopping synchronization, frequency hopping release and the like are realized. After the ith illegal eavesdropping device realizes frequency hopping synchronization, the discrete form of the obtained baseband signal can be expressed as:
Figure BDA0003647549000000047
wherein the content of the first and second substances,
Figure BDA0003647549000000048
and
Figure BDA0003647549000000049
respectively representing an equivalent channel gain, a normalized propagation delay and a normalized frequency offset at the i-th transmitting device to the eavesdropping device,
Figure BDA00036475490000000410
is composed of
Figure BDA00036475490000000411
Ψ (n) is a combined form of root-raised cosine roll-off filter impulse responses at the transmitting device and the illegal eavesdropping device, which is equivalent to the impulse response of the raised cosine roll-off filter.
Then calculating the signal-to-noise ratio of the ith illegal eavesdropping device
Figure BDA00036475490000000412
It is defined as the power of the information component divided by the total power of the artificial noise and the thermal noise, and the expression is:
Figure BDA00036475490000000413
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00036475490000000414
representing the normalized power budget at the ith eavesdropping device.
S4, in a multi-eavesdropping scene with transceiving frequency offset, legal receiving equipment calculates the minimum secret capacity performance of the frequency hopping system, and designs a frequency hopping system transmitting power distribution scheme with frequency error robustness;
the step S4 includes the following sub-steps:
s401. in the case of N illegal eavesdropping devices, the security performance of the frequency hopping system can be ensured by using the minimum security capacity C s By weight, the expression is:
Figure BDA0003647549000000051
wherein [. I [ ]] + ＝max{0,*}，
Figure BDA0003647549000000052
h E And η E The channel gain and the normalized power budget at the eavesdropping device with the largest signal-to-noise ratio, respectively.
S402, in order to maximize the system secret capacity, the transmission power distribution ratio of the information sequence and the artificial noise sequence needs to be optimized. Let x be | h r | 2 η r [2-2sinc(L·ΔF r )]+1，y＝|h r | 2 η r +1，z＝|h E | 2 η E +1, then the optimal transmit power allocation problem can be modeled as:
Figure BDA0003647549000000053
Figure BDA0003647549000000054
recording the optimal solution of the transmit power allocation problem as λ * The expression is:
Figure BDA0003647549000000055
wherein alpha is 1 Is shown as
Figure BDA0003647549000000056
And S5, the legal receiving equipment feeds the power distribution scheme back to the frequency hopping transmitting equipment. And according to the feedback parameters, the frequency hopping transmitting equipment adjusts a transmission power distribution strategy.
The invention has the beneficial effects that: the invention provides a frequency hopping system optimization method with frequency error robustness based on a communication environment with a plurality of eavesdropping devices, and the robustness of the system to frequency synchronization errors can be effectively improved by adjusting the transmitting power ratio of an information sequence and artificial noise, and the secrecy capacity performance of the system in a scene with a plurality of illegal eavesdropping devices is improved.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of a frequency hopping communication system in an embodiment;
FIG. 3 is a diagram illustrating an optimal power allocation factor for different frequency offsets in an embodiment;
FIG. 4 is a diagram illustrating security performance of the frequency hopping system under different frequency offsets in an embodiment.
Detailed Description
The technical solutions of the present invention are further described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the following.
As shown in fig. 1, a frequency hopping system optimization method with frequency error robustness includes the following steps:
s1, a frequency hopping transmitting device transmits a sum signal of an information sequence and an artificial noise sequence after aliasing with a frequency hopping carrier;
s2, under the scene of receiving and sending frequency offset, firstly, carrying out frequency hopping artificial noise cancellation on legal receiving equipment, then carrying out mathematical modeling on residual artificial noise caused by the frequency offset, and finally calculating a mathematical expression of a signal-to-noise ratio at the legal receiving equipment;
s3, the legal receiving equipment respectively carries out mathematical modeling on the receiving signals of the N illegal eavesdropping equipment and respectively calculates mathematical expressions of signal-to-noise ratios of the N illegal eavesdropping equipment;
s4, in a multi-eavesdropping scene with transceiving frequency offset, legal receiving equipment calculates the minimum secret capacity performance of the frequency hopping system, and designs a frequency hopping system transmitting power distribution scheme with frequency error robustness;
and S5, the legal receiving equipment feeds back the power distribution scheme to the frequency hopping transmitting equipment. And adjusting the transmission power distribution strategy by the frequency hopping transmission equipment according to the feedback parameters.
