CN102843588A - Method and system for intrusion detection for CMMB (China Mobile Multimedia Broadcasting) play system based on watermark technology - Google Patents
Method and system for intrusion detection for CMMB (China Mobile Multimedia Broadcasting) play system based on watermark technology Download PDFInfo
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Abstract
The invention relates to the field of detection application of CMMB (China Mobile Multimedia Broadcasting) video broadcast information, in particular to a method and a system for intrusion detection for a CMMB play system based on a watermark technology. The method comprises the following steps of: 1, watermark embedment, wherein CMMB broadcast message data are transformed into a transform domain, and a watermark is embedded into a CMMB broadcast message; 2, message transmission, wherein the watermark-embedded CMMB broadcast message is transmitted after being processed by a CMMB transmitting system; 3, message receiving, wherein a CMMB receiving terminal receives the broadcast message from a transmitting terminal and then processing and extracting the CMMB broadcast message and a watermark message; and 4, watermark detecting, wherein the watermark message extracted in the 3 is compared with a promissory watermark for monitoring, and an alarm is triggered when no watermark is monitored or the monitored watermark is wrong. According to the method and the system, the watermark message is used for encrypting the CMMB message, so that the characteristics of concealment, robustness and key uniqueness are achieved, therefore the reliability in intrusion detection can be effectively ensured and the track certification of the CMMB broadcast content can be realized.
Description
Technical field
The present invention relates to CMMB video broadcasting detection of information application, relate in particular to CMMB broadcasting detection system and method based on digital watermark.
Background technology
Digital watermark technology is a kind of Information Hiding Techniques in fact, and its basic thought comes from the secret writing art in ancient times.Video watermark is meant relevant with content of multimedia or more incoherent flag informations is directly embedded in the middle of the content of multimedia; But do not influence the use value of raw content; And be not easy to be discovered or notice to have only through the watermark detector of special use and just can monitor out hiding digital watermark information by people's vision system.It has characteristics such as robustness, fail safe, the transparency.Different research fields and different application environment according to the video watermark technology can have multiple different sorting technique.For example, can be divided into time domain watermark and frequency domain water mark etc. according to the research of watermark at different transform domains.And whether be compressed processing according to video data, can be divided into the video watermark of compression domain and uncompressed domain.
Watermark information forms after by the original watermark image conversion; The process watermark encoder is embedded into watermark signal in the middle of the video data stream; Before embed watermark, can be earlier to watermark information upset, encryption so that each watermark information that adds all is not quite similar; In transmission course, the video data stream of embed watermark may be subjected to various attacks to video content, the situation that simultaneously because wireless transmission, can decline, multipath interference, Doppler frequency shift etc. influences the acknowledge(ment) signal quality; At receiving terminal; Watermark decoder comes out watermark extracting through corresponding watermark extracting algorithm earlier; Then according to key to extracting to such an extent that watermark information such as deciphers at handled, and the video watermark that uses the Mathematical Modeling of normalizated correlation coefficient to judge to extract and the correlation of original embed watermark.
CMMB is the wireless video broadcast technology that China releases, and begins to take shape in the development of China.Because radio transmission not only receives various interference easily, and receives various attack more easily in communication process.It is reported; The prosperous promise satellite of China once repeatedly received the attack of hostile forces such as Falun Gong; Utilize China's satellite to carry out reaction propaganda, the satellite information transmission of China, long-distance education, television broadcasting etc. are caused have a strong impact on, influence country, social stable; The image of infringement China also influences the people's normal life in the world.Therefore, must take the necessary technology measure, the containment attack.In addition; If use wireless transmission method, then can be anywhere or anytime through wireless launcher emission information, the video information that shielding is really sent from the base station; In case cracked information by the lawless person; Or seize facilities such as base station, and then can have a strong impact on the communication of normal information, this has created opportunity for some lawless persons are engaged in illegal activity.
Yet in the standard about CMMB of domestic present formulation, do not comprise content, and security mechanism realizes safety monitoring based on the CMMB secure context of digital watermark.Therefore. development is carried out automatic monitoring technical accurately and rapidly to DTV broadcast quality, transmission quality and broadcast content and is become the professional task of top priority of broadcast television monitoring.
