Abstract:
An ultra wide bandwidth, high speed, spread spectrum communications system uses short wavelets of electromagnetic energy to transmit information through objects such as walls or earth. The communication system uses baseband codes formed from time shifted and inverted wavelets to encode data on a RF signal. The combination of short duration wavelets and encoding techniques are used to spread the signal energy over an ultra wide frequency band such that the energy is not concentrated in any particular narrow band and is not detected by conventional narrow band receivers so it does not interfere with those communication systems. The use of pulse codes composed of time shifted and inverted wavelets gives the system according to the present invention a spatial resolution on the order of 1 foot which is sufficient to minimize the negative effects of multipath interference and permit time domain rake processing.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application No. 10/295,888, filed Sep. 30, 2002, now U.S. Pat No. 6,931,078, which is a continuation of U.S. patent application No. 09/209,460, filed Dec. 11, 1998, now U.S. Pat. No. 6,700,939 which was converted from U.S. provisional application Ser. No. 60/069,594, filed Dec. 12, 1997, both of which are hereby incorporated by reference in their entirety. 
    
    
     STATEMENT REGARDING GOVERNMENT INTEREST 
     The Government of the United States of America, as represented by the Secretary of the Army, as certain non-exclusive license rights to the Invention as set forth in rights determination ARL No. 998-679-16. 
    
