Abstract:
Systems and methods of ultra-wideband communication are provided. In one embodiment, an ultra-wideband communication system divides a stream of data conveying symbols into a plurality of unspread substreams. A common spreading code is generated at the ultra-wideband transmitter, and each of the unspread substreams are spread using the common spreading code to form a plurality of spread substreams. The spread substreams are combined to form a composite signal that is transmitted. This Abstract is provided for the sole purpose of complying with the Abstract requirement rules that allow a reader to quickly ascertain the subject matter of the disclosure contained herein. This Abstract is submitted with the explicit understanding that it will not be used to interpret or to limit the scope or the meaning of the claims.

Description:
This application is a continuation-in-part of U.S. application Ser. No. 09/670,054 filed Sep. 25, 2000 now U.S. Pat. No. 7,031,371 entitled “METHOD AND APPARATUS FOR WIRELESS COMMUNICATIONS.” 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     The invention relates generally to ultra-wideband communications, and more particularly to systems and methods for communication using ultra-wideband technology. 
     BACKGROUND OF THE INVENTION 
     The electromagnetic spectrum used to convey radio communications is a precious commodity. Communication systems seek to use this spectrum as efficiently as possible to maximize the capacity or quantity of information, which can be conveyed using the spectrum. 
     Various multiple access techniques have been developed to transfer information among a number of users, all while efficiently using spectrum. Time division multiple access (TDMA) techniques assign different users to different time slots. Capacity is hard limited by the number of time slots available. To prevent intolerable interference, the portion of the spectrum used in one radio coverage area or cell has conventionally been unusable in adjacent cells. Thus, only a fraction, typically less than one-third, of the entire spectrum available for conveying communications has been conventionally usable in any one location. In other words, conventional TDMA systems employ a frequency reuse pattern of at least three, indicating an inefficient use of spectrum. 
     Conventional direct sequence spread spectrum (DSSS) code division multiple access (CDMA) techniques theoretically use the spectrum more efficiently than TDMA techniques. However, in practice conventional DSSS-CDMA techniques typically fail to provide results significantly better than TDMA. DSSS-CDMA techniques assign different users to different codes. The different codes have conventionally been selected because of orthogonality or low cross correlation properties with the codes of other users. These properties minimize interference. All communications are broadcast using the same spectrum, so the frequency reuse pattern equals one. While the commonly used spectrum conveys a composite of communications for all users, each individual user&#39;s communications are extracted from the composite by correlating a received signal against the individual user&#39;s assigned code. 
     Capacity in conventional DSSS-CDMA systems is interference limited. In other words, more and more codes can be assigned so that the given amount of spectrum can service more and more users until interference reaches a level where only a minimally acceptable quality of service results. In practice, most conventional DSSS-CDMA systems can assign far fewer codes than appear theoretically possible due to a near-far effect and multipath. The near-far effect results when signals from different users are received with greatly differing field strengths, but this detrimental effect may be ameliorated somewhat by power control. 
     Multipath results when the transmitted signal takes multiple paths to the receiver due to being reflected from and deflected around obstacles in the environment. As the signal propagates over the multiple paths, different propagation delays are experienced. Thus, a signal transmitted at a precise instant in time is received spread over an interval, causing the signal to interfere with itself. In conventional DSSS-CDMA communication systems, multipath tends to destroy the orthogonality of spreading codes, resulting in dramatically increased interference. 
     SUMMARY OF THE INVENTION 
     In order to combat the above problems, systems and methods described herein provide a novel ultra-wideband communication system. In one embodiment, an ultra-wideband communication system divides a stream of data conveying symbols into a plurality of unspread substreams. A common spreading code is generated at the ultra-wideband transmitter, and each of the unspread substreams are spread using the common spreading code to form a plurality of spread substreams. The spread substreams are combined to form a composite signal that is transmitted. 
     In another embodiment, an ultra-wideband communication system comprises a demultiplexer for dividing a stream of data conveying symbols into a plurality of unspread substreams. A spreading section is coupled to the demultiplexer and configured to generate a plurality of spread substreams from the plurality of unspread substreams. A combining section is coupled to the spreading section and configured to form a composite signal from the plurality of spread substreams, and a transmission section is coupled to the combining section and configured to transmit the composite signal over an ultra-wideband communication channel. 
     These and other features and advantages of the present invention will be appreciated from review of the following Detailed Description of the Preferred Embodiments, along with the accompanying figures in which like reference numerals are used to describe the same, similar or corresponding parts in the several views of the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A more complete understanding of the present invention may be derived by referring to the detailed description and claims when considered in connection with the Figures, wherein like reference numbers refer to similar items throughout the Figures, and: 
         FIG. 1  shows a layout diagram of an exemplary environment in which the present invention may be practiced; 
         FIG. 2  shows a timing diagram, which depicts a temporal format of a TDMA communication signal; 
         FIG. 3  shows a block diagram of a transmitter and a receiver configured in accordance with the teaching of the present invention; 
         FIG. 4  shows a timing diagram depicting how a cyclic spreading code is applied to blocks of unspread data streams in accordance with first, second and third embodiments of a DSSS modulation section in the transmitter of the present invention; 
         FIG. 5  shows a block diagram of the first embodiment of the DSSS modulation section; 
         FIG. 6  shows a block diagram of the second embodiment of the DSSS modulation section; 
         FIG. 7  shows a block diagram of the third embodiment of the DSSS modulation section; 
         FIG. 8  shows a first embodiment of a CDM to TDM converter section in the receiver of the present invention; 
         FIG. 9  shows an exemplary spectral analysis of a suitable spreading code usable in connection with the present invention, the spectral analysis showing a substantially flat response; 
         FIG. 10  shows an exemplary timing diagram of various individual signal components present in a composite signal output from a matched filter portion of a mismatched filter in the CDM to TDM converter; 
         FIG. 11  shows a timing diagram depicting how a cyclic spreading code is applied to blocks of unspread data streams in fourth and fifth embodiments of the DSSS modulation section; 
         FIG. 12  shows a block diagram of the fourth and fifth embodiments of the DSSS modulation section; 
         FIG. 13  shows a second embodiment of the CDM to TDM converter for use with the fourth embodiment of the DSSS modulation section; 
         FIG. 14  shows a third embodiment of the CDM to TDM converter for use with the fifth embodiment of the DSSS modulation section; 
         FIG. 15  is an illustration of different communication methods; and 
         FIG. 16  is an illustration of two ultra-wideband pulses. 