When realization is monitored digital broadcast video technical security, should not influence the quality of video image as far as possible or this influence is reduced to minimum.Will consider that simultaneously monitoring system should be simple, and cost is little, because later on maybe be with carrying out a large amount of deployment in China, cost is too high will to suppress its development.Monitoring system also should have real-time, and whether promptly be used for monitoring the content of being sent at any time legal.
Broadcast television monitoring is operated in the broadcast that ensures safety, strengthens governability, promotes to play an increasingly important role in the cause industry development.Therefore set up the CMMB safety monitoring system platform of a cover, realize that the safety monitoring to the CMMB video content is very necessary based on digital watermark.
Summary of the invention
The present invention is directed to the problems referred to above, effectively transmit, designed a kind of based on digital watermark CMMB Play System intrusion detection method and system for solving the CMMB information security.
At first aspect the CMMB transmitter module, realize the realization of watermark embedded technology.The embedded technology of watermark requires to accomplish to embed that algorithm is simple, complexity is low, and the embedding of watermark simultaneously should not produce significantly influence to video quality.Before watermark embeds, some simple processing are carried out in watermark, as watermark information being encrypted etc., can make watermark information more reliable, and in transmission course, have a mind to or attack unintentionally that for various stronger adaptive capacity is arranged at secure context.
The work that the work done and transmitter module do is just in time opposite receive surveying, and carry out the extraction work of watermark, and the watermark information that proposes is deciphered and compared with former watermark information.If do not monitor watermark information, then LED etc. lights and sends alarm sound simultaneously; If monitor watermark information, then complete new the and restorability of watermark information etc. is analyzed, if watermark receives continuous serious attack, send alarm signal.To select suitable Rules of Assessment in addition, the quality of the performance of watermark is assessed, the assessment monitoring of watermark is generally comprised the content of two aspects, the visual quality quality after the stack watermark is evaluated and tested, and to the evaluation and test of watermark robustness.
According to above-mentioned requirements, a kind of based on digital watermark CMMB Play System intrusion detection method, step is following:
Step 1, embed watermark: the data conversion of CMMB broadcast message embeds watermark in the CMMB broadcast message to transform domain;
Step 2, transmission information: the CMMB broadcast message of embed watermark is handled the back through the CMMB emission system send;
Step 3, message pick-up: the CMMB receiving terminal receives the broadcast message of transmitting terminal, handles the back and extracts CMMB broadcast message and watermark information;
Step 4, watermark detection: the watermark information that step 3 is extracted compares monitoring with the watermark of agreement, if do not monitor watermark or the watermark that monitors wrong, trigger warning.
Said method has just simply been realized watermark detection technique, but from fail safe, because the opening of wireless messages transmission is easy to intercepted and captured and crack.Therefore need to use safer encryption technology, information is further encrypted.Designed thus and have a kind of based on digital watermark CMMB Play System intrusion detection method of encryption technology, step is following:
Step 1, embed watermark: the data conversion of CMMB broadcast message embeds watermark in the CMMB broadcast message to transform domain;
Step 2, watermark ID encrypt: the watermark in the step 1 through the hash function computing, is generated ID, adopt symmetric encipherment algorithm that ID is encrypted, generate and encrypt ID;
Step 3, secret key encryption: adopt oval algorithm to encrypt the symmetric key of symmetric cryptography in the step 2; Promptly corresponding each CMMB receiving terminal is provided with a private key; Adopt with the corresponding PKI of private key of each receiving terminal and encrypt symmetric key, each receiving terminal is to having an encrypted symmetric key, a plurality of composition encrypted symmetric key groups; Then the encrypted symmetric key group and the encryption ID in the step 2 that generate are packaged into one group of data, are called the watermark keys bag;
Step 4, transmission information: the CMMB broadcast message of embed watermark is handled the back through the CMMB emission system send, simultaneously the watermark keys bag is also outwards sent;
Step 5, message pick-up: the CMMB receiving terminal receives the information of transmitting terminal, will distribute the CMMB broadcast message and the watermark keys bag of band watermark after the scanning, and watermark is extracted from CMMB information;
Step 6, watermark detection: with the watermark keys bag that receives in the step 5; Extract and encrypt ID and encrypted symmetric key group; Private key with receiving terminal is unique is deciphered the encrypted symmetric key group, decrypts the unique encrypted symmetric key to untiing of this receiving terminal, obtains symmetric key; Decipher encrypting ID with the close spoon of symmetry, obtain former ID; Whether the watermark of extracting in the step 5 is generated contrast ID with the hash function computing, and the ID that deciphering is obtained compares with contrast ID, detect consistently, if detect wrongly, or does not detect ID, triggers warning.