    
     COPYRIGHT NOTICE 
     Copyright, 1998, XTREMESPECTRUM, Inc. A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to reproduction by anyone of the patent document or the patent disclosure, as it appears in the U.S. Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     Not Applicable 
     REFERENCE TO MICROFICHE APPENDIX 
     Not Applicable 
     BACKGROUND OF THE INVENTION 
     1. Technical Field of the Invention 
     The present invention pertains to a radio communications system, particularly to a wireless digital communications system, and more particularly to an ultra wide bandwidth (UWB), spread-spectrum, wireless digital communications system. 
     2. Description of the Prior Art 
     There are numerous radio communications techniques for digital data. Most recently, wireless digital communications have been applied to mobile telephone systems, pagers, remote data collection, and wireless networking of computers as well as other applications. One of many books on the subject is “Wireless Digital Communications, Modulation &amp; Spread Spectrum Applications,” by Kamilo Feher. This book and others deal with conventional modulation of a carrier with, for example, phase or frequency shift keying (i.e. FSK, MSK, GMSK, BPSK, DBPSK, QPSK, O-QPSK, FQPSK, π/4-DEQPSK). The American and Japanese cellular standard, for example, uses π/4-DEQPSK. These systems have used either time division multiple access (TDMA) or code division multiple access (CDMA) in order to share the aggregate bandwidth between multiple users. They use either FHSS (frequency hop spread spectrum) or the CDMA codes to spread the spectrum. There remains a need, however, for higher data rates to be accommodated, with simultaneous ability to communicate through barriers such as buildings, walls, or even through soil or through tunnels. The spectrum that is capable of penetrating walls and soil (i.e. frequencies below about 3 GHz), however, is in use. Therefore, there is a need to have a communication system that can coexist in that part of the spectrum where penetration occurs. Current spread-spectrum and narrowband systems cannot coexist with other narrow bandwidth users of the same spectrum due to mutual interference. 
     Too much interference is impinged on the other users, who themselves cause too much interference to the communication system. Typically, high-speed links operate on microwave carriers that are easily blocked by terrain and intervening objects. Prior techniques are based on modulating a carrier frequency. Such a framework assumes that all components, (e.g. the antenna) have a reasonably flat frequency response over the bandwidth used and therefore do not affect the waveform. The present invention does not. They also assume that there are several to many cycles of the carrier between transitions (e.g. zero crossings) in the modulating waveform. Again, the present invention does not. It is this fact allows the present invention to simultaneously operate at low frequencies, yet -resolve multipath, and maintain high data rates. This combination has substantial benefits be low frequencies both penetrate lossy media, and minimize reflections off objects because they become smaller relative to the wavelength. But conventional systems typically have less than 10% bandwidth, and therefore have poor resolution at low frequencies. Furthermore, in contrast to current techniques, the present invention is optimized to not only be robust to multipath, but to take advantage of it. 
     Other UWB systems have been based on producing and receiving short one-to two cycle impulses at a relatively low duty cycle. Examples include deRosa (U.S. Pat. No. 2,671,896), Robbins (U.S. Pat. No. 3,662,316), Morey (U.S. Pat. No. 3,806,795), Ross and Mara (U.S. Pat. No. 5,337,054), and Fullerton and Kowie (U.S. Pat. No. 5,677,927). Impulses on the order of Ins are emitted at a 1 to 10 MHz rate, giving rise to a 100:1 to 1000:1 duty cycle. Due to this poor duty cycle, it is difficult to impossible to generate significant average power efficiently, or in an integrated circuit, because the peak voltages are higher than breakdown voltage of state-of-the-art low voltage CMOS and Bipolar processes. The waveform used in the present invention is, instead, an essentially continuous wave. The prior-art systems also use pseudo-random time intervals between unchanging (essentially identical) pulses, for the purpose of spreading the spectrum conveying information, are used in each of these systems. By contrast, the present invention, while allowing the pulse position to be randomized, communicates information by changing the pulse shape. Yet another difference is interference. The present invention does not require pulse position modulation to make the output power spectrum smooth. Instead, the spectrum is smoothed by the modulation of the pulse shape. 
     SUMMARY OF INVENTION 
     It is an object of the present invention to construct an ultra wide bandwidth (UWB) high-speed digital communications system that directly produces short, spatially compact, electromagnetic wavelets, (or impulses, or energy packets). The wave-shape of these wavelets is tailored to propagate in free space and communicate information, for example, through use of inverted or non-inverted copies. It is an object of the present invention to communicate information by sending sequences of these impulses, where the spectrum is constrained by both the selection of the sequence coding, and the shape of the wavelet. It is also an object of the present invention to construct an UWB high-speed digital communications system that penetrates through obstructing objects (e.g. walls), or media (e.g. earth). It is also an object of the present invention to construct an UWB high-speed digital communications system that not only tolerates significant multipath, but can take advantage of it. It is also an objective of the present invention to operate in the presence of interference from other users of the same spectrum, yet with little interference to those other users. It is also an object of the present invention to provide the above objectives in a device that can be largely constructed with a large-scale semiconductor integrated-circuit (LSI). 
     The foregoing and other objects and advantages of the invention will appear from the following description. In the description reference is made to the accompanying drawings which form a part hereof, and in which there is shown by way of illustration and not of limitation a preferred embodiment. Such description does not represent the full extent of the invention, but rather the invention may be employed in different arrangements according to the breadth of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1 . shows a block diagram of a transmitter section of the new UWB high-speed digital communications system using an embodiment with Concatenated Digital &amp; Analog Code 
         FIGS. 2A-2B . Show a block diagram of the receiver section of the new UWB high-speed digital communications system using an embodiment with a mixer/multiplier “LO” having the full code. 
         FIG. 3 . shows a simplified block diagram for a wavelet generator that generates a pseudo derivative-of-Gaussian (DOG) wavelet shape typically used in the transmitter. 
         FIG. 4 . shows a timing diagram for the wavelet generator shown in  FIG. 3   
         FIG. 5 . shows the wave-shape of the first derivative of a Gaussian (a monocycle) approximated by the wavelet generator. 
         FIG. 6 . shows the spectrum of the DOG monocycle wavelet shown in  FIG. 5 . 
         FIG. 7 . shows a diagram for a wavelet generator with selectable shapes of the n th  derivative of a Gaussian where n=0, 1, or 2. 
         FIG. 8 . shows a timing diagram for the wavelet generator shown in  FIG. 7  with 2 nd  derivative of a Gaussian wave-shape selected as is typically used for the receiver. 
         FIG. 9  shows an embodiment for switching a common antenna between the transmitter and the receiver, and sharing the same dispersive analog code hardware, even when the dispersive analog code construction is directional. 
         FIG. 10 . shows a block diagram for a simple example analog code h a =[1, 1, −1, 1]. 
         FIG. 11 . shows a timing diagram and the waveforms involved with constructing the analog code shown in for  FIG. 10 . 
         FIG. 12 . shows a block diagram for generating the data-modulated digital code for transmit and receive modes. 
         FIG. 13 . shows an expansion of the delayed locked loop receiver 
         FIG. 14 . shows a block diagram of an embodiment of the programmable delay (or phase shift) function using a DDS (Direct Digital Synthesizer). 
         FIG. 15 . shows a block diagram for a programmable delay embodiment using concatenated programmable one-shots. 
         FIG. 16 . shows a plot of example data stream, d k =[1, 0, 1, 1, 0, 1, 0], which would be convolved with the wavelet function and the code stream. 
         FIG. 17 . shows a plot of an example, equispaced code stream, h n =[1, 1, 1, 0, 0, 1, 0], which would be convolved with the wavelet function 
         FIG. 18 . shows a plot of the convolved data and code streams y(t)=h(t)*d(t) from  FIG. 16  and  FIG. 17 . 
         FIG. 19 . shows the autocorrelation of a transmit code, illustrating the high spatial resolution which allows operation in severe multipath. 
         FIG. 20 . shows the received power spectral density of RFI in Alexandria Va. 
         FIGS. 21A-21B  show a plot of the received signal before and after RFI extraction, with RFI in Alexandria Va. 
         FIG. 22  shows an embodiment for jittering the clock using a jitter code stored in RAM. 
         FIG. 23  shows an embodiment for jittering the clock using a linear feedback shift register. 
         FIG. 24  shows an alternate embodiment for jittering using a ciphered data sequence. 
         FIG. 25  shows an embodiment of a programmable dispersive-analog-code using couplers and a lattice structure that allows the transmission lines to be implemented on a printed circuit board. 
         FIG. 26  shows an embodiment of a programmable dispersive-analog-code using inverting amplifiers instead of a hybrid coupler to obtain programmable polarity. 
         FIG. 27  shows an embodiment of a programmable dispersive-analog-code using a tapped transmission line and an active network suitable for integrating in a monolithic integrated circuit. 
         FIG. 28  shows a block diagram of an embodiment for a continuous-time integrator. 
         FIGS. 29A-29B  show an alternative block diagram for the receiver, differing from that of  FIGS. 2A-2B  in that the dispersive analog code is in the path of the signal as opposed to the mixer “local-oscillator” path. 
         FIG. 30  is an exemplary receiver circuit according to the present invention. 
         FIG. 31  is an exemplary wavelet generator circuit according to the present invention. 
         FIG. 32  is an exemplary receiver circuit according to the present invention. 
         FIG. 33  is another exemplary wavelet generator circuit according to the present invention. 
         FIG. 34  shows an embodiment of a programmable dispersive-analog code generator. 
     
