Abstract:
The present invention teaches method and apparatus to transform a featureless, unpredictable, and non-repeatable chaos waveform into digital chaos waveforms that maintain featureless characteristics to serve as a for wireless communications protocol, whereby unintended observers cannot detect or disrupt yet imprint a small measure of predictability and repeatability to aid intend observers in recovering embedded information. The invention comprises a radio frame constructed from a plurality of buffered digital chaos signals.

Description:
[0001]    This invention was produced in part using funds obtained through a grant from the Army Small Business Innovation Research. Consequently, the federal government has certain rights in this invention. 
       RELATED APPLICATION 
       [0002]    This application claims priority to commonly owned U.S. Provisional Patent Application No. 61/367,800, titled “Method and apparatus for communicating communication data in a digital chaos communication system,” filed Jul. 26, 2010. This application is a continuation of U.S. application Ser. No. 13/190,478, filed Jul. 26, 2011, entitled “Method and Apparatus for Communicating Data in a Digital Chaos Communication System.” Both applications are commonly owned by the present inventor. The contents of both applications are incorporated herein, in their entirety by reference. 
       FIELD OF INVENTION 
       [0003]    This invention relates generally to wireless communication systems. In particular, this invention relates to embedding digital signals and digital information within digital chaos waveforms. 
       BACKGROUND OF INVENTION 
       [0004]    A wireless communication device in a communication system communicates directly or indirectly with other wireless communication devices. For direct/point-to-point communications, the participating wireless communication devices tune their receivers and transmitters to the same channel(s) and communicate over those channels. For indirect wireless communications, each wireless communication device communicates directly with an associated base station and/or access point via an assigned channel. 
         [0005]    Each wireless communication device participating in wireless communications includes a built-in radio transceiver (i.e., transmitter and receiver) or is coupled to an associated radio transceiver. Typically, the transmitter includes one antenna for transmitting radiofrequency (RF) signals, which are received by one or more antennas of the receiver. When the receiver includes two or more antennas, the receiver selects one of antennas to receive the incoming RF signals. This type of wireless communication between the transmitter and receiver is known as a single-output-single-input (SISO) communication. 
         [0006]    Well known communications system provide a range extension on a SISO system by reducing the data rate and, as a result, increase the symbol duration and/or increasing transmit power. However, increasing transmit power can lead to increase interference to other users sharing the network. The preferred method for improved range reception does not lead to decreased network capacity. For popular multicarrier systems such as SISO WLANs, range improvement is achieved by taking an 802.11a/802.11g signal and cutting the symbol rate. Specifically, the current communications system achieves range extension by dividing a symbol clock by 24, i.e., the inverse of Super-G, which doubles the clock frequency. When the symbol clock is divided, the maximum symbol duration is 96 usec and the corresponding rate is 250 kbps. For example, the current communications system takes an 802.11a/802.11g signal that is 16.5 MHz, divides the symbol clock by 24 and cuts the signal to 687.5 kHz. When the bandwidth for a signal is reduced, the integrated thermal noise density of the receiver is also reduced. Therefore, when the bandwidth is reduced by a factor of 24, the thermal noise floor is decreased by 10*log10(24). This results in a 13 dB “gain” in the sensitivity of the receiver which is equivalent to at least 3 times improvement in the range of a typical wireless system. The cost of this implementation, however, is that the data rate is also decreased by a factor of 24. What is needed is a communication device, system and method that increases the transmission range of a WLAN without reducing the data rate. A suitable invention would improve transmission characteristics without data rate reduction or increased interference at the expense of bandwidth expansion of the wireless system. 
