US 20030228017 A1 Abstract A transmitted signal exploits unique higher order statistics of temporally dependent waveforms to encode message symbols with unique durations enabling low power transmission of the covert message. The message is independent of the characteristics or encoded data of the transmitted waveform. The method uses spatial fourth order cumulants or spatial second order moments in a Blind Source Separation and generalized eigenvalue decomposition to determine unique matrix pencil eigenvalues. Sequential detection in successive blocks determine the duration of the eigenvalue. The durations of the detected eigenvalues are sorted sequentially and can be sorted spatially by Steering vectors, AoA or geolocation into signal tracks that are mapped to recover the transmitted cover message. Generation of the transmitted signals with unique high order statistics may be accomplished using combination of noise generators, temporal filters, signal sources, combiners and switches. The receiver includes a multi-element array and does not need a priori knowledge of the transmitted signal source to recover the message. The methods and apparatus for covert communication does not require typical demodulation. The covert communication system is multiple access.
Claims(150) 1. A communication device for providing a communication signal from a data signal comprised of a sequence of bits, comprising:
a noise generator for generating a first signal comprised of a bit stream; a filter for receiving said first signal and generating a temporal dependence between immediately adjacent bits in said first signal to thereby provide a third signal; a plurality of signal sources each providing a source signal with a characteristic unique from the others; a switch for selectively operatively connecting as a function of said data signal one of said plurality of signal sources in sequence to a combining means to thereby provide a second signal; and said combining means for combining said third signal with said second signal to thereby provide the communication signal from said data signal. 2. The communication device of 3. The communication device of 4. The communication device of 5. The communication device of 6. The communication device of 7. The communication device of 8. The communication device of 9. The communication device of 10. The communication device of 11. The communication device of 12. The communication device of 13. The communication device of 14. The communication device of 15. The communication device of 16. The communication device of 17. The communication device of 18. The communication device of 19. The communication device of 20. The communication device of 21. The communication device of 22. The communication device of 23. The communication device of 24. The communication device of 25. A communication device for providing a communication signal from a sequence of bits comprising:
first means for providing a first signal; second means for providing a second signal comprising, in sequence, as a function of said sequence of bits, one of a plurality of third signals each with a matrix pencil eigenvalue unique among said third signals; and third means for combining said first and second signals to thereby provide the communication signal. 26. The communication device of 27. The communication device of 28. The communication device of 29. The communication device of 30. The communication device of 31. The communication device of 32. The communication device of 33. The communication device of 34. The communication device of 35. The communication device of 36. The communication device of 37. The communication device of 38. The communication device of 39. The communication device of 40. The communication device of 41. The communication device of 42. The communication device of 43. The communication device of 44. The communication device of 45. The communication device of 46. The communication device of 47. The communication device of 48. In a receiver including an antenna with a plurality of antenna elements for receiving a communication signal comprised of a plurality of symbols and a digitizer for providing a bit stream from the received symbols, the improvement comprising a filter for generating a temporal dependence between immediately adjacent bits of said bit stream. 49. The receiver of 50. The receiver of 51. The receiver of 52. The receiver of 53. The receiver of 54. The receiver of 55. A communication system comprising a transmitter and a receiver geographically separated from the transmitter for communicating a communication signal formed from a sequence of bits wherein said communication signal is comprised of a plurality of symbols, comprising:
a transmitter comprising:
first means for providing a first signal;
second means for providing a second signal comprising in sequence as a function of said sequence of bits one of a plurality of third signals each with a matrix pencil eigenvalue unique among said third signals;
third means for combining said first and second signals to thereby provide said communication signal; and
transmitting means for transmitting said communication signal; and
a receiver comprising:
receiving means for receiving and digitizing the symbols of said communication signal to thereby produce a first received signal;
means for determining a matrix pencil eigenvalue for at least one of said first received signal symbols;
means for determining the generalized eigenvalue decomposition of said matrix pencil eigenvalue;
means for determining the duration of said matrix pencil eigenvalue; [ditto]
means for filtering said symbols as a function of the determined duration of the associated matrix pencil eigenvalue; [ditto]
means for spatially correlating the filtered matrix pencil eigenvalues; and
means for sequentially mapping the correlated matrix pencil eigenvalues to thereby determine at the receiver the sequence of bits in the communication signal.
