Patent Publication Number: US-8989764-B2

Title: Robust location distinction using temporal link signatures

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present invention claims priority to and the benefit of Provisional Application No. 60/970,094 to Patwari et al., entitled “Robust Location Distinction Using Temporal Link Signatures,” filed on Sep. 5, 2007, which is herein incorporated by reference in its entirety. 
    
    
     FIELD OF INVENTION 
     The present invention relates to the field of wireless networks. Specifically, the present invention relates to a temporal link signature that uniquely identifies the link between a transmitter and a receiver. 
     THE RELEVANT TECHNOLOGY 
     Location distinction is critical in many wireless network situations, including motion detection in wireless sensor networks, physical security of objects using wireless tags, and information security against replication attacks. Some applications requiring location distinction and motion detection include wireless sensor networks, active radio frequency identification (RFID), and secure wireless networks. 
     For instance, in wireless sensor networks, sensor location can be associated with measured sensor data for use in geographic location-based routing methods. Some wireless networks are deployed purely to be able to locate active RF transmitter tags placed in objects for logistical purposes, such as those used in warehouses or factories. In one particular application, location estimation must be done in an energy efficient manner, especially for networks of sensors with small batteries that must last for years. 
     In addition, active wireless tags can be used to protect the physical security of objects. For example, RFID tags are fast replacing bar-codes and are used as a means for improved logistics and security for products in stores and warehouses. Active RFID in particular is desired for its greater range, but a tag must be in range of multiple base stations (BS) in order to be able to estimate its location. Location distinction is critical to provide a warning and to be able to focus resources (e.g., security cameras, personnel) on moving objects. 
     Security is of utmost concern when protecting wireless networks. In particular, wireless networks can be vulnerable to medium access control (MAC) address spoofing. That is, an adversary, at a different location, can claim to be another node by spoofing its address. Traditional cryptography methods can be implemented to prevent this spoofing; however, these methods are susceptible to node compromise. 
     As described above, many applications including those listed above require location distinction. However, existing techniques fail to do so in an efficient and robust manner. For example the use of accelerometers, Doppler, and received signal strength each have their own disadvantages, as described below. 
     An accelerometer detects changes in velocity. However, accelerometers can be cost prohibitive. The additional device cost of an accelerometer may be acceptable for protection of high-value assets, but would be prohibitive for applications such as bar-code replacement and large-scale sensor networks. Furthermore, an accelerometer needs continuous power that would excessively drain battery power since the accelerometer cannot detect motion from a sleep state. 
     Doppler is the frequency shift caused by the velocity of a transmitter and can be used to detect movement of an object. However, the use of Doppler measurements is limited to situations only in which the object is moving. That is, Doppler measurements provide limited information after object has stopped moving. Thus, transmission of a Doppler signal could not be intermittent like a packet radio, and would require excessive use of battery power. 
     Further, received signal strength (RSS) can be used to detect movement of a transmitter. However, RSS measurements vary due to small-scale and frequency-selective fading, such that its use in location distinction requires multiple measurements at different receivers. However, for wireless sensor networks, multi-node collaboration is expensive in terms of energy requirements and usage. 
     SUMMARY OF THE INVENTION 
     Accordingly, what is needed is an energy efficient manner for performing location distinction in wireless sensor networks. 
     In one embodiment, a radio channel identifier defines a signature. Specifically, the radio channel identifier comprises a temporal link signature between a transmitter and a receiver. The transmitter is located at a first location. The receiver is located at a second location. The temporal link signature comprises a characteristic of an impulse response of a transmitted signal from the transmitter over a channel between the transmitter and the receiver. 
     In another embodiment, a method for detecting a change in transmitter location is described. 
     The method begins by determining a baseline temporal link signature of a channel between a transmitter located at a first location and a receiver at a second location. The baseline temporal link signature is characteristic of a first impulse response of at least one transmitted signal over the channel. A signal is received at the receiver, wherein the signal is based on a second transmitted signal from an unknown transmitter at an unknown location. The unknown transmitter is presumably the transmitter. A temporal link signature is determined based on the signal that is received. The temporal link signature is characteristic of an impulse response of the second transmitted signal over an unknown channel between the unknown transmitter and the receiver. A change between the first location and the second location is detected by determining if the temporal link signature is different from the baseline temporal link signature.\ 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments are illustrated in referenced figures of the drawings which illustrate what is regarded as the preferred embodiments presently contemplated. It is intended that the embodiments and figures disclosed herein are to be considered illustrative rather than limiting. 
         FIG. 1  is a network illustrating a robust location distinction mechanism, in accordance with one embodiment of the present invention. 