Wherein the step S1 includes the following sub-steps:
s101, frequency hopping transmitting equipment generates an information sequence s (l), wherein the information sequence s (l) is not related to an artificial noise sequence p (l);
superposing the information sequence s (l) with the artificial noise sequence p (l) to obtain a sum signal, carrying out aliasing operation on the sum signal and a frequency hopping carrier wave, and then transmitting the m-th hop transmission signal
Figure BDA0003647549000000061
Expressed as:
Figure BDA0003647549000000062
where l and m are integers and m is 0, s (t) and p (t) are continuous time versions of information sequence s (l) and artificial noise sequence p (l), psi (t) represents the impulse response of the root-raised cosine roll-off filter,' indicates convolution operation, f m Is the carrier frequency of the m-th hop signal,
Figure BDA0003647549000000063
transmitting a signal for the mth hop
Figure BDA0003647549000000064
The initial phase of (a). T ═ L.T b Denotes the period of each signal hop, L denotes the number of bits per signal hop, T b Representing the duration of the signal per bit. g (T) a rectangular window function representing the start and end times of each hop signal when T e (0, T)]The value is 1, otherwise 0.
The step S2 includes the following sub-steps:
s201, a radio frequency receiving signal at a legal receiving device may be represented as:
Figure BDA0003647549000000071
wherein
Figure BDA0003647549000000072
τ r And f r Respectively representing the channel gain, propagation delay and frequency offset between the transmitting device and the legitimate receiving device, w r (t) is additive white gaussian noise from the transmitting device to the legitimate receiving device.
After frequency hopping synchronization and matched filtering are performed on the received signal r (t), the resulting baseband received signal r (n) can be represented as:
r(n)＝r s (n)+r p (n)+w r (n),
wherein the content of the first and second substances,
Figure BDA0003647549000000073
Figure BDA0003647549000000074
respectively representing an information component and an artificial noise component. h is r 、D r And F r Respectively representing equivalent channel gain, normalized propagation delay and normalized frequency offset, w, at a transmitting device to a legitimate receiving device r (n) is w r The discrete form of (t), Ψ (t), is the combination of the raised cosine impulse response function of the transmitting device and the legitimate receiving device, equivalent to the impulse response of the raised cosine roll-off filter.
S202, the legal receiving equipment executes the reference artificial noise reconstruction operation. It is assumed that the channel gain and propagation delay have been accurately estimated. Performing frequency offset estimation on the baseband signal, and recording the frequency offset estimation error as
Figure BDA0003647549000000075
Wherein
Figure BDA0003647549000000076
Is the frequency offset estimate. Reconstruction of reference artificial noise sequence by using channel gain, propagation delay and frequency offset estimation value
Figure BDA0003647549000000077
The resulting reference sequence can be expressed as:
Figure BDA0003647549000000078
and S203, the legal receiving equipment executes artificial noise cancellation operation. Subtracting the reconstructed reference artificial noise sequence from the baseband received signal r (n)
Figure BDA0003647549000000079
It is possible to obtain:
Figure BDA00036475490000000710
wherein
Figure BDA00036475490000000711
The residual artificial noise after the artificial noise cancellation is shown to reduce the signal-to-noise ratio performance of the frequency hopping communication system.
And S204, assuming that the receiver updates the frequency estimation value once every time the receiver receives one-hop signals, namely the frequency compensation period is L symbols. Note r p (n) and
Figure BDA00036475490000000712
the fast Fourier transform results of (A) are respectively R p (k) And
Figure BDA00036475490000000713
both satisfy:
Figure BDA0003647549000000081
wherein the content of the first and second substances,
Figure BDA0003647549000000082
is an inter-frequency interference component caused by a frequency error. Let P {. cndot } denote to obtain the power of {. cndot
Figure BDA0003647549000000083
Wherein P is p Representing the transmit power of the artificial noise signal p (t).