     
    
    
     It will be recognized that some or all of the Figures are schematic representations for purposes of illustration and do not necessarily depict the actual relative sizes or locations of the elements shown. The Figures are provided for the purpose of illustrating one or more embodiments of the invention with the explicit understanding that they will not be used to limit the scope or the meaning of the claims. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the following paragraphs, the present invention will be described in detail by way of example with reference to the attached drawings. While this invention is capable of embodiment in many different forms, there is shown in the drawings and will herein be described in detail specific embodiments, with the understanding that the present disclosure is to be considered as an example of the principles of the invention and not intended to limit the invention to the specific embodiments shown and described. That is, throughout this description, the embodiments and examples shown should be considered as exemplars, rather than as limitations on the present invention. As used herein, the “present invention” refers to any one of the embodiments of the invention described herein, and any equivalents. Furthermore, reference to various feature(s) of the “present invention” throughout this document does not mean that all claimed embodiments or methods must include the referenced feature(s). 
     The present invention provides several advantages and features, for example, the present invention combines TDMA and spread spectrum techniques so that wireless communications capacity is increased over the capacities achievable through conventional TDMA and/or CDMA systems using an equivalent amount of spectrum. 
     Another advantage of the present invention is that robust, simple, and inexpensive processing techniques are usable, making the present invention suitable for hubs, subscriber units, mobile stations/fixed stations, portable stations, and the like. 
     Another advantage is that the present invention may be adapted to and used in conjunction with a variety of modulation and multiple access techniques, such as frequency division multiple access (FDMA) and orthogonal frequency division multiplexing (OFDM). 
     Another advantage of the present invention is that a composite RF communication signal includes signal components obtained by modulating diverse branches of a single user&#39;s data stream using cyclic variants of a common spreading code. 
     Another advantage is that the present invention is configured to tolerate self-interference and is better able to tolerate multipath than conventional DSSS-CDMA communication systems. 
     These and other features and advantages of the present invention will be appreciated from review of the following discussion: 
       FIG. 1  shows a layout diagram of an exemplary environment in which a communication system  20  configured in accordance with the teaching of the present invention may be practiced. Communication system  20  includes any number of transmitters (TX&#39;s)  22  (three shown) and any number of receivers (RX&#39;s)  24 (five shown). Transmitters  22  wirelessly broadcast messages through RF time domain multiple access (TDMA) communication signals  26  which are receivable by receivers  24  located within radio coverage areas  28  for the transmitters  22 . Radio coverage areas  28  may also be called cells or sectors. As illustrated in  FIG. 1 , various ones of radio coverage areas  28  may be adjacent to one another and even overlap to some extent. In the preferred embodiment, a common spectrum is used in all radio coverage areas  28  so that communication system  20  has a frequency reuse pattern substantially equal to one. 
     For the sake of clarity,  FIG. 1  depicts only a forward link in which radio equipment is viewed as being only a transmitter  22  or a receiver  24 . However, those skilled in the art will appreciate that a reverse link may also be implemented and that each item of equipment may have both a transmitter and receiver. The reverse link may use the same or a different spectrum from the forward link. If a forward link conforms to the teaching of the present invention, then the reverse link may or may not conform, and vice versa. 
       FIG. 2  shows a timing diagram, which depicts an exemplary temporal format for TDMA communication signal  26 .  FIG. 2  specifically depicts two frames  30 , each of which is temporally subdivided into any number of timeslots  32 . Different timeslots  32  are preferably assigned to different receivers  24  ( FIG. 1 ) in a manner well understood in the art so that different recipients are distinguished from one another by being assigned to the different time slots  32 . In the preferred embodiments, TDMA communication signal  26  consumes the entire common spectrum for each time slot  32 . Nothing requires a time slot  32  to be assigned to receivers  24  for an indefinite period or to be of the same duration as other time slots  32 . 
     Each time slot  32  of TDMA communication signal  26  is subdivided into successive blocks  34  of symbols  36 .  FIG. 2  labels blocks  34  with the identifiers B k , for k=0 to K−1, where K is an integer number. Any number of blocks  34  may be included in each timeslot  32 . Each block B k  includes M symbols  36 , labeled as a k,m  for m=0 to M−1, where M is an integer number.  FIG. 2  illustrates each of symbols  36  within a block  34  as being concurrently present throughout the entire duration of a block period because certain preferred embodiments discussed below configure symbols  36  to remain present for block periods. 
       FIG. 2  further illustrates that the M symbols  36  of each block  34  are spread using an N-chip spreading code  38 , labeled as C n , for n=0 to N−1, where N is an integer number. As discussed in more detail below, each symbol  36  is independently spread using cyclic variations of the same common code  38 . The number M of symbols  36  in a block may equal the number N of chips in a spreading code, in which case the spreading factor equals one. However, performance improvements result when N is greater than M. 
       FIG. 3  shows a block diagram of a single transmitter  22  and a single receiver  24  configured in accordance with the teaching of the present invention. Those skilled in the art will appreciate that all transmitters  22  and receivers  24  may be configured similarly. In addition, any number of receivers  24  may, at any given instant, receive TDMA communication signal  26  from a given transmitter  22  and, in fact, may receive TDMA communication signals  26  from more than one transmitter  22 . 
     Transmitter  22  includes a TDMA modulation section  40 , which generates a TDMA-configured stream  42  of data conveying symbols  36 . Stream  42  feeds a direct sequence spread spectrum (DSSS) modulation section  44 , which generates a composite signal  46 . Composite signal  46  feeds a transmission section  48 , which forms TDMA communication signal  26  from composite signal  46  and wirelessly broadcasts TDMA communication signal  2   6  for reception by receivers  24  located within radio coverage area  28  ( FIG. 1 ) of transmitter  22   
     Within TDMA modulation section  40  any number of data sources  50  supply digital data to a multiplexer (MUX)  52 . The digital data from data sources  50  may be intended for any number of receivers  24 . Multiplexer  52  groups the digital data so that data intended for different receivers  24  are serially fed to a cyclic redundancy check (CRC) section  54  in accordance with the assignment of timeslots  32  ( FIG. 2 ) to receivers  24 . CRC section  54  provides forward error correction in a manner well understood by those skilled in the art. 
     From CRC section  54 , the input data stream may be fed through a scrambler  56  which randomizes the data to an encode and interleave section  58 . Section  58  may apply another type of error correction, such as convolutional or turbo encoding, to the input stream, and interleave the data. CRC section  54  and section  58  may utilize a form of block encoding. The block size or boundaries of such encoding need have no relationship to blocks  34  ( FIG. 1 ), discussed above. 