         FIG. 2  is a flow diagram illustrating a method for location distinction, in accordance with one embodiment of the present invention. 
         FIG. 3  is a system capable of implementing a method for location distinction, in accordance with one embodiment of the present invention. 
         FIG. 4  is a flow diagram illustrating a particular implementation of a method for location distinction, in accordance with one embodiment of the present invention. 
         FIG. 5  is a diagram of a history of temporal link signatures, in accordance with one embodiment of the present invention. 
         FIG. 6  is a block diagram of a system including multiple receivers for implementing a method for location distinction, in accordance with one embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Reference will now be made in detail to the preferred embodiments of the present invention, a method and system for performing location distinction in a wireless network for purposes of detecting a change in transmitter or receiver location, or a combination of both. While the invention will be described in conjunction with the preferred embodiments, it will be understood that they are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents which may be included within the spirit and scope of the invention as defined by the appended claims. 
     Accordingly, embodiments of the present invention provide for a robust location distinction mechanism that uses a physical layer characteristic of the radio channel between a transmitter and a receiver, that comprises a temporal link signature. The temporal link signature is the sum of the effects of the multiple paths from the transmitter to the receiver, each with its own time delay and complex amplitude (e.g., real or complex). Such a signature changes when the relative position between the transmitter and receiver changes, because the multiple paths in the link change with the positions of the endpoints of the radio link. Embodiments of the present invention are capable of detecting the change in signature. As a result, additional response steps may be implemented based on the change of the temporal link signature. 
     Method and System for Location Distinction: 
       FIG. 1  illustrates a network  100  including transmitters i and receivers j that is capable of performing location distinction, in accordance with one embodiment of the present invention. In particular, the network  100  illustrates a known relationship between receiver j 1  at node  110  and transmitter i 1  at node  120 A at an initial state. That is, transmitter i 1  is located at a first location node  120 A and receiver j 1  is located at a second location, node  110 . The present embodiment is capable of determining if a temporal link signature of the radio channel  125  between transmitter i 1  at node  120 A and receiver j 1  at node  110  has changed. A change in the temporal link signature may indicate that either transmitter i 1  or receiver j 1  has moved, that both transmitter i 1  or receiver j 1  have moved, or that an adversary transmitter i 2  at node  130  is impersonating transmitter i 1  at node  120 A. 
     In particular, in the network  100 , a radio link exists between transmitter i 1  at node  120 A and receiver j 1  at node  110 . The receiver j 1  can measure and record the temporal link signature of link (i 1 ,j 1 ). When transmitter i 1  moves to node  120 B, the present embodiment can then distinguish the new link signature from one or more previously recorded link signatures, and declare that transmitter i 1  has moved, in one embodiment. 
     Alternatively, if an adversary, transmitter i 2 , impersonates transmitter i 1  from node  130 , the adversary&#39;s transmission to receiver j 1  at node  110  will be detected to be from a different location. Thereafter, an appropriate action may be taken. 
     In still another embodiment, while the detection of a temporal link signature change between transmitter i 1  and receiver j 1  can be reliably performed at one receiver, receiver j 2  at node  115  can also participate in the detection process for higher reliability and robustness. Specifically, measurements at multiple receivers can be used to achieve even higher robustness of location distinction. 
     In contrast to existing techniques, location distinction using temporal link signatures does not require continuous operation, in one embodiment. That is, a sensor transmitting a signal can schedule one or more sleep periods, and a wireless network can send packets intermittently. When awakened from sleep or upon reception of the subsequent packet, a receiver can detect that a neighboring transmitter has moved since its past transmission. As an added advantage, temporal link signatures in embodiments of the present invention can be measured at a single receiver and require no additional complexity at the transmitter, which keeps tag cost and energy consumption low. 
     For secure wireless networks, such as that illustrated in network  100 , temporal link signatures are particularly robust to impersonation attacks because of three physical barriers. First, an attacker (e.g., transmitter i 2  at node  130 ) cannot measure the link signature of the legitimate links between a transmitter and corresponding receivers, unless it is at exactly the same location as all receivers. As such, the link signature acts as a form of secrecy, which in combination with the reciprocity of the channel  125  impulse response, can be used to obtain a shared secret for purposes of a secure wireless communication. Second, even if an attacker (transmitter i 2 ) can measure a link signature, it will not have the same link signature at the receiver j 1  unless the attacker (e.g., transmitter i 2 ) is at exactly the same location as the legitimate transmitter (e.g., transmitter i 1 ), which is difficult, if not impossible to achieve. Furthermore, an attacker (transmitter i 2 ) can change its measured link signature, but cannot ‘spoof’ an arbitrary link signature. 
     These three physical barriers exist because the link between a legitimate transmitter (e.g., transmitter i 1 ) and the attacker&#39;s receiver (e.g., receiver at node  130 ) is a different physical channel compared to the one between the legitimate transmitter (e.g., transmitter i 1 ) and legitimate receiver (e.g., receiver j 1  at node  110 ). Further, any signal sent by the attacker (e.g., transmitter i 2 ) to the legitimate receiver (e.g., receiver j 1  at node  110 ) must be filtered by a third different physical channel between them. 
       FIGS. 2 and 3  together illustrate a method and system for performing location distinction in order to determine a change in the physical relationship between a transmitter and a receiver, in accordance with one embodiment of the present invention. For instance, the method and system of  FIGS. 2 and 3  can be used to determine if either the transmitter or receiver, or a combination of both, has moved from a previous location. 
     In particular,  FIG. 2  is a flow chart  200  illustrating a method for location distinction, in accordance with one embodiment of the present invention. The system  300  of  FIG. 3  is capable of implementing the method of  FIG. 2 , in accordance with one embodiment of the present invention. In particular, system  300  can be located at a receiver (e.g., receiver j 1  or receiver j 2 ), in one embodiment. In another embodiment, system  300  can be located at a remote location separate from either receiver j 1  or receiver j 2  in a multiple receiver network, or in a single receiver network. 
     Returning to  FIG. 2 , at  210 , a baseline temporal link signature of channel between a transmitter located at a first location and a receiver at a second location is determined. The baseline temporal link signature is characteristic of an impulse response of at least one transmitted signal over the channel, such as a first transmitted signal. In one embodiment, the baseline temporal link signature module  310  of system  300  determines the baseline temporal link signature. 
     At  220 , a signal is received at the receiver. The received signal is based on a second transmitted signal from an unknown transmitter at an unknown location. In one embodiment, the unknown transmitter is presumably the transmitter associated with the baseline temporal link signature. In one embodiment, the receiver  320  receives the signal from the unknown transmitter. 
     At  230 , a temporal link signature is determined. The temporal link signature is based on the received signal. In addition, the temporal link signature is characteristic of an impulse response of the second transmitted signal over an unknown channel between the unknown transmitter and the receiver. In one embodiment, the temporal link signature module  330  determines the temporal link signature. 
     At  240 , a change between the first location and the second location is determined by determining if the temporal link signature from  230  is substantially different from the baseline temporal link signature. That is, in one embodiment, assuming that the unknown transmitter is the same transmitter used for determining the baseline temporal link signature, if the temporal link signature is substantially different from the baseline, then the location of the transmitter has changed, assuming the receiver location stays constant. In another embodiment, an intruder can be detected when the temporal link signature is substantially different from the baseline, such that the intruder is trying to impersonate the transmitter used for the baseline temporal link signature. In one embodiment, the comparator  340  determines if there has been a change between the two temporal link signatures. 
     Temporal Link Signature 
     The power of the temporal link signature comes from the variability in the multiple paths over which radio waves propagate on a link. A single radio link is composed of many paths (also referred to as multiple paths or multi-paths) from the transmitter to the receiver. For example, referring to  FIG. 1 , the radio link over channel  125  is composed of many paths from transmitter i 1  to receiver j 1 . These multiple paths are caused by the reflections, diffractions, and scattering of the radio waves interacting with the physical environment. Each path has a different length, so a wave propagating along that path takes a different amount of time to arrive at the receiver. Each path has attenuation caused by path losses and interactions with objects in the environment, so each wave undergoes a different attenuation and phase shift. At the receiver, many copies of the transmitted signal arrive, but each copy arrives with a different time delay, and with a different amplitude and phase. The sum of these time delayed, scaled, and phase shifted transmitted signals is the received signal. 
     As will be explained below in detail, the temporal link signature is based on a plurality of time delays and a plurality of amplitudes of the multipath components of the transmitted signal over the channel  125 . In one embodiment, the temporal link signature comprises an impulse response of a transmitted signal over the channel  125  between the transmitter i 1  and receiver j 1 , wherein the impulse response is based on the plurality of time delays and the plurality of amplitudes of the multipath components. For instance, the impulse response can be configured as a list, or vector of the plurality of time delays and plurality of amplitudes. In one embodiment, the impulse response is a complex-valued impulse response, where the amplitude has both a magnitude and a phase angle. In another embodiment, the impulse response is a real-valued impulse response, wherein only the magnitude of the amplitude is considered. 
     Since the received signal is a linear combination of the transmitted signal, we can consider the radio channel or link as a linear filter. For the link or channel in between transmitter i and receiver j, the channel impulse response (CIR), denoted h i,j (t), is given by Eq. 1, as follows: 
                         h     i   ,   j       ⁡     (   τ   )       =       ∑     l   =   1     L     ⁢           ⁢       α   l     ⁢     ⅇ   jϕⅈ     ⁢     δ   ⁡     (     τ   -     τ   l       )             ,           (   1   )               
In particular, α l  and φ l  are the amplitude and the phase of the lth multipath component, τ l  is the time delay, L is the total number of multipaths, and δ(τ) is the Dirac delta function. Essentially, the filter impulse response is the superposition of many impulses, each one representing a single path in the multiple paths of a link. Each impulse is delayed by the path delay, and multiplied by the amplitude and phase of that path.
 
     The received signal, r(t), is then the convolution of the channel filter and the transmitted signal s(t), as described in Eq. 2.
 
 r ( t )= s ( t )* h   i,j ( t ),  (2)
 
     All receivers measure r(t) in order to demodulate the information bits sent by the transmitter. 
     Estimation of the Temporal Link Signature 
     In one embodiment, the received signal, r(t), is used to make a band-limited estimate of h i,j (t). If the bits are correctly demodulated, s(t), the transmitted signal, can be recreated in the receiver. In general, estimating h i,j (t) from known r(t) and s(t) in Eq. 2 is a de-convolution problem, however, in one embodiment, a de-convolution process need not be performed. 
     For instance, once the transmitted signal, s(t), is known, the transmitter can be identified. Specifically, the transmitter is associated with an identifying signal (e.g., RFID) that is periodically transmitted. In that way, a transmitter can be distinguished from a plurality of transmitters based on the identifying signal. In one embodiment, the identifying signal is also used for purposes of determining the temporal link signature, although this is not a requirement. For instance, one or more signals that are different than the identifying signal may be transmitted for purposes of determining the temporal link signature. 
     In particular, generally, digital signals have power spectral densities which are flat inside the band (the frequency range of the channel) in order to maximize spectral efficiency. Specifically, |S(f)| 2  is approximately equal to a known constant, denoted P s , for all f within the band. In addition, an approximation of h i,j (t) is sufficient, as there is no need to exactly recreate h i,j (t), in one embodiment. 
     As a result, in one embodiment, the temporal link signature is calculated using only convolution, rather than de-convolution. To show this, Eq. 2 is rewritten in the frequency domain below as Eq. 2A.
 
 R ( f )= S ( f ) H   i,j ( f ),  (2A)
 
In Eq. 2A, R(f), S(f), and H i,j (f) are the Fourier transforms of r(t), s(t), and h i,j (t), respectively.
 
     Thereafter, R(f) is multiplied with the complex conjugate of the Fourier transform of the re-created transmitted signal, S*(f), in Eq. 3.
 
 S *( f ) R ( f )=| S ( f )| 2   H   i,j ( f ),  (3)
 
Note that this multiplication in the frequency domain is a convolution in the time domain. As |S(f)| 2  is nearly constant within the band, Eq. 3 is a band limited version of H i,j (f).
 
     Finally, the temporal domain is recovered from Eq. 3 by taking the inverse Fourier transform. The impulse response estimate obtained from the nth received packet from transmitter i at receiver j is denoted below in Eq. 3A, where    −1  {−} indicates an inverse Fourier transform is performed. 
     
       
         
           
             
               
                 
                   
                     
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     Since the received signal is sampled, the following sampled impulse response vector can be determined in Eq. 4.
 
 h   i,j   (n)   =[h   i,j   (n) (0), . . . ,  h   i,j   (n) (κ T   r )] T ,  (4)
 
In Eq. 4, T r  is the sampling rate at the receiver, and κ+1 is the number of samples. As shown in Eq. 4, the impulse response includes a plurality of time delays and amplitudes of the multipath components of the transmitted signal over the channel. As described previously, the impulse response may be a complex-valued impulse response, where the amplitude has both a magnitude and a phase angle, or the impulse response may be a real-valued impulse response, where the amplitude only has a magnitude.
 
     In one embodiment, the calculation of Eq. 4 can be done regardless of modulation, but for particular modulation types, the process is even easier. For example, consider receivers for orthogonal frequency division multiplexing (OFDM)-based standards, such as in IEEE 802.11a/g and 802.16. Such receivers can be readily adapted to calculate temporal link signatures since the signal amplitude and phase in each sub-channel provides a sampled version of the Fourier transform of the signal. In effect, the Fourier transform operation is already implemented, and R(f) is directly available. In one embodiment, calculation of the temporal link signature requires an additional inverse FFT operator. 
     In embodiments of the present invention, the calculation necessary for the computation of temporal link signatures can be performed in existing code-division multiple access (CDMA) cellular base station receivers, in access points for wireless local area networks (WLANs) operating on the 802.11b standard, and ultra-wideband (UWB) receivers. Specifically, CDMA receivers first correlate the received signal with the known pseudo-noise (PN) signal. Then, the correlator output in a rake receiver is used, which adds in the power from each multipath component. In one embodiment, the temporal link signature is just the average of the correlator output over the course of many bits. UWB receivers also measure a signal which shows an approximate impulse response. In either case, little or no additional calculation would be required to implement a temporal link signature-based method for these standard PHY protocols. 
     Normalization 
     When describing time measurements, transmitters and receivers are typically not synchronized. As such, the temporal link signature, h i,j   (n+1) (t) has only a relative notion of time t. If the next temporal link signature on the same link (i,j), h i,j   (n+1) (t), is equal to h i,j   (n) (t+Δt), where Δt is a significant offset compared to the duration of the link signature, the temporal link difference between the nth and n+1st measurement will be very high, simply because of the lack of synchronization. 
     To address the synchronization problem, normalization is performed, in one embodiment. That is, the time delay axis is normalized at each new link signature measurement by setting the time delay of the line-of-sight (LOS) multipath to be zero. In Eq. 1, this means that τ 1 =0, and can be implemented with a threshold detector. That is, when a measured impulse response first exceeds a threshold, the delay is set to 0. In another embodiment, all link signatures in this discussion are time-delay normalized. 
     In another embodiment, for purposes of replication attack detection, robustness to attacks requires that signatures be also normalized by amplitude. This is because a transmit power can be easily increased or decreased. For purposes of clarity, in this specification, normalized link signatures refers to amplitude normalization. However, other embodiments of the present invention are well suited to applications in which amplitude normalization is not required. 
     In the present embodiment, for a normalized link signature, the measured impulse response is normalized to unit norm in Eq. 5.
 
  h   i,j   (n)   =h   i,j   (n)   /∥h   i,j   (n) ∥  (5)
 
In Eq. 5, ∥·∥ indicates the Euclidean (l 2 ) norm. For purposes of the present invention, h i,j   (n)  refers to the link signature. In other embodiments, when using a normalized link signature, the term  h   i,j   (n)  is substituted into any expression in place of h i,j   (n) .
 
Particular Location Distinction Methodology
 
       FIG. 4  is a flow chart  400  illustrating a method for location distinction, in accordance with one embodiment of the present invention. The method illustrated in  FIG. 4  can be used to determine movement of either a transmitter, or receiver, or combination of the two. In addition, the method of  FIG. 4  can be used to determine when a replication attack is detected, in another embodiment. The method of flow chart  400  can be implemented within an environment described in  FIG. 3 . As such, a receiver is designated as j, and a transmitter is designated as i. 
     At  410 , a plurality of signals (N−1) is received at a receiver j and a history of temporal link signatures can be created. That is, at least one temporal link signature is used to determine a baseline temporal link signature. More specifically, given receiver j and nodes iε   J (where    J  is the set of neighbors of j), a history of N−1 link signatures is measured and stored, as Eq. 5A.
 
   i,j   ={h   i,j   (n) } n=1   N−1 (5A)
 
These histories are assumed to be recorded while transmitter i is not moving and not under a replication attack, in one embodiment. Still, h i,j   (n)  will differ due to normal temporal variations in the radio channel. To quantify this variation, receiver j calculates the historical average difference (σ i,j ) between the N−1 measurements in    i,j , as presented below in Eq. 7.
 
     At  420 , the Nth measurement h (N)  is then taken. That is, the Nth transmitted signal is received as a received signal at the receiver j. More specifically, the received signal is based on an Nth transmitted signal from an unknown transmitter from an unknown location. It is presumed that the unknown transmitter is the transmitter i, but it is not necessarily the case, as will be described below. The presumption can be made, in one embodiment, if the transmitted signal, as demodulated from the received signal, matches the identifying signal of the transmitter i. For instance, the transmitted signal may be used for both identifying transmitter i, and for purposes of determining the temporal link signature. In another case, a separate signal is used for identification purposes. 
     Also, at  430 , the temporal link signature of the Nth transmitted signal is determined. The temporal link signature is characteristic of an impulse response of the Nth transmitted signal over the unknown channel between the unknown transmitter and the receiver j. 
     In one embodiment, the temporal link signature is estimated, as is provided in Eq. 4. More specifically, in the present application, h (N)  denotes the Nth measurement of the temporal link signature as given in Eq. 4. The subscript  i,j  is left out since it isn&#39;t known yet that the signature matches with link (i,j) between the transmitter i and the receiver j. 
     At  432 , a plurality of distances between the temporal link signature, as determined by the Nth transmitted signal, and each of the history of temporal link signatures is calculated, or determined. 
     Thereafter, at  435 , a representative temporal link signature from the history of temporal link signatures is selected that is associated with the closest distance calculated. In this case, the representative temporal link signature acts as the baseline temporal link signature. Moreover, the distance d i,j  between h (N)  and the history    i,j  that is associated with the representative temporal link signature is calculated using Eq. 6. 
                     d     i   ,   j       =       1     σ     i   ,   j         ⁢       min     h   ∈     H   ij         ⁢          h   -     h     (   N   )                          (   6   )               
Eq. 6 is the normalized minimum Euclidean (l 2 ) distance between the Nth measurement and the history vectors. In other embodiments, many other distance measurements are possible, but in the present embodiment, l 2  is chosen as a simple proof-of-concept measure.
 
     Next, at decision step  440 , the difference, or distance d i,j , is compared to a threshold to determine if there is a relative change between the locations of the transmitter i and the receiver j. Specifically, d i,j  is compared to a threshold γ, for a constant γ&gt;0. When d i,j &gt;γ, the method proceeds to  450 . Specifically, the difference in the measured temporal link signature, from the Nth transmitted signal, and its history is not due to normal temporal variations, but the measured link signature is that of a different link over a different channel (e.g., from a new transmission location), and as such a relative location change between the transmitter i and receiver j is detected. 
     More particularly, a movement of the transmitter may be detected when eh temporal link signature is different from the baseline temporal link signature. That is, movement of the transmitter is determined when the receiver location remains static, and the distance d i,j  exceeds the threshold γ. 
     At  450 , appropriate action is taken. The action taken when a transmitter is detected to be at a distinct location is application dependent. If it is determined that the unknown transmitter is transmitter i, then the process may begin anew to build a history of temporal link signature for the new link. On the other hand, if it is determined that the unknown transmitter is not transmitter i, then the process outlined in  FIG. 4  may proceed back to  420  in anticipation of the next received signal, from the Nth transmitted signal, since the previously received signal is not considered in the history of temporal link signatures. 
     In one embodiment, in the case of the sensor motion detection or object security applications, where it is expected that no movement would occur, a cooperative sensor localization methodology may be implemented, as discussed below. In other cases, an alarm may be triggered leading to other actions, such as pointing cameras to a particular location, physically investigating why there was movement detected, etc. 
     In another application, when a replication attack is suspected, the receiver might collaborate with other receivers to confirm the change in the location of node i (from the unknown transmitter), or an authentication process or re-authentication process may be implemented with the unknown transmitter. For instance, if re-authentication fails, then the Nth transmitted signal may be determined to be from an adversary transmitter, and not transmitter i. Specifically, an adversary transmitter posing as the transmitter i can be determined when the receiver location remains static, the distance d i,j  exceeds the threshold γ, and the re-authentication process fails. An alarm may also be triggered when the replication attack is verified, or suspected. 
     On the other hand, if the difference is less than the threshold, then the method proceeds to  460  and adds the temporal link signature into the history of temporal link signatures. Specifically, when d i,j  is less than the threshold γ, the measurement is assumed to be from the same link (e.g., channel between transmitter i and receiver j), such that h i,j   (N) =  h   (N) . Thereafter, the temporal link signature is included in the history,    i,j . In one embodiment, for constant memory usage, the oldest measurement in    i,j  can be discarded. 
     Thereafter, the method returns to  420  in anticipation for the N+1 measurement. 
       FIG. 5  is a diagram  500  illustrating a history    i,j  of temporal link signatures, new measurement h (N) , and a dotted line connecting h (N)  to its closest point in the history. The diagram  500  is illustrative of flow diagram  400 , in accordance with one embodiment of the present invention. The normalized distance d i,j  is the length of the line divided by σ i,j . 
     In one embodiment,  FIG. 5  is analogous to a clustering algorithm operating on high-dimensional data. In one embodiment, it is not assumed that points in    i,j  come from a particular distribution. Instead, the spread of the points in the cluster (history) is quantified as the average distance between pairs of points in the cluster in Eq. 7. 
     
       
         
           
             
               
                 
                   
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                               \ 
                               ⁢ 
                               g 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                              
                             
                               h 
                               - 
                               g 
                             
                              
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The normalization constant 
             1       (     N   -   1     )     ⁢     (     N   -   2     )             
comes from N−1 size of the history set,    i,j , In one embodiment, half of the terms ∥h−g∥ are calculated since the distance is symmetric.
 
Evaluation Methodology
 
     In one embodiment, a methodology is described for determining the accuracy of the location distinction process of embodiments of the present invention. First, a methodology is developed to demonstrate that the link signature due to a transmitter at a location i′ and the receiver at a location j, is different from the link signature history between i and j, where i′≠i by more than the threshold γ. This difference is denoted by d i-i′,j  and is referred to as the spatial link difference. 
     Second, the link signature measured while the transmitter is at the same location i and the receiver is at j, will be different from the link signature history between i and j by less than the threshold γ. This difference is denoted by d i,j   (N) , and is referred to as the temporal link difference. 
     As such, the location change detection test can be viewed as a choice between two events H 0  and H 1 , in which these terms are defined as follows in Eqs. 8A and 8B.
 
H 0 :d i,j =d i,j   (N)   (8A)
 
H 1 :d i,j =d i-v,j   (8B)
 
Since d i,j s are random variables, their conditional density functions are denoted f d     i,j   (d|H 0 ) and f d     i,j   (d|H 1 ). Detection theory gives the performance of a detector, using the probability of false alarm P FA  and probability of detection P D , as follows in Eqs. 9A and 9B.
 
P FA =∫ χ=γ   ∞ ∫d i,j (x|H 0 )dx  (9A)
 
P D =∫ χ=γ   ∞ ∫d i,j (x|H 1 )dx  (9B)
 
It is important to note that the probability of missed detection is referred to as P M , where P M =1−P D . Since the probabilities are a function of γ, the lower false alarm rate can be traded for lower probability of detection, and vice versa.
 
Collaborative Sensor Receivers
 
     As shown in  FIG. 1 , multiple receivers can be used for a more robust system for determining location distinction, in accordance with one embodiment of the present invention. In particular, the present embodiment relies on the collaboration between two or more nodes (receivers). 
     In sensor networks, although collaboration may expend additional communication energy, it may be used in order to confirm with higher reliability that a transmitter&#39;s location has changed. Sensor and ad hoc networks typically rely on redundancy of links, so each node is expected to have multiple neighbors. For prevention of replication attacks, collaboration may be normal, and any access points in radio range would collaborate, in one embodiment. For example, WLAN coverage regions often overlap, and hence multiple access points may receive signals from the same transmitter. As WLANs become more ubiquitous, access point densities may increase and would create more overlap. 
       FIG. 6  is a block diagram of a system  600  including multiple receivers for implementing a method for location distinction, in accordance with one embodiment of the present invention. As shown in  FIG. 6 , each of the multiple receivers  610 A-N is analogous to the system  300  shown in  FIG. 3 . As such, each of the multiple receivers  610 A-N includes a baseline temporal link signature module, a receiver for receiving a transmitted signal, a temporal link signature module, and a comparator. In addition, a central module  620  is communicatively coupled with each of the multiple receivers  610 A-N. The central module  620  includes a central comparator  623  and a locator  625 . 
     For purposes of discussion, the term   is defined to be the set of receivers  610 A-N involved in the collaborative location distinction process for transmitter i. The process proceeds as follows: 
     Each node jε  records a history    i,j  with length N−1. An average difference σ i,j  between the link signatures in the history can be calculated. For instance, each of the baseline temporal link signature modules (e.g.,  611 A) records the history of temporal link signatures for a corresponding node. 
     In addition, each node records the new, Nth temporal link signature h (N)  and calculates the distance d i,j  between it and the history, as in Eq. 6. For instance, the each of the temporal link signature modules (e.g.,  613 A) calculates or determines the Nth temporal link signature h (N)  for a corresponding node. In addition, each of the comparators (E.g.,  615 A) is able to calculate the distance d i,j  between it and the history of temporal link signatures associated with its corresponding node. 
     For collaboration, in one embodiment nodes jε  send differences d i,j  to a central processor, or central comparator  623 , which then combines the results into a mean distance d i   , represented as follows in Eq. 10. In one embodiment, the central comparator  623  is located in one of the receivers. In another embodiment, the central comparator  623  is at a remote location, different from any of the receivers. Eq. 10 is listed below. 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       i 
                       , 
                     
                   
                   = 
                   
                     
                       1 
                       
                          
                          
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           j 
                           ∈ 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           d 
                           
                             i 
                             , 
                             j 
                           
                         
                         ⁢ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     In the central comparator  623 , the result d i,J  is compared to a threshold γ. If the difference is above the threshold, it can be determined that the new measurement is from a different transmitter location, in one embodiment. Otherwise, it can be determined that the new measurement is from the same transmitter location. This process is similar to the process outlined in  440 ,  450 , and  460 . As such, each receiver adds  (N)=h (N)  to its history for the link (i,j). 
     In addition, denoting d i,j   (N)  to be the temporal link difference, and d i-v,J  to be the spatial link difference, a choice can be made between the two events in Eqs. 11A and 11B, in another embodiment.
 
H 0 :d i,j =d i,J   (N)   (11A)
 
H 1 :d i,j =d i,J   (11B)
 
     The conditional density functions (pdfs) are now denoted ∫ di,J (d|H 0 ) and ∫ di,J (d|H 1 ). In addition, the probability of false alarm, P FA , and probability of detection, P D  are determined in Eqs. 12A and 12B.
 
P FA =∫ χ=γ   ∞ ∫d i,J (x|H 0 )dx  (12A)
 
P D =∫ χ=γ   ∞ ∫d i,j (x|H 1 )dx  (12B)
 
     Furthermore, locator  625  is used to determine a location of the transmitter, in one embodiment. Given the received signals at each of the multiple receivers  610 A-N, a location algorithm may be used to determine a geographic location of the transmitter, knowing the locations of each of the multiple receivers  610 A-N. As such, not only can a change in location between the relative positions of a transmitter and receiver be determined, but the geographic location of the transmitter can be determined to substantiate the change in location. 
     As a result, embodiments of the present invention that provide location distinction in wireless networks can be implemented in various applications, such as for purposes of providing wireless security for wireless networks, active RFID, wireless sensor networks, forensics information, etc. For instance, for purposes of wireless security, when a imposter is detected, a re-authentication process may be triggered. In the case of active RFID, when movement is detected, corrective action can be taken, such as confirming that the movement occurred through video, or physical investigation, or additional transmission at higher power for triangulation. Further, in wireless sensor networks, if movement is detected, multiple receiver collaboration can be activated to verify the movement. Also, in the field of forensics, embodiments of the present invention are capable of identifying the location from which a network break-in was committed. That is, through correlation of event timing, location distinction can be implemented to provide additional information showing that a breach occurred. 
     A method and system for determining location distinction in wireless networks is thus described. While the invention has been illustrated and described by means of specific embodiments, it is to be understood that numerous changes and modifications may be made therein without departing from the spirit and scope of the invention as defined in the appended claims and equivalents thereof. Furthermore, while the present invention has been described in particular embodiments, it should be appreciated that the present invention should not be construed as limited by such embodiments, but rather construed according to the below claims.