    
    
     BRIEF OVERVIEW OF THE PRINCIPLES OF OPERATION 
     The present communication system is a departure from conventional narrower band transmission systems in that it uses baseband transmission of codes built from time shifted and inverted replicas of short RF pulses rather than a modulated carrier. It is innovative compared to other pulsed waveform systems because it exploits phase as well as time position to create the transmit waveform. This feature allow s the system to smoothly vary the peak to average power ratios of both the spectrum and the time domain waveforms and to generate larger collections of codes. 
     Typical pulse durations are on the order of 100 to 1000 picoseconds with bandwidths of roughly 1 GHz to 8 GHz respectively. The combination of short duration pulses and the coding techniques used spread the signal energy over such a broad frequency band that little energy appears in any narrowband user&#39;s band. The result is that the UWB transmitted signal is below the detection threshold of conventional narrowband receivers. 
     The system makes it practical to transmit information at very high data rates through walls, tunnels, buildings, and other obstructions using signals with high enough spatial resolution to resolve the obstructions that lead to multipath fading in conventional systems. 
     Multipath occurs when time delayed and attenuated copies of the transmitted waveform arrive at the receiver simultaneously. In urban environments this is due in large part to reflection and transmission of architectural features, e.g. walls, floors, ceilings, and windows. 
     When the range resolution of the receiver is large compared to the multipath differences, constructive and destructive interference occurs which reduces system performance. This is multipath fading. If, on the other hand, multipath components are resolved by the receiver, then no interference occurs, and the multipath components can be used to improve system performance. 
     The range resolution of the receiver is roughly inverse to the bandwidth of the transmit signal. So, 10 MHz systems have range resolution of 
     