     However, the output of section  58  feeds an optional peak-to-average (P/A) block encoding section  60 . P/A block encoding section  60  applies a type of encoding which primarily reduces the peak-to-average power ratio in composite signal  46  and thereby lessens the demands placed on a power amplifier included in transmission section  48  to faithfully reproduce communication signal  26  with a minimum amount of distortion. This type of encoding may, but is not required to, provide additional coding gain. In the preferred embodiments, when P/A block encoding section  60  is included, it applies block encoding so that encoded blocks coincide with successive blocks of symbols  36  ( FIG. 2 ), discussed above. In other words, the data are encoded so that P/A encoded blocks begin with symbol  36  a k,0  ( FIG. 2 ) and end with symbol  36  a k,m  ( FIG. 2 ). 
     P/A block encoding section  60  feeds a constellation encoding section  62  which converts the data into complex symbols in accordance with a predetermined phase constellation. As an example, each four-bit group of data output from P/A block encoding section  60  may be mapped by section  62  into a single complex symbol having in-phase and quadrature components in accordance with a 16-QAM phase constellation. However, those skilled in the art will appreciate that the present invention may be used with any type or size of phase constellation. 
     The stream of complex symbols output from constellation encode section  62  passes through a synchronization multiplexer (SYNC MUX)  64 , where a preamble  66  is inserted into the stream at appropriate intervals. Preamble  66  is a known code which helps receivers  24  obtain synchronization and determine the timing of frames  30  and time slots  32  ( FIG. 2 ). The resulting TDMA-configured complex stream  42  serves as the output from TDMA modulation section  40  and feeds DSSS modulation section  44 . 
     Within DSSS modulation section  44 , a demultiplexer (DEMUX)  68  divides TDMA-configured stream  42  of complex symbols  36  into blocks  34  ( FIG. 2 ) of symbols  36 . As a result, M unspread complex symbol substreams  70  are provided by demultiplexer  68  so that each unspread substream  70  contributes a single complex symbol  36  during each block  34 , and each block  34  has a block period T*M, where T is the symbol period of TDMA-configured stream  42 . 
     Unspread substreams  70  feed a spreading section  72 . Within spreading section  72 , cyclic variations of common spreading code  38  ( FIG. 2 ) are applied to the M unspread substreams  70  to form M spread substreams  74  of “chips.” The chip period in each spread substream  74  is T*M/N. The M spread substreams  74  may be passed through an optional peak-to-average (P/A) reduction section  76  which adjusts phase angles of the complex chips conveyed in the spread substreams  74  in a manner understood by those skilled in the art to reduce peak-to-average power ratio and lessen demands placed on a power amplifier. Following P/A reduction section  76 , a combining section  78  combines spread substreams  74  to form composite signal  46 . Various embodiments of DSSS modulation section  44  are discussed in more detail below. 
     Transmission section  48  includes any number of components and functions well known to those skilled in the art. For example, scrambling section  56  and/or synchronization multiplexer  64 , discussed above, may be included in transmission section  48  rather than in TDMA modulation section  40 . A pulse shaping section (not shown) is desirably included in transmission section  48  to spread the energy from each chip over a number of chip intervals using a suitable filter which minimizes inter-symbol or inter-chip interference so that spectral constraints may be observed. Transmission section  48  may also include digital-to-analog conversion, quadrature modulation, up-conversion, and power amplification functions, all implemented in conventional fashion. Power control may be implemented in transmission section  48  at the power amplifier to ameliorate a potential near-far problem, which should be much less pronounced in communication system  20  ( FIG. 1 ) than in traditional CDMA communication systems. After pulse shaping, analog conversion, up-conversion, and amplification, TDMA communication signal  26  is formed from composite signal  46  and wirelessly broadcast from transmission section  48 . Receiver  24  receives TDMA communication signal  26 . 
     Within receiver  24 , communication signal  26  is processed through a receiving section  80  and passed to a code division multiplex (CDM) to time division multiplex (TDM) converter  82 . CDM to TDM converter  82  produces a baseband signal  84 , which is further demodulated in a TDM demodulation section  86 , with individual users receiving their respective data streams  88 . Of course, nothing requires a receiver  24  to serve multiple users and TDM demodulation section  86  may simply provide a data stream intended for a single user. 
     Receiving section  80  includes any number of components and functions well known to those skilled in the art. For example, amplifying, filtering, and down-conversion may be performed to form an intermediate frequency (IF) signal. The IF signal may be converted from an analog form into a digital form, and automatic gain control (AGC) may be provided. In the preferred embodiments, the digitized form of the down-converted communication signal  26  passes to CDM to TDM converter  82 . 
     Generally, CDM to TDM converter  82  performs despreading and optionally performs equalization on the communication signal. Various embodiments of CDM to TDM converter  82  are discussed in more detail below. 
     TDM demodulation section  86  includes any number of components and functions well known to those skilled in the art. For example, channel estimation and synchronization may be performed in TDM demodulation section  82 . A rake receiver and/or equalizer may be included. De-interleaving, error correction decoding, and descrambling are desirably performed, and preambles and other control data are evaluated to detect time slots assigned to the receiver  24 . These and other components and functions conventionally used in digital demodulators may be included in TDM demodulation section  86 . 
       FIG. 4  shows a timing diagram depicting how common spreading code  38  ( FIG. 2 ) is applied to blocks  34  ( FIG. 2 ) of unspread data substreams  70  ( FIG. 3 ) in accordance with first, second and third embodiments of DSSS modulation section  44  ( FIG. 3 ) in transmitter  22  ( FIG. 3 ).  FIG. 4  is presented in tabular form, with rows representing the application of the chips of common spreading code  38  to symbols  36  ( FIG. 2 ). Columns in  FIG. 4  depict successive blocks  34 . As indicated by a shaded region in  FIG. 4 , spreading code  38  is applied to unspread substreams  70  so that composite signal  46  is influenced, at least for a portion of the time, by symbols  36  from two different blocks  34 . In particular, in the specific embodiment depicted by  FIG. 4 , for only a single chip of each block period is composite signal  46  influenced by symbols  36  from a common block  34  of symbols. The manner of application of common spreading code  38  ( FIG. 2 ) to blocks  34  ( FIG. 2 ) of unspread data substreams  70  depicted in  FIG. 4  may be contrasted with an alternate embodiment, discussed below in connection with  FIG. 11 . 
       FIG. 5  shows a block diagram of the first embodiment of DSSS modulation section  44 . Demultiplexer  68  is omitted from  FIG. 5  for convenience. The unspread substream  70  conveying symbols a k,0  experiences no delay before being fed to a first input of a multiplier  90 . However, the unspread substreams  70  conveying symbols a k,1  through a k,M−1  are respectively delayed in delay elements  92  by 1 through M−1 symbol periods (T) before being fed to respective first inputs of other multipliers  90 . 