For each CMMB receiving terminal, be furnished with unique private key, decrypt the enciphered message of its corresponding PKI.To the hash function that computing is carried out in watermark, can be the same hash function of choosing in the pool of keys, or the hash function of picked at random in the pool of keys.And the watermark of adopting also can be same watermark, perhaps adopts the watermark of real-time change, constantly changes.
A kind of based on digital watermark CMMB Play System intruding detection system, include the transmitting terminal and the receiving terminal that have the CMMB broadcast system now, also comprise in addition with lower module:
The watermark merge module is used for watermark is embedded into original CBBM broadcast message;
Watermark encrypting embedding module is used for the hash function computing is carried out in watermark, carries out symmetric cryptography and SSH and encrypts;
The watermark information deciphering module is used to extract the ID of the enciphered message of reception, and with the watermark information computing that receives after the contrast ID that generates compare detection information;
Alarm module is used for not monitoring watermark or the watermark that monitors has the warning of false triggering;
The video quality monitoring device is used for monitoring at any time watermark and embeds the influence of CMMB information to video quality.
The present invention has designed a kind of effective CMMB information intrusion detection method and system; Adopt watermark information that CMMB information is encrypted; Uniqueness characteristics with disguise, robustness and close spoon can effectively guarantee the reliability of intrusion detection, can realize the CMMB broadcasted content carried out and follow the tracks of authentication; In time find illegally to intercut, disorderly broadcast phenomenon, and send warning.System is simple, and is cheap, is convenient to promote.Adopt two-way emission data simultaneously, carry out fast detecting, guarantee the real-time of data, do not influence video image quality, have practicality.Whether whether realization have pirate radio in the monitoring broadcast band and have the lawless person to forge video information and perhaps revise former video information, simultaneously to monitoring to such an extent that information is in time fed back the safety monitoring of CMMB.Guarantee that the CMMB broadcast video has a safety, health, stable broadcast platform, the video information for broad masses of the people provide high-quality promotes Social Culture development, prosperity.
Description of drawings
Fig. 1 is a CMMB safety monitoring system structure chart;
Fig. 2 is a CMMB safety monitoring flow chart;
Fig. 3 is the transmitting terminal schematic diagram;
Fig. 4 is the receiving terminal schematic diagram.
Embodiment
Below in conjunction with specific embodiment and Figure of description the present invention is described further.Specific embodiment described herein is only in order to explaining the present invention, and is not used in qualification the present invention.
Embodiment: a kind of based on digital watermark CMMB Play System intrusion detection method, step is following:
Step 1, embed watermark: the data conversion of CMMB broadcast message embeds watermark in the CMMB broadcast message to transform domain;
Step 2, transmission information: the CMMB broadcast message of embed watermark is handled the back through the CMMB emission system send;
Step 3, message pick-up: the CMMB receiving terminal receives the broadcast message of transmitting terminal, handles the back and extracts CMMB broadcast message and watermark information;
Step 4, watermark detection: the watermark information that step 3 is extracted compares monitoring with the watermark of agreement, if do not monitor watermark or the watermark that monitors wrong, trigger warning.
Said method has just simply been realized watermark detection technique, but from fail safe, because the opening of wireless messages transmission is easy to intercepted and captured and crack.Therefore need to use safer encryption technology, information is further encrypted.Designed thus and have a kind of based on digital watermark CMMB Play System intrusion detection method of encryption technology, step is following:
Step 1, embed watermark: the data conversion of CMMB broadcast message embeds watermark in the CMMB broadcast message to transform domain;
Step 2, watermark ID encrypt: the watermark in the step 1 through the hash function computing, is generated ID, adopt symmetric encipherment algorithm that ID is encrypted, generate and encrypt ID;
Step 3, secret key encryption: adopt oval algorithm to encrypt the symmetric key of symmetric cryptography in the step 2; Promptly corresponding each CMMB receiving terminal is provided with a private key; Adopt with the corresponding PKI of private key of each receiving terminal and encrypt symmetric key, each receiving terminal is to having an encrypted symmetric key, a plurality of composition encrypted symmetric key groups; Then the encrypted symmetric key group and the encryption ID in the step 2 that generate are packaged into one group of data, are called the watermark keys bag; Step 4, transmission information: the CMMB broadcast message of embed watermark is handled the back through the CMMB emission system send, simultaneously the watermark keys bag is also outwards sent;
Step 5, message pick-up: the CMMB receiving terminal receives the information of transmitting terminal, will distribute the CMMB broadcast message and the watermark keys bag of band watermark after the scanning, and watermark is extracted from CMMB information;
Step 6, watermark detection: with the watermark keys bag that receives in the step 5; Extract and encrypt ID and encrypted symmetric key group; Private key with receiving terminal is unique is deciphered the encrypted symmetric key group, decrypts the unique encrypted symmetric key to untiing of this receiving terminal, obtains symmetric key; Decipher encrypting ID with the close spoon of symmetry, obtain former ID; Whether the watermark of extracting in the step 5 is generated contrast ID with the hash function computing, and the ID that deciphering is obtained compares with contrast ID, detect consistently, if detect wrongly, or does not detect ID, triggers warning.