56. The communication system of 57. The communication system of 58. The communication system of 59. The communication system of 60. A communication system comprising a transmitter and a receiver geographically separated from the transmitter for communicating a communication signal formed from a sequence of bits wherein said communication signal is comprised of a plurality of symbols, comprising:
a transmitter comprising:
first means for providing a first signal;
second means for providing a second signal comprising in sequence as a function of said sequence of bits one of a plurality of third signals each with a matrix pencil eigenvalue unique among said third signals;
third means for combining said first and second signals to thereby provide said communication signal; and
transmitting means for transmitting said communication signal; and
a receiver comprising:
receiving means for receiving and digitizing the symbols of said communication signal to thereby produce a first received signal;
means for determining a matrix pencil eigenvalue for at least one of said first received signal symbols;
means for determining the generalized eigenvalue decomposition of said matrix pencil eigenvalue;
means for determining the duration of said matrix pencil eigenvalue;
means for filtering said symbols as a function of the determined duration of the associated matrix pencil eigenvalue;
means for sorting the filtered matrix pencil eigenvalues into at least one group of like eigenvalues; and
means for sequentially mapping the correlated matrix pencil eigenvalues to thereby determine at the receiver the sequence of bits in the communication signal.
61. A method for providing a communication signal from a data signal comprised of a sequence of bits, comprising the steps of:
providing a first signal comprised of a bit stream; receiving said first signal and generating a temporal dependence between immediately adjacent bits in said first signal to thereby provide a third signal; providing a plurality of signal sources each providing a source signal with a characteristic unique from the others; providing a combining means; selectively operatively connecting as a function of said data signal one of said plurality of signal sources in sequence to said combining means to thereby provide a second signal; and combining at said combining means said third signal with said second signal to thereby provide the communication signal from said data signal. 62. The method of 63. The method of 64. The method of 65. The method of 66. The method of 67. The method of 68. The method of 69. The method of 70. The method of 71. The method of 72. The method of 73. The method of 74. The method of 75. The method of 76. The method of 77. The method of 78. The method of 79. The method of 80. A method for providing a communication signal from a sequence of bits comprising:
providing a first signal; providing a second signal comprising, in sequence, as a function of said sequence of bits, one of a plurality of third signals each with a matrix pencil eigenvalue unique among said third signals; and combining said first and second signals to thereby provide the communication signal. 81. The method of 82. The method of 83. The method of 84. The method of 85. The method of 86. The method of 87. The method of 88. The method of 89. The method of 90. The method of 91. The method of 92. The method of 93. The method of 94. The method of 95. The method of 96. The method of 97. The method of 98. The method of 99. The method of 100. The method of 101. The method of 102. The method of 103. In a method of receiving a communication signal comprised of a plurality of symbols in a receiver including an antenna with a plurality of antenna elements and a digitizer for providing a bit stream from the received symbols, the improvement comprising the step of providing a temporal dependence between immediately adjacent bits of said bit stream. 104. The method of 105. The method of 106. The method of 107. The method of 108. The method of 109. The method of 110. A method of communicating between a transmitter and a receiver including a multi-element array antenna which is geographically spaced apart from said transmitter a communication signal formed from a sequence of bits wherein said communication signal is comprised of a plurality of symbols, comprising the steps of:
in the transmitter:
providing a first signal;
providing a second signal comprising in sequence as a function of said sequence of bits one of a plurality of third signals each with a matrix pencil eigenvalue unique among said third signals;
combining said first and second signals to thereby provide said communication signal; and
transmitting said communication signal; and
in the receiver:
receiving and digitizing the symbols of said communication signal to thereby produce a first received signal;
determining a matrix pencil eigenvalue for at least one of said first received signal symbols;
determining the generalized eigenvalue decomposition of said matrix pencil eigenvalue;
determining the duration of said matrix pencil eigenvalue;
filtering said symbols as a function of the determined duration of the associated matrix pencil eigenvalue;
spatially correlating the filtered matrix pencil eigenvalues; and
sequentially mapping the correlated matrix pencil eigenvalues to thereby determine at the receiver the sequence of bits in the communication signal.
111. The method of 112. The method of 113. The method of 114. The method of 115. The method of 116. The method of 117. The method of 118. The method of 119. The method of 120. The method of 121. The method of 122. The method of 123. The method of 124. The method of 125. The method of 126. The method of 127. The method of 128. The method of 129. The method of 130. The method of 131. The method of 132. A method of communicating between a transmitter and a receiver including a multi-element array antenna which is geographically spaced apart from said transmitter a communication signal formed from a sequence of bits wherein said communication signal is comprised of a plurality of symbols, comprising the steps of:
in the transmitter:
providing a first signal;
providing a second signal comprising in sequence as a function of said sequence of bits one of a plurality of third signals each with a matrix pencil eigenvalue unique among said third signals;
combining said first and second signals to thereby provide said communication signal; and
transmitting said communication signal; and
in the receiver:
receiving and digitizing the symbols of said communication signal to thereby produce a first received signal;
determining a matrix pencil eigenvalue for at least one of said first received signal symbols;
determining the generalized eigenvalue decomposition of said matrix pencil eigenvalue;
determining the duration of said matrix pencil eigenvalue;
filtering said symbols as a function of the determined duration of the associated matrix pencil eigenvalue;
sorting the filtered matrix pencil eigenvalues into at least one group of like eigenvalues; and
sequentially mapping the correlated matrix pencil eigenvalues to thereby determine at the receiver the sequence of bits in the communication signal.
