security of wireless communications has becoming increasingly important .openness of wireless networks makes them vulnerable to spoofing attacks where an unauthorized user masquerades as another legitimate user . in the past, conventional cryptographic security mechanisms were used to foil such attacks , in which the identity of a user should be authenticated through a challenge - response process , namely , authentication and key agreement ( aka ) protocol . the aka protocolwas revised for stronger security from second - generation ( 2 g ) to fourth - generation ( 4 g ) systems .a recent aka protocol , known as evolved packet system aka ( eps - aka ) , has been proposed for the long term evolution ( lte ) system .the security of state - of - the - art eps - aka protocol comes from computational complexity , namely , the adversary has limited computational power .it is believed that more efforts should be done to prevent potential innovative attacks since the wireless medium offers novel avenues for intrusion .  in recent years , various efforts have been made in authenticating the transmitter and receiver at the physical layer . in general, these physical layer authentication schemes can be classified as key based or keyless , according to whether a secret key shared between the transmitter and receiver is exploited to authenticate each other or not . in the keyless authentication schemes , some specific features of either the transmitting device or the specific channel between the legitimate users were exploited in order to authenticate the transmission . as an initial trusted transmissionis often required for identifying the features , they might be difficult to implement in some practical scenarios . instead , various key based authentication schemes are closer to the traditional challenge - response mechanism , but less prone to attacks due to the protection from the unique randomness of physical characteristics .  for key based challenge - response authentication schemes , two legitimate users , alice and bob , shared a secret key .whenever alice transmits a random number as the challenge , bob sends back a response ( often called a tag ) , which is the output of a cryptographic hash function with both the challenge and key as its inputs . by verifying the response with a locally generated tag ,bob s identity can be confirmed .indeed , both schemes in follow this authentication mechanism , which are implemented at the physical layer . in ,both alice and bob presume public challenges , which are used to generate tags with the shared key , and the tag is physically encapsulated as an embedded fingerprint , which is conveyed with the primary transmission by superposition .the embedded fingerprint is often allocated with low power , which is further corrupted by the channel noise .hence , its recovery is in general difficult for the adversary , as she / he faces a fundamental information - theoretic challenge , not purely a computational one .the physical layer challenge - response authentication mechanism ( phy - cram ) proposed in implements the conventional challenge - response process at the physical layer , where the randomness of fading channel s amplitude is used to protect both challenge and response ( tag ) .recently , we proposed a physical layer phase challenge - response authentication scheme ( phy - pcras ) for multicarrier transmission in .it requires the channel reciprocity and the randomness of channel - phase response for the protection of the shared key from possible eavesdropping .  by exploiting the randomness of physical channels, various physical layer authentication schemes may ensure unconditional security at least for some bits of the shared key ( which can not be broken even if the adversary has unlimited computational power ) .however , this enhanced security depends heavily on the underlying physical channel , which is often out of our control . in the worst case of static channels ( for example , line - of - sight communications ), this kind of unconditional security may not be guaranteed .in this paper , we consider to develop an improved version of phy - pcras for practical ofdm transmission , which can guarantee enhanced security even in the worst case of static channels .the main contributions of this paper are summarized as follows :  1 .we propose a novel artificial - noise - aided phy - pcras ( ana - phy - pcras ) for practical ofdm transmission , where the tikhonov - distributed artificial noise is introduced to interfere with the phase - modulated key for resisting possible attacks .a strictly - positive key equivocation can be ensured even for the worst case scenario .we make a fine improvement on phy - pcras , where the estimate of phase differences between subcarriers is simply replaced by the direct estimate of subcarrier phases .this makes the implementation of phy - pcras simpler .a time - separated subchannel allocation scheme is provided to obtain a sufficient number of uncorrelated subchannels .then , a modified ana - phy - pcras is proposed for use of time - separated subchannels , which shows its robustness in verification for alleviating the discontinuity of channel phase at far - separated time slots .various practical issues are discussed with non - ideal ofdm transmission , including imperfect carrier and timing recoveries . in particular , we show that small sampling offsets often result in significant frequency offsets along the allocated subcarriers , which should be compensated for proper verification . 