CN114928375B - Frequency hopping system optimization method with frequency error robustness - Google Patents
Frequency hopping system optimization method with frequency error robustness Download PDFInfo
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Abstract
The invention discloses a frequency hopping system optimization method with frequency error robustness, which comprises the following steps: s1, at a frequency hopping transmitting device, mixing a sum signal of an information sequence and an artificial noise sequence with a frequency hopping carrier wave and transmitting the mixture; s2, calculating a mathematical expression of a signal-to-noise ratio at legal receiving equipment under the condition that receiving and transmitting frequency offset exists; s3, respectively calculating by legal receiving equipmentNMathematical expressions of signal-to-noise ratios at the illegal eavesdropping device; s4, designing a transmission power distribution scheme of the frequency hopping system with frequency error robustness under a multi-eavesdropping scene with receiving and transmitting frequency offset; s5, the legal receiving device feeds back the power distribution scheme to the frequency hopping transmitting device, and the frequency hopping transmitting device adjusts the transmitting power distribution strategy. The invention can effectively improve the robustness of the system to the frequency synchronization error and the existence of the system by adjusting the transmission power proportion of the information sequence and the artificial noise in the frequency hopping transmission equipmentNThe secret capacity performance of the frequency hopping system when an illegal eavesdropping device.
Description
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 artificial noise auxiliary lower frequency hopping communication system 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 transmitting power of the secret signal, so that the ratio of the artificial noise to the transmitting power of the secret signal needs to be optimized while the artificial noise is introduced. In addition, 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 own receiver can be reduced. In addition, there are generally a plurality of illegal interception devices in a communication environment, and mathematical modeling and optimization of the communication environment in a strong interception scene are required. In summary, the influence of the receiving frequency offset and the environment of the multi-eavesdropping device needs to be considered in the process of optimizing the transmitting power, so that the artificial noise suppression effect of the receiving device on the own side is optimized.
In view of this, this patent considers the communication environment that has a plurality of eavesdropping equipment, has put forward a frequency hopping system optimization method with frequency error robustness, through adjusting the transmission power proportion of information sequence and artificial noise, can improve the robustness of system to the frequency synchronization error effectively, promotes the secret capacity performance of system under the scene that has a plurality of illegal eavesdropping equipment.
Disclosure of Invention
The invention aims to overcome the defects of the prior scheme, considers the communication environment with a plurality of eavesdropping devices, and provides a frequency hopping system optimization method with frequency error robustness.
The aim 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, at a frequency hopping transmitting device, mixing a sum signal of an information sequence and an artificial noise sequence with a frequency hopping carrier wave and transmitting the mixture;
said step S1 comprises the sub-steps of:
s101, generating an information sequence s (l) by frequency hopping transmitting equipment, wherein the information sequence s (l) is not related to an artificial noise sequence p (l);
the information sequence s (l) and the artificial noise sequence p (l) are overlapped to obtain a sum signal, the sum signal and the frequency hopping carrier wave are transmitted after being subjected to aliasing operation, and the mth hop transmits the signal
Expressed as:
wherein l and m are integers and m is equal to or greater than 0, s (t) and p (t) are continuous time versions of the information sequence s (l) and the artificial noise sequence p (l), ψ (t) represents the impulse response of the root raised cosine roll-off filter,' represents the convolution operation, f m For the carrier frequency of the mth-hop signal,
transmitting a signal for the mth hop->
Is used to determine the initial phase of the phase. T=l·t b Representing the period of each hop signal, L representing the number of bits per hop signal, T b Representing the duration of the signal per bit. g (t) represents a rectangular window function of the start and end times of each hop signal, when t e (0, T]The value is 1, otherwise, the value is 0.
S2, under the scene of receiving-transmitting frequency offset, firstly performing frequency hopping artificial noise cancellation on legal receiving equipment, then performing mathematical modeling on residual artificial noise caused by the frequency offset, and finally calculating a mathematical expression of signal-to-noise ratio at the legal receiving equipment;
said step S2 comprises the sub-steps of:
s201. the radio frequency received signal at the legal receiving device may be expressed as:
wherein the method comprises the steps of
τ r And f r Respectively representing channel gain, propagation delay and frequency offset, w, between transmitting device and legal receiving device r (t) is additive white gaussian noise at the transmitting device to the legitimate receiving device.