133. A method of communicating information comprised of a sequence of bits from a transmitter to a receiver comprising the steps of:
modulating a carrier wave with a data signal to thereby produce a first signal wherein the data signal does not represent the information to be communicated; transmitting the first signal from the transmitter; receiving the first signal at the receiver; determining at the receiver the communicated information independently of the data signal. 134. The method of 135. The method of 136. The method of sequentially grouping a predetermined number of bits in said sequence of bits into symbols to thereby provide symbols of an M-ary alphabet;
providing a plurality of third signals each with a matrix pencil eigenvalue unique among said third signals;
providing a switch whereby for each of said symbols said switch operatively connects one of said third signals other than the third signal that was operatively connected for the preceding symbol to thereby form said second signal.
137. The method of 138. The method of 139. In a method of communicating information from a transmitter to a receiver using a communication signal comprised of a carrier wave modulated by a data signal, the improvement comprising determining the information at the receiver independent of the data signal. 140. In a method of communicating information from a transmitter to a receiver using a communication signal containing a plurality of symbols comprised of a carrier wave modulated by a data signal, the improvement comprising determining the information at the receiver as a function of a higher-order statistic of the received symbols. 141. The method of 142. The method of 143. In a method of communicating a first information stream from a transmitter to a receiver using a communication signal containing a plurality of symbols comprised of a carrier wave modulated by a data signal, the improvement comprising communicating a second information stream from the transmitter to the receiver by selectively altering a characteristic of said communication signal wherein said second information stream is different than said first information stream. 144. The method of 145. In a method of communication using plural waveforms where the duration of the transmission of each waveform represents a symbol, the improvement wherein the duration of transmission is determined by the state of a high-order statistic of a characteristic of the waveforms. 146. The method of 147. The method of 148. A method for communication of a message comprising a plurality of sequenced M-ary alphabet symbols, said method comprising the steps of:
assigning each M-ary alphabet symbol a unique symbol duration; generating a waveform for which both the spatial 2nd order moment or the spatial 4 ^{th }order cumulant are constant and not zero; and for each symbol, transmitting the waveform for the assigned symbol duration immediately followed by a pause in waveform transmission. 149. A method for communication of a message comprising a plurality of sequenced M-ary alphabet symbols, said method comprising the steps of:
assigning each M-ary alphabet symbol a unique symbol duration; generating plural waveforms for which the spatial 2nd order moment and the spatial 4 ^{th }order cumulant are constant, nonzero, and unique; and for each symbol, transmitting one of the plural waveforms for the assigned symbol duration so that immediately adjacent symbols are transmitted by different waveforms. 150. A method for communicating a message comprising a plurality of sequenced M-ary alphabet symbols represented by M-ary durations, said method comprising the steps of:
receiving a signal in a multiple element array; determining a high order statistic of a signal characteristic of each symbol, and determining the duration of each symbol by the state of the determined high order statistic. Description [0001] The present application is related to and co-pending with commonly-assigned U.S. patent application Ser. No. 10/360,631 entitled “Blind Source Separation Utilizing A Spatial Fourth Order Cumulant Matrix Pencil”, filed on Feb. 10, 2003, the disclosure of which is hereby incorporated herein by reference. [0002] The present application is related to and co-pending with U.S. Provisional Patent Application Serial No. 60/374,149 filed Apr. 22, 2002 entitled “Blind Source Separation Using A Spatial Fourth Order Cumulant Matrix Pencil”, the entirety of which is hereby incorporated herein by reference. [0003] The present application is related to and filed concurrently with U.S. Provisional Patent Application Serial No. ______ entitled “Cooperative SIGINT for Covert Communication and Location Provisional”, the entirety of which is hereby incorporated herein by reference. [0004] In the advent of globalization, information is a fundamental and valuable commodity. Information and intelligence regarding national defense and security comes at an even a higher premium. In may instances this information and intelligence can only be obtained covertly so as to not reveal the source. Information regarding location of a source such as for surveillance or combat search and rescue can be degraded in value if detected by unfriendly entities, such as enemy forces in the case of a downed pilot or a marked terrorist under surveillance. Additionally, command and control among conventional and/or special operation forces can betray missions by alerting hostile governments or organization of their presence. Embedded voice and data bugs can also expose the existence of these forces if their transmissions are detected resulting in the desired information moving out of reach of the bugging device. These are but a view of the many possible scenarios where a message is desirably sent covertly from a mobile or fixed transmitter to a remote receiver or, more importantly, a friendly or cooperative receiver with out the presence of a signal being detected by an unintended receiver. Covertly transmitting a signal may be necessary to reflect the fact that the transmission is conducted in such a way as to avoid intentional or inadvertent detection by systems monitoring