         [0007]    Generally speaking, transmission systems compliant with the IEEE 802.11a and 802.11g or “802.11a/g” as well as the 802.11n standards achieve their high data transmission rates using Orthogonal Frequency Division Modulation (OFDM) encoded symbols mapped up to a 64 quadrature amplitude modulation (QAM) multi-carrier constellation. In a general sense, the use of OFDM divides the overall system bandwidth into a number of frequency sub-bands or channels, with each frequency sub-band being associated with a respective sub-carrier upon which data may be modulated. Thus, each frequency sub-band of the OFDM system may be viewed as an independent transmission channel within which to send data, thereby increasing the overall throughput or transmission rate of the communication system. Similarly, multi-code spread spectrum system comprised of perfectly orthogonal high-speed chaos spreading codes transporting independent modulated data can be used to increase its overall throughput or transmission rate of the SISO system. The high-speed “spreading signals” belong to the class of signals referred to as Pseudo Noise (PN) or pseudo-random signal. This class of signals possesses good autocorrelation and cross-correlation properties such that different PN sequences are nearly orthogonal to one other. The autocorrelation and cross-correlation properties of these PN sequences allow the original information bearing signal to be spread at the transmitter. 
         [0008]    Transmitters used in the wireless communication systems that are compliant with the aforementioned 802.11a/802.11g/802.11n standards as well as other standards such as the 802.16a IEEE Standard, typically perform multi-carrier OFDM symbol encoding (which may include error correction encoding and interleaving), convert the encoded symbols into the time domain using Inverse Fast Fourier Transform (IFFT) techniques, and perform digital to analog conversion and conventional radio frequency (RF) upconversion on the signals. These transmitters then transmit the modulated and upconverted signals after appropriate power amplification to one or more receivers, resulting in a relatively high-speed time domain signal with a high peak-to-average ratio (PAR). 
         [0009]    Transmitters used in direct sequence spread spectrum (DSSS) wireless communication systems such as those compliant with commercial telecommunication standards WCDMA and CDMA 2000 perform high-speed spreading of data bits after error correction, interleaving and prior to symbol mapping. Thereafter, the digital signal is converted to analog form and frequency translated using conventional RF upconversion methods. The combined signals for all DSSS signals are appropriately power amplified and transmitted to one or more receivers. 
         [0010]    Likewise, the receivers used in the wireless communication systems that are compliant with the aforementioned 802.11a/802.11g/802.11n and 802.16a IEEE standards typically include an RF receiving unit that performs RF downconversion and filtering of the received signals (which may be performed in one or more stages), and a baseband processor unit that processes the OFDM encoded symbols bearing the data of interest. The digital form of each OFDM symbol presented in the frequency domain is recovered after baseband downconverting, conventional analog to digital conversion and Fast Fourier Transformation of the received time domain signal. Whereas receivers used for reception for DSSS must de-spread the high signal after baseband downconverting to restore the original information signal band but yields a processing gain equal to the ratio the high speed signal to information bearing signal. Thereafter, the baseband processor performs demodulation and frequency domain equalization (FEQ) to recover the transmitted symbols, and these symbols are then processed with an appropriate FEC decoder, e.g. a Viterbi decoder, to estimate or determine the most likely identity of the transmitted symbol. The recovered and recognized stream of symbols is then decoded, which may include deinterleaving and error correction using any of a number of known error correction techniques, to produce a set of recovered signals corresponding to the original signals transmitted by the transmitter. 
         [0011]    To further increase the number of signals which may be propagated in the communication system and/or to compensate for deleterious effects associated with the various propagation paths, and to thereby improve transmission performance, it is known to use multiple transmission and receive antennas within a wireless transmission system. Such a system is commonly referred to as a multiple-input, multiple-output (MIMO) wireless transmission system and is specifically provided for within the 802.11 n IEEE Standard now being adopted. As is known, the use of MIMO technology produces significant increases in spectral efficiency, throughput and link reliability, and these benefits generally increase as the number of transmission and receive antennas within the MIMO system increases. 
         [0012]    In particular, in addition to the frequency channels created by the use of OFDM, a MIMO channel formed by the various transmissions and receive antennas between a particular transmitter and a particular receiver includes a number of independent spatial channels. As is known, a wireless MIMO communication system can provide improved performance (e.g., increased transmission capacity) by utilizing the additional dimensionalities created by these spatial channels for the transmission of additional data. Of course, the spatial channels of a wideband MIMO system may experience different channel conditions (e.g., different fading and multi-path effects) across the overall system bandwidth and may therefore achieve different signal-to-noise ratio (SNRs) at different frequencies (i.e., at the different OFDM frequency sub-bands) of the overall system bandwidth. Consequently, the number of information bits per modulation symbol (i.e., the data rate) that may be transmitted using the different frequency sub-bands of each spatial channel for a particular level of performance may differ from frequency sub-band to frequency sub-band. Whereas DSSS signal occupies the entire channel band, the number of information bits per modulation symbol (i.e., the data rate) that may be transmitted using the different chaos sequence for each spatial channel for a particular level of performance. 