       
         
           
             
               R 
               res 
             
             = 
             
               
                 c 
                 BW 
               
               = 
               
                 
                   
                     3 
                     × 
                     
                       10 
                       8 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     m 
                     ⁢ 
                     
                       / 
                     
                     ⁢ 
                     sec 
                   
                   
                     10 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     MHz 
                   
                 
                 = 
                 
                   30 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     m 
                     . 
                   
                 
               
             
           
         
       
     
     likewise, a 100 MHz system has 3 meter (10 foot) resolution, and a 1 GHz system has resolution on the order of 0.3 meters (1 foot). Since architectural features (walls, floors, etc.) are separated by distances that are on the order of 10 feet, systems that resolve them well require resolution that is order of 1 foot. 
     The pulse codes built by the present system are composed of biphase modulated and time shifted replicas of an underlying short wavelet pulse. The receiver compresses the transmitted pulse code using a matched filter (correlation processing). The width of the compressed pulse that results is nominally that of a single pulse. This gives the prototype system spatial resolution that is on the order of one foot—sufficient to avoid the negative effects of multipath, and to allow time domain rake processing. 
     Theory 
     The present ultrawideband (UWB) short pulse (SP) communication system uses baseband transmission of codes built from time shifted and inverted replicas of short RF pulses. No carrier is used. Typical pulse durations are on the order of 100 to 1000 picoseconds, and typical bandwidths are greater than 1 GHz. Below, is a short review of time and frequency domain issues related to the UWB communication system. Top level views of the transmitter and receiver are given in  FIG. 1  and  FIGS. 2A-2B . 
     Time Domain 
     A waveform with good bandwidth and derivative properties is the Gaussian monocycle, which is formulated by taking the first derivative of a Gaussian. It has the form of a ramp with a Gaussian envelope
 
 s ( t )= te   −kt     2     (1)
 
     The pulse&#39;s duration is a function of the constant k, which controls the rate of decay of the Gaussian envelope.  FIG. 5  illustrates the case where the constant k has been selected to generate a pulse duration of roughly 1.5 nanoseconds. Equations (3) to (5) relate the pulse duration to bandwidth. 
     Circuits for generating these signals include: avalanche transistors; step recovery diodes (SRD) in comb filter circuits; and high speed logic and transistors. The present system currently uses a pulse forming network of high speed discrete logic together with signal conditioning. 
     Frequency Domain 
     An important property of UWB signals is the relationship between pulse duration and bandwidth. In general, the narrower a pulse is made in time, the broader the frequency band over which its energy is spread. Thus, if energy per Hertz is fixed, wider bandwidth pulses transmit more energy than narrower ones. From this perspective, shorter in time is always better. 
     Other criterion effecting the selection of pulse duration include the propagation properties of the band that results. In general, the lower frequencies, HF (3-30 MHz), VHF (30-300 MHz), and UHF (300-1000 MHz) have been shown to have superior materials (building and foliage) penetration relative to higher frequency bands. A good compromise for in-building operation is to span the VHF and UHF bands. This represents a trade-off of energy spreading against the propagation model and engineering feasibility. 
     To tie pulse duration to bandwidth, consider the Gaussian monocycle of (1). Its frequency domain representation is also Gaussian, and is given by 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁡ 
                     
                       ( 
                       ω 
                       ) 
                     