After the artificial noise cancellation, the frequency domain expression of the residual artificial noise can be expressed as:
Figure BDA0003647549000000084
the power of the residual artifacts can be expressed as:
P{ΔR p (k)}＝[2-2sinc(L·ΔF r )]|h r | 2 P p .
after the legal receiving equipment completes the artificial noise cancellation operation, the signal-to-noise ratio of the obtained signal is recorded as gamma r The expression is:
Figure BDA0003647549000000085
wherein, P s Representing the transmit power of the security signal s (t),
Figure BDA0003647549000000086
representing the normalized transmit power budget at the legitimate receiving device,
Figure BDA0003647549000000087
representing the transmission power allocation factor of the artificial noise sequence and the information sequence at the transmitting device.
Further, the step S3 includes the following sub-steps:
s301, assuming that N illegal eavesdropping devices exist in the system. The radio frequency signal received by the ith illegal eavesdropping device is:
Figure BDA0003647549000000088
wherein i is more than or equal to 1 and less than or equal to N,
Figure BDA0003647549000000089
and
Figure BDA00036475490000000810
respectively representing the channel gain, propagation delay and frequency offset between the transmitting device to the i-th illegal eavesdropping device,
Figure BDA00036475490000000811
is additive white gaussian noise at the ith eavesdropping device.
In a strong eavesdropping scene, the illegal eavesdropping equipment can accurately detect and acquire frequency hopping signal parameters, so that the operations of frequency hopping synchronization, frequency hopping release and the like are realized. After the ith illegal eavesdropping device realizes frequency hopping synchronization, the discrete form of the obtained baseband signal can be expressed as:
Figure BDA0003647549000000091
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003647549000000092
and
Figure BDA0003647549000000093
respectively representing an equivalent channel gain, a normalized propagation delay and a normalized frequency offset at the i-th transmitting device to the illegal eavesdropping device,
Figure BDA0003647549000000094
is composed of
Figure BDA0003647549000000095
Ψ (n) is a combined form of the root-raised cosine roll-off filter impulse responses at the transmitting device and the illegal eavesdropping device, which is equivalent to the impulse response of the raised cosine roll-off filter.
Then calculating the signal-to-noise ratio of the ith illegal eavesdropping device
Figure BDA0003647549000000096
It is defined as the power of the information component divided by the total power of the artificial noise and the thermal noise, and the expression is:
Figure BDA0003647549000000097
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003647549000000098
representing the normalized power budget at the ith eavesdropping device.
Further, the step S4 includes the following sub-steps:
s401, in the case of N illegal eavesdropping devices, the security performance of the frequency hopping system can use the minimum security capacity C s In terms of scale, the expression is:
Figure BDA0003647549000000099
wherein [ ] A] + ＝max{0,*}，
Figure BDA00036475490000000910
h E And η E The channel gain and the normalized power budget at the eavesdropping device with the largest signal-to-noise ratio, respectively.
S402, in order to maximize the security capacity of the system, the transmission power distribution ratio of the information sequence and the artificial noise sequence needs to be optimized. Let x be | h r | 2 η r [2-2sinc(L·ΔF r )]+1，y＝|h r | 2 η r +1，z＝|h E | 2 η E +1, then the optimal transmit power allocation problem can be modeled as:
Figure BDA0003647549000000101
Figure BDA0003647549000000102
let λ be the optimal solution of the transmit power allocation problem * The expression is:
Figure BDA0003647549000000103
wherein alpha is 1 Is shown as
Figure BDA0003647549000000104
In the embodiment of the present application, the optimal power allocation factor λ in the step S4 * The derivation process of (2) includes:
C s the first derivative on λ is:
Figure BDA0003647549000000105
wherein the content of the first and second substances,
Figure BDA0003647549000000106
order to
Figure BDA0003647549000000107
Then
Xλ 2 +Yλ+Z＝0.
Case 1: consider the case where X is 0, i.e., X + yz is xz + z: when y is less than or equal to z, lambda belongs to phi; when y > z, λ ∈ [0, + ∞).
When y ≦ z, the optimal power allocation factor λ * Is phi.
When Y > Z, Y < 0, Z < 0, and further, when λ ∈ [0, + ∞) are always present
Figure BDA0003647549000000108
Shows C s Monotonically decreasing with increasing λ (λ > 0), and thus the optimum powerDivision factor lambda * Is 0.
Case 2: consider the case where X > 0, i.e., X + yz < xz + z: when y is less than or equal to z, lambda belongs to phi; when y > z, λ ∈ [0, λ ∈ [ X ] B 0 ) Wherein
Figure BDA0003647549000000109
When y ≦ z, the optimal power allocation factor λ * Is phi.