After the received signal r (t) is subjected to frequency hopping synchronization and matched filtering, the obtained baseband received signal r (n) can be expressed as:
r(n)＝r s (n)+r p (n)+w r (n),
wherein,,
representing the information component and the artificial noise component, respectively. h is a r 、D r And F r Representing equivalent channel gain, normalized propagation delay and normalized frequency offset, w, respectively, at transmitting device to legal receiving device r (n) is w r And (t) is a combination of a raised cosine impulse response function of the 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 device executes a reference artificial noise reconstruction operation. It is assumed that the channel gain and propagation delay have been accurately estimated. Frequency offset estimation is carried out on the baseband signal, and the frequency offset estimation error is recorded as
Wherein->
Is a frequency offset estimate. Reconstructing a reference artificial noise sequence with channel gain, propagation delay, frequency offset estimate>
The resulting reference sequence can be expressed as:
s203, legal receiving equipment executes manual workNoise cancellation operation. Subtracting reconstructed reference artificial noise sequence from baseband received signal r (n)
The method can obtain the following steps:
wherein the method comprises the steps of
Representing the residual artificial noise after the artificial noise cancellation, can reduce the signal-to-noise ratio performance of the frequency hopping communication system.
S204. assume that the receiver updates the frequency estimation value once every time it receives a signal, i.e. the frequency compensation period is L symbols. R is recorded p (n) and
the fast fourier transform results of (a) are respectively R p (k) And->
The two are as follows:
wherein,,
is an inter-frequency interference component caused by a frequency error. Record->
Representing the power of solving {.cndot }, can be obtained +.>
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:
the power of the residual artifacts can be expressed as:
after 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:
wherein P is s Representing the transmit power of the secret signal s (t),
representing normalized transmit power budget at legal receiving device, < >>
A transmit power allocation factor representing an artificial noise sequence and an information sequence at a transmitting device.
S3, the legal receiving equipment respectively carries out mathematical modeling on the received signals of the N illegal interception equipment, and respectively calculates mathematical expressions of signal-to-noise ratios of the N illegal interception equipment;
said step S3 comprises the sub-steps of:
s301, assume that N illegal eavesdropping devices exist in the system. The radio frequency signal received by the i-th illegal eavesdropping device is:
wherein i is more than or equal to 1 and less than or equal to N,
and->
Respectively representing the channel gain, propagation delay and frequency offset between the transmitting device and the ith illegal eavesdropping device, < >>
Is an additive white gaussian noise at the ith illegal eavesdropping device.
In a strong eavesdropping scene, illegal eavesdropping equipment can accurately detect and acquire the frequency hopping signal parameters, so that operations such as frequency hopping synchronization and frequency hopping unlocking are realized. After the i-th illegal eavesdropping device realizes frequency hopping synchronization, the discrete form of the obtained baseband signal can be expressed as:
wherein,,
and->
Representing equivalent channel gain, normalized propagation delay and normalized frequency offset, respectively, at the ith transmitting device to the illegal eavesdropping device,/->
Is->
Is the combination of the impulse responses of the root raised cosine roll-off filter at the transmitting device and the illegal eavesdropping device, is equivalent to the impulse response of the raised cosine roll-off filter.
Then calculate the signal-to-noise ratio at the ith illegal eavesdropping device
It is defined as the power of the information component divided by the total power of the artificial noise and the thermal noise expressed as:
wherein,,
representing the normalized power budget at the ith illegal eavesdropping device.
S4, in a multi-eavesdropping scene with receiving-transmitting frequency offset, legal receiving equipment calculates the minimum secret capacity performance of a frequency hopping system, and designs a transmitting power distribution scheme of the frequency hopping system with frequency error robustness;
said step S4 comprises the sub-steps of:
s401 in case of N illegal eavesdropping devices, the security performance of the frequency hopping system can be improved by using the minimum security capacity C s The expression is:
wherein [ (x)] + ＝max{0,*}，
h E And eta E Channel gain and normalized power budget at the eavesdropping device with maximum signal-to-noise ratio, respectively.
S402. in order to maximize the system secret capacity, the transmission power allocation ratio of the information sequence and the artificial noise sequence needs to be optimized. Let x= |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:
recording the optimal solution of the transmit power allocation problem as lambda * The expression is:
wherein lambda is 1 Represented as
S5, the legal receiving device feeds back the power distribution scheme to the frequency hopping transmitting device. And adjusting a transmitting power distribution strategy by the frequency hopping transmitting equipment according to the feedback parameters.
The beneficial effects of the invention are as follows: 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 can effectively improve the robustness of the system to the frequency synchronization error and the confidentiality capacity performance of the system under the scene with a plurality of illegal eavesdropping devices by adjusting the transmission power proportion of an information sequence and artificial noise.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
fig. 2 is a schematic diagram of a transmission and reception of a frequency hopping communication system according to an embodiment;
FIG. 3 is a diagram illustrating the optimal power distribution factor for different frequency offsets according to an embodiment;
fig. 4 is a schematic diagram of security performance of a frequency hopping system with different frequency offsets in an embodiment.
Detailed Description
The technical solution of the present invention will be described in further detail with reference to the accompanying drawings, but the scope of the present invention is not limited to the following description.
As shown in fig. 1, a frequency hopping system optimization method with frequency error robustness includes the following steps:
s1, at a frequency hopping transmitting device, mixing a sum signal of an information sequence and an artificial noise sequence with a frequency hopping carrier wave and transmitting the mixture;
s2, under the scene of receiving-transmitting frequency offset, firstly performing frequency hopping artificial noise cancellation on legal receiving equipment, then performing mathematical modeling on residual artificial noise caused by the frequency offset, and finally calculating a mathematical expression of signal-to-noise ratio at the legal receiving equipment;
s3, the legal receiving equipment respectively carries out mathematical modeling on the received signals of the N illegal interception equipment, and respectively calculates mathematical expressions of signal-to-noise ratios of the N illegal interception equipment;
s4, in a multi-eavesdropping scene with receiving-transmitting frequency offset, legal receiving equipment calculates the minimum secret capacity performance of a frequency hopping system, and designs a transmitting power distribution scheme of the frequency hopping system with frequency error robustness;
s5, the legal receiving device feeds back the power distribution scheme to the frequency hopping transmitting device. And adjusting a transmitting power distribution strategy by the frequency hopping transmitting equipment according to the feedback parameters.
Wherein, the step S1 comprises the following substeps:
s101, generating an information sequence s (l) by frequency hopping transmitting equipment, wherein the information sequence s (l) is not related to an artificial noise sequence p (l);
the information sequence s (l) and the artificial noise sequence p (l) are overlapped to obtain a sum signal, the sum signal and the frequency hopping carrier wave are transmitted after being subjected to aliasing operation, and the mth hop transmits the signal
Expressed as:
wherein l and m are integers and m is equal to or greater than 0, s (t) and p (t) are continuous time versions of the information sequence s (l) and the artificial noise sequence p (l), ψ (t) represents the impulse response of the root raised cosine roll-off filter,' represents the convolution operation, f m Load for mth hop signalThe frequency of the wave is such that,
transmitting a signal for the mth hop->
Is used to determine the initial phase of the phase. T=l·t b Representing the period of each hop signal, L representing the number of bits per hop signal, T b Representing the duration of the signal per bit. g (t) represents a rectangular window function of the start and end times of each hop signal, when t e (0, T]The value is 1, otherwise, the value is 0.
Said step S2 comprises the sub-steps of:
s201. the radio frequency received signal at the legal receiving device may be expressed as:
wherein the method comprises the steps of
τ r And f r Respectively representing channel gain, propagation delay and frequency offset, w, between transmitting device and legal receiving device r (t) is additive white gaussian noise at the transmitting device to the legitimate receiving device.
After the received signal r (t) is subjected to frequency hopping synchronization and matched filtering, the obtained baseband received signal r (n) can be expressed as:
r(n)＝r s (n)+r p (n)+w r (n),
wherein,,
representing the information component and the artificial noise component, respectively。h r 、D r And F r Representing equivalent channel gain, normalized propagation delay and normalized frequency offset, w, respectively, at transmitting device to legal receiving device r (n) is w r And (t) is a combination of a raised cosine impulse response function of the 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 device executes a reference artificial noise reconstruction operation. It is assumed that the channel gain and propagation delay have been accurately estimated. Frequency offset estimation is carried out on the baseband signal, and the frequency offset estimation error is recorded as
Wherein->
Is a frequency offset estimate. Reconstructing a reference artificial noise sequence with channel gain, propagation delay, frequency offset estimate>
The resulting reference sequence can be expressed as:
s203, the legal receiving device executes artificial noise cancellation operation. Subtracting reconstructed reference artificial noise sequence from baseband received signal r (n)
The method can obtain the following steps:
wherein the method comprises the steps of
Representing the residual artificial noise after the artificial noise cancellation, can be reducedSignal-to-noise ratio performance of a low frequency hopping communication system.
S204. assume that the receiver updates the frequency estimation value once every time it receives a signal, i.e. the frequency compensation period is L symbols. R is recorded p (n) and
the fast fourier transform results of (a) are respectively R p (k) And->
The two are as follows:
wherein,,
is an inter-frequency interference component caused by a frequency error. Record->
Representing the power of solving {.cndot }, can be obtained +.>
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:
the power of the residual artifacts can be expressed as:
after 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:
wherein P is s Representing the transmit power of the secret signal s (t),
representing normalized transmit power budget at legal receiving device, < >>
A transmit power allocation factor representing an artificial noise sequence and an information sequence at a transmitting device.
Further, the step S3 includes the following substeps:
s301, assume that N illegal eavesdropping devices exist in the system. The radio frequency signal received by the i-th illegal eavesdropping device is:
wherein i is more than or equal to 1 and less than or equal to N,
and->
Respectively representing the channel gain, propagation delay and frequency offset between the transmitting device and the ith illegal eavesdropping device, < >>
Is an additive white gaussian noise at the ith illegal eavesdropping device.
In a strong eavesdropping scene, illegal eavesdropping equipment can accurately detect and acquire the frequency hopping signal parameters, so that operations such as frequency hopping synchronization and frequency hopping unlocking are realized. After the i-th illegal eavesdropping device realizes frequency hopping synchronization, the discrete form of the obtained baseband signal can be expressed as:
wherein,,
and->
Representing equivalent channel gain, normalized propagation delay and normalized frequency offset, respectively, at the ith transmitting device to the illegal eavesdropping device,/->
Is->
Is the combination of the impulse responses of the root raised cosine roll-off filter at the transmitting device and the illegal eavesdropping device, is equivalent to the impulse response of the raised cosine roll-off filter.
Then calculate the signal-to-noise ratio at the ith illegal eavesdropping device
It is defined as the power of the information component divided by the total power of the artificial noise and the thermal noise expressed as:
wherein,,
representing the normalized power budget at the ith illegal eavesdropping device.
Further, the step S4 includes the following substeps:
s401 in case of N illegal eavesdropping devices, the confidentiality of the frequency hopping system can be the mostSmall security capacity C s The expression is:
wherein [ (x)] + ＝max{0,*}，
h E And eta E Channel gain and normalized power budget at the eavesdropping device with maximum signal-to-noise ratio, respectively.
S402. in order to maximize the system secret capacity, the transmission power allocation ratio of the information sequence and the artificial noise sequence needs to be optimized. Let x= |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:
recording the optimal solution of the transmit power allocation problem as lambda * The expression is:
wherein lambda is 1 Represented as
In the embodiment of the present application, the optimal power distribution factor λ in step S4 * The derivation process of (1) comprises:
C s the first derivative to λ is:
wherein,,
order the
Then
Xλ 2 +Yλ+Z＝0.
Case 1: consider the case of x=0, i.e., x+yz=xz+z: when y is less than or equal to z, lambda is epsilon phi; when y is greater than z, lambda is e-0, ++ infinity A kind of electronic device.
When y.ltoreq.z, the optimum power division factor lambda * Phi.
When Y > Z, Y < 0 and Z < 0 can be found, and thus the constant can be found when lambda E [0, + ] is
Indication C s Monotonically decreasing with increasing λ (λ > 0), thus optimizing the power division factor λ * 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 is epsilon phi; when y > z, lambda e [0, lambda 0 ) Wherein
When y.ltoreq.z, the optimum power division factor lambda * Phi.
When y > Z, Z < 0 can be obtained. X lambda is taken up 2 The two solutions for +yλ+z=0 are denoted as λ 1 And lambda (lambda) 2 The expression is:
in addition, in the case of the optical fiber,
the expression of (2) is:
it can be found that
Thereby obtaining lambda 2 ＜0＜λ 0 ＜λ 1 . Thus, when λ ε [0, λ 0 ) We always have
At this time, the optimal power distribution factor lambda * Is 0.
Case 3: consider the case of X < 0, i.e., x+yz > xz+z: when y is less than or equal to z, the feasible domain is lambda E (lambda) 0 , + -infinity a) is provided; when y is greater than z, the feasible region is lambda E [0, + ] infinity.
When y.ltoreq.z, we have Z > 0,
and lambda is 2 ＜0＜λ 0 ＜λ 1 . Can obtain the time lambda E (lambda) 0 ,λ 1 ) Time of day
When lambda is epsilon (lambda) 1 , + -infinity at->
The optimal power distribution factor is lambda * ＝λ 1 。
When Y > z and z (x+yz) < Y (xz+z), we have Y < 0,
z < 0, and thus ++infinity when lambda is E0 ++infinity>
The optimal power distribution factor is lambda * ＝0。
When Y > z and z (x+yz). Gtoreq.y (xz+z), we have Y < 0,
z is greater than or equal to 0, at this time lambda 2 ＜0≤λ 1 . When lambda is E [0, lambda 1 ) Time->
When lambda is epsilon (lambda) 1 , + -infinity at->
The optimal power distribution factor is lambda * ＝λ 1 。
From the above analysis, it can be confirmed that λ was found in step S4 * Is an expression of (2).
The optimal power distribution factor lambda of the frequency hopping system can be calculated by integrating all the steps * . The legal receiver will find lambda * After being fed 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, so that the power optimization of the frequency hopping system with frequency error robustness in the multi-eavesdropping scene is realized.
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 proposed power distribution method is verified by means of MATLAB software tool simulation, and simulation parameters are shown in the following table:
fig. 3 shows the trend of the optimal power allocation factor with frequency offset. It can be seen that as the frequency offset increases, the optimum power distribution factor overall tends to decrease, indicating that the transmit power ratio of the noise artifact to the secret signal should decrease as the frequency offset increases. By comparing curves (1) - (2), it can be found that the optimal power allocation factor decreases with increasing frequency hopping period. Furthermore, by comparison of curves (2) - (3) - (4), it can be found that the optimal power allocation factor decreases continuously with increasing relative channel quality.
Fig. 4 shows the 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 overall security capacity of the system tends to decrease, indicating that the frequency offset significantly reduces the security performance of the system. By comparing the curves (1) - (2), it can be found that shortening the frequency hopping period can effectively improve the secret capacity performance of the system. Furthermore, by comparing curves (2) - (3) - (4), it can be seen that system privacy performance increases with relative channel quality.
The present invention has been described and illustrated in detail herein to enable those skilled in the art to make and use the invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. And that modifications and variations which do not depart from the spirit and scope of the invention are intended to be within the scope of the appended claims.
Claims (3)
1. A frequency hopping system optimization method with frequency error robustness is characterized in that: the method comprises the following steps:
s1, at a frequency hopping transmitting device, mixing a sum signal of an information sequence and an artificial noise sequence with a frequency hopping carrier wave and transmitting the mixture;
said step S1 comprises the sub-steps of:
s101, generating an information sequence s (l) by frequency hopping transmitting equipment, wherein the information sequence s (l) is not related to an artificial noise sequence p (l);
the information sequence s (l) and the artificial noise sequence p (l) are overlapped to obtain a sum signal, the sum signal and the frequency hopping carrier wave are transmitted after being subjected to aliasing operation, and the mth hop transmits the signal
Expressed as:
wherein l and m are integers and m is equal to or greater than 0, s (t) and p (t) are continuous time versions of the information sequence s (l) and the artificial noise sequence p (l), ψ (t) represents the impulse response of the root raised cosine roll-off filter,' represents the convolution operation, f m For the carrier frequency of the mth-hop signal,
transmitting a signal for the mth hop->
Is a phase of the initial phase of (a); t=l·t b Representing the period of each hop signal, L representing the number of bits per hop signal, T b Representing the duration of each bit of the signal; g (t) represents a rectangular window function of the start and end times of each hop signal, when t e (0, T]The value is 1 when the time is taken, otherwise, the value is 0;
s2, under the scene of receiving-transmitting frequency offset, firstly performing frequency hopping artificial noise cancellation on legal receiving equipment, then performing mathematical modeling on residual artificial noise caused by the frequency offset, and finally calculating the signal-to-noise ratio at the legal receiving equipment;
said step S2 comprises the sub-steps of:
s201, in the scene of receiving-transmitting frequency offset, the radio frequency receiving signal at legal receiving equipment is expressed as:
wherein the method comprises the steps of
τ r And f r Respectively representing channel gain, propagation delay and frequency offset, w, between transmitting device and legal receiving device r (t) is additive white gaussian noise at the transmitting device to the legitimate receiving device;
after the received signal r (t) is subjected to frequency hopping synchronization and matched filtering, the obtained baseband received signal r (n) is:
r(n)＝r s (n)+r p (n)+w r (n),
wherein,,
r s (n) and r P (n) represents an information component and an artificial noise component, respectively; h is a r 、D r And F r Representing equivalent channel gain, normalized propagation delay and normalized frequency offset, w, respectively, at transmitting device to legal receiving device r (n) is w r A discrete form of (t), ψ (t) being the combination of the raised cosine impulse response functions of the transmitting device and the legal receiving device, equivalent to the impulse response of a raised cosine roll-off filter;
s202, the legal receiving device executes a reference artificial noise reconstruction operation:
assuming 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
Wherein->
Reconstructing a reference artificial noise sequence for the frequency offset estimate using the channel gain, propagation delay, frequency offset estimate>
The resulting reference sequence is expressed as:
s203, the legal receiving device executes artificial noise cancellation operation: subtracting reconstructed reference artificial noise sequence from baseband received signal r (n)
The method comprises the following steps:
wherein the method comprises the steps of
Representing the residual artificial noise after the artificial noise cancellation;
s204, assuming that the receiver updates the frequency estimation value once every time a jump signal is received, namely the frequency compensation period is L symbols, r is recorded p (n) and
the fast fourier transform results of (a) are respectively R p (k) And->
The two are as follows:
wherein,,
is an inter-frequency interference component caused by a frequency error; recording device
Representing the power of solving {.cndot }, get +.>
Wherein P is p Representing the transmit power of the artificial noise signal p (t);
after artificial noise cancellation, the frequency domain of the residual artificial noise is expressed as:
the power of the residual artifacts is expressed as:
after 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:
wherein P is s Representing the transmit power of the secret signal s (t),
representing normalized transmit power budget at legal receiving device, < >>
Indicating the transmitting devicePreparing a transmission power distribution factor of the artificial noise sequence and the information sequence;
s3, the legal receiving equipment respectively carries out mathematical modeling on the received signals of the N illegal interception equipment, and respectively calculates the signal to noise ratios of the N illegal interception equipment;
s4, in a multi-eavesdropping scene with receiving-transmitting frequency offset, legal receiving equipment calculates the minimum secret capacity performance of a frequency hopping system, and designs a transmitting power distribution scheme of the frequency hopping system with frequency error robustness;
s5, the legal receiving device feeds back the power distribution scheme to the frequency hopping transmitting device, and the frequency hopping transmitting device adjusts the transmitting power distribution strategy according to the feedback parameters.
2. The method for optimizing a frequency hopping system with robustness to frequency errors according to claim 1, wherein: said step S3 comprises the sub-steps of:
s301, setting N illegal interception devices in the system, wherein radio frequency signals received by the ith illegal interception device are as follows:
wherein i is more than or equal to 1 and less than or equal to N,
and->
Respectively representing the channel gain, propagation delay and frequency offset between the transmitting device and the ith illegal eavesdropping device, < >>
Additive white gaussian noise at the ith illegal eavesdropping device;
in a strong eavesdropping scene, illegal eavesdropping equipment accurately detects and acquires frequency hopping signal parameters, frequency hopping synchronization and debounce operation are realized, and after the i-th illegal eavesdropping equipment realizes the frequency hopping synchronization, the discrete form of the obtained baseband signal is expressed as follows:
wherein,,
and->
Representing equivalent channel gain, normalized propagation delay and normalized frequency offset, respectively, at the ith transmitting device to the illegal eavesdropping device,/->
Is->
Is the combination of impulse responses of a root raised cosine roll-off filter at a transmitting device and an illegal eavesdropping device, and is equivalent to the impulse responses of the raised cosine roll-off filter;
then calculate the signal-to-noise ratio at the ith illegal eavesdropping device
It is defined as the power of the information component divided by the total power of the artificial noise and the thermal noise expressed as:
wherein,,
representing the normalized power budget at the ith illegal eavesdropping device.
3. The frequency hopping system optimization method with frequency error robustness according to claim 2, wherein: said step S4 comprises the sub-steps of:
s401 in the case of N illegal eavesdropping devices, the security performance of the frequency hopping system uses a minimum security capacity C s The expression is:
wherein [ (x)] + ＝max{0,*}，
h E And eta E Channel gain and normalized power budget at the eavesdropping device with maximum signal-to-noise ratio, respectively;
s402, optimizing the transmission power distribution ratio of an information sequence and an artificial noise sequence in order to maximize the security capacity of the system; let x= |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:
recording the optimal solution of the transmit power allocation problem as lambda * The expression is:
wherein lambda is 1 Represented as
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