5 .we also provide an application model for generating the shared keys between two legitimate nodes in 4 g mobile networks .hence , the conventional challenge - response authentication scheme employed in 4 g networks might be replaced by ana - phy - pcras with enhanced security .the rest of the paper is organized as follows . in sectionii , we propose an ana - phy - pcras for perfect ofdm transmission , and a time - separated subchannel allocation scheme is presented , along with a modified ana - phy - pcras .section - iii is devoted to practical issues with non - ideal ofdm transmission .the security analysis of ana - phy - pcras is given in sectiion - iv .simulation results are presented in section - v , and the conclusion is made in section - vi .in this paper , we employ a common alice - bob - eve model , where two trusting parties , alice and bob , share some common secrets and they want to authenticate each other , while eve , as an opponent , has no any knowledge about the shared secrets and wants to impersonate alice or bob .  from the viewpoint of modern cryptography ,the development of cryptographic primitives should consider the worst case scenario . in the past ,various physical layer authentication schemes were proposed and claimed enhanced security of information - theoretic nature , which , however , depends heavily on the randomness of the underlying physical channel . whenever the physical channel happens to be static ,there is simply no guarantee of enhanced security .therefore , it is essential to consider the worst case of static channels between alice and bob for developing physical layer authentication schemes .we propose a novel ana - phy - pcras for ofdm transmission , which makes two nontrivial improvements on phy - pcras .firstly , channel uncertainty has been proved to be essential for ensuring enhanced security in various physical layer cryptographic approaches . for ana - phy - pcras , we introduce the tikhonov - distributed artificial noise to interfere with the phase - modulated key , which could be used to create artificial channel uncertainty . therefore , the minimum amount of enhanced security of information - theoretic nature can be guaranteed even in the worst case scenario .this contrasts sharply to various reported physical layer authentication schemes , which rely solely on the randomness of the physical channel .whenever the channel randomness appears , ana - phy - pcras can be protected by the uncertainty from both the physical channel and artificial noise .secondly , we make a fine improvement on phy - pcras , where the estimate of phase differences between subcarriers is simply replaced by the direct estimate of subcarrier phase .it does work as we use a noncoherent metric for verification , which remains unchanged for any random but constant phase increment over all subcarriers .in this paper , we assume a multipath fading channel between alice and bob .it is often associate with a channel coherence time , below which the channel is considered as temporally correlated .assuming an ofdm system with subcarriers , a bandwidth of hz and symbol length of seconds , of which , seconds are due to the length of cyclic prefix ( cp ) , and . in the following , we use to denote the sampling period .the transmitter uses the waveforms \\  0 , \quad \quad \quad \quad \quad \quad \quad \quad \text{otherwise}\end{array}\right.\end{aligned}\ ] ] and the transmitted baseband for an ofdm symbol is where are complex numbers from a signal constellation .since we focus on a phase challenge - response scheme , -ary psk modulation is preferred , and hence .the signal is transmitted over a frequency - selective fading channel where is the delay of the -th path and is the corresponding complex amplitude . assuming the receiver filter is flat within the signal bandwidth , the received signal is where is an additive white gaussian noise process .  sampling the signal at time instants yields for convenience ,assume that the delays s are integer multiples of . with the sampling period of ,the number of resulting samples for each ofdm symbol is , where denotes the length of cp . after removing the guard interval and taking the fast fourier transform ( fft ) to the received signal, we get where with , and which keeps constant at least over one ofdm symbol .  let denote the carrier frequency at the subcarrier . with perfect ofdm transmission, it can be viewed as parallel multicarrier transmission with a set of carriers .   as a challenge - response process for ana - phy - pcras, alice sends a challenge signal to bob , bob sends back a response signal , which can be verified by alice with the shared secret key . with ofdm transmission , subcarriers are selected .we shall show later that the perfect security of ana - phy - pcras requires independent fading among carriers .hence , these carriers should be well separated .let  ]. in practice , the allocated subchannels are often equally spaced , and the value of determines the minimum mutual correlation .   consider a time - invariant version of the multipath fading channel model ( [ eq : htau ] ) , where s are zero - mean complex gaussian variables with a power delay profile and .the normalized delays s are assumed to be uniformly and independently distributed over the length of cp (  ] , namely , .\end{aligned}\ ] ]  with perfect ofdm transmission , the waveforms can be viewed as `` mutually orthogonal '' at the receiver even they undergo multipath fading channels ( after insertion and deletion of the cp ) .equivalently , the received signal at bob can be represented as .\end{aligned}\ ] ] where are assumed to be constant during  ] in the form of .\end{aligned}\ ] ] where since we assume -ary psk modulation , and denotes the introduced artificial noise .we assume that are independent and identically distributed ( i.i.d . ) with the same probability - density - function ( pdf ) . here , we employ the tikhonov distribution for , namely , .\end{aligned}\ ] ] where determines the dispersion of the distribution , and is the modified bessel function of the first kind and 0-th order , and is confined to a support of length in the vicinity of 0 .the use of tikhonov distributed artificial noise is due to the fact that the tikhonov distribution maximizes the entropy when the mean and variance of ( or the circular mean and circular variance of ) are specified .then , the received signal at alice is given by where  ] , and each sub - key can be delivered through carriers .when alice challenges at time instants with subcarriers for each time instant , bob extracts subcarrier phases at each time instant , and responds to alice at time instant with a tagged signal containing the -th sub - key . finally , the received signal at alice during  ] , and } ] , which means that channel phase discontinuity is observed over far - separated time slots .hence , this discontinuity at different time slots should be seriously considered for verification , and a noncoherent combining method is preferred . here, we propose a suboptimum hypothesis testing method , which employs a noncoherent combining metric   with sufficient separation in time , s are independent complex gaussian variables of the same variance .the sum of squares of independent complex gaussian variables of the same variance is noncentrally chi - squared distributed with degrees of freedom , which yields the pdf of where both and can be again estimated from the moments of as shown in ( [ eq : riceest ] ) .the cumulative distribution of can be described by the generalized marcum q - function , which is given by with .the authentication is typically claimed if . the threshold of this test is determined for a false acceptance rate ( or false alarm probability ) according to the distribution of  the successful authenticate rate ( or detection probability ) can be simply computed as   compared to ana - phy - pcras , the use of ( [ eq : mod1 ] ) results in noncoherent combining loss for the modified scheme , which , however , does not require the assumption of phase continuity among different time slots .for a practical ofdm receiver , there is often a local carrier frequency oscillator for demodulation , with which the received radio signal can be converted from radio frequency into baseband .then , the baseband signal is sampled and discrete - time samples are obtained for subsequent processing , where the sampling clock is derived from a local oscillator . practically , both timing and carrier references are asynchronous between the transmitter and receiver .hence , in a real - world passband transmission system , the following parameters can cause disturbances in the receiver .  1.  the carrier frequency oscillator for demodulation at the receiver can be different with the transmitter oscillator , resulting in a carrier frequency offset of and a random but constant phase offset of .the sampling time at the receiver has a constant symbol offset compared to the transmitter time .the sampling time at the receiver has a sampling clock frequency offset of compared to the transmitter time , where the sampling period employed at the receiver is deviated from the desired sampling period ._ for simplicity of notation and in order to focus on the pure imperfections at the receiver , we do not include the artificial noise in this section , which , however , is fully considered in simulations_.   whenever the condition 1 ) occurs , the received samples can be written as where , and is included in for convenience .as the multipath channel is assumed to be constant during at least one ofdm symbol , we simply use instead of for the path gain .  after the removal of guard interval from the received samples , the application of fft yields where denotes the interchannel interference ( ici ) . due to the use of noncoherent metric ( [ eq : mod1 ] ) for verification, the extra phase has no impact .it should be noted that with the presence of carrier frequency offset , the direct loss in snr is db and the frequency offset noise power due to the introduction of ici can be approximated by  for the normalized channel gains , namely , .   with a non - zero symbol offset ,the channel impulse response `` seen '' by the receiver is also shifted in the time scale by , which yields since is assume to be constant during at least one ofdm symbol .just like in ( [ eq : hk ] ) , the equivalent channel gain at the carrier can now be written as   with a time - shift of , the input samples for demodulation are also shifted by , which results in both intersymbol interference ( isi ) and ici .the isi arises since one ofdm symbol window with a nonzero shift will actually be covered by two ofdm symbols , while ici is due to the corruption of orthogonality among subcarriers when .hence , by neglecting a minor loss ( ) in snr for large , demodulation of the subcarrier via fft yields  where is the disturbance caused by both ici and isi .the disturbance can be well approximated by gaussian noise with power  where   with a challenge - response process , ana - phy - pcras involves two rounds of communications .hence , the receiver imperfections from both alice and bob should be considered together .let , be the normalized sampling symbol offsets of alice s and bob s receivers , respectively . when alice challenges , bob estimates the channel phase at subcarrier . with the sampling symboloffset , this phase estimate must include an extra increment over frequency , namely , where is the non - biased estimation error with zero mean , and .when bob responds to alice , alice also introduces her sampling symbol offset , and she can finally manage to obtain parallel channels at subcarriers as where , , and denotes the interference due to the sampling offset at alice .   with a sampling clock period of ,the received samples at can be written as } \nonumber \\    & = & \sum_k \left(x_k e^{j2\pi k \frac{n_g\varsigma}{n}}\right ) h_k e^{j2\pi n\frac{k+k\varsigma}{n}}.\end{aligned}\ ] ] demodulation of the subcarrier yields  where and is the disturbance caused by ici .consider a sampling clock frequency offset up to ppm ( ) for an ofdm system of subcarriers .the multiplicative factor results in some loss in snr , which is less than 0.3 db in the worst carrier .the sampling frequency offset also results in an incremental phase rotation over subcarriers , which is the same to ( [ eq : fy ] ) .   