When y > Z, Z < 0 can be obtained. Will X lambda 2 The two solutions of + Y λ + Z ═ 0 are denoted λ 1 And λ 2 The expression is:
Figure BDA0003647549000000111
Figure BDA0003647549000000112
in addition to this, the present invention is,
Figure BDA0003647549000000113
the expression of (a) is:
Figure BDA0003647549000000114
can find out
Figure BDA0003647549000000115
Further obtain the lambda 2 ＜0＜λ 0 ＜λ 1 . Thus, when λ ∈ [0, λ 0 ) When we are constantly at all
Figure BDA0003647549000000116
At this time, the optimal power distribution factor λ * Is 0.
Case 3: consider the case where X < 0, i.e., X + yz > xz + z: when y is less than or equal to z, the feasible domain is lambda epsilon (lambda 0 , + ∞); when y > z, the feasible domain is λ ∈ [0, + ∞).
When y ≦ Z, we have Z > 0,
Figure BDA0003647549000000117
and lambda 2 ＜0＜λ 0 ＜λ 1 . Can obtain the time when the lambda belongs to the lambda (lambda) 0 ,λ 1 ) Time of flight
Figure BDA0003647549000000118
When λ ∈ (λ ∈) 1 , + ∞) time
Figure BDA0003647549000000119
When the optimal power distribution factor is lambda * ＝λ 1 。
When Y > z and z (x + yz) < Y (xz + z), we have Y < 0,
Figure BDA00036475490000001110
z < 0, and further when λ ∈ [0, + ∞)
Figure BDA00036475490000001111
When the optimal power distribution factor is lambda * ＝0。
When Y > z and z (x + yz) ≧ Y (xz + z), we have Y < 0,
Figure BDA00036475490000001112
z is greater than or equal to 0, at the moment lambda 2 ＜0≤λ 1 . When λ ∈ [0, λ ∈ 1 ) Time of flight
Figure BDA00036475490000001113
When λ ∈ (λ ∈) 1 , + ∞) in
Figure BDA00036475490000001114
When the optimal power distribution factor is lambda * ＝λ 1 。
Combining the above analysis, it can be confirmed that λ is in step S4 * Is described in (1).
By combining all the steps, the optimal power distribution factor lambda of the frequency hopping system can be calculated * . Lambda to be solved by a legitimate receiver * After the feedback is sent back to the frequency hopping transmitting equipment, the transmitting equipment adjusts the transmitting power proportion of the information sequence and the artificial noise sequence according to the received optimal power distribution factor, and then the power optimization of the frequency hopping system with frequency error robustness in a multi-eavesdropping scene is achieved.
In an embodiment of the present application, a frequency hopping communication system model is constructed according to the inventive method shown in fig. 1, as shown in fig. 2. The secret signal is a Binary Phase Shift Keying (BPSK) signal and the artificial noise is a zero-mean Gaussian signal. The MATLAB software tool is used for simulating and verifying the power distribution method, and the simulation parameters are shown in the following table:
Figure BDA0003647549000000121
fig. 3 shows the variation trend of the optimal power allocation factor with frequency offset. It can be found that the optimal power allocation factor is decreased as a whole with the increasing frequency offset, which indicates that the transmission power ratio of the artificial noise to the secret signal should be decreased with the increasing frequency offset. By comparing the curves of (i) - (ii), it can be found that the optimal power allocation factor decreases with the increase of the frequency hopping period. In addition, through the comparison of the curves (c) - (d), it can be found that the optimal power allocation factor is continuously reduced along with the improvement of the relative channel quality.
Fig. 4 shows the variation trend of the secret capacity of the frequency hopping system with the frequency offset. It can be seen that as the frequency offset increases, the security capacity of the system as a whole tends to decrease, indicating that the frequency offset significantly reduces the security performance of the system. Through the comparison of the curves (i) - (ii), it can be found that shortening the frequency hopping period can effectively improve the secrecy capacity performance of the system. In addition, through the comparison of the curves- (c), it can be found that the system security performance is continuously increased along with the improvement of the relative channel quality.