                   
                   = 
                   
                     
                       ω 
                       
                         2 
                         ⁢ 
                         k 
                       
                     
                     ⁢ 
                     
                       
                         π 
                         k 
                       
                     
                     ⁢ 
                     
                       ⅇ 
                       
                         
                           ω 
                           2 
                         
                         
                           4 
                           ⁢ 
                           k 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The spectrum of a 1 GHz Gaussian monocycle that spans the VHF and UHF bands is shown in  FIG. 6 . The time duration and bandwidth are both controlled by parameter k. The operating frequency is best described by the peak of the power spectrum which is 
     
       
         
           
             
               
                 
                   
                     
                       ω 
                       max 
                     
                     = 
                     
                       
                         2 
                         ⁢ 
                         k 
                       
                     
                   
                   , 
                   
                     
                       f 
                       max 
                     
                     = 
                     
                       
                         
                           ω 
                           max 
                         
                         
                           2 
                           ⁢ 
                           π 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     The bandwidth is determined by the upper and lower frequencies to the 6 dB down power levels
 
ƒ lo =0.3191057ƒ max 
 
ƒ hi =1.9216229ƒ max   (4)
 
     and the center frequency is 
     
       
         
           
             
               
                 
                   
                     f 
                     c 
                   
                   = 
                   
                     
                       
                         
                           f 
                           lo 
                         
                         + 
                         
                           f 
                           hi 
                         
                       
                       2 
                     
                     = 
                     
                       1.12 
                       ⁢ 
                       
                         
                           f 
                           max 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     If √{square root over (k)}=2.5×10 9 , then ƒ max =560 MHz the bandwidth is 1 GHz, and the pulse duration is 1.5 nanoseconds. Typical of UWB signals, the power is spread over a band greater than 100% of the operating frequency. 
     Codes for Integration and Channelization 
     The transceivers of the present invention use pulse codes for integration gain, channelization, whitening, and notch filtering. The pulse coded transmit signal is formed from shifted (time hopped) and inverted (biphase) copies of the underlying ultrawideband short pulse. 
     The time shifts and phase inversions are implemented with a combination of analog and digital circuitry: fixed and programmable delays; phase inverters (hybrid tees); splitters and combiners; GaAs switches; and digital circuits to generate control. 
     A template for a biphase-time hopped code h(t) can be written as a sum of weighted and shifted impulses as 
     
       
         
           
             
               
                 
                   
                     
                       h 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           n 
                           = 
                           0 
                         
                         
                           
                             N 
                             c 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           h 
                           n 
                         
                         ⁢ 
                         
                           δ 
                           ⁡ 
                           
                             ( 
                             
                               t 
                               - 
                               
                                 T 
                                 n 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     where, T n  is the relative position of chip n, N c  is the length of the code, and the coefficients of the code are h n ∈{−1, 1} for biphase (antipodal) operation. The frequency domain representation of the code h(t) is 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           H 
                           ⁡ 
                           
                             ( 
                             ω 
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               0 
                             
                             
                               
                                 N 
                                 c 
                               
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               h 
                               n 
                             
                             ⁢ 
                             
                               δ 
                               ⁡ 
                               
                                 ( 
                                 
                                   t 
                                   - 
                                   
                                     T 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 
                                   - 
                                   jω 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 t 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ⅆ 
                               t 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               0 
                             
                             
                               
                                 N 
                                 c 
                               
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               h 
                               n 
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 
                                   - 
                                   jω 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   T 
                                   n 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The pulse code is formed from the short pulse in equation (1) and the code template in equation (6) as 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           p 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             s 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           * 
                           
                             h 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             s 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           * 
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 0 
                               
                               
                                 
                                   N 
                                   c 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 h 
                                 n 
                               
                               ⁢ 
                               
                                 δ 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     
                                       T 
                                       n 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                             
                           ⁢ 
                           
                             
                               ∫ 
                               
                                 - 
                                 ∞ 
                               
                               ∞ 
                             
                             ⁢ 
                             
                               
                                 s 
                                 ⁡ 
                                 
                                   ( 
                                   τ 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   
                                     