with a challenge - response approach , we focus on the final verification in the response stage . as depicted in section - iii.c , an equivalent frequency offset due to sampling offset at the stage of challengingshould be considered .  by including all the above imperfections , the demodulated subcarrier at given by where  and is the disturbance caused by both ici and isi .consider the modified ana - phy - pcras for the time - separated subchannels . with the channel model ( [ eq : imodel ] ) under practical imperfections ,we propose to employ a refined non - coherent combining metric where , and time slots starting at are employed .compared to ( [ eq : mod1 ] ) , the refined metric includes the effect of residual frequency - offset ( [ eq : resfq ] ) due to various imperfections .  for the scenario .[ s1 ] with , we have that , which can result in a very large frequency offset ( [ eq : resfq ] ) even with a small value of .therefore , the search of frequency shown in ( [ eq : rmod ] ) should be seriously considered in practice .noting that the contribution of in ( [ eq : resfq ] ) due to sampling clock frequency offset is minor compared to sampling offset .in this section , security analysis is presented . for ease of analysis ,we focus on the basic ana - phy - pcras over a single ofdm symbol .   as a passive attacker , eve only monitors all frames inside the network during authentication , and tries to learn from whatever it gets .  by monitoring the response signal from bob , the received signal at eveis given by where , is eve s channel - phase response when bob transmits a zero - phase sinusoidal signal at frequency , is bob s estimate of channel response when alice challenges , and is the noise process observed by eve .  due to the orthogonality among different subcarriers , one can retrieve the discrete signal vector from ( [ eq : pa ] ) as ^t ] .   for wireless rich - scattering fading channels ,the observations of eve remain independent from the channel - specific observations of alice and bob , if eve is located more than half a wavelength away from these two users . in this case , eve can not get a feasible estimate about based on the monitoring signal when alice initiates a challenge . hence , it is fair to assume that eve has no any knowledge about either or .let  ] .if is uniformly distributed over  ] , which is irrespective of the distribution of .let denote the pdfs of , respectively .for a uniformly distributed random variable on a circle , we have that if  ] .if the parallel fading channels at subcarriers between alice and bob are independent , we have that either or their estimates are i.i.d , each of which is uniformly distributed over  ] .this means that therefore , there is no hope for eve to extract any reliable information about the key . in this case ,information - theoretic security can be perfectly ensured .the worst case for the purpose of authentication is to consider the scenario , where the parallel channels between bob and alice ( or eve ) are all assumed to be static over a long period .this means that can be well estimated before the start of authentication and further compensated in ( [ eq : phi ] ) by eve , who may get a clean version of the received signal   as eve can be located very close to bob , her observation may be free of noise , which is the worst case for addressing the security issue . in this case , eve can directly extract the phase of , namely , where .  hence , the mutual information between and can now be computed as where ^l}\end{aligned}\ ] ] with denoting the modified bessel function of the first kind and 1-th order .since s are uniformly , i.i.d . over the discrete values , where for equally - distributed -psk constellations .  consider the worst case scenario , where the channel between alice and bob is static and eve can get a noise - free version of the transmitted signal by either alice or bob. with ana - phy - pcras , eve s key equivocation can be lower bounded as \end{aligned}\ ] ] if the introduced artificial noise is with the pdf of .it was shown in that \nonumber \\   & = & i(\phi_0^{l-1 } ; \varphi_0^{l-1}|\lambda ) - i(\lambda;\phi_0^{l-1}|\varphi_0^{l-1}),\end{aligned}\ ] ] where as is independent of , and the first term denotes the coherent mutual information . by assuming a coherent channel model of , it can be efficiently computed as \nonumber \\         & = & \log_2 m -  e_{\varphi,\upsilon}\left[\log_2\frac{\sum_{\bar{\varphi } \in \omega}f_\upsilon(\varphi+\upsilon-\bar{\varphi})}{f_\upsilon(\upsilon)}\right].\end{aligned}\ ] ] by noting that , the conditional equivocation can be bounded as ,\end{aligned}\ ] ] which could be strictly positive for a properly chosen distribution .in developing ana - phy - pcras , we have assumed that alice and bob share two secret keys , namely , . in practical wireless network scenarios ,it is interesting to investigate how alice and bob can share secrets before authentication .this , indeed , depends on the underlying wireless network .  for 4 g mobile networks ,we consider a typical scenario where a user equipment ( ue / alice ) , wants to authenticate with an evolved node - b ( enb / bob ) .the possibility of sharing common secrets between alice and bob comes from the long - term secret key ( ) stored on the universal subscriber identity module ( usim ) and in the authentication center ( auc ) .the challenge - response authentication process can be depicted in fig .