         [0013]    In the MIMO-OFDM communication system using a typical scheme, a high Peak-to-Average Power Ratio (PAPR) may be caused by the multiple carrier modulation. That is, because data are transmitted using multiple carriers in the MIMO-OFDM scheme, the final OFDM signals have amplitude obtained by summing up amplitudes of each carrier. The high PAPR results when the carrier signal phases are added constructively (zero phase difference) or destructively (±180 phase difference). Notably, OFDM signals have a higher peak-to-average ratio (PAPR) often called a peak-to-average power ratio (PAPR) than single-carrier signals do. The reason is that in the time domain, a multicarrier signal is the sum of many narrowband signals. At some time instances, this sum is large and at other times is small, which means that the peak value of the signal is substantially larger than the average value. Similarly, MIMO-DSSS schemes can have high PAPR for periodic sequence or binary-valued sequence; however chaos spreading sequences do not exhibit either of these characteristics and therefore have better PAPR performance for SISO and MIMO operations. 
         [0014]    The continually increasing reliance on SISO and especially MISO wireless forms of communication creates reliability and privacy problems. Data should be reliably transmitted from a transmitter to a receiver. In particular, the communication should be resistant to noise, interference, and possibly to interception by unintended parties. 
         [0015]    In the last few years there has been a rapidly growing interest in ultra-wide bandwidth (UWB) impulse radio (IR) communication systems. These systems make use of ultra-short duration pulses that yield ultra-wide bandwidth signals characterized by extremely low power spectral densities. UWB-IR systems are particularly promising for short-range wireless communications as they combine reduced complexity with low power consumption, low probability of detection (LPD), immunity to multipath fading, and multi-user capabilities. Current UWB-IR communication systems employ pseudo-random noise (PN) coding for channelization purposes and pulse-position modulation (PPM) for encoding the binary information. 
         [0016]    Others have proposed a periodic sequences of pulses in the context of chaos-based communication system. Additional work has relied upon the self-synchronizing properties of two chaotic systems. In such a system, data is modulated into pulse trains using variable time delays and is decodable by a coherent receiver having a chaotic generator matched to the generator used in the transmitter. Such system is known in the art as a Chaotic Pulse Position Modulation (CPPM) scheme. 
         [0017]    Such chaotic dynamical systems have been proposed to address the problem of communication privacy. Chaotic signals exhibit a broad continuous spectrum and have been studied in connection with spread-spectrum applications. The irregular nature of a chaotic signal makes it difficult to intercept and decode. In many instances a chaotic signal will be indistinguishable from noise and interference to receivers not having knowledge of the chaotic signal used for transmission. In the context of UWB systems the use of non-periodic (chaotic) codes enhances the spread-spectrum characteristics of the system by removing the spectral features of the signal transmitted. This results in a lower probability of interception/detection (LPI/LPD) and possibly less interference towards other users. This makes the chaos-based communication systems attractive. 
         [0018]    There remains a need for improved chaotic coding/modulation methods to produce such attractive communication systems. One prior art, U.S. Pat. No. 6,882,689, issued Apr. 15, 2005 to Maggio et al., attempts to improve chaotic coding using pseudo-chaotic coding/modulation method that exploits the symbolic dynamics of a chaotic map at the transmitter to encode data. The method uses symbolic dynamics as “coarse-grained” description of the evolution of a dynamic system. The state space is partitioned and a symbol is associated with each partition. The Maggio invention uses a trajectory of the dynamic system and analyzes it as a symbolic system. A preferred transmitter of the Maggio prior art accepts digital data for coding and the digital data is allocated to symbolic states according to a chaotic map using a shift register to approximate the Bernoulli shift map acting as a convolution code with a number of states equal to the symbolic states defined on the chaotic map. The pseudo-chaotically coded data is converted to analog form and modulated into synchronization frames in a transmitted signal. 
         [0019]    The Maggio prior art has limitations in that it uses only one chaos map (e.g., Bernoulli shift map) that is generated based on the data transmitted. By confining the mapping to Bernoulli shift, information that is repeated in each transmission or repeat symbol can be recognized after observing the waveform over an extended period of time. Once compromised, all future data will be detectable and decodable by a hostile system. 
         [0020]    Generally, the most fundamental issue in wireless communication lies in how efficiently and reliably data can be transmitted through a channel. The next generation multimedia mobile communication system, which has been actively researched in recent years, requires a high speed communication system capable of processing and transmitting various forms of information such as images and wireless data, different than an initial communication system providing a voice-based service. 
         [0021]    Then according to the prior art, what is needed is a system and method that does not sacrifice data rate in favor of range, provides increased robustness, while improving LPI/LFD. 
       SUMMARY OF INVENTION 
       [0022]    The present invention teaches improvements not found in the prior art. The invention teaches a system, device and method for wirelessly transmitting data using a digital chaos spreading sequence for wirelessly transmitting data. In one aspect, the invention teaches a constructing and storing a digital chaos spreading code sequence. 
         [0023]    In another aspect of the invention the digital chaos waveform is chosen based on the intended application. For example, one chaos waveform typical characteristics include, for example, unity autocorrelation and very low cross-correlation, and cyclostationary properties. The particular digital chaos waveform family such as Bernoulli mapping, Chen&#39;s system, or Ikeda map as examples. 
         [0024]    In another aspect of the invention, a plurality of constructed digital chaos spreading code are stored in a volatile memory. 
         [0025]    Within a single group, the volatile memory includes slots for storing a constructed digital chaos spreading sequence of a length N. The digital chaos spread sequence may be partitioned into M number of groups of equal number of even number of digital chaos spreading code subsequences. Users are assigned a group ID from are stored in a sequential order. The sequential ordering can be a known order, such as formal ordering of natural numbers (e.g., 1, 2, 3, . . . ). However, the ordering does not need to be consecutive. The number is the index to sequences stored in at both the transmitter and receiver in a manner such as to provide a one-to-one correspondence between selected digital chaos spreading code sequence at the transmitter and detected and recovered index at the receiver. 
         [0026]    In yet another aspect, the invention discloses a data payload wherein the pre-ambles and mid-ambles are constructed so that multiple embedded signals can be detected at one or more locations without interference with native performance of each constituent signal. The data payload may be comprised of at least one high PAPR signal and at least one other signal that is part of a common network protocol. The pre-amble and mid-amble are also constructed by repeating the digital chaos sequence of sign flipping a copy of the digital chaos sequence in the next symbol period. 
         [0027]    In still another aspect, the invention teaches a transmitter system including a volatile memory storing a digital chaos sequence. 
         [0028]    In still another aspect, the invention teaches a receiver system including a volatile memory storing a digital chaos sequence. 
         [0029]    In still another aspect, the invention teaches a system for transmitting data using a digital chaos spreading sequence. 
         [0030]    In another aspect, the invention discloses a method for embedding control information in pre-ambles and mid-ambles for a network based on relative amplitude over the replication period. The control information is conveyed using a pre-selected digital chaos sequence. 
         [0031]    In yet another aspect, the invention teaches a method for selecting a digital chaos waveform for use in a digital chaos spread sequence. 