the electromagnetic (EM) environment local to the covert transmitter. However, any transmission, covert or not, may be desired to be received only by intended receivers. [0005] Intentional detection of the signal or message can be accomplished in military systems that use specially designed electronic support measures (ESM) receivers. These ESM receivers are often found in signal intelligence (SIGINT) applications. In commercial applications, devices employed by service providers (i.e. spectral monitors, error rate testers) can be used to detect intrusion on their spectral allocation. Inadvertent detection can also occur, such as when a user or service provider notices degradation in link performance (e.g., video quality, audio quality, or increased bit error rate). [0006] The term covert also implies the additional goals of evading interception and exploitation by unintended receivers. Interception is the measurement of waveform features or parameters useful for classifying/identifying a transmitter and/or the waveform type and/or deriving information useful for denying (i.e. jamming) the communication. Exploitation is processing a signal by an unintended receiver in the attempt to locate the transmitter and/or recover the message content. In the broad literature on covert communications these characteristics as applied to transmitted information signals are referred to as low probability of detection (LPD), low probability of intercept (LPI), and/or low probability of exploitation (LPE) by an unintended receiver. [0007] Typically an LPD communication system shown in FIG. 1 is designed by minimizing the radiated energy in all directions. The goal is to have the emitter [0008] Given the desirability to transmit messages covertly, it is helpful to understand considerations that enhance or degrade LPD, LPI and LPE. An unintended receiver such as the receiver [0009] In prior art LPD systems, the bandwidth of the message signal is artificially broadened to reduce the energy loading on the band, as is done in direct sequence spread spectrum (DSSS) communication, the intended receiver has a processing gain over the unintended receivers that use the same co-channel receiver bandwidth to capture the signal. However, for prior art DSSS, the intended receiver [0010] Minimizing transmit power has two direct system benefits. First, the total signal power used will be a small fraction of the total noise power present in the same band. Thus, if the message is limited in time duration, the total energy measured by an unintended receiver [0011] Therefore, as naturally arise in military environments such as depicted in FIG. 2, there is a need for a low power message system and method, covert or otherwise, such as covert communications for Intel or Special Forces, “stealth” IFF for low observable ground vehicles, and combat search and rescue (CSAR). There is also such a need in a number of civilian or public safety applications as well, such as asset tracking/location or “lost child” detection/location and surveillance. In particular in these latter-described applications it may be particularly desirable to receive both a message and location the source of the message. [0012] Embodiments of the present inventive system and method address the above needs while requiring only an extremely low power signal. [0013]FIG. 1 is a general representation of a prior art approach to LPD. [0014]FIG. 2 depiction of covert scenarios. [0015]FIG. 3 is a representation of an embodiment of a waveform independent covert communication system. [0016]FIG. 4 is a depiction of a binary symbol message 101011 according to an embodiment of the invention. [0017]FIG. 5 [0018]FIG. 5 [0019]FIG. 6 [0020]FIG. 6 [0021]FIG. 6 [0022]FIG. 6 [0023]FIG. 6 [0024]FIG. 6 [0025]FIG. 7 is a schematic representation of a Laplacian noise generator with multiple signal sources according to an embodiment of the invention. [0026]FIG. 8 is a representation of eigenvalue tracks for a frequency shifter laplacian noise waveform for message “101011” according to an embodiment of the invention. [0027]FIG. 9 is a representation of block-to-block eigenvalue correlations. [0028]FIG. 10 is a schematic representation of a message recovery system with spatial information according to an embodiment of the invention. [0029]FIG. 11 is a flow diagram for covert communication via message recovery with spatial information according to an embodiment of the invention. [0030]FIG. 12 is a schematic representation of a message recovery system without spatial information according to an embodiment of the invention. [0031]FIG. 13 is a flow diagram for covert communication via message recovery without spatial information according to an embodiment of the invention. [0032]FIG. 14 is a flow diagram for covert communication via encoded eigenvalues according to an embodiment of the invention. [0033]FIG. 15 is a representation of a binary message sequence 101011 encoded using different carrier waveforms. [0034] A useful feature of embodiments described herein is the use of time duration to convey information, while the individual waveforms used to convey the message (in the time duration of the fourth-order characteristic) are in a sense superfluous or independent of the message to be conveyed. This is a significant advantage for ubiquitous application, allowing for parasitic use of present communication infrastructure and devices. Thus there are few restrictions on the pairing between potential covert transmitters and the intended receiver using the disclosed covert communication methods and apparatus because of the independence of the information transfer on the “carrier waveform”. This is unlike prior art systems where the receivers designed or instantiated for a certain signal type cannot accurately recover the message if the receiver is presented with another signal type. However, embodiments of the present invention by contrast can function equally well for any waveform, and the receiver does not require any a priori knowledge of the “carrier waveform”. In fact, embodiments of the covert transmitter can be waveform agile without informing the