The invention has been described and illustrated in detail herein to enable those skilled in the art to understand and practice the invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. A frequency hopping system optimization method with frequency error robustness is characterized in that: the method comprises the following steps:
s1, a frequency hopping transmitting device transmits a sum signal of an information sequence and an artificial noise sequence after aliasing with a frequency hopping carrier;
s2, under the scene of transmitting and receiving frequency offset, firstly, carrying out frequency hopping artificial noise cancellation on legal receiving equipment, then carrying out mathematical modeling on residual artificial noise caused by the frequency offset, and finally calculating the signal-to-noise ratio of the legal receiving equipment;
s3, the legal receiving equipment respectively carries out mathematical modeling on the received signals of the N illegal eavesdropping equipment and respectively calculates the signal-to-noise ratio of the N illegal eavesdropping equipment;
s4, under a multi-eavesdropping scene with receiving and sending frequency deviation, legal receiving equipment calculates the minimum secret capacity performance of the frequency hopping system, and a frequency hopping system transmitting power distribution scheme with frequency error robustness is designed;
and S5, the legal receiving equipment feeds the power distribution scheme back to the frequency hopping transmitting equipment, and the frequency hopping transmitting equipment adjusts a transmission power distribution strategy according to the feedback parameters.
2. The method of claim 1 for optimizing a frequency hopping system with frequency error robustness, wherein: the step S1 includes the following sub-steps:
s101, frequency hopping transmitting equipment generates an information sequence s (l), wherein the information sequence s (l) is not related to an artificial noise sequence p (l);
superposing the information sequence s (l) with the artificial noise sequence p (l) to obtain a sum signal, carrying out aliasing operation on the sum signal and a frequency hopping carrier wave, and then transmitting the m-th hop transmission signal
Figure FDA0003647548990000011
To representComprises the following steps:
Figure FDA0003647548990000012
where l and m are integers and m is 0, s (t) and p (t) are continuous time versions of information sequence s (l) and artificial noise sequence p (l), psi (t) represents the impulse response of the root-raised cosine roll-off filter,' indicates convolution operation, f m Is the carrier frequency of the m-th hop signal,
Figure FDA0003647548990000013
transmitting a signal for the mth hop
Figure FDA0003647548990000014
The initial phase of (a). T ═ L.T b Representing the period of each signal hop, L representing the number of bits per signal hop, T b Representing the duration of the signal per bit. g (T) a rectangular window function representing the start and end times of each hop signal when T e (0, T)]The value is 1, otherwise 0.
3. A method as claimed in claim 1, wherein the frequency hopping system is frequency error robust, and wherein: the step S2 includes the following sub-steps:
s201, under the scene of existence of transceiving frequency deviation, representing the radio frequency receiving signal at a legal receiving device as follows:
Figure FDA0003647548990000015
wherein
Figure FDA0003647548990000021
τ r And f r Respectively representing the channel gain, propagation delay and frequency offset between a transmitting device and a legitimate receiving device, w r (t) additive white gaussian noise from the transmitting device to the legitimate receiving device;
after frequency hopping synchronization and matched filtering are carried out on the received signal r (t), the obtained baseband received signal r (n) is:
r(n)＝r s (n)+r p (n)+w r (n),
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003647548990000022
Figure FDA0003647548990000023
r s (n) and r P (n) representing an information component and an artificial noise component, respectively; h is r 、D r And F r Respectively representing equivalent channel gain, normalized propagation delay and normalized frequency offset, w, at a transmitting device to a legitimate receiving device r (n) is w r In a discrete form of (t), Ψ (t) is a combination of a raised cosine impulse response function of a transmitting device and a legal receiving device, which is equivalent to the impulse response of a raised cosine roll-off filter;
s202, the legal receiving equipment executes a reference artificial noise reconstruction operation:
assuming that the channel gain and propagation delay have been accurately estimated, the frequency offset estimation is performed on the baseband signal, and the frequency offset estimation error is recorded as
Figure FDA0003647548990000024
Wherein
Figure FDA0003647548990000025
Reconstructing a reference artificial noise sequence for the frequency offset estimation by using the channel gain, propagation delay and frequency offset estimation
Figure FDA0003647548990000026
The resulting reference sequence is represented as:
Figure FDA0003647548990000027
s203, the legal receiving equipment executes artificial noise cancellation operation: subtracting the reconstructed reference artificial noise sequence from the baseband received signal r (n)
Figure FDA0003647548990000028
Obtaining:
Figure FDA0003647548990000029
wherein
Figure FDA00036475489900000210
Representing residual artificial noise after the artificial noise is cancelled;
s204, assuming that the receiver updates the frequency estimation value once when receiving one-hop signal, namely the frequency compensation period is L symbols, and r is recorded p (n) and
Figure FDA00036475489900000211
the fast Fourier transform results of (A) are respectively R p (k) And
Figure FDA00036475489900000212
both satisfy:
Figure FDA0003647548990000031
wherein the content of the first and second substances,
Figure FDA0003647548990000032
is an inter-frequency interference component caused by a frequency error; let P {. cndot } denote to obtain the power of {. cndot
Figure FDA0003647548990000033
Wherein P is p Representing the transmit power of the artificial noise signal p (t);
after the artificial noise cancellation, the frequency domain of the residual artificial noise is represented as:
Figure FDA0003647548990000034
the power of the residual artifacts is expressed as:
P{ΔR p (k)}＝[2-2sinc(L·ΔF r )]|h r | 2 P p .