         [0032]    In yet another aspect the invention teaches a method for embedding multiple disparate communication signals within digital chaos communication waveforms originating from a single antenna subsystem. The method according to this aspect can include multiple antenna element for introducing low probability intercept (LPI) and low probability of detection (LPD), reduced peak-to-average ratio (PAPR), and increased network system capacity. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0033]    A more complete understanding of the present invention may be derived by referring to the various embodiments of the invention described in the detailed descriptions and drawings and figures in which like numerals denote like elements, and in which: 
           [0034]      FIG. 1  is an exemplary SISO wireless transmission system that may be used with the various embodiments of the invention; 
           [0035]      FIG. 2  is an exemplary wireless transmitter in accordance with various embodiments of the invention; 
           [0036]      FIG. 3  is an exemplary wireless receiver in accordance with various embodiments of the invention; 
           [0037]      FIG. 4  is a flowchart of an exemplary method for constructing of a digital chaos sequence according to various embodiments of the present invention; 
           [0038]      FIG. 5  is an exemplary receiver synchronization process according to various embodiments of the invention; and 
           [0039]      FIG. 6  Is an exemplary embodiment of packet formation according to various embodiments of the invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0040]    The brief description of exemplary embodiments of the invention herein makes reference to the accompanying drawing and flowchart, which show the exemplary embodiment by way of illustration and its best mode. While these exemplary embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, it should be understood that other embodiments may be realized and that logical and mechanical changes may be made without departing from the spirit and scope of the invention. Thus, the description herein is presented for purposes of illustration only and not of limitation. For example, the steps recited in any of the method or process descriptions may be executed in any order and are not limited to the order presented. 
         [0041]    The present invention may be described herein in terms of functional block components and various processing steps. It should be appreciated that such functional blocks may be realized by any number of hardware and/or software components configured to perform the specified functions. For example, the present invention may employ various integrated circuit (IC) components (e.g., memory elements, processing elements, logic elements, look-up tables, and the like), which may carry out a variety of functions under the control of one or more microprocessors or other control devices. Similarly, the software elements of the present invention may be implemented with any programming or scripting language such as C, C++, java, COBOL, assembler, PERL, or the like, with the various algorithms being implemented with any combination of data structures, objects, processes, routines or other programming elements. Further, it should be noted that the present invention may employ any number of conventional techniques for data transmission, signaling, data processing, network control, and the like. Still further, the invention could be used to detect or prevent security issues with a scripting language, such as JavaScript, VBScript or the like. For a basic introduction of cryptography, please review a text written by Bruce Schneider which is entitled “Applied Cryptography: Protocols Algorithms, And Source Code In C,” published by john Wiley &amp; Sons (second edition, 1996), which is hereby incorporated by reference. 
         [0042]    It should be appreciated that the particular implementations shown and described herein are illustrative of the invention and its best mode and are not intended to otherwise limit the scope of the present invention in any way. Indeed, for the sake of brevity; conventional wireless data transmission, transmitter, receivers, modulators, base station, data transmission concepts and other functional aspects of the systems (and components of the individual operating components of the systems) may not be described in detail herein. Furthermore, the connecting lines shown in the various figures contained herein are intended to represent exemplary functional relationships and/or physical couplings between the various elements. It also should be noted that many alternative or additional functional relationships or physical connections may be present in a practical electronic transaction or file transmission system. 
         [0043]    As will be appreciated by one of ordinary skill in the art, the present invention may be embodied as a method, a data processing system, a device for data processing, and/or a computer program product. Accordingly, the present invention may take the form of an entirely software embodiment, an entirely hardware embodiment, or an embodiment combining aspects of both software and hardware. Furthermore, the present invention may take the form of a computer program product on a computer-readable storage medium having computer-readable program code means embodied in the storage medium. Any suitable computer-readable storage medium may be utilized, including hard disks, CD-ROM, optical storage devices, magnetic storage devices, and/or the like. 
         [0044]    To simplify the description of the exemplary embodiment, the invention is described as pertaining to a SISO DSSS system, the invention is applicable to MIMO systems as well. It will be appreciated, however, that many applications of the present invention could be formulated. For example, the system could be used to facilitate any conventional wireless communication medium, and the like. Further, it should be appreciated that the network described herein may include any system for exchanging data or transacting business, such as the Internet, an intranet, an extranet, WAN, WLAN, WPAN, Ad hoc Networks, mobile ad hoc networks (MANET), satellite communications (SATCOM), and/or the like. 
         [0045]      FIG. 1  is an exemplary embodiment block diagram of a SISO system  100  useful for the invention. In  FIG. 1  shows a block diagram of an exemplary single-input-single-output (SISO) communication system  100 . The exemplary SISO communication system  100  and its sub-components will be described below when required to facilitate the description of the present invention. The exemplary SISO communication system  100  may be implemented as a wireless system for the transmission and reception of data across a wireless channel  111 . For example, the SISO communication system  100  may be implemented as part of a wireless local area network (LAN) or metropolitan area network (MAN) system, a cellular telephone system, or another type of radio or microwave frequency system incorporating one-way or two-way communications over a range of distances. 
         [0046]    SISO communication system  100  may employ various signal modulation and demodulation techniques, such as single-carrier frequency domain equalization (SCFDE), direct sequence spread spectrum (DSSS) or orthogonal frequency division multiplexing (OFDM), for example. However, throughout this description, references will be made with respect to a SISO communication system or a system including a transmitter and receiver merely to facilitate the description of the invention. 
         [0047]    SISO communication system  100  includes a transmitter  102  and a receiver  104 . The transmitter  102  transmits signals across the channel  111  to the receiver  104 . The transmitter  102  may include an encoder  204  for encoding data and/or other types of signals received, for example, from a data source  202  (information sequence  202 ). The signal may then be modulated  103  prior to being transmitted to the receiver  104  by antenna  218 . Such signals may alternatively be referred to collectively as “data,” “signals,” “information sequence,” and/or “data signals.” 
         [0048]    The signal is received at the receiver antenna  326 . The receiver  104  also includes a decoder  320 , which is connected to the demodulator  105 . The decoder  320  typically combines and decodes the demodulated signals from the demodulator  105 . In this regard, the decoder  320  typically recovers the original signals that were provided by the data source  202 . As depicted in  FIG. 1 , the original signals recovered by the decoder  320  may be transmitted to a connected data sink  107 , which may include one or more devices configured to utilize or process the recovered signals  322 . As is well known, receivers may additionally include other elements such as symbol mapper  318 , symbol detection unit  316 , Doppler Correction unit  314 , packet detection circuit  308 , AD converters  304  and the like which are of the type which may be found in the prior art. 
         [0049]    As previously noted, traditional SISO WLAN transmission has problems addressed by the present invention. Namely, prior art systems such 802.11x compliant system are more susceptible to interference, wireless collisions, and interception by unintended parties. 
         [0050]    The present invention addresses these problems by providing a system and method for embedding multiple information-bearing communication signals within digital chaos communication waveforms occupying the same frequency channel bandwidth . By digital chaos what is meant is a waveform generated by sampling a chaos signal, where chaos signal are determined by nonlinear dynamics: either stochastic or deterministic. Digital chaos sequences generated according to the invention as described below, is used as a spreading sequence in a digital chaos transmitter  102  shown in  FIG. 1 . 
         [0051]    With reference to  FIG. 2 , transmitter  102  includes a channel encoder  204 , a symbol mapper  206 , multiplexer  208 , wherein channel encoder  204 , symbol mapper  206  and multiplexer  208  are traditional elements as are found in the prior art. As such, their construction and operation is not discussed in here for brevity. 
         [0052]    Transmitter  102  further includes a chaos sequence memory  208  for storing digital chaos sequences in accordance with the present invention. 
         [0053]    The digital chaos sequences stored in chaos sequence memory  208  are constructed according to the digital chaos sequence generation method of  FIG. 4 . With reference to  FIG. 4 , digital chaos construction method  400 , the digital chaos spreading code sequence is constructed by recording native analog chaos circuit or computer simulated non-linear dynamics of deterministic or stochastic mapping characteristics (Step  402 ). The recorded segments are sampled such that successive samples appear independent and segments of a predefined length and variable quantity have low cross correlation.(Step  404 ) Those samples may then be stored in memory (Step  406 ). Sampling rate can be varied or irregular, but the number of samples taken is fixed for a particular spreading factor and can be any number (Step  408 ). Moreover, the period over which you sample can be varied. In accordance with the invention, the segments are quantized (Step  410 ). The quantized recorded segments undergo the Gram-Schmidt (GS) process (Step  412 ). The GS process on the sequence ensures that autocorrelation peak occurs at unity or near unity and cross-correlation between sequences is zero or nearly zero (e.g. m low cross-correlation)—within the precision of the quantization process. In one exemplary embodiment, the cross-correlation is less than 10 dB[ 0059 ] An Irregular sampling interval according to the invention may be, for example, determined by modulo counting of known sequence generator such as Fibonacci numbers, Lucas numbers, Perrin numbers or any pseudo random number generators. For implementation ease with semiconductor technologies for digital system, the amplitudes may be quantized to finite levels based on the maximum allow cross-correlation (½ L , where is L is the number of bits used to represent by each sample amplitude) between code sequences. Independent segments or the digital chaos sequences are grouped together to form a vector span for transmitting the information-bearing communication signals or training signals. It is well-known in mathematic that any signal in an n-dimensional subspace can be unique represented an n-tuple of scalar corresponds to the projection of the signal onto the orthonormal bases of the n-dimensional. The final step of the digital chaos process is to convert the independent digital chaos segments into a group of orthonormal sequences spanning the same subspace as the original segment. This process is performed using the Gram-Schmidt orthogonalization process. 
         [0054]    The memory can be partitioned such that groups of digital chaos spreading codes are stored independently of each other. For example, the distinct groups may be organized according to the application for it will be used. Typical applications include any wireless applications requiring voice over IP (VoIP) capability, video capability, and data capability for point-to-point operation and/or point-to-multi-point. Inside the groups, the volatile memory is further partitioned into slots for storing a digital chaos sequence code. The slot is further partitioned into a plurality of sub-slots for storing subsets of the of the digital chaos sequence. 
         [0055]    Once the chaos sequence memory  208  is fully populated with digital chaos spreading sequences, the memory  208 , the entire memory  208  is subjected to Gram-Schmidt processing, which converts the independent digital chaos segments into a group of orthonormal sequences spanning the same subspace as the original segment. The memory requirement after the Gram-Schmidt process is unchanged from those of the quantized segments. It is well-known in mathematics that any signal in an n-dimensional subspace can be unique represented an n scalar values that corresponds to the projection of the signal onto the orthonormal bases of the n-dimensional thus the need for Gram-Schmidt process in this invention method of apparatus 
         [0056]    A preferred embodiment of the invention for the packet formation is shown in  FIG. 6  In this exemplary embodiment the sample rate at the receiver is targeted at 20 MHz and the chipping rate is proposed at 4 Mcps at the transmitter. The minimum center frequency spacing between adjacent systems will be 5 MHz. The framing structure may be a radio frame of 10 ms divided into 5 sub-frames of equal duration 2 milliseconds (ms) ( 600 ). These sub-frames may be configured as transmit or receive slot for any user. 
         [0057]    A super-frame consists of several frames transmitted in succession with 2 ms gap spacing between frames ( 610 ). Each frame to be transmitted consists of a preamble training sequence, mid-amble training sequence, and data payload. The flexibility of frame structure can accommodate a number of other embodiments cater to specific application. In this embodiment (other might exists that make different trades for different application requirements), sufficient training information is included to present securely and reliably. 
         [0058]    As is well known, the key to a successful wireless design is to incorporate sufficient training information to recognize the arrival of packets, align symbol boundaries, estimate channel characteristic and correct for frequency offset. This embodiment utilizes a header field comprises of a ten symbol preamble ( 602 ) and  48  symbol signal field ( 604 ) that defines the configuration state for the receiver. The data portion of the frame varies from 0-200 symbols or 1-250 symbols ( 606 ) depending if it is the first frame of a super frame. The mid-amble, if transmitted, consists of five additional training sequences in the middle of the frame ( 608 ). All training sequences are modulated using differential chaos shift keying (DCSK) and repeated a predetermined number of times; nine times and five times are shown for the preamble and mid-ambles, respectively, in  FIG. 6 . Each repetition is modulated with either a 1 or −1 according to normal DCSK techniques. The modulation input can be an alternating sequence of positive and negative ones, which embeds with control information for the rest of the packet. The preamble and mid-ambles can have their powers significantly higher that the data to aid in the synchronization at the receiver. For example, one embodiment used a 3 dB boosted in relative power to the data samples. This will permit the high probability of detection without an overly burdensome overhead for the frame. If total overhead is 10% or less in duration for the frame, significant improvement in detection and synchronization at the receiver is achievable for sacrificing only 0.79 dB is signal power compared to no power boost. Each symbol is comprised of a chaos sequence of predetermined length that can range from 16 chips to 4000 chips, depending on the application requirements for throughput and covertness. The signal field is comprised on a 6 bit scrambling seed, which is used to initialize the pseudorandom number (pn) generator for sequence pattern. The state of the registers of the pn determines which of 2 ̂6  stored sequence is selected or, optionally, which sequence in the chaos family should be transmitted for the current symbol. 