intended receiver. [0035] The embodiments herein are predicated on selecting and transmitting carrier waveforms with unique higher order spatial statistics. Such higher order statistics include 2 [0036] To recover the message information, the waveform is not conventionally demodulated. Rather, a straightforward block or batch estimation algorithm estimates the generalized eigenvalues of the SFOCMP for each signal in the receiver field-of-view (FOV) over time using only the array output. For this discussion we assume the data has been digitized appropriately. The sizing for the block processing (e.g., the block of contiguous array observations, sometimes known as “snapshots”) is dependent on several factors. Chiefly we must ensure that each block has enough sample support so that the eigenvalue estimates from the GEVD of the SFOCMP in each block over a symbol duration nominally match. This means that estimation error is negligible. Accordingly, changes in the eigenstructure can be reliably detected, and this change indicates a symbol boundary. The degree to which a nominal match is required within a block depends on the complexity of the signal environment (e.g., extraneous co-channel signals), the communication errors (e.g., partially received messages) tolerable in a given application, and the receiver processing resources to recover the message in a timely manner. [0037] Further, in practical situations, as power sources become impaired (e.g., batteries running low on power), transmitted waveforms become increasingly distorted. This situation limits the effectiveness of matched filtering as used in prior art systems, since the concept of matched filter relies on knowledge of the transmitted waveform in the receiver. Embodiments of the inventive technique are impervious to such distortion since it is the duration and not the actual value of the eigenvalues of the SFOCMP that matter. So as long as the eigenstructure characteristic of the distorted signals is nominally constant during a message symbol, the inventive system and method is robust as to degraded transmitter performance. Therefore, the present inventive system and method will operate successfully under conditions that would normally be detrimental to conventional systems. The use of lower order matrix pencils are also contemplated by the present inventive system and method. [0038] In FIG. 3, the source [0039] The binary symbol stream is from source [0040] The minimum duration and duration increment must be such that synchronizing the data block boundaries used in the receiver to that of the symbol timing in the transmitter [0041] Defining S as the array snapshots/block, “b” blocks for the minimum length symbol, “B” blocks for the maximum length symbol, and “R” as ADC (analog to digital converter) conversion rate in the receiver, the minimum and maximum symbol durations for a binary alphabet are: [0042] The values b=10 and B=20 along with S=5,000 and R=1 Gsamples/sec are subject to implementation choice, and used here for illustration only. Assuming that a system would have an equal number of binary symbols of each type, the average (over the long-term) data rate is nominally 13 kbps. If M-ary signaling is implemented with the same maximum and minimum symbol durations, the data rate can be improved by factor of log [0043] The receiver [0044] As may be apparent to those of skill in the art, there may be some advantage to overlapping blocks of the data. However, the following discussion deals with non-overlapping blocks. On each block, the two fourth-order spatial cumulant matrices required to form the SFOCMP are formed using pre-selected delay triplets. The delays can be either pre-selected, or subjected to online modification using a programmed search routine (if necessary). This search routine might be necessary when certain conditions, such as repeated eigenvalues for different signals are encountered. Processing of the received covert message this difficulty is likely of no consequence. However, provisions are made for signals whose eigenstructure match at the delays selected to be repressed at different delays to provide improved discrimination if desirable. After the matrix pencil is formed, the GEVD is computed. From the GEVD, the eigenvalues and eigenvectors are used to determine the signal environment over time block b. Subsequently, the eigenvectors are used to determine the signal steering vectors and then the eigenstructure is correlated block wise in the Blockwise Eigenvalue Correlator [0045] An important function of a tracker is the track initiation and deletion logic. An embodiment of the tracks uses a fixed distance and a fixed number of consecutive “good associations” for initiation and a single “no association” for a track deletion. A “good association” is any measurement that is “close enough” to track. A “no association” condition occurs when all the measurements are “Too far” from a particular track. the distance indicative of an good association can be set empirically or experimentally. Track initiation and track deletion strategies can also be used to adapt to various situation. A Kalman-like approach to association gates can be adapted as the number of observation for a track are accumulated. Such an approach also has the advantage of replacing fixed averaging of the measurements. [0046] To recover the covert message, in the covert communication receive processor [0047] The design also allows for multiple access for communications. Consider the case where multiple remote covert emitters are sending data. It is unlikely that they would have exactly the same fourth-order cumulant representation, even if they are using the same base waveform. This is because any deviation from nominal waveform implementation (e.g., frequency change, waveform change, matrix pencil eigenvalue change, phase noise, I/Q imbalance, timing jitter, phase jitter, symbol rate change, pulse shape change, a fourth-order statistic change, relative rotational alignment of a signal constellation change, power amplifier rise/fall time change, and Doppler shift change) causes the fourth-order statistics of these