                                       N 
                                       c 
                                     
                                     - 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     h 
                                     n 
                                   
                                   ⁢ 
                                   
                                     δ 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         
                                           T 
                                           n 
                                         
                                         - 
                                         τ 
                                       
                                       ) 
                                     
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ⅆ 
                                     t 
                                   
                                 
                               
                             
                           
                         
                         , 
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               0 
                             
                             
                               
                                 N 
                                 c 
                               
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               h 
                               n 
                             
                             ⁢ 
                             
                               
                                 ∫ 
                                 
                                   - 
                                   ∞ 
                                 
                                 ∞ 
                               
                               ⁢ 
                               
                                 
                                   s 
                                   ⁡ 
                                   
                                     ( 
                                     τ 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   δ 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       
                                         T 
                                         n 
                                       
                                       - 
                                       τ 
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ⅆ 
                                   t 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             ∑ 
                             
                               n 
                               = 
                               0 
                             
                             
                               
                                 N 
                                 c 
                               
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               h 
                               n 
                             
                             ⁢ 
                             
                               s 
                               ⁡ 
                               
                                 ( 
                                 
                                   t 
                                   - 
                                   
                                     T 
                                     n 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     a collection of shifted and inverted (weighted ±1) replicas of the underlying pulse. The frequency domain representation of the pulse code shown in equation (8) is
 
 P (ω)= H (ω) S (ω)  (9)
 
     If the data are treated as a set of equispaced impulses, they have the time and frequency domain representations 
     
       
         
           
             
               
                 
                   
                     
                       d 
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           0 
                         
                         
                           
                             N 
                             d 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           d 
                           k 
                         
                         ⁢ 
                         
                           δ 
                           ⁡ 
                           
                             ( 
                             
                               t 
                               - 
                               
                                 kT 
                                 c 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       D 
                       ⁡ 
                       
                         ( 
                         ω 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           0 
                         
                         
                           
                             N 
                             d 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           d 
                           k 
                         
                         ⁢ 
                         
                           ⅇ 
                           
                             
                               - 
                               jω 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               kT 
                               c 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       d 
                       k 
                     
                     ∈ 
                     
                       { 
                       
                         
                           - 
                           1 
                         
                         , 
                         1 
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Temporarily restricting the system to only biphase modulation of the pulse code in equation (8), the transmit signal is 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           x 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                         
                           
                             d 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           * 
                           
                             h 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           * 
                           
                             s 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               
                                 N 
                                 d 
                               
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               d 
                               k 
                             
                             ⁢ 
                             
                               p 
                               ⁡ 
                               
                                 ( 
                                 
                                   t 
                                   - 
                                   
                                     kT 
                                     c 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               
                                 N 
                                 d 
                               
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 0 
                               
                               
                                 
                                   N 
                                   c 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 d 
                                 k 
                               
                               ⁢ 
                               
                                 h 
                                 n 
                               
                               ⁢ 
                               
                                 s 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     
                                       T 
                                       n 
                                     
                                     - 
                                     
                                       kT 
                                       c 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Which has the spectrum 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           X 
                           ⁡ 
                           
                             ( 
                             ω 
                             ) 
                           
                         
                         = 
                         
                           
                             D 
                             ⁡ 
                             
                               ( 
                               ω 
                               ) 
                             
                           
                           ⁢ 
                           
                             P 
                             ⁡ 
                             
                               ( 
                               ω 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             D 
                             ⁡ 
                             
                               ( 
                               ω 
                               ) 
                             
                           
                           ⁢ 
                           
                             H 
                             ⁡ 
                             
                               ( 
                               ω 
                               ) 
                             
                           
                           ⁢ 
                           
                             S 
                             ⁡ 
                             
                               ( 
                               ω 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     If the data are assumed white, or whitened by preprocessing, then the spectrum of the transmit waveform is that of the coded pulse of equation (8). Proper selection of the delays and weights of the pulse code preserve the pulse&#39;s spectