CN111224764A - Physical layer security algorithm based on subcarrier power distribution scheme - Google Patents

Physical layer security algorithm based on subcarrier power distribution scheme Download PDF

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CN111224764A
CN111224764A CN201911153415.1A CN201911153415A CN111224764A CN 111224764 A CN111224764 A CN 111224764A CN 201911153415 A CN201911153415 A CN 201911153415A CN 111224764 A CN111224764 A CN 111224764A
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bit error
power
error rate
subcarrier
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李鸣岩
郭志民
吕卓
陈岑
张铮
蔡军飞
李暖暖
张伟
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State Grid Corp of China SGCC
Electric Power Research Institute of State Grid Henan Electric Power Co Ltd
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Electric Power Research Institute of State Grid Henan Electric Power Co Ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path
    • H04L5/003—Arrangements for allocating sub-channels of the transmission path
    • H04L5/0053—Allocation of signaling, i.e. of overhead other than pilot signals
    • H04L5/0057—Physical resource allocation for CQI
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00—Arrangements affording multiple use of the transmission path
    • H04L5/003—Arrangements for allocating sub-channels of the transmission path
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
    • 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
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention belongs to the technical field of wireless communication physical layer security, and particularly relates to a physical layer security algorithm based on a subcarrier power distribution scheme, which is suitable for a multicarrier communication network combining the characteristics of an OFDM system. The algorithm utilizes a power distribution mode of a bit error rate optimization criterion to carry out power distribution on subcarriers to optimize the bit error rate performance of a system, provides an empirical function power distribution scheme based on the application of the power optimization distribution mode to the algorithm provided by the invention, and obtains a closed solution of a power distribution coefficient. The simulation result of the algorithm shows that the legal receiver can decode reliably, the bit error rate of the eavesdropper approaches 0.5, the simulation result of the power optimization distribution algorithm shows that the bit error rate performance is optimized by 10 to 20 percent under the condition of low signal-to-noise ratio, and the bit error rate performance is improved by one order of magnitude under the condition of 20 dB.

Description

Physical layer security algorithm based on subcarrier power distribution scheme
Technical Field
The invention belongs to the technical field of wireless communication physical layer security, and particularly relates to a physical layer security algorithm based on a subcarrier power distribution scheme, which is suitable for a multicarrier communication network combining the characteristics of an OFDM system and has a positive effect on enhancing the information security performance of a 5G network.
Background
With the development of information technology, 5G has become the focus of attention in the field of mobile communication at home and abroad. The OFDM technology has become one of the key technologies of the physical layer in LTE and LTE-Advanced systems due to its technical advantages of high spectrum utilization, strong multipath fading resistance, etc., and will also be more widely applied in 5G systems. The problem of secure transmission of data in a 5G mobile communication system faces more serious challenges due to the broadcastability and openness of wireless channel transmission, uncertainty of user distribution, and complexity of network structure. The research of a physical layer security scheme combining the characteristics of the OFDM technology has a positive effect on enhancing the information security performance of the 5G network. Physical layer security algorithms combined with OFDM modulation have attracted a lot of attention in recent years. Because of its multi-carrier uniqueness, each sub-carrier channel will undergo different fading, so that each sub-carrier has different transmission capability, and the difference of wireless channel characteristics is exactly the essence that physical layer security can be implemented, so it is necessary to consider the physical layer security technology under the OFDM system.
On the premise that the physical layer safety scheme can be realized, different modulation modes and flexible transmission power distribution are reasonably used, and information data can be transmitted more safely. Moreover, due to the frequency selectivity and time variability of the wireless channel, the channel condition needs to be monitored in real time, so that the frequency resource is utilized more effectively. The traditional OFDM system can switch between different modes according to the requirement of the required transmission rate, but the same modulation mode (for example, ieee802.11a and DVB-T) is adopted on each sub-channel, which is beneficial to the implementation of the system, reduces the complexity of coding and decoding, but the frequency resource of the system is not fully utilized. For an OFDM system where all subcarriers are fixed modulation schemes, the overall error probability is mainly determined by the subcarriers on the channel experiencing the most severe fading. Therefore, in a frequency selective fading channel, the overall error probability of the OFDM system decreases very slowly as the average signal-to-noise ratio increases.
Disclosure of Invention
The invention aims to provide a physical layer security algorithm based on a subcarrier power allocation scheme aiming at the problems in the prior art, the algorithm utilizes a power allocation mode of a bit error rate optimization criterion to allocate power to subcarriers so as to optimize the bit error rate performance of a system, provides an empirical function power allocation scheme based on the power allocation optimization mode applied to the algorithm provided by the invention, and solves a closed solution of a power allocation coefficient. The simulation result of the algorithm shows that the legal receiver can decode reliably, the bit error rate of the eavesdropper approaches 0.5, the simulation result of the power optimization distribution algorithm shows that the bit error rate performance is optimized by 10-20% under the condition of low signal-to-noise ratio, and the bit error rate performance is improved by one order of magnitude under the condition of 20 dB.
The technical scheme of the invention is as follows:
a physical layer security algorithm based on a sub-carrier power distribution scheme is suitable for a multi-carrier communication network combining the characteristics of an OFDM system, and comprises the following steps:
s1, firstly, the total bit error rate P of the OFDM systemberExpressed as the transmit power p on K sub-carrierskK is a function of 1, 2.. multidata, K }, and the K-th subcarrier is used for MPSK or MQAM modulationBit error rate p ofberCan be expressed as a function p of the signal-to-noise ratio of the channelber＝f(γk) K is 1,2, …, K, and the signal-to-noise ratio on the K-th subcarrier can be expressed as a function y of the allocated power for the channelk＝αkpkThe total bit error rate may be determined by the given channel state information αkThe arithmetic average of the bit error rates of the respective channels of (a) is obtained as:
Figure BDA0002284182880000021
s2, bit symbols carried by front K/2 sub-carriers corresponding to front K/2 sub-channels with larger channel quality module value square at a sending end are unchanged, bit symbols of rear K/2 sub-carriers corresponding to rear K/2 sub-channels are exclusive OR operations of original symbols and symbols on the front K/2 sub-carriers corresponding to the rear K/2 sub-channels, and when a receiving end decodes, the bit error rate of the front K/2 sub-carriers is unchanged gber(βkpk)＝f(βkpk) K is more than or equal to 1 and less than or equal to K/2, the bit error rates of the last K/2 sub-carriers are influenced by the bit error rates of the first K/2 sub-carriers in a one-to-one correspondence manner, and the bit error rate function of the receiving end is set to be g (β)kpk) Then, there are: gber(βkpk)＝f(βkpk)(1-f(βk-K/2pk-K/2))+(1-f(βkpk))f(βk-K/2pk-K/2),K/2+1≤k≤K；
S3. to reduce the iterative computation, f is ignored (β)kpk)f(βk+K/2pk+K/2) The influence on the total bit error rate of the system is obtained to obtain the total bit error rate function of the system
Figure BDA0002284182880000031
S4. in formula
Figure BDA0002284182880000032
Under the constraint of the set total transmitting power limit, introducing Lagrange function and Lagrange multiplier lambda to obtain extreme value, and substituting into approximate expression of channel bit error rate function corresponding to subcarrier under BPSK modulation mode,solving lambda and power distribution coefficient vector { p) for the power distribution schemekClosed solution, there are:
Figure BDA0002284182880000033
s5. if the subcarrier power p occurs in the process of solvingkAnd solving according to an iterative operation method under the condition of a negative value.
Specifically, in the OFDM system, input data is divided into K parallel sub-data after serial-to-parallel conversion, and the transmission power on the K-th sub-channel is pkThen, the sub data stream is sent out through each orthogonal sub carrier by IFFT transformation and parallel-to-serial transformation to form an OFDM transmission signal.
Specifically, the Lagrange function in step S4 is:
Figure BDA0002284182880000034
λ is Lagrange multiplication factor, p in the formulakAnd solving the partial derivatives and setting the partial derivatives as 0 to obtain an equation set of a physical layer security algorithm based on the subcarrier power distribution scheme:
Figure BDA0002284182880000041
specifically, in step S5, the method for obtaining the power distribution coefficient through iterative computation includes the following steps:
firstly, initializing, determining signal-to-noise ratio (SNR) and obtaining total transmitting power under the condition of energy normalization
Figure BDA0002284182880000048
Setting iteration number i, and setting step length mu (0) to mu0；
Generating an initial power distribution value to satisfy
Figure BDA0002284182880000042
Generating a set of p under constraintk(0) And calculating λ (0), wherein
Figure BDA0002284182880000043
When the total emission power is evenly distributed to each subcarrier, the average emission power of each subcarrier and the number of subcarriers in the system is K, so that
Figure BDA0002284182880000044
For total transmit power, to reduce the iterative operation, corresponds to { β }kAllocate by size { p }k(0)}；
Thirdly, the step size is approximated, and the power coefficient { p of the subcarrier is updatedk}，λ(i)：
Figure BDA0002284182880000045
Four, negative power handling if { pkIf a negative value appears in (i +1) }, it is set to
Figure BDA0002284182880000046
And always maintaining the subcarrier power distribution coefficient p in the iterative operationkIs composed of
Figure BDA0002284182880000047
Wherein the subcarrier power coefficient { p ] is not calculated and updated any morekAnd d, updating mu (i +1), and returning to the step three for iterative operation.
In frequency selective fading channels, the problem that the overall error probability of the OFDM system decreases very slowly with the increase of the average snr can be solved by applying different modulation schemes to different sub-channels, and the modulation scheme used must be adapted to the snr of each sub-channel, i.e. an adaptive modulation scheme is applied. Applying OFDM systems with adaptive modulation in a frequency selective fading channel environment, a large fraction of the subcarriers may not be used. For example, under the multi-user system condition using static Time Division Multiple Access (TDMA) or Frequency Division Multiple Access (FDMA) as the Multiple Access technology, each user is allocated a fixed Frequency band, each user applies OFDM in adaptive modulation to an expected Time slot or Frequency band, the sub-carriers allocated to the users in the deep fading channel may not be applied to other users again, which results in waste of system resources, and the sub-channels with the best performance are only used in part of Time, which results in waste of resources. However, the sub-carriers exhibiting deep fading in a user only occupy a part of the sub-carriers, and not all the sub-carriers are necessarily in deep fading, because the fading coefficients of each sub-carrier in the OFDM multi-carrier system can be considered to be independent of each other, so that an adaptive resource allocation method for allocating resources to each sub-carrier according to the instantaneous channel characteristics can be considered, and this method allocates an appropriate number of resources to each sub-carrier according to a certain algorithm, so that all the sub-carriers can be utilized more effectively, i.e., a dynamic resource allocation method. The method can dynamically allocate resources according to the instantaneous characteristics of the channel state, and the invention adopts an optimization algorithm of the dynamic resource allocation method.
The design idea of the invention is based on a Wyner three-node eavesdropping channel model, aiming at a single-antenna multi-carrier system, by utilizing the characteristics of CSI and OFDM multi-carrier modulation, a physical layer safe transmission algorithm based on subcarrier power distribution is designed without a legal receiver CSI being superior to an eavesdropper. In the invention, in order to improve the performance of the algorithm scheme, the OFDM spectrum resources are required to be fully utilized, and each subcarrier is allocated to be an effective carrier, so that the subcarriers can be reasonably allocated according to the instantaneous state information of a channel, namely, a dynamic allocation scheme is adopted to allocate the resources, and the method for flexibly allocating the bits and the transmission power is more suitable for a physical layer safe transmission algorithm of joint subcarrier power allocation.
The invention has the beneficial effects that: in consideration of the requirement of fully utilizing and allocating each subcarrier in order to improve the performance of the algorithm scheme, the subcarriers can be reasonably allocated according to the instantaneous state information of the channel, namely, a dynamic allocation scheme is adopted for resource allocation; 2, the security algorithm provided by the invention does not need to know the channel information of an eavesdropper, and can be suitable for the situation that the eavesdropper eavesdrops passively; 3 under different fading channels, such as frequency selective fading channels, the invention can improve the secrecy capacity of the OFDM system by reasonably distributing the subcarrier power; 4, the invention completely distributes the total power to each subcarrier, does not cause additional expenditure and power waste, and has better system performance; the power distribution algorithm provided by the invention distributes more power to the subcarriers with better channel quality in the first half, ensures the transmission of data and obviously improves the error code performance of the system.
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FIG. 1 is a system schematic block diagram of a physical layer secure transmission algorithm based on a subcarrier power allocation algorithm according to the present invention;
fig. 2 is a schematic diagram of a simulation analysis for a physical layer security algorithm based on a subcarrier power allocation scheme.
Detailed Description
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.
In OFDM system, input data is divided into K paths of parallel subdata after serial-parallel conversion, and transmitting power on K path of subchannel uses pkThen, the sub data stream is sent out through each orthogonal sub carrier by IFFT transformation and parallel-to-serial transformation to form an OFDM transmission signal. Assuming that the received signals all reach the receiving end through each mutually independent multipath rayleigh fading channel, for the receiving end, the signal on the k-th subcarrier after IFFT processing can be expressed as:
Figure BDA0002284182880000061
in the formula
Figure BDA0002284182880000062
Is the multiplicative fading factor of the channel on the k sub-carrier, assuming
Figure BDA0002284182880000063
The channel quality estimation method is a complex Gaussian random variable which is independent from each other, has the same distribution mean value of 0 and the variance of 1, and the modulus value of the complex Gaussian random variable represents the channel quality on the channel. x is the number ofkAfter modulation of the systemAnd (4) a symbol.
Figure BDA0002284182880000064
Is a mean of 0 and a variance of σ2White additive gaussian noise. p is a radical ofkIs the transmit power on the k-th subcarrier and satisfies the following equation:
Figure BDA0002284182880000071
in the formula (I), the compound is shown in the specification,
Figure BDA0002284182880000072
when the total emission power is evenly distributed to each subcarrier, the average emission power of each subcarrier and the number of subcarriers in the system is K, so that
Figure BDA0002284182880000073
Is the total transmit power. The signal-to-noise ratio on the k sub-carrier can be expressed as γk＝αkpkIn the formula
Figure BDA0002284182880000074
The ratio of the gain of the kth sub-channel to the noise power represents the channel state information of the kth sub-channel, and the key point of the algorithm research is to reasonably distribute the transmitting power on each sub-carrier according to the channel state information.
To minimize the total bit error rate, first we will refer to the system total bit error rate PberExpressed as the transmit power p on K sub-carrierskK is a function of 1, 2.. K), and for a general MPSK, MQAM modulation scheme, the bit error rate of the K-th subcarrier can be expressed as a function of the signal-to-noise ratio of the channel, so that the channel state information α of the subcarrier is givenkThe bit error rate function of the channel is expressed as:
pber＝f(αkpk),k＝1,2,…,K (3)
where f () is a function determined by a certain modulation scheme, and when MPSK or MQAM modulation scheme is used, for convenience, the literature is usedGoldsmith A.J., ChuaS.G., MQAM adaptive modulation with variable rate and variable power in fading channel, IEEE communication journal 1997, 45(10), 1218-kWhen the modulation mode is MQAM with more than 4 orders, the bit error rate function of the channel corresponding to the subcarrier can be approximately expressed as:
Figure BDA0002284182880000075
bithe MQAM modulation mode determines the BPSK modulation mode as follows:
fBPSK(βkpk)≈0.2exp(-1.1βkpk) (5)
the bit error rate empirical formula can be uniformly expressed as:
Figure BDA0002284182880000076
in equation (6), BPSK modulation c is 1.1, and MQAM modulation c of 4 th order or more is 1.5.
Assuming that each subcarrier carries as much bit stream data as each subcarrier transmits received data over its corresponding channel, the total bit error rate for the system may be given by the channel state information αkThe arithmetic average of the bit error rates of the respective channels of (a) is obtained as:
Figure BDA0002284182880000081
for a physical layer security algorithm based on a subcarrier power allocation scheme, the system block diagram is shown in fig. 1, and after subcarriers are sorted according to channel transmission quality, channel state information α of a sending endkNot changed, but αkThe data information carried on the corresponding sub-carriers is changed. Setting:
{βk,k＝1,2,…,K}＝sorted{αk,k＝1,2,…,K} (8)
is β1≥β2≥…≥βkSetting the bit error rate function of the receiving end to be g (β)kpk) Because the bit symbols carried by the first K/2 sub-carriers corresponding to the better channel transmission quality at the sending end are not changed, and because the bit symbols carried by the first K/2 sub-carriers corresponding to the first K/2 sub-channels with the larger square of the channel quality modulus at the sending end are not changed, the bit symbols of the last K/2 sub-carriers corresponding to the last K/2 sub-channels are the exclusive or operation of the original symbols and the symbols on the corresponding first K/2 sub-carriers, when the receiving end decodes, the bit error rate of the first K/2 sub-carriers is not changed, and the method comprises the following steps:
gber(βkpk)＝f(βkpk),1≤k≤K/2 (9)
then the bit error rates of the K/2 sub-carriers are affected by the bit error rates of the first K/2 sub-carriers in a one-to-one correspondence manner, and the following are carried out:
gber(βkpk)＝f(βkpk)(1-f(βk-K/2pk-K/2))+(1-f(βkpk))f(βk-K/2pk-K/2),K/2+1≤k≤K (10)
the total bit error rate function is then:
Figure BDA0002284182880000082
to reduce iterative computations, f (β) may be omittedkpk)f(βk+K/2pk+K/2) Impact on the overall bit error rate of the system. The overall bit error rate function of the system is changed to:
Figure BDA0002284182880000091
under the constraint of the total transmission power limit set by the formula (2), introducing Lagrange multiplier to obtain an extreme value, wherein the Lagrange function is as follows:
Figure BDA0002284182880000092
wherein λ is Lagrange multiplication factor, for p in formula (13)kAnd solving the partial derivatives and setting the partial derivatives as 0 to obtain an equation set of a physical layer security algorithm based on the subcarrier power distribution scheme:
Figure BDA0002284182880000093
taking BPSK modulation mode in this text, substituting formula (6) into (2) and (14) to obtain K +1 closed function expressions of K +1 unknowns, and solving lambda and power distribution coefficient vector { p) of the power distribution schemekAnd (4) the following steps:
Figure BDA0002284182880000094
if p occurs during the solving processkNegative values, for { pkThe problem of negative values in p in the related literaturekSet to 0, i.e. the corresponding subcarrier does not participate in transmitting signals, and remove the corresponding equation, after which p is reallocatedkThe solution is performed in a cyclic manner. In order to meet the requirement of fully utilizing the frequency spectrum resource of the OFDM system in a physical layer security algorithm system combining subcarrier sequencing and XOR operation, negative value p occurskIs arranged as
Figure BDA0002284182880000101
The treatment is carried out on the raw materials,
Figure BDA0002284182880000102
for the average transmitting power in the equal power distribution method, theta is a minimum value and can be set in advance according to requirements. And then the power distribution coefficient is obtained through iterative operation.
The iterative operation method comprises the following steps:
firstly, initializing, determining signal-to-noise ratio (SNR) and obtaining total transmitting power under the condition of energy normalization
Figure BDA0002284182880000103
Setting the number of iterationsi, setting step size mu (0) to mu0；
Secondly, generating an initial power distribution value which satisfies the formula (2)
Figure BDA0002284182880000104
Generating a set of p under constraintk(0) And calculating lambda (0), corresponding to { β } for reducing iterative operationkAllocate by size { p }k(0)}；
Thirdly, the step size is approached, and the power coefficient { p of the subcarrier is updatedk}，λ(i)：
Figure BDA0002284182880000105
Figure BDA0002284182880000106
Four, negative power handling if { pkIf a negative value appears in (i +1) }, it is set to
Figure BDA0002284182880000107
And always maintaining the subcarrier power distribution coefficient p in the iterative operationkIs composed of
Figure BDA0002284182880000108
In equation (16), the subcarrier power coefficient { p ] is not updated by calculationkAnd d, updating mu (i +1), and returning to the step three to carry out iterative operation again.
Simulation analysis
For the physical layer security algorithm based on the subcarrier power allocation scheme provided by the invention, simulation analysis is shown in fig. 2. In simulation analysis, a channel is modeled into a multi-path channel model, each path adopts a mutually independent Rayleigh fading channel model, a noise model is additive white Gaussian noise, the adopted modulation modes are BPSK modulation and QPSK modulation, the number of subcarriers K is 64, the length of a cyclic prefix is 16, and the ISI is completely eliminated on the assumption that time synchronization is finished. Through an MATLAB simulation platform, 1e5 independent experiments are respectively carried out on OFDM symbols sent by a sending end under the conditions of different signal to noise ratios in a simulation mode, and the bit error rate (BER, BitErrorRate) conditions of a legal receiver and an eavesdropper are counted. It can be seen from the figure that under the state of low signal-to-noise ratio, the power optimization distribution effect is closer to the performance of power average distribution error rate, and the performance of error rate is optimized by 10% -20%; when the signal-to-noise ratio is increased to more than 10dB, the error rate performance after power optimization is greatly improved, the power distribution of the total subcarriers is considered, more power is distributed to the first half of subcarrier channels with better channel characteristics under the condition of high signal-to-noise ratio, and the second half of carriers are restrained by the bit error rate performance of the first half of carriers, so that the accumulated error is reduced, and the total bit error rate performance of the system is improved; more power is distributed to the sub-carrier with poor channel quality of the second half to the channel with poor channel characteristics, so that the receiving signal-to-noise ratio of the sub-channel with relatively poor channel quality is improved, the signal-to-noise ratio of the sub-channel with relatively good channel characteristics is reduced, the channel with relatively good channel characteristics is not easily subjected to noise interference under the condition of high signal-to-noise ratio, and the error rate performance is improved by the channel with relatively poor channel characteristics, so that the total error rate performance of the system is improved; when the signal-to-noise ratio of the system is increased to be about 20dB, the power distribution curve chart shows a trend of 'back-up', because the bit error rate performance tends to be stable to the limit under the condition of high signal-to-noise ratio, the performance effect of optimizing the bit error rate by power distribution is gradually reduced, but the bit error rate is still higher than the bit error rate value of the average power distribution scheme by one order of magnitude, and the bit error rate performance of a legal receiver can be greatly improved by a physical layer security algorithm based on the subcarrier power distribution scheme.
Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present invention and not to limit the same; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art will understand that: modifications to the specific embodiments of the invention or equivalent substitutions for parts of the technical features may be made; without departing from the spirit of the present invention, it is intended to cover all aspects of the invention as defined by the appended claims.

Claims (4)

1. A physical layer security algorithm based on a sub-carrier power allocation scheme is suitable for a multi-carrier communication network combining the characteristics of an OFDM system, and is characterized by comprising the following steps:
s1, firstly, the total bit error rate P of the OFDM systemberExpressed as the transmit power p on K sub-carrierskK is a function of 1, 2.. K }, and the bit error rate p of the kth subcarrier is the bit error rate p of the MPSK or MQAM modulation systemberCan be expressed as a function p of the signal-to-noise ratio of the channelber＝f(γk) K is 1,2, …, K, and the signal-to-noise ratio on the K-th subcarrier can be expressed as a function y of the allocated power for the channelk＝αkpkThe total bit error rate may be determined by the given channel state information αkThe arithmetic average of the bit error rates of the respective channels of (a) is obtained as:
Figure FDA0002284182870000011
s2, bit symbols carried by front K/2 sub-carriers corresponding to front K/2 sub-channels with larger channel quality module value square at a sending end are unchanged, bit symbols of rear K/2 sub-carriers corresponding to rear K/2 sub-channels are exclusive OR operations of original symbols and symbols on the front K/2 sub-carriers corresponding to the rear K/2 sub-channels, and when a receiving end decodes, the bit error rate of the front K/2 sub-carriers is unchanged gber(βkpk)＝f(βkpk) K is more than or equal to 1 and less than or equal to K/2, the bit error rates of the last K/2 sub-carriers are influenced by the bit error rates of the first K/2 sub-carriers in a one-to-one correspondence manner, and the bit error rate function of the receiving end is set to be g (β)kpk) Then, there are: gber(βkpk)＝f(βkpk)(1-f(βk-K/2pk-K/2))+(1-f(βkpk))f(βk-K/2pk-K/2),K/2+1≤k≤K；
S3. to reduce the iterative computation, f is ignored (β)kpk)f(βk+K/2pk+K/2) The influence on the total bit error rate of the system is obtained to obtain the total bit error rate function of the system
Figure FDA0002284182870000012
S4. in formula
Figure FDA0002284182870000013
Under the constraint of the set total transmitting power limit, introducing a Lagrange function and a Lagrange multiplier lambda to solve an extreme value, substituting an approximate expression of a channel bit error rate function corresponding to a subcarrier under a BPSK (binary phase Shift keying) modulation mode, and solving lambda and a power distribution coefficient vector { p ] of the power distribution schemekClosed solution, there are:
Figure FDA0002284182870000014
s5. if the subcarrier power p occurs in the process of solvingkAnd solving according to an iterative operation method under the condition of a negative value.
2. The OFDM system of claim 1, wherein the input data is divided into K parallel sub-data after serial-to-parallel conversion, and the transmission power on the K sub-channel is pkThen, the sub data stream is sent out through each orthogonal sub carrier by IFFT transformation and parallel-to-serial transformation to form an OFDM transmission signal.
3. The method as claimed in claim 1, wherein the Lagrange function in step S4 is:
Figure FDA0002284182870000021
λ is Lagrange multiplication factor, p in the formulakAnd solving the partial derivatives and setting the partial derivatives as 0 to obtain an equation set of a physical layer security algorithm based on the subcarrier power distribution scheme:
Figure FDA0002284182870000022
4. the method according to claim 1, wherein in step S5, the step of calculating the power distribution coefficient by iterative operation comprises:
firstly, initializing, determining signal-to-noise ratio (SNR) and obtaining total transmitting power under the condition of energy normalization
Figure FDA0002284182870000023
Setting iteration number i, and setting step length mu (0) to mu0；
Generating an initial power distribution value to satisfy
Figure FDA0002284182870000024
Generating a set of p under constraintk(0) And calculating λ (0), wherein
Figure FDA0002284182870000025
When the total emission power is evenly distributed to each subcarrier, the average emission power of each subcarrier and the number of subcarriers in the system is K, so that
Figure FDA0002284182870000026
For total transmit power, to reduce the iterative operation, corresponds to { β }kAllocate by size { p }k(0)}；
Thirdly, the step size is approximated, and the power coefficient { p of the subcarrier is updatedk}，λ(i)：
Figure FDA0002284182870000031
Four, negative power handling if { pkIf a negative value appears in (i +1) }, it is set to
Figure FDA0002284182870000032
And always maintaining the subcarrier power distribution coefficient p in the iterative operationkIs composed of
Figure FDA0002284182870000033
Wherein the subcarrier power coefficient { p ] is not calculated and updated any morekAnd d, updating mu (i +1), and returning to the step three for iterative operation.
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