         [0059]    Transmitter  102  receives information bearing signals  202 . The format of data information of  202  may be bits, symbols, or sampled analog waveforms. The high speed chaos spreading sequence  208  multiplies the channel coded bits or symbol or directly the sampled analog waveform. The high speed chaos spreading transform the bit, symbol, or sample analog waveform into a digital chaos waveform with information embedded in the amplitude and phase of the digital chaos waveform compared to an exact replica  306  at the receiver. 
         [0060]    The signal transmitted by transmitter  102  is received by digital chaos receiver  104  which recovers the embedded data.  FIG. 3  is an exemplary embodiment of a receiver  104  according to the present invention. Receiver  104  includes an antenna  306  for receiving the transmitted signal, channel filter  302  to reject signals not in the band of interest, analog-to-digital (ND) converter is used to sample and quantization the analog signal suitable for digital processing, chaos replica repository  306  need for despreading, packet detection  308  to determine when a packet arrives, matched filter  310  to recover symbol timing, channel estimate  312  to estimate and compensate the distortions to the waveform due to multipath fading, Doppler Correction  314  to estimate and correct frequency offsets to due oscillator drift and mobility, symbol detect  316  to estimate the mapping symbol sent by the transmitter, symbol D-map look-up table  318  to recover informational symbol, Channel Decode  320  to recover the original transmitted bits. 
         [0061]    In recovering the data, receiver  104  receives the transmitted signal and recovers the data signal by 1) The packets are continually searched until the receiver detects the arrival of a valid packet ( 502 ). The detection of the packet is based on the output of a free-running correlation ( 308 ) that exploits the preamble structure. The validity of the packet is determined from the cyclic redundancy check (CRC) of the signal field ( 604 ). After the packet has been declared valid, the preamble is used to perform two synchronization processes: symbol timing estimation &amp; correction ( 504 ) and frequency estimation &amp; correction ( 506 ). A match filter or bank of matched filter ( 310 ) is used to estimate the timing error and the appropriate correction is made in the receiver timing. A separate correlator is used to estimate the frequency errors ( 314 ) and the appropriate correction is applied to the baseband received signal. The channel estimate is computed using the pre-computed convolution matrix based on the training symbols from the preamble. The pseudo inverse of this matrix, which can be also computed off since it doesn&#39;t change unless the preamble changes, is used to compute the minimum mean square estimate of the channel taps ( 312 ) ( 508 ). Averaging is possible for each of process steps  502 ,  504 ,  506 , and  508  based on the repetition of the training symbols in both the preamble and mid-amble. The final processing step to process the payload ( 510 ), which consists of symbol detect ( 316 ), Symbol D-Map ( 318 ), Channel Decode ( 320 ), and finally, recovery of the information bits ( 322 ). It should be noted that there are two common receiver modes as preferred embodiments. One, the high speed multiplication with Chaos replica  306  occurs directly after the A/D. This embodiment is preferred when a sampled analog waveform is the information-bearing signal as shown in  FIG. 2 . Two, the high speed multiplication with Chaos replica  306  occurs prior symbol detect  316  and after Doppler Correction  314  and Channel Estimation. This embodiment is bested suited when the information-bearing signals where bits or symbols. Either configuration works for the information-bearing signals in the form of bits or symbol, however configuration two has the best performance and configuration one has the lower power consumptions. 
         [0062]    It should be appreciated by one skilled in art, that the present invention may be utilized in any device that implements the DSSS OFDM encoding scheme. The foregoing description has been directed to specific embodiments of this invention. It will be apparent that other variations and modifications may be made to the described embodiments, with the attainment of some or all of their advantages. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.