after the legal receiving equipment completes the artificial noise cancellation operation, the signal-to-noise ratio of the obtained signal is recorded as gamma r The expression is:
Figure FDA0003647548990000035
wherein, P s Representing the transmit power of the security signal s (t),
Figure FDA0003647548990000036
representing the normalized transmit power budget at the legitimate receiving device,
Figure FDA0003647548990000037
representing the transmission power allocation factor of the artificial noise sequence and the information sequence at the transmitting device.
4. The method of claim 1 for optimizing a frequency hopping system with frequency error robustness, wherein: the step S3 includes the following sub-steps:
s301, N illegal eavesdropping devices are arranged in the system, and the radio frequency signal received by the ith illegal eavesdropping device is as follows:
Figure FDA0003647548990000038
wherein i is more than or equal to 1 and less than or equal to N,
Figure FDA0003647548990000039
and
Figure FDA00036475489900000310
respectively representing the channel gain, propagation delay and frequency offset between the transmitting device to the i-th illegal eavesdropping device,
Figure FDA00036475489900000311
the additive white Gaussian noise at the ith illegal eavesdropping device is obtained;
in a strong eavesdropping scene, an illegal eavesdropping device accurately detects and acquires frequency hopping signal parameters and realizes frequency hopping synchronization and debounce operation, and after the ith illegal eavesdropping device realizes frequency hopping synchronization, the discrete form of an obtained baseband signal is expressed as:
Figure FDA0003647548990000041
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003647548990000042
and
Figure FDA0003647548990000043
respectively representing an equivalent channel gain, a normalized propagation delay and a normalized frequency offset at the i-th transmitting device to the eavesdropping device,
Figure FDA0003647548990000044
is composed of
Figure FDA0003647548990000045
Ψ (n) is a combined form of root raised cosine roll-off filter impulse responses at the transmitting device and the illegal eavesdropping device, and is equivalent to the impulse response of the raised cosine roll-off filter;
then calculating the signal-to-noise ratio of the ith illegal eavesdropping device
Figure FDA0003647548990000046
It is defined as the power of the information component divided by the total power of the artificial noise and the thermal noise, and the expression is:
Figure FDA0003647548990000047
wherein the content of the first and second substances,
Figure FDA0003647548990000048
representing the normalized power budget at the ith eavesdropping device.
5. A method as claimed in claim 1, wherein the frequency hopping system is frequency error robust, and wherein: the step S4 includes the following sub-steps:
s401, in the case of N illegal eavesdropping devices, the minimum security capacity C is used for the security performance of the frequency hopping system s In terms of scale, the expression is:
Figure FDA0003647548990000049
wherein [ ] A] + ＝max{0,*}，
Figure FDA00036475489900000410
h E And η E Channel gain and normalized power budget at the eavesdropping device with the largest signal-to-noise ratio, respectively;
s402, in order to maximize the system secret capacity, the transmission power distribution proportion of an information sequence and an artificial noise sequence needs to be optimized; let x be | h r | 2 η r [2-2sinc(L·ΔF r )]+1，y＝|h r | 2 η r +1，z＝|h E | 2 η E +1, then the optimal transmit power allocation problem is modeled as:
Figure FDA0003647548990000051
Figure FDA0003647548990000052
recording the optimal solution of the transmit power allocation problem as λ * The expression is:
Figure FDA0003647548990000053
wherein alpha is 1 Is shown as
Figure FDA0003647548990000054
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