signals to differ. Further, the multiple access signals are assumed distinguishable by spatial location. Of course this requires enough data to be collected to resolve the location, and the array must also provide such resolving power. But, if automated location is not possible at the receiver, due to, for instance, no calibration, the covert transmitters may still have multiple access if the multiple access signals can be assured uniqueness amongst themselves and the environment of sufficient degree in the SFOCMP eigenvalues. The receiver need not know the exact eigenvalues that will be used, but in this mode it is incumbent on the individual transmitters to use one and only one eigenvalue and not switch waveforms. In principle, correlation algorithms to properly sort this data are readily imaginable, though the details depend specifically on the signal designs. And of course if location of the covert emitter is still is necessary, the remote covert emitter could encode his position, say from his GPS, into the data stream. This might make the encryption more important, and certainly elevates the need for LPD/LPI capability. [0048] Returning to the concept of the SFOCMP, it is not correct to think of the possible eigenvalues for a given transmission to constitute a signaling constellation. While signaling using the eigenvalues could be approached this way, it is not a requirement. This would restrict the choices and implementation and performance for the system. The full flexibility of the proposed approach is reached when we allow a non-constant mapping of the baseband symbols (i.e. time durations) to the potential plurality “carrier waveform” options available in the transmitter. The number of “carrier waveforms” can exceed the M-ary alphabet. For example, some alternative “carrier waveforms” might be encountered as distortions of the canonical set such as when power systems or components degrade over time or for some reason the system designer desires a larger signal set be available. [0049] A specific example of waveform design to be feature-less is shown in FIG. 4 and FIGS. 5 [0050]FIG. 5 [0051] Given an environment with several interferers and the already negative received SNR an unintended receiver (even using a front-end filter) will likely not reliably detect the presence of the covert signal. But even if a machine detects the presence of the signal energy, it would likely not be acted upon since it would fail all modulation recognition tests and show no exploitable temporal structure. The signal represented in FIG. 4 [0052] A mathematical element of the invention is the use of spatial high order statistics to separate signal sources, such as a blind source separation algorithm that utilizes a normalized spatial fourth-order cumulant matrix pencil and its generalized eigenvalue decomposition (GEVD). The equations presented herein use the following subscripting convention. Quantities relating to the array observations available to the system are denoted with a boldface subscript x. However, the subscript should not be confused with the representation of the vector observation from the array output, also denoted as a boldface x. From the context the meanings shall be clear to those of skill in the art. Further, quantities relating to the propagating signals impinging on a receive array are denoted with a boldface subscript r. Following this convention, the matrix pencil of the array output data is given as is given as equation 1. An assumption is made that the received signals r comprising the vector observation of the array output x are independent. Therefore the spatial fourth-order cumulant matrix pencil (SFOCMP) of the array output P [0053] where the arguments of the pencil P [0054] in the field of view (FOV) during the observation interval. The terms C [0055] where the matrix is N×N, and the subscript rc indicates the element in the r [0056] Because of the unique definition of the pencil of the array output data P [0057] The quantity V shown in equation 2 is a N×M [0058] Since P [0059] contributes one finite eigenvalue, and it is expressed as the inverse normalized fourth-order autocumulant for that signal as expressed by equation 3.
[0060] where the terms
[0061] represent the individual fourth-order cumulant terms for each signal. These terms are actually the diagonal terms of the pencil P [0062] Thus the GEVD of the two pencils P [0063] These eigenvalues are available to an analysis system, and in theory are independent of system Gaussian noise level given sufficient length data records. The eigenvalues are implicit characteristics of the signals carrying the emitter's covert message in each symbol duration. To exploit this property, as mentioned before, the receiver will typically form blocks or batches of received data for the purpose of correlating the eigenstructure over time to determine patterns of persistent values (FIG. 3) augmented by the availability of spatial data. It is important to recall that only the time duration of the emitter's statistical characteristic as measured by the SFOCMP is relevant, and not the exact values. Hence, the emitter is completely free to choose the “carrier waveforms” at will (FIGS. 6 [0064] The steering vectors can be estimated from the cumulant data for each signal in the FOV of the receiver. A cumulant matrix formed by the receive data, say C [0065] The last equality follows directly from the fact that each eigenvector of the SFOCMP P [0066] In FIG. 3, the Blind Source Separation processor [0067] There are numerous ways the covert transmitter can control the desired characteristic of its emitted waveform, some of which leave lower-order statistics unchanged. For example altering the channel filter (i.e. Nyquist pulse shaping) between maximum phase and minimum phase realizations is undetectable in the second-order domain (i.e. power spectra), but evident in the fourth-order domain as measured by our SFOCMP. Also one could conceive on signaling with kurtosis, a fourth-order statistic, applied in the transmitter. Or, one could simply shift between classic waveforms, for example, BPSK, GMSK, QPSK, QAM, or