     A spreading code generation section  94  generates cyclic variations of common spreading code  38 .  FIG. 5  illustrates code generation section  94  in matrix form, which matrix takes on a cyclic Toeplitz form because the matrix elements hold cyclic variations of the same spreading code  38 . As depicted in  FIG. 5 , different columns of the matrix supply code chips C o  through C N−1  to second inputs of respective multipliers  90 . Different rows of the matrix indicate different code chips to apply during different chip intervals. So long as the number (N) of chips in spreading code  38  is greater than or equal to the number (M) of symbols  36  per block  34 , different code chips of the same code are applied to different symbols during any and all chip intervals. 
     Outputs of multipliers  90  provide respective spread substreams  74 .  FIG. 5  omits depiction of optional P/A reduction section  76  ( FIG. 3 ) for convenience. Combining section  78  takes the form of an adder, so that composite signal  46  during each chip interval equals the sum of M symbols  36 , with each of the M symbols being premultiplied by designated chips of common spreading code  38 . Accordingly, DSSS modulating section  44  temporally offsets application of common spreading code  38  to unspread substreams  70  so that the resulting spread substreams  74  correspond to unspread substreams  70  modulated by cyclic variations of common spreading code  38 . 
       FIG. 6  shows a block diagram of the second embodiment of DSSS modulation section  44 . This second embodiment is equivalent to the first embodiment of  FIG. 5 , but it is implemented differently. Demultiplexer  68  ( FIG. 3 ) is omitted from  FIG. 6  for convenience. In this embodiment, spreading code generation section  94  need not be implemented as a two-dimensional matrix having a different row to define the different chips to be applied during different chip intervals, as discussed above in connection with  FIG. 5 . Rather, spreading code generation section  94  may be implemented as a one-dimensional matrix having different columns, and only one of those columns is simultaneously applied to different unspread substreams  70 . Spreading code generation section  94  may be implemented as a shift register configured to shift cyclically at the chip rate. In order to achieve the appropriate temporal offsetting, delay elements  92  are now positioned between multipliers  90  and the adder of combining section  78 . Accordingly, in this second embodiment of DSSS modulating section  44 , DSSS modulating section  44  temporally offsets the application of common spreading code  38  to unspread substreams  70  so that the resulting spread substreams  74  correspond to unspread substreams  70  modulated by cyclic variations of common spreading code  38 . 
       FIG. 7  shows a block diagram of the third embodiment of DSSS modulating section  44 . This third embodiment is also equivalent to the first embodiment of  FIG. 5 , but is implemented differently. This third embodiment is a finite impulse response (FIR) implementation. In this third embodiment, symbol stream  42  ( FIG. 3 ) is fed to a series of delay elements  96 , each of which imparts a one-chip interval delay. The series of delay elements  96  serves the role of demultiplexer  68  ( FIG. 3 ) in this third embodiment, with the input to the first delay element  96  and the outputs of all delay elements  96  providing unspread substreams  70 . Delay elements  92  ( FIGS. 5-6 ) from the first and second embodiments of spreading section  72  are omitted. 
     Spreading code generation section  94  simply provides common spreading code  38 , and need not be cycled because unspread substreams  70  to which spreading code  38  is applied are configured to perform the temporal offsetting requirements. Accordingly, symbol delay elements  92  are omitted and spreading code generating section  94  need not cycle the common spreading code or explicitly provide separate versions of spreading code  38  to separate unspread substreams  70 . Nevertheless, in this third embodiment of DSSS modulation section  44 , spreading section  72  temporally offsets application of common spreading code  38  by sequentially delaying symbols  36  to form unspread substreams  70  and applying spreading code  38  to the delayed symbols in unspread substreams  70  so that the resulting spread substreams  74  correspond to unspread substreams  70  modulated by cyclic variations of common spreading code  38 . 
       FIG. 8  shows a first embodiment of CDM to TDM converter  82  included in receiver  24  ( FIGS. 1 and 3 ). Desirably, CDM to TDM converter  82  is configured to complement DSSS modulation section  44  of transmitter  22  ( FIGS. 1 and 3 ). In particular, this first embodiment of CDM to TDM converter  82  is configured to complement any of the first through third embodiments of DSSS modulation section  44  discussed above in connection with  FIGS. 4-7 . 
     CDM to TDM converter  82  includes a pulse shaping matched filter  98 , the output of which feeds a mismatched filter  100 . Pulse shaping matched filter  98  complements a pulse shaping filter (not shown) desirably implemented in transmission section  48  of transmitter  22  ( FIG. 3 ) to optimize signal-to-noise ratio and band-limit the signal. Pulse shaping matched filter  98  is desirably implemented using conventional techniques known to those skilled in the art. 
     Mismatched filter  100  accomplishes two functions. One function is despreading and the other function is sidelobe suppression. In fact, mismatched filter  100  is desirably implemented to correspond to a spreader matched filter  102  upstream of a sidelobe suppression filter  104 . One technique for implementing mismatched filter  100  is simply to implement two filters coupled in series for the despreading and sidelobe suppression functions. In another technique (not shown) the two functions may be combined in a common filter. 
     Mismatched filter  100  experiences a signal-to-noise ratio typically worse than that of a matched filter. However, in the preferred embodiments, mismatched filter  100  is desirably configured to achieve a relative efficiency of greater than 60%, and more preferably greater than 90%, compared to a matched filter. 
     Those skilled in the art will appreciate that the configuration of common spreading code  38  is a strong determinant of the relative efficiency of mismatched filter  100 . For example, conventional orthogonal pseudonoise (PN) codes commonly used in conventional CDMA applications are unacceptable because their mismatched filters achieve relative efficiencies roughly around only 50%. 
     While a wide variety of different codes may be used with the present invention, codes which have low aperiodic autocorrelation sidelobes and a substantially flat spectral analysis are preferred in this embodiment. Barker codes make suitable codes because of aperiodic autocorrelation sidelobes having magnitudes less than or equal to one. However, for many applications the limited length (i.e., N≦13) and/or prime numbered length of many Barker codes proves a detriment. In such cases, other codes having a greater length and slightly greater aperiodic autocorrelation sidelobes, such as magnitudes less than or equal to two or three are acceptable and may be easily derived by those skilled in the art. 
       FIG. 9  shows an exemplary spectral analysis of a suitable spreading code usable in connection with the present invention. In particular,  FIG. 9  represents an arbitrary code for which a spectral analysis can be performed using a time-frequency domain transformation, such as a Fourier transform. While a code having a precisely flat spectral analysis result is not a requirement, better results are achieved when no frequency bin shows substantially more or less signal level than other bins, as depicted in  FIG. 9 . As an example, the signal level in each bin is desirably within ±25% of the average signal level taken over all bins. In particular, for best results no bins should exhibit a nearly zero signal level. 
     The implementation of mismatched filter  100  illustrated in  FIG. 8  will be readily understood by those skilled in the art. Spreader matched filter  102  may be implemented using the complex conjugate of spreading code  38  ( FIG. 2 ) presented in a reverse order. Sidelobe suppression filter  104  may be implemented using well-known FFT or linear programming techniques. 
     The output of spreader matched filter  102  in mismatched filter  100  is a composite signal  106  equivalent to the autocorrelation function applied to each of the M unspread and spread substreams  70  and  74  (FIGS.  3  and  5 - 7 ) discussed above. 
       FIG. 10  shows an exemplary timing diagram of the various individual signal components present in composite signal  106  output from the matched filter  102  portion of mismatched filter  100 . For convenience,  FIG. 10  depicts an exemplary situation where the number of substreams  70  and  74  (i.e., M) equals seven and the number (i.e., N) of chips in spreading code  38  equals seven. Thus, each row in  FIG. 10  represents one of the seven substreams, and each row depicts autocorrelation with an assumed rectangular pulse. Of course, composite signal  106  is the sum of all rows in  FIG. 10  rather than seven distinct signals. 
     Assuming ideal synchronization where samples are taken at the integral chip intervals of 0, 1, 2, . . . , then in this example, seven successive samples yield the signal levels of the seven substreams. However, each sample in composite signal  106  is corrupted by self-interference  108 , caused by sidelobes of the autocorrelation function. Accordingly, sidelobe suppression filter  104  ( FIG. 8 ) substantially attenuates the self-interference  108  of the sidelobes while not severely attenuating the autocorrelation peak. 
     Referring back to  FIGS. 3 and 8 , the output sidelobe suppression filter  104  provides baseband signal  84 , which also serves as the output of CDM to TDM converter  82 . Baseband signal  84  is routed to TDM demodulation section  86 . Depending upon the severity of multipath remaining in baseband signal  84  after processing through sidelobe suppression filter  104 , a rake receiver (not shown) or equalizer (not shown) may be used in TDM demodulation section  86  to compensate for the multipath. While some inefficiency may result from using a mismatched filter to despread communication signal  26 , any such inefficiency is more than compensated for by a marked improvement in multipath tolerance. 
     While receiver  24  receives a communication signal  26  from one transmitter  22 , it may simultaneously receive other communication signals  26  from other transmitters  22  in adjacent radio coverage areas  28  ( FIG. 1 ). Conventional CDMA techniques may be used to prevent interference between such diverse communication signals  26 . For example, different spreading codes  38  may be selected for use at different transmitters  22 . Such different spreading codes  38  are desirably configured to have low cross-correlation sidelobes among all spreading codes  38 . If this option is selected, only a few (e.g., 3-7) of such codes need be used to prevent interference because interference should not be a problem between communication signals  26  from non-adjacent radio coverage areas  28  ( FIG. 1 ). Alternatively, transmitter  22  and receiver  24  may include other stages to further scramble/descramble spread spectrum signals using other spreading codes. 
     The embodiments of the present invention discussed above and characterized by the timing depicted in  FIG. 4 , wherein composite signal  46  is influenced, at least for a portion of the time, by symbols  36  from two different blocks  34 , show advantageous resilience in the presence of multipath. However, alternate embodiments, discussed below, may provide even better performance in the presence of multipath for some applications. 
       FIG. 1  shows a timing diagram depicting how common spreading code  38  ( FIG. 2 ) is applied to blocks  34  ( FIG. 2 ) of unspread data substreams  70  ( FIG. 3 ) in accordance with fourth and fifth embodiments of DSSS modulation section  44  ( FIG. 3 ) in transmitter  22  ( FIG. 3 ). Like  FIG. 4  discussed above,  FIG. 11  is presented in tabular form, with rows representing the application of the chips of common spreading code  38  to symbols  36  ( FIG. 2 ). Columns in  FIG. 11  depict successive blocks  34 . As indicated by a shaded region in  FIG. 11 , spreading code  38  in the fourth and fifth embodiments is applied to unspread substreams  70  so that composite signal  46  is influenced, at all times, by symbols  36  from only common blocks  34 . 
       FIG. 12  shows a block diagram of the fourth and fifth embodiments of DSSS modulation section  44 . Demultiplexer  68  ( FIG. 3 ) is omitted from  FIG. 12  for convenience. In addition, in order to enable matrix multiplication operations discussed below,  FIG. 12  represents that N symbols  36  (i.e. a k,0  through a k,N−1 ) are provided from demultiplexer  68  during each block  34  ( FIG. 2 ). In other words,  FIG. 12  represents that the number (M) of symbols  36  per block  34  equals the number (N) of chips in spreading code  38 . Those skilled in the art will appreciate that when M&lt;N, the number M of symbols  36  per block  34  may be made equal to N by padding with zeros so that the zeros are evenly distributed among the symbols  36 . As an example, if M equals 4 and N equals 12, then 12 symbols  36  may be provided by following each symbol  36  in each block  34  with two zeros. 
     Unspread substreams  70 , which provide N symbols  36  per block  34 , pass to an optional time-frequency domain transformation section  110 . Time-frequency domain transformation section  110  may be implemented as an inverse fast Fourier transform (IFFT). For purposes of the present discussion, the fourth embodiment of DSSS modulation section  44  shall be deemed to omit section  110 , while the fifth embodiment shall be deemed to include section  110 . Thus, unspread substreams  70  convey time domain data to spreading section  72  in the fourth embodiment and frequency domain data to spreading section  72  in the fifth embodiment. 
     While section  110  is not a requirement of the present invention, certain benefits may be achieved by the addition of section  110  as will be discussed below. Moreover, section  110 , or the equivalent, is conventionally included in digital communication transmitters which implement an orthogonal frequency division multiplexed (OFDM) modulation format. In such situations, section  110  may be present for use in connection with the present invention at little additional complexity or expense. 
     Delay elements  92  ( FIGS. 5-6 ) are omitted in the fourth and fifth embodiments of DSSS modulation section  44  to permit only symbols  36  concurrently present during a common block  34  to influence composite signal  46 . However, spreading section  72  and spreading code generating section  94  are implemented in a manner similar to that discussed above in connection with the first and second embodiments of DSSS modulation section  44  ( FIGS. 5-6 ). In particular, cyclic variations of a single common spreading code  38  are applied in the form of a cyclic Toeplitz matrix (see  FIG. 5 ). While spreading code generating section  94  acts to multiply the 1×N matrix of symbols  36  in each block  34  by spreading code  38  effectively in the form of an N×N cyclic Toeplitz matrix, it may do so simply through a one-dimensional matrix having different columns applied to different unspread substreams  70  at different multipliers  90 . Instead of selecting a spreading code  38  with low aperiodic autocorrelation sidelobes as discussed above in connection with the first, second and third embodiments of DSSS modulation section  44 , the fourth and fifth embodiments of DSSS modulation section  44  are better served with a spreading code  38  having low periodic autocorrelation sidelobes and a substantially flat spectrum. Spreading code generation section  94  may be implemented as a shift register configured to shift cyclically at the chip rate. Spread substreams  74  output from multipliers  90  are combined in an adding circuit  78  to form a pre-composite signal  46 ′, which is converted back into parallel streams at a demultiplexer (DEMUX)  112  into N chips per block  34 , labeled b k,0  through b k,N−1  in  FIG. 12 . 
     Demultiplexer  112  provides one technique for forming a cyclic prefix  114 . Chips b k,0  through b k,N−1  and cyclic prefix  114  are routed in parallel to inputs of a multiplexer (MUX)  116  for conversion into serial composite signal  46 . In particular, chips b k,0  through b k,N−1  are associated with an intended order, in which chips b k,0 , b k,1 , b k,2 , . . . b k,P  occur first in pre-composite signal  46 ′, and chips b k,q , . . . b k,N−3 , b k,N−2 , b k,N−1 , occur last in pre-composite signal  46 ′.  FIG. 12  illustrates an example where the p=2 first-occurring spread substreams in pre-composite signal  46 ′ are repeated as cyclic prefix  114  so that they also occur last in composite signal  46 . Of course, those skilled in the art will appreciate that the clock rate of multiplexer  116  is desirably sufficiently higher than the clock chip rate to accommodate cyclic prefix  114 . 
     Transmission section  48  forms blocks  34  of communication signal  26  from blocks  34  of composite signal  46 . Blocks  34  of communication signal  26  propagate to receiver  24  through a communication channel, which may be unique to a specific transmitter  22  location and receiver  24  location. Blocks  34  of communication signal  26  experience multipath and other types of distortion when propagating through this channel. The mathematical effect of this distortion is equivalent to multiplying composite signal  46  by the transfer function of the channel, which imposes the multipath. 
     As discussed above, each block  34  of composite signal  46  is formed from the matrix multiplication of the spreading code  38  with a block  34  of symbols  36 . The effect of multipath distortion is then the matrix multiplication of the matrix expression of the channel transfer function with this matrix product. Normally, a matrix multiplication does not observe a communicative mathematical property. In other words, the product of the channel transfer function by the spreading matrix does not necessarily equal the product of spreading matrix by the channel transfer function. 
     Due to the failure of the mathematical communicative property in matrix multiplication, normally equalization to compensate for multipath should be performed before despreading in receiver  22 . Unfortunately, such equalization is exceedingly difficult to successfully perform, due at least in part to requiring the implementation of a filter with characteristics equivalent to the inverse of the channel transfer function. The characteristics of the channel cannot be easily controlled, and channel transfer function quite possibly has elements near zero. Attempting to form inverse filters of such characteristics often leads to unstable implementations. 
     However, the use of cyclic variations of common spreading code  38 , when combined with cyclic prefix  114  and processed as discussed below in receiver  24 , enables the mathematical communicative property. Consequently, despreading may now occur prior to equalization for multipath, thereby making effective equalization a relatively simple task. 
       FIG. 13  shows a second embodiment of CDM to TDM converter  82  for use with the fourth embodiment of the DSSS modulation section  44  (i.e., the time domain embodiment). The digitized IF form of communication signal  26 , after being distorted through the communication channel, is applied to a demultiplexer (DEMUX)  118  and a synchronization (SYNC) section  120 . An output of synchronization section  120  feeds a cyclic prefix removal section  122  of demultiplexer  118 . Synchronization section  120  identifies the start of blocks  34 , and cyclic prefix removal section  122  removes the first-occurring p chips from each block  34 . As discussed above, the last-occurring p chips duplicate the first-occurring p chips, and the last-occurring p chips and all other chips remain in each block  34 . The first-occurring p chips are removed because they are influenced by multipath from the previous block  34  of communication signal  26 . All chips, which remain in each block  34 , are influenced only by multipath from that block  34 . 
     The block  34  of chips, with cyclic prefix  114  ( FIG. 12 ) removed, passes to mismatched filter  100  for despreading and equalization. As discussed above, due to the use of cyclic variations of spreading code  38  to spread symbols  36  and the inclusion of cyclic prefix  114 , the matrix multiplication which characterizes the channel now observes the communicative mathematical property. Consequently, despreading may occur before equalization. 
     Despreading may take place using a despreading code generator  124 , a despreading section  126 , and a combining section  128 . Despreading code generator  124 , despreading section  126 , and combining section  128  are identical in structure to spreading code generator  94 , spreading section  72 , and combining section  78  in DSSS modulator section  44  of transmitter  22  ( FIG. 12 ), with the despreading code generated in despreading code generator  124  being related to spreading code  38 . In particular, despreading code chips D n =IFFT(1/FFT(C n )), where IFFT and FFT denote inverse fast Fourier transform and fast Fourier transform, respectively, and C n  represents the chips of spreading code  38 . 
     Spread substreams  130  are provided by demultiplexer  118  to multipliers  132  in despreading section  126  along with the despreading code matrix from despreading code generator  124 . The despreading code is applied in the form of a cyclic Toeplitz matrix due to the use of cyclic variations of a common spreading code to which the despreading code is related. Multipliers  132  provide despread substreams  134  to combiner  128  to add despread substreams  134  on a chip by chip basis into a serial pre-composite baseband signal  136 . Pre-composite baseband signal  136  is converted into parallel symbol substreams  140  at a demultiplexer (DEMUX)  138 , and symbol substreams  140  are applied to a maximum likelihood sequence estimation (MLSE) equalizer  142  or the equivalent. MLSE equalizer  142  may also be called a Viterbi equalizer. Parallel outputs from MLSE equalizer  142  feed a multiplexer (MUX)  144  which converts the parallel symbol substreams into baseband signal  84  for further processing by TDM demodulation section  86  ( FIG. 3 ). 
     Those skilled in the art will appreciate that an MLSE equalizer is a simple structure, which is stable and can be effectively configured to compensate for multipath. The coupling of MLSE equalizer  142  downstream of despreading section  126  is possible due to the use of cyclic variations of common spreading code  38  in transmitter  22  and cyclic prefix  114  to enable matrix multiplication exhibiting the mathematical communicative property. 
       FIG. 14  shows a third embodiment of CDM to TDM converter  82  for use with the fifth embodiment of DSSS modulation section  44  (i.e., the frequency domain embodiment), discussed above in connection with  FIG. 12 . The digitized IF form of communication signal  26 , after being distorted through the communication channel, is applied to demultiplexer (DEMUX)  118  and synchronization (SYNC) section  120 , as discussed above in connection with  FIG. 13 . Likewise, cyclic prefix  114  ( FIG. 12 ) is removed at cyclic prefix removal section  122  of demultiplexer  118 , as discussed above in connection with  FIG. 13 . 
     Spread substreams  130  are provided by demultiplexer  118  to a time-frequency domain transformation section  146 , which complements time-frequency domain transformation section  110  ( FIG. 12 ). Thus, if time-frequency domain transformation section  110  in DSSS modulation section  44  implements an inverse fast Fourier transform (IFFT), then time-frequency domain transformation section  146  desirably implements a fast Fourier transform (FFT). 
     Mismatched filter  100  couples downstream of time-frequency domain transformation section  146 . In this third embodiment of CDM to TDM converter  82  mismatched filter  100  may be implemented in a manner that joins despreading and equalization functions in a common frequency domain equalizer. As illustrated in  FIG. 14 , coefficients for the frequency domain equalizer take the form D* H(n) /D C(n) , where represents despreading code chips that are related to spreading code  38  in the manner discussed above in connection with  FIG. 13  and D* H(n)  represents the complex conjugate of the transfer function of the channel. One reason why a frequency domain equalizer is easy and effective to implement is that coefficients are not proportional to the inverse of the transfer function of the channel. While despreading code chips are related to the inverse of the FFT of the spreading code, such coefficients do not pose problems because the designer controls the FFT of the code through code selection, and a spreading code having a substantially flat spectral response may be selected, as discussed above in connection with  FIG. 9 . 
     Parallel outputs of mismatched filter  100  pass in parallel to hard decision sections  148 , and parallel outputs of hard decision sections  148  are combined into serial baseband signal  84  in multiplexer (MUX)  144  for further processing in TDM demodulation section  86  ( FIG. 3 ). 
     Due to the enabling of the mathematical communicative property for matrix multiplication discussed above, mismatched filter  100  may reside downstream of time-frequency transformation section  146 , which improves the efficacy and simplicity of the equalization and despreading functions. 
     The present invention provides an improved method and apparatus for wireless communications. The present invention contemplates the combination of TDMA and spread spectrum techniques so that wireless communications capacity is increased over the capacities achievable through conventional TDMA and/or CDMA systems using an equivalent amount of spectrum. Furthermore, robust, simple, and inexpensive processing techniques are usable in the present invention, making the present invention suitable for hubs, subscriber units, mobile stations, fixed stations, portable stations, and the like. The present invention may be adapted to and used in conjunction with a variety of modulation and multiple access techniques, such as frequency division multiple access (FDMA) and orthogonal frequency division multiplexing (OFDM). The advantages and improvements of the present invention are achieved, at least in part through the use of a composite RF communication signal which includes signal components obtained by modulating diverse branches of a single user&#39;s data stream using cyclic variants of a common spreading code. The present invention is configured to tolerate self-interference and is better able to tolerate multipath than conventional DSSS-CDMA communication systems. 
     With reference to  FIGS. 15 and 16 , additional embodiments of the present invention will now be described. The embodiments described below employ ultra-wideband communication technology. Referring to  FIGS. 15 and 16 , ultra-wideband (UWB) communication technology employs discrete pulses of electromagnetic energy that are emitted at, for example, nanosecond or picosecond intervals (generally tens of picoseconds to hundreds of nanoseconds in duration). For this reason, ultra-wideband is often called “impulse radio.” That is, the UWB pulses may be transmitted without modulation onto a sine wave, or a sinusoidal carrier, in contrast with conventional carrier wave communication technology. Thus, UWB generally requires neither an assigned frequency nor a power amplifier. 
     Another example of sinusoidal carrier wave communication technology is illustrated in  FIG. 15 . IEEE 802.11a is a wireless local area network (LAN) protocol, which transmits a sinusoidal radio frequency signal at a 5 GHz center frequency, with a radio frequency spread of about 5 MHz. As defined herein, a carrier wave is an electromagnetic wave of a specified frequency and amplitude that is emitted by a radio transmitter in order to carry information. The 802.11 protocol is an example of a carrier wave communication technology. The carrier wave comprises a substantially continuous sinusoidal waveform having a specific narrow radio frequency (5 MHz) that has a duration that may range from seconds to minutes. 
     In contrast, an ultra-wideband (UWB) pulse may have a 2.0 GHz center frequency, with a frequency spread of approximately 4 GHz, as shown in  FIG. 16 , which illustrates two typical UWB pulses.  FIG. 16  illustrates that the shorter the UWB pulse in time, the broader the spread of its frequency spectrum. This is because bandwidth is inversely proportional to the time duration of the pulse. A 600-picosecond UWB pulse can have about a 1.8 GHz center frequency, with a frequency spread of approximately 1.6 GHz and a 300-picosecond UWB pulse can have about a 3 GHz center frequency, with a frequency spread of approximately 3.2 GHz. Thus, UWB pulses generally do not operate within a specific frequency, as shown in  FIG. 15 . In addition, either of the pulses shown in  FIG. 16  may be frequency shifted, for example, by using heterodyning, to have essentially the same bandwidth but centered at any desired frequency. And because UWB pulses are spread across an extremely wide frequency range, UWB communication systems allow communications at very high data rates, such as 100 megabits per second or greater. 
     Also, because the UWB pulses are spread across an extremely wide frequency range, the power sampled in, for example, a one megahertz bandwidth, is very low. For example, UWB pulses of one nano-second duration and one milliwatt average power (0 dBm) spreads the power over the entire one gigahertz frequency band occupied by the pulse. The resulting power density is thus 1 milliwatt divided by the 1,000 MHz pulse bandwidth, or 0.001 milliwatt per megahertz (−30 dBm/MHz). 
     Generally, in the case of wireless communications, a multiplicity of UWB pulses may be transmitted at relatively low power density (milliwatts per megahertz). However, an alternative UWB communication system may transmit at a higher power density. For example, UWB pulses may be transmitted between 30 dBm to −50 dBm. 
     Several different methods of ultra-wideband (UWB) communications have been proposed. For wireless UWB communications in the United States, all of these methods must meet the constraints recently established by the Federal Communications Commission (FCC) in their Report and Order issued Apr. 22, 2002 (ET Docket 98-153). Currently, the FCC is allowing limited UWVB communications, but as UWB systems are deployed, and additional experience with this new technology is gained, the FCC may expand the use of UWB communication technology. It will be appreciated that the present invention may be applied to current forms of UWB communications, as well as to future variations and/or varieties of UWB communication technology. 
     For example, the April 22 Report and Order requires that UWB pulses, or signals occupy greater than 20% fractional bandwidth or 500 megahertz, whichever is smaller. Fractional bandwidth is defined as 2 times the difference between the high and low 10 dB cutoff frequencies divided by the sum of the high and low 10 dB cutoff frequencies. However, these requirements for wireless UWB communications in the United States may change in the future. 
     Communication standards committees associated with the International Institute of Electrical and Electronics Engineers (IEEE) are considering a number of ultra-wideband (UWB) wireless communication methods that meet the current constraints established by the FCC. One UWB communication method may transmit UWB pulses that occupy 500 MHz bands within the 7.5 GHz FCC allocation (from 3.1 GHz to 10.6 GHz). In one embodiment of this communication method, UWB pulses have about a 2-nanosecond duration, which corresponds to about a 500 MHz bandwidth. The center frequency of the UWB pulses can be varied to place them wherever desired within the 7.5 GHz allocation. In another embodiment of this communication method, an Inverse Fast Fourier Transform (IFFT) is performed on parallel data to produce 122 carriers, each approximately 4.125 MHz wide. In this embodiment, also known as Orthogonal Frequency Division Multiplexing (OFDM), the resultant UWB pulse, or signal is approximately 506 MHz wide, and has a 242 nanosecond duration. It meets the FCC rules for UWB communications because it is an aggregation of many relatively narrow band carriers rather than because of the duration of each pulse. 
     Another UWB communication method being evaluated by the IEEE standards committees comprises transmitting discrete UWB pulses that occupy greater than 500 MHz of frequency spectrum. For example, in one embodiment of this communication method, UWB pulse durations may vary from 2 nanoseconds, which occupies about 500 MHz, to about 133 picoseconds, which occupies about 7.5 GHz of bandwidth. That is, a single UWB pulse may occupy substantially all of the entire allocation for communications (from 3.1 GHz to 10.6 GHz). 
     Yet another UWB communication method being evaluated by the IEEE standards committees comprises transmitting a sequence of pulses that may be approximately 0.7 nanoseconds or less in duration, and at a chipping rate of approximately 1.4 giga pulses per second. The pulses are modulated using a Direct-Sequence modulation technique, and is called DS-UWB. Operation in two bands is contemplated, with one band is centered near 4 GHz with a 1.4 GHz wide signal, while the second band is centered near 8 GHz, with a 2.8 GHz wide UWB signal. Operation may occur at either or both of the UWB bands. Data rates between about 28 Megabits/second to as much as 1,320 Megabits/second are contemplated. 
     Thus, described above are three different methods of wireless ultra-wideband (UWB) communication. It will be appreciated that the present invention may be employed using any one of the above-described methods, variants of the above methods, or other UWB communication methods yet to be developed. 
     Certain features of the present invention may be employed by an ultra-wideband (CUB) communication system. For example, one embodiment of an UWB communication system divides a stream of data conveying symbols into a plurality of unspread substreams. A common spreading code is generated at the ultra-wideband transmitter, and each of the unspread substreams are spread using the common spreading code to form a plurality of spread substreams. The spread substreams are combined to form a composite signal that is transmitted using a plurality of discrete electromagnetic pulses. 
     In another embodiment, an ultra-wideband communication system comprises a demultiplexer for dividing a stream of data conveying symbols into a plurality of unspread substreams. A spreading section is coupled to the demultiplexer and configured to generate a plurality of spread substreams from the plurality of unspread substreams. A combining section is coupled to the spreading section and configured to form a composite signal from the plurality of spread substreams, and a transmission section is coupled to the combining section and configured to transmit the composite signal over an ultra-wideband communication channel. 
     The UWB devices, systems and/or methods in the above-described embodiments communicate with each other by transmitting and receiving a plurality of discrete electromagnetic pulses, as opposed to a substantially continuous carrier wave. Each pulse may have a duration that can range between about 10 picoseconds to about 1 microsecond, and a power that may range between about +30 dBm to about −60 dBm, as measured at a single frequency. 
     The present invention may be employed in any type of network, be it wireless, wire, or a mix of wire media and wireless components. That is, a network may use both wire media, such as coaxial cable, and wireless devices, such as satellites, or cellular antennas. As defined herein, a network is a group of points or nodes connected by communication paths. The communication paths may use wires or they may be wireless. A network as defined herein can interconnect with other networks and contain sub-networks. A network as defined herein can be characterized in terms of a spatial distance, for example, such as a local area network (LAN), a personal area network (PAN), a metropolitan area network (MAN), a wide area network (WAN), and a wireless personal area network (WPAN), among others. A network as defined herein can also be characterized by the type of data transmission technology used by the network, such as, for example, a Transmission Control Protocol/Internet Protocol (TCP/IP) network, a Systems Network Architecture network, among others. A network as defined herein can also be characterized by whether it carries voice, data, or both kinds of signals. A network as defined herein may also be characterized by users of the network, such as, for example, users of a public switched telephone network (PSTN) or other type of public network, and private networks (such as within a single room or home), among others. A network as defined herein can also be characterized by the usual nature of its connections, for example, a dial-up network, a switched network, a dedicated network, and a non-switched network, among others. A network as defined herein can also be characterized by the types of physical links that it employs, for example, optical fiber, coaxial cable, a mix of both, unshielded twisted pair, and shielded twisted pair, among others. 
     The present invention may be employed in any type of wireless network, such as a wireless PAN, LAN, MAN, or WAN. In addition, the present invention may be employed in wire media, as the present invention dramatically increases the bandwidth of conventional networks that employ wire media, such as hybrid fiber-coax cable networks, or CATV networks, yet it can be inexpensively deployed without extensive modification to the existing wire media network. 
     Thus, it is seen that systems and methods of ultra-wideband communications are provided. One skilled in the art will appreciate that the present invention can be practiced by other than the above-described embodiments, which are presented in this description for purposes of illustration and not of limitation. For example, those skilled in the art will appreciate that the order of time-frequency domain transformation and spreading functions may be reversed from that shown in  FIG. 12 . The specification and drawings are not intended to limit the exclusionary scope of this patent document. It is noted that various equivalents for the particular embodiments discussed in this description may practice the invention as well. That is, while the present invention has been described in conjunction with specific embodiments, it is evident that many alternatives, modifications, permutations and variations will become apparent to those of ordinary skill in the art in light of the foregoing description. Accordingly, it is intended that the present invention embrace all such alternatives, modifications and variations as fall within the scope of the appended claims. The fact that a product, process or method exhibits differences from one or more of the above-described exemplary embodiments does not mean that the product or process is outside the scope (literal scope and/or other legally-recognized scope) of the following claims.