For each CMMB receiving terminal, be furnished with unique private key, decrypt the enciphered message of its corresponding PKI.To the hash function that computing is carried out in watermark, can be the same hash function of choosing in the pool of keys, or the hash function of picked at random in the pool of keys.And the watermark of adopting also can be same watermark, perhaps adopts the watermark of real-time change, constantly changes.
A kind of based on digital watermark CMMB Play System intruding detection system, include the transmitting terminal and the receiving terminal that have the CMMB broadcast system now, also comprise in addition with lower module:
The watermark merge module is used for watermark is embedded into original CBBM broadcast message;
Watermark encrypting embedding module is used for the hash function computing is carried out in watermark, carries out symmetric cryptography and SSH and encrypts;
The watermark information deciphering module is used to extract the ID of the enciphered message of reception, and with the watermark information computing that receives after the contrast ID that generates compare detection information;
Alarm module is used for not monitoring watermark or the watermark that monitors has the warning of false triggering;
The video quality monitoring device is used for monitoring at any time watermark and embeds the influence of CMMB information to video quality.
Can know that from Fig. 1 and Fig. 2 this system at first is input to watermark encoder with original CMMB video and the pretreated watermark information of process and carries out watermark embedding processing; Carry out the RS coding and the OFDM modulation treatment of base band then; The signal map that to pass through Base-Band Processing is a radiofrequency signal, mails to the CMMB synchronous satellite through up broadcast channel and up distribution channels.To pass through ground supplement forwarding net at receiving terminal receives to such an extent that signal carries out the conversion of radio frequency to base band earlier; Carry out Base-Band Processing then, RS decoding/OFDM demodulation etc. are carried out wavelet transformation with the information that obtains at last; Whether monitoring contains the correlation of watermark and contained watermark and original watermark; If do not detect watermark or the correlation of the watermark of monitoring and original watermark be lower than threshold values, then send warning, and inform the staff through network.This system is based on the proposition of video digital watermark technology.
Watermark embeds: earlier watermarking images is done the conversion on the time domain, purpose is watermark information to be carried out out of order, reaches the effect of encryption.Employing is technological based on the image scrambling of Arnold conversion:
The size of N representing matrix, mod is modular arithmetic.Digital picture can be seen as a two-dimentional square, can arrange again through the location of pixels of image after the conversion, and it is disorderly and unsystematic that this sampled images can seem, thereby realized the scrambling encryption effect to image.Because the Arnold conversion has periodically, if repeat carry out the Arnold conversion, through restoring original image after certain number of times.Such as the watermarking images size of using among this paper is 64 * 64, and the cycle is 48.
Adopt the Daubechies wavelet transformation that the original two field picture X of embed watermark that wants is carried out three grades of wavelet decomposition then, obtain low frequency component wavelet coefficient x (LL
, i, j), horizontal component wavelet coefficient x (LH
, i, j), vertical component wavelet coefficient x (HL
, i is j) with diagonal components wavelet coefficient x (HH
, i, j), n=1,2,3; With reference to analysis, press the vertical component wavelet coefficient x (HL that following formula is revised original video two field picture bottom in the value of each sampled point according to the watermark bianry image to embedded location
3, i is j) with horizontal component wavelet coefficient x (LH
3, i, j):
1) when the watermarking images sampled point (i, value j) is 0 o'clock:
2) when the watermarking images sampled point (i, value j) is 1 o'clock:
Wherein (i j) is the embed watermark wavelet subband coefficients of images to X', and (i j) is the original video frame wavelet subband coefficients of images to X.This algorithm is according to the value of watermarking images sampled point, revises horizontal component wavelet coefficient x (LH behind three grades of wavelet transformations of original video two field picture
3, i is j) with vertical component wavelet coefficient x (HL
3, i, j), because through behind the wavelet transformation, the energy of two field picture mainly concentrates on low frequency LL subband, high-frequency sub-band mainly is vertical, level and cornerwise marginal information, the energy that contains is less.Usually, the vision of human eye is responsive to image smoothing part details and slight change, and not too responsive to the minor variations of image border or texture part.Therefore can't cause big influence to the reconstruct of original image to its modification, and, make that adding watermarking images has good robustness through modification to wavelet coefficient.
is watermark embed strength in the formula; Its value should be weighed invisibility and robustness requirement;
is big more; Though watermark is strong more, but the picture quality of embed watermark will reduce.Otherwise value is little, though picture quality has improved, can weaken the robustness of watermark simultaneously.The best interval of
is (3.5～12) in this experiment.At last, horizontal component wavelet coefficient after use was revised and vertical component wavelet coefficient carry out three grades of wavelet reconstructions and obtain final embed watermark image.
The leaching process of watermark: when extracting watermark; Also need carry out segmentation to the original video watermark; In every section video, choose the frame of video of specific embed watermark earlier, the two field picture of original embed watermark is carried out three grades of wavelet decomposition, obtain low frequency component wavelet coefficient x (LL<img file="635073DEST_PATH_IMAGE002.GIF" he="24" img-content="drawing" img-format="GIF" inline="no" orientation="portrait" wi="9" />, i, j), horizontal component wavelet coefficient x (LH<img file="509619DEST_PATH_IMAGE003.GIF" he="25" img-content="drawing" img-format="GIF" inline="no" orientation="portrait" wi="12" />, i, j), vertical component wavelet coefficient x (HL<img file="793970DEST_PATH_IMAGE003.GIF" he="25" img-content="drawing" img-format="GIF" inline="no" orientation="portrait" wi="12" />, i is j) with diagonal components wavelet coefficient x (HH<img file="268813DEST_PATH_IMAGE003.GIF" he="25" img-content="drawing" img-format="GIF" inline="no" orientation="portrait" wi="12" />, i, j), n=1,2,3; Compare its corresponding horizontal component wavelet coefficient and vertical component wavelet coefficient x (LH<sub >3</sub>, i, j) and x (HL<sub >3</sub>, i, difference j)<img file="296812DEST_PATH_IMAGE007.GIF" he="18" img-content="drawing" img-format="GIF" inline="no" orientation="portrait" wi="16" />If,<img file="291444DEST_PATH_IMAGE007.GIF" he="18" img-content="drawing" img-format="GIF" inline="no" orientation="portrait" wi="16" >0, represent that then watermarking images is 0 in the value of this sampled point, otherwise, if<img file="481117DEST_PATH_IMAGE007.GIF" he="18" img-content="drawing" img-format="GIF" inline="no" orientation="portrait" wi="16" /><0, be expressed as 1.Carry out the watermark information that portfolio restructuring obtains embedding according to obtaining watermark information in the value of each sampled point; Then the watermark information that obtains is carried out T-k scramble (T is the Arnold scramble cycle of watermarking images, the scramble number of times of watermarking images when k is embedding) and obtain final watermarking information.
Fig. 3 transmitter operation principle: transmitter will realized the CMMB emission function: on sampling, carrier frequency, the basis of encoding, interweaving etc., to be implemented in embed watermark information among the information code current that collects, do not influence video quality simultaneously.
Fig. 4 operation of receiver principle: the working method of receiver and transmitter are just in time opposite, need to realize functions such as deinterleaving, decoding, can from the signal that receives, monitor whether contain watermark information simultaneously.
Monitoring result and watermark additive effect to receiver are analyzed.If monitor watermark, then integrality of the watermark information that monitors etc. is analyzed, if watermark is imperfect or do not conform to former watermark information, then send warning, inform the monitoring personnel.
The purpose of CMMB safety monitoring system is in order to guarantee that it broadcasts safely, in time finds signal interruption, illegally problem such as intercuts, and examines the broadcast effect, guarantees programme content safety.
Claims (6)
1. one kind based on digital watermark CMMB Play System intrusion detection method, it is characterized in that said method step is following:
Step 1, embed watermark: the data conversion of CMMB broadcast message embeds watermark in the CMMB broadcast message to transform domain;
Step 2, transmission information: the CMMB broadcast message of embed watermark is handled the back through the CMMB emission system send;
Step 3, message pick-up: the CMMB receiving terminal receives the broadcast message of transmitting terminal, handles the back and extracts CMMB broadcast message and watermark information;
Step 4, watermark detection: the watermark information that step 3 is extracted compares monitoring with the watermark of agreement, if do not monitor watermark or the watermark that monitors wrong, trigger warning.
2. one kind based on digital watermark CMMB Play System intrusion detection method, it is characterized in that said method step is following:
Step 1, embed watermark: the data conversion of CMMB broadcast message embeds watermark in the CMMB broadcast message to transform domain;
Step 2, watermark ID encrypt: the watermark in the step 1 through the hash function computing, is generated ID, adopt symmetric encipherment algorithm that ID is encrypted, generate and encrypt ID;
Step 3, secret key encryption: adopt oval algorithm to encrypt the symmetric key of symmetric cryptography in the step 2; Promptly corresponding each CMMB receiving terminal is provided with a private key; Adopt with the corresponding PKI of private key of each receiving terminal and encrypt symmetric key, each receiving terminal is to having an encrypted symmetric key, a plurality of composition encrypted symmetric key groups; Then the encrypted symmetric key group and the encryption ID in the step 2 that generate are packaged into one group of data, are called the watermark keys bag;
Step 4, transmission information: the CMMB broadcast message of embed watermark is handled the back through the CMMB emission system send, simultaneously the watermark keys bag is also outwards sent;
Step 5, message pick-up: the CMMB receiving terminal receives the information of transmitting terminal, will distribute the CMMB broadcast message and the watermark keys bag of band watermark after the scanning, and watermark is extracted from CMMB information;
Step 6, watermark detection: with the watermark keys bag that receives in the step 5; Extract and encrypt ID and encrypted symmetric key group; Private key with receiving terminal is unique is deciphered the encrypted symmetric key group, decrypts the unique encrypted symmetric key to untiing of this receiving terminal, obtains symmetric key; Decipher encrypting ID with the close spoon of symmetry, obtain former ID; Whether the watermark of extracting in the step 5 is generated contrast ID with the hash function computing, and the ID that deciphering is obtained compares with contrast ID, detect consistently, if detect wrongly, or does not detect ID, triggers warning.
3. method according to claim 2 is characterized in that being furnished with unique private key for each CMMB receiving terminal, decrypts the enciphered message of its corresponding PKI.
4. method according to claim 2 is characterized in that described hash function is the same hash function of choosing in the pool of keys, or the hash function of picked at random in the pool of keys.
5. method according to claim 2 is characterized in that described watermark can be same watermark, perhaps adopts the watermark of real-time change.
6. one kind based on digital watermark CMMB Play System intruding detection system, it is characterized in that comprising:
The watermark merge module is used for watermark is embedded into original CBBM broadcast message;
Watermark encrypting embedding module is used for the hash function computing is carried out in watermark, carries out symmetric cryptography and SSH and encrypts;
The watermark information deciphering module is used to extract the ID of the enciphered message of reception, and with the watermark information computing that receives after the contrast ID that generates compare detection information;
Alarm module is used for not monitoring watermark or the watermark that monitors has the warning of false triggering;
The video quality monitoring device is used for monitoring at any time watermark and embeds the influence of CMMB information to video quality.
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| CN110838999A (en) * | 2019-11-19 | 2020-02-25 | 济南大学 | OFDM system peak power optimization method based on Arnold transformation |
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| CN102361480A (en) * | 2011-06-29 | 2012-02-22 | 武汉理工大学 | Digital watermarking method applicable to safety of data transmission of smart grid |
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| CN110838999A (en) * | 2019-11-19 | 2020-02-25 | 济南大学 | OFDM system peak power optimization method based on Arnold transformation |
| CN110838999B (en) * | 2019-11-19 | 2022-05-03 | 济南大学 | OFDM system peak power optimization method based on Arnold transformation |
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