[ fig : sysmodel ] .as shown , a pair of shared keys can be derived from the long - term key , namely , where rand , sqn , amf can be considered as random numbers , and are the message authentication function used to compute mac and res ( xres ) , respectively. please refer to for more details .consider that the system operates at carrier frequency of ghz with a bandwidth of mhz , which is divided into tones with a total symbol period of 108.8 , of which 6.4 constitutes the cp .hence , and . parallel subchannels are obtained using both ifft and fft . for ana - phy - pcras , subchannels with equal bandwidth interval ( ) are selected with the minimum normalized correlation of 0.7136 among subchannels .for the modified ana - phy - pcras , subchannels with equal bandwidth interval ( ) are selected with the minimum normalized correlation of 0.2468 . to allocate sub - channels ,we repeatedly employ such carriers at times , where and can be employed for example . with the use of large , the allocated subchannels at different time slots could be nearly uncorrelated .however , it should be noted that the use of large could cause noticeable end - to - end delay . in the case of and ,the end - to - end delay is at least ms , which is comparable to the time delay due to authentication in lte .  in simulations ,we employ the channel model with exponentially decaying power - delay profile , where a total of 20 multipaths are assumed , the normalized delays are assumed to be uniformly and independently distributed over the length of cp (  ] is employed .the key equivocation decreases when increases .when no artificial noise is introduced , the key equivocation is simply reduced to zero for this worst case scenario , which means that there is no guarantee of information - theoretic security for phy - pcras .clearly , the use of higher - order modulation scheme can strengthen the system security as the key equivocation increases ._ we comment here that there is simply no guarantee of information - theoretic security for various reported physical - layer authentication schemes if eve is very close to bob and hence she can get a noise - free version of the transmitted signal by bob , and in the same time the channel between alice and bob is unfortunately static over the period of authentication . _   through extensive monte - carlo simulations ,we investigate the pdfs of under two hypothesis , which can be well employed to evaluate both successful authentication and false acceptance rates .the proper choice of the threshold can also be determined from the pdfs of .    and at snr = 5 db for phy - pcras.,scaledwidth=50.0% ]   and at snr = 10 db and for ana - phy - pcras.,scaledwidth=50.0% ]  s.,scaledwidth=50.0% ]  ) .,scaledwidth=50.0% ]  with subchannels selected among ofdm subchannels ( ) for a single ofdm symbol , fig .[ fig : pdf1 ] shows empirical pdfs of and at snr=5 db for phy - pcras , while fig .[ fig : pdf2 ] shows empirical pdfs of and at snr=10 db for ana - phy - pcras with . in both figures ,bpsk constellation is assumed . as claimed in section - iii , and both chi - square distributed . hence , chi - square distributions are also given in both figures , where are directly estimated through monte - carlo simulations . as shown , the theoretical chi - square distributions are coincided well with the empirical distributions even though subchannels are correlated . since the pdf of is far apart from that of even at the snr of 5 db in fig .[ fig : pdf1 ] , almost ideal roc curve can be observed . with the introduction of artificial noise ,the roc performance of ana - phy - pcras is clearly inferior to that of phy - pcras as indicated by fig .[ fig : pdf2 ] .next , we investigate the effect of on the roc curves for ana - phy - pcra , which is depicted in fig .[ fig : rocbeta ] for different s . from both fig .[ fig : rocbeta ] and fig .[ fig : eqv ] , we conclude that there is a fundamental tradeoff between the roc performance and security , which is controlled by the amount of artificial noise ( ) .  in fig .[ fig : eqv ] , we have shown that the use of qpsk constellation is significantly superior to the use of bpsk constellation for the security of ana - phy - pcras . here, we show their roc curves in fig .[ fig : rocbq ] for ana - phy - pcras with both bpsk and qpsk constellations , where is used .noting that the use of qpsk constellation requires the size of key doubled compared to the use of bpsk constellation .as shown , the same roc curves are observed for both bpsk and qpsk .hence , the use of higher order constellations can significantly improve the security of ana - phy - pcras , which is very helpful in practical scenarioes whenever the number of allocated subchannels is not enough compared to the size of the shared key .and at snr=10 db with time - separated subchannel allocation ( ) and .,scaledwidth=50.0% ]  we also consider the modified ana - phy - pcras , where subchannels allocated for four ( ) far - separated ofdm symbols with subchannels allocated for each ofdm symbol .[ fig : pdf3 ] shows its empirical pdfs of and at snr=10 db and .although the modified ana - phy - pcras can be better protected by the randomness of the physical channel ( due to well - separated subchannels in both time and frequency ) , it , however , is slightly inferior to ana - phy - pcras in the roc performance as indicated in fig .[ fig : pdf2 ] and fig .[ fig : pdf3 ] , due to noncoherent combining loss .we consider practical imperfections in both the challenge and response stages .imperfects at the receiver of bob in the challenge stage are assume to be independent from the receiver of alice in the response stage .  in simulations , both the effects of carrier frequencyoffset and sampling offset are considered , while the sampling frequency offset is not considered , as its effect can be well included in the equivalent channel model as shown in ( [ eq : imodel ] ) . the residual carrier frequency offset assumed to be uniformly distributed in  ] . by referring to ( [ eq : rmod ] ), the verification should be searched over the range of , due to the sampling offsets introduced by the receivers at the sides of both bob and alice .clearly , , \varpi_{\max}=2\pi \times \frac{2n_\varepsilon^{\max}\delta \ell}{n}\ ] ] with a step size of for search of , there are candidate frequencies to be tested for maximizing ( [ eq : rmod ] ) .  in fig .[ fig : pdf4 ] , the modified ana - phy - pcras is considered for , and . clearly , $ ] .one can show that the snr loss due to both carrier frequency offset and sampling offset is negligible when the working snr is db , which was verified by extensive simulations .  by comparing fig .[ fig : pdf4 ] with fig .[ fig : pdf3 ] , there is actually minor difference between the scenarios of zero- and non - zero sampling / carrier frequency offsets for the empirical pdfs when is set to 200 .even with , it still works with slightly degraded roc performance .therefore , the number of candidate frequencies to be tested can be very small for authentication , and the increase in complexity due to the search of frequency can be well controlled .and at snr=10db ( ) and .,scaledwidth=50.0% ]   .,scaledwidth=50.0% ]  as a mutual physical challenge - response authentication scheme , the phy - cram proposed in was shown to be simple , low complexity , robust , and flexible .hence , it is interesting to compare ana - phy - pcras with phy - cram .[ fig : comp ] shows the comparison result in the roc performance at snr=5 db , where is used for ana - phy - pcras .therefore , a normalized key equivocation of can be achieved in the worst case scenario .this , however , is not true for phy - cram .even with the introduction of artificial noise , ana - phy - pcras is still better than phy - cram in the roc performance as shown in fig .[ fig : comp ] .indeed , phy - cram employs amplitude modulation , which is often worse than phase modulation in performance . for implementation , high peak fluctuations may occur with phy - cram , due to the employment of amplitude modulation .hence , it requires to suppress the high peak in practice with additional complexity .ana - phy - pcras , however , is more sensitive to the frequency offset compared to phy - cram .in this paper , we proposed a novel ana - phy - pcras for practical ofdm transmission , where the tikhonov - distributed artificial noise is introduced to interfere with the phase - modulated key for resisting potential key - recovery attacks .thanks to the introduced artificial noise , the proposed ana - phy - pcras was proved to be secure even in the worst case scenario , where a static channel between alice and bob is assumed , and eve can even get a noise - free version of the transmitted signal by either alice or bob .various practical issues are addressed for ana - phy - pcras with ofdm transmission , including correlation among subchannels , imperfect carrier and timing recoveries .the effect of sampling offset was shown to be significant for the practical implementation of ana - phy - pcras , and a search procedure in the plane of frequency should be seriously considered for verification even with very small sampling offsets .we also proposed a modified ana - phy - pcras for time - separated subchannels , which shows its robustness in verification whenever the local oscillator at the receiver may change over time .compared to the traditional challenge - response authentication scheme implemented at the upper layer , we conclude that ana - phy - pcras ( or its modified version ) can be further protected by the uncertainty from both the wireless channel and introduced artificial noise , which is of information - theoretic nature and could not be broken even with unlimited computational power .d. shan , k. zeng , w. xiang , p. richardson , and y. dong , `` phy - cram : physical layer challenge - response authentication mechanism for wireless networks , '' _ ieee j. sel .areas commun ._ , vol . 31 , pp . 18171827 , 2013 .     a. ferrante , n. laurenti , c. masiero , m. pavon , and s. tomasin , `` on the error region for channel estimation based physical layer authentication over rayleigh fading , '' _ ieee trans .forensics security _ , vol .941952 , may 2015 .l. xiao , l. j. greenstein , n. b. mandayam , and w. trappe , `` using the physical layer for wireless authentication in time - variant channels , '' _ ieee trans .wireless commun ._ , vol . 7 , pp . 25712579 , jul. 2008 .   x. liang , l. greenstein , n. b. mandayam , and w. trappe , `` using the physical layer for wireless authentication in time - variant channels , '' _ ieee trans .wireless commun ._ , vol . 7 , pp . 25712579 , jul. 2008 .             c. ye , s. mathur , a. reznik , y. shah , w. trappe , and n. mandayam , `` information - theoretically secret key generation for fading wireless channels , '' _ ieee trans .forensics security _ , vol . 5 ,240254 , jun . 2010 .

Abstract: recently , we have developed a physical layer phase challenge - response authentication scheme ( phy - pcras ) for independent multicarrier transmission . in this paper , we make a further step by proposing a novel artificial - noise - aided phy - pcras ( ana - phy - pcras ) for practical orthogonal frequency division multiplexing ( ofdm ) transmission , where the tikhonov - distributed artificial noise is introduced to interfere with the phase - modulated key for resisting potential key - recovery attacks whenever a static channel between two legitimate users is unfortunately encountered . then , we address various practical issues for ana - phy - pcras with ofdm transmission , including correlation among subchannels , imperfect carrier and timing recoveries . among them , we show that the effect of sampling offset is very significant and a search procedure in the frequency domain should be incorporated for verification . with practical ofdm transmission , the number of uncorrelated subchannels is often not sufficient . hence , we employ a time - separated approach for allocating enough subchannels and a modified ana - phy - pcras is proposed to alleviate the discontinuity of channel phase at far - separated time slots . finally , the key equivocation is derived for the worst case scenario . we conclude that the enhanced security of ana - phy - pcras comes from the uncertainty of both the wireless channel and introduced artificial noise , compared to the traditional challenge - response authentication scheme implemented at the upper layer .   authentication , physical layer authentication , ofdm transmission , information - theoretic security .


pi and pid controllers ( see , _ e.g. _ , ) are still by far the most popular feedback design in industry . to the best of our knowledge, there is no clear - cut explanation of their strange ubiquity for a wide range of systems .remember that , from a purely mathematical standpoint , they are only fully justified until now for first and second order linear differential equations with constant coefficients !we solve here this long - standing and quite irritating open problem via the newly introduced _intelligent _ pids ( ) , which have already been utilized quite successfully in several concrete situations ( see , _ e.g. _ , ) .the proof relies on a crude time - sampling of both types of regulators .it shows that the gains in a classic pi or pid take into account , if they are properly tuned , the estimated `` structural '' part of the intelligent controllers .thus the efficiency of these intelligent controllers with respect to arbitrary nonlinear plants ( ) is enough for fulfilling our purpose .let us nevertheless emphasize that the classic tuning rules are quite intricate whereas their counterparts for intelligent controllers are obvious .only few references ( see , _e.g. _ , ) in the huge literature on pids exhibit some connections with our viewpoint .  our paper is organized as follows .section [ mfc ] is devoted to a brief review of _ model - free _ control and of the corresponding intelligent pid controllers .section [ connect ] , which establishes our results by comparing the sampling of classical and intelligent controllers , gives a table for the connections between classic and intelligent gains .the computer simulations in section [ applications ] confirms the superiority of the intelligent controllers ( see , also , for other examples ) .some concluding remarks are given in section [ conclusion ] .the input - output behavior of the system , which for simplicity s sake is assumed to be monovariable , is `` approximatively '' governed within its operating range by an * unknown * finite - dimensional ordinary differential equation , which is not necessarily linear , replace equation by the following `` phenomenological '' model , which is only valid during a very short time interval , the derivation order , which is in general equal to or , and the constant parameter are chosen by the practitioner .it implies that is not necessarily equal to the derivation order of in equation ( [ e ] ) .the numerical value of at any time instant is deduced from those of and , thanks to our quite efficient numerical differentiators , which are moreover real - time .the desired behavior is obtained by implementing , if , for instance , , the _ intelligent pid controller _ ( _ i - pid _ ) where  * is the output reference trajectory , which is determined e.g. via the rules of flatness - based control ; * is the tracking error ; * , , are the usual tuning gains .let us consider the following special cases :  * if again , we may use an _ intelligent pd controller _( _ i - pd _ ) * if , we can restrict ourselves to * * an _ intelligent pi controller _ ( _ i - pi _ ) * * or even to an _ intelligent p controller _ ( _ i - p _ )   if ( resp . ) , plugging equations or ( resp . or ) in equationyields the control of a pure double ( resp .simple ) integrator .this is why tuning the gains of our intelligent controllers is quite straightforward.  it should be emphasized , if ( resp . ) , that equation ( resp . ) is mathematically sufficient for ensuring stability around the reference trajectory . the integral term in equation ( resp . )nevertheless adds some well known robustness properties .consider the classic continuous - time pi controller a crude sampling of the integral through a riemann sum leads to where is the sampling interval .the corresponding discrete form of equation reads : combining the above equation with yields   a trivial sampling of the `` velocity form '' of equation yields which is equivalent to equation .utilize , if in equation , the i - p , which may be rewritten as replace , according to the computer implementation in , by and therefore by it yields    * fact*.- equations and become * identical * if we set   it should be emphasized that the above property , defined by equations , does not hold for continuous - time pis and i - ps .this equivalence is strictly related to time sampling , _i.e. _ , to computer implementation , as demonstrated by taking in equations .extending the calculations of section [ 1 ] is quite obvious .the velocity form of the pid reads .it yields the obvious sampling if on the other hand , equation yields . from the computer implementation , we derive   * fact*.- equations and become * identical * if we set    equation becomes with the i - pid introduce the pii controller where a double integral appears . to its velocity form corresponds the sampling which is identical to equation if one sets the connection between ipis and pii follows at once .the previous calculations yield the following correspondence table between the gains of our various controllers :  [ table ]  [ cols="<,<,<,<,<,<",options="header " , ]   due to the form of equation ( [ f ] ) , it should be noticed that the tuning gains of the classic regulators ought to be negative .   the previous calculations and table 1explain why sampled classic pi and pid controllers take into account , if their gains are properly tuned , the structural term , which contains all the structural information of the unknown nonlinear systems , in equations , , , .the superiority of intelligent controllers , which was already noted in , is however confirmed :  1 .  tuning the gains of intelligent controllers is straightforward whereas it is complex and painful for classic pids in spite of all the numerous existing rules in the literature ( see , _ e.g. _ , ) .contrarily to intelligent controllers , a correctly tuned classic pi or pid controller is unable to take into account heat effects , ageing processes , characteristic dispersions due to mass production , .fault tolerant control is much better handled by intelligent controllers than by classic ones .for the nonlinear system we deduce a classic pi controller thanks to a method due to broda and dindeleux which improves the well - known ziegler - nichols rules ( see , _ e.g. _ , ) .note however that the open loop response of system , with , is somehow difficult to exploit as shown by figure [ x1bo ] .it yields  * a delay system where , , ; * a pi where , .figures [ x1pi ] and [ x1ipi ] , which depict the simulation results for the above pi and an i - pi , do not show any significant difference .remember however that the i - pi , where , , , does not necessitate any cumbersome identification procedure .  without any new calibration of the pi for another operating range figure [ x1pi5 ]shows a deterioration of the performances , whereas the performances of the i - pi , which are depicted in figure [ x1ipi5 ] , remain good .introduce now a fault accommodation via a control power loss , , where the sampling time .the i - pi behaves then much better ( figure [ x1ipipp ] ) than the pi ( figure [ x1pipp ] ) .note nevertheless a small deviation of the i - pi controller when the power loss becomes quite important ( figure [ x1ipipp]-(b ) ) .the above numerical simulations as well as many existing experimentations ( see , and ) demonstrate that intelligent pid controllers yield better performances than classic ones .this is achieved moreover thanks to a quite straightforward and natural gain tuning , which contrasts with the numerous complex rules for classic pids .those considerations as well as the results of this communication imply therefore   99 b. dandra - novel , c. boussard , m. fliess , o. el hamzaoui , h. mounier , b. steux , commande sans modle de vitesse longitudinale dun vhicule lectrique , _ 6 conf. internat .automatique _ , nancy , 2010 ( online http//hal.inria.fr / inria-00463865/en/ ) .chang , j.h .jung , a systematic method for gain selection of robust pid control for nonlinear plants of second - order controller canonical form , _ ieee trans .control systems technology _ , vol .473 - 483 , 2009 .s. choi , b. dandra - novel , m. fliess , h. mounier , model - free control of automotive engine and brake for stop - and - go scenario , _ 10 ieee conf .control conf ._ , budapest , 2009 ( online http//hal.inria.fr / inria-00419445/en/ ) .m. fliess , c. join , model - free control and intelligent pid controllers : towards a possible trivialization of nonlinear control ? , _ 15 ifac symp . system identif ._ , saint - malo , 2009 ( online http//hal.inria.fr / inria-00372325/en/ ).   garca collado f.a ., dandra - novel b. , fliess m. , mounier h. , analyse frquentielle des drivateurs algbriques , _xxii coll .gretsi _ , dijon , 2009 ( online http//hal.inria.fr / inria-00394972/en/ ) .gdouin , c. join , e. delaleau , j .-bourgeot , s. arbab - chirani , s. calloch , model - free control of shape memory alloys antagonistic actuators , _17 ifac world congress _ ,seoul , 2008 ( online http//hal.inria.fr / inria-00261891/en/ ) .gdouin , c. join , e. delaleau , j .-bourgeot , s. arbab - chirani , s. calloch , a new control strategy for shape memory alloys actuators , _8 europ .martensitic transformations _ , prague , 2009 ( online http//hal.inria.fr / inria-00424933/en/ ) .c. join , j. masse , m. fliess , tude prliminaire dune commande sans modle pour papillon de moteur , _ j. europ .337 - 354 , 2008 ( online http//hal.inria.fr / inria-00187327/en/ ) .c. join , g. robert , m. fliess , vers une commande sans modle pour amnagements hydrolectriques en cascade , _6 conf ._ , nancy , 2010 ( online http//hal.inria.fr / inria-00460912/en/ ) .s. riachy , m. fliess , c. join , j .-barbot , vers une simplification de la commande non linaire : lexemple dun avion dcollage vertical ,_ 6 conf .automatique _ , nancy , 2010 ( online http//hal.inria.fr / inria-00463605/en/ ) .  j. villagra , b. dandra - novel , s. choi , m. fliess , h. mounier , robust stop - and - go control strategy : an algebraic approach for non - linear estimation and control , _ int . j. vehicle autonomous systems _ , vol . 7 , pp . 270 - 291 , 2009 ( online http//hal.inria.fr / inria-00419445/en/ ) .

Abstract: the ubiquity of pid controllers in the industry has remained mysterious until now . we provide here a mathematical explanation of this strange phenomenon by comparing their sampling with the the one of `` intelligent '' pid controllers , which were recently introduced . some computer simulations nevertheless confirm the superiority of the new intelligent feedback design . +  + * _ keywords_* pid , model - free control , intelligent pid , sampling .