potentially even just variants (i.e. constellation rotations, different pulse shape filters) of a fixed modulation type. There also exists the possibility that the “carrier waveforms” might be chosen as chaotic to appear more noise-like or designed using numerical techniques and generated using direct synthesis in a transmitter. [0068] In any scheme adopted, the information transfer from the transmitter to the receiver is contained in the duration of the change in the eigenvalues of the SFOCMP, not the particular eigenvalues. Since our technique is independent of the particular eigenvalue, it is independent of the waveforms used by the emitter. Which allows, in principle, any transmitter to make use of the receiver having the capability to exploit fourth-order cumulants. The degree to which a specific emitter wishes to “hide” from say conventional ESM receivers holds the implications on the implementation details of the “carrier waveforms”. [0069]FIG. 6 [0070]FIG. 6 [0071]FIG. 6 [0072]FIG. 6 [0073]FIG. 6 [0074] Combinations of the specific implementation described and others that should be readily apparent from an understanding of this disclosure are likewise envisioned. FIG. 6F is but one of the many possible combinations. The implementation of the noise generator [0075]FIG. 7 is an embodiment using a Laplacian generator [0076] As shall be understood by those of skill in the art, the specific example discussed above may be extended to use random mappings of frequency offsets over time. Also, we could alter the channel filter. There is no requirement that the filter be IIR as shown in the Figure. A number of alternative implementations could be chosen depending on the application. The key feature of the filter is to introduce a temporal dependence of the input noise waveform. Further one could also consider altering the input noise generator. However, a consideration is to select a source with suitable fourth-order properties. Any or all of these parameters can be modified to control the fourth-order properties for the transmitted waveform so long as the “codebook” constraints (time duration and alphabet size) are maintained. A natural alternative to frequency shifting, would be to pulse the carrier on/off. However, this approach reduces the number of signal samples available for geolocation given a fixed observation interval as discussed hereafter. [0077] If one wished to use standard waveforms as the “carrier waveforms” this mode of operation is also possible with this invention. The transmitter shown in FIG. 7 could be modified to look like alternatives shown in FIGS. 6 [0078] An example of a potential message recovery embodiment is shown in FIG. 8. To recover a message the receiver requires three parameters relative to the time durations of the message symbols. The receiver must know the minimum symbol duration [0079] Spatially correlated eigenvalue time durations [0080] An illustration of a portion of the block-to-block eigenvalue correlation result is shown in FIG. 9. For block [0081] As mentioned above, using a simple time-gating operation in the receiver, it is possible to determine which eigenvalues are potentially information carrying. By correlating the GEVD over many blocks of data the persistence of the eigenvalues can be measured. The persistence of eigenvalues of the SFOCMP over time from the covert transmitter provides the signaling mechanism. However, there may be a number of extraneous pulsed signals in the FOV time coincident with the desired communication signal. This makes message recovery complicated, though with proper message construction and error recovery/correction (i.e. FEC), the system is robust to several types of errors such as “erasures” when ambiguous results may be obtained in the decoding and symbol recovery errors. These results can be encountered due to signal fades (i.e. erasures) or symbol recovery errors in the receiver due to statistical fluctuations in time duration measurements exceeding a tolerable threshold. We can correct improper decisions regarding the detection of a symbol in the message in the receiver using typical error control coding. [0082] An embodiment of the receiver [0083] Spatial correlation can be broaden to include simply steering vectors. This is useful when the array and transmitter have a stable geometry. Relative motion between the transmitter and sensing array causes the steering vectors to have a detrimental time dependency. Again, if the spatial variable for correlating the message data is “slowly” varying then small incremental changes can be tolerated. The covert messages is indented to be recovered using a “consistency” of the spatial domain information of the computed eigenstructure from the SFOCMP for the signals of interest. But to account for the possibility of “fixed” location emitters and other emitter who are not of interest to the communication process, a time-gate decision process as noted earlier is advantageously applied. This way the receiver need only attempt to decode “message strings” that emanate from “consistent” spatial locations with the appropriate time character. [0084] Although access to the spatial variables using only the receive array output data has been previously described. It is useful to note a blind source separation algorithm based on a fourth-order cumulant matrix pencil produces eigenvectors that are orthogonal all but one signal's steering vector. Thus using the eigenvectors it is possible to estimate each corresponding signal's steering vector. Two methods are possible. The first method is to use the blockwise estimates directly available from the BSS process as described in relation to FIG. 3 such as averaging across the blocks. A second method is to use the time stamps available from the blockwise correlation process [0085] Signal tracks [0086] The recovered messages are composed of sequentially ordered matrix pencil eigenvalues with a duration within the time gate originating from the same location as determined by the steering vector estimate, AoA or geolocation. The “signal sequence 1” [0087] The advantages of incorporating spatial variables into the message recovery process warrant explanation. First, the spatial variables aid in rejecting extraneous pulsed emitters based on their spatial locations being anti-correlated over time to the persistent spatial locations of the covert emitter(s). By the same token, spatial variables allow the basic signaling approach to support multiple access of covert emitters without undue burden in the receiver for properly assembling the pulsed message sequences. This is because the additional covert emitters will very likely emanate from resolvable spatial locations, and the receiver can use the consistency of the spatial locations over time to associate the proper message sequence. For each transmitted signal, the message sequence is represented by the time durations of the eigenvalues of the appropriately selected matrix pencil, where we have preferred the SFOCMP approach. [0088] The spatial location of any emitter is independent of the exact value of its corresponding eigenvalues available from the GEVD of the SFOCMP. Lastly, the spatial variables provide additional “distance” in the recovery process, since it is now multi-dimensional. For example, two signals may have very similar eigenvalues. But, if their spatial locations are resolvable by the receiver, and fairly constant, then the eigenvalues corresponding to those spatial locations can be easily assigned. Then the message can be recovered using the time duration of each eigenvalue in the sequence assigned a given spatial location using the same technique as previously described when only a single covert signal was in view. [0089] The ability to resolve spatial location has system implications that are interrelated. Some top-level practical design issues that must be reconciled, are desired proximity of transmitters, expected noise environment, block processing sample support for estimating spatial locations and the eigenvalues available from the SFOCMP, digitizer sample rates, signal bandwidths and center frequencies, aperture design (i.e. element type, size, number of ports, operating frequency), and the like. This is of course in addition to having an appropriate level of calibration and positional knowledge of the receive platform. Many of these considerations are direct carry-overs from standard array-based signal processing systems. [0090]FIG. 11 is a flow chart for covert communication with a transmitter [0091] The receiver [0092] If spatial data is unavailable, say because calibration of the sensing array has been degraded, the communication process can still operate. However, the freedom of waveform selection by the transmitter is reduced. In this case the transmitter must select a specific waveform type and use it exclusively (in a pulsed fashion) over the entire message (FIG. 4). Unfortunately with this implementation option the achievable data rate is reduced because of the need to introduce “deadtime” to define symbol boundaries. Thus it is possible to use a single “carrier waveform” that can be pulsed “ON” for each symbol followed by a period of “OFF” time. In this way the covert transmitter need only use a single waveform and need not modify it's fourth-order cumulant signature. This could be an advantage in systems where additional spatial correlation variables preferred to aid unambiguous assignment of the received eigenvalues are unavailable, since we identify one and only one eigenvalue. But as mentioned this is disadvantageous in a multi-emitter environment. For such an environment we prefer a waveform agile emitter where the “carrier waveform” sequencer logic can be designed to select the “carrier waveform” for a specific duration, controlled by the message symbol, in either a fixed map or in some other manner. The mapping choice would be up to the transmitter designer and need not be known to the receiver. The receiver processing is shown in FIG. 12. [0093]FIG. 12 presents a receiver [0094]FIG. 13 is a flow chart for covert communication with a transmitter [0095] The receiver [0096]FIG. 14 is a flow diagram for covert communication using encoded eigenvalues and spatial information. The source [0097] The receiver [0098]FIG. 15 is a representation of a binary message sequence 101011 transmitted via data carrying waveforms according to an embodiment. In the embodiment shown the symbol are transmitted by alternating waveforms of BPSK, QPSK and GMSK. As the message is independent of the encoded data, for LPI it is preferred that the carrier waveforms be modulated with random data at a rate greatly exceeding the covert message symbol rate. The random data may be modulated for a BPSK waveform at 5 sample/per random symbol with a frequency offset of 0.1 f [0099] As discussed previously the waveform duration discriminates the message symbol. As shown in FIG. 15 the symbol 1 has a duration of 20 blocks and the symbol “0” has a duration of 10 blocks. The message is transmitted as a GMSK waveform for a duration of 20 blocks indicating a symbol “1”. The next symbol is transmitted as a different waveform QPSK for a duration of 10 block indicating a symbol “0”. The next symbol is transmitted by the GMSK waveform for a duration of 20 blocks again indicating a “1” symbol and a QPSK waveform is used to transmit the “0” symbol. As illustrative of the independent of the waveform and message content the symbol “1” is then transmitted as a BPSK waveform for a 20 block duration and the next symbol “1” is transmitted by the QPSK waveform for a duration of 20 block. Evident in FIG. 15 is that identical waveforms can communicate different symbols while maintaining waveform content and message independence. [0100] While preferred embodiments of the present inventive system and method have been described, it is to be understood that the embodiments described are illustrative only and that the scope of the embodiments of the present inventive system and method is to be defined solely by the appended claims when accorded a full range of equivalence, many variations and modifications naturally occurring to those of skill in the art from a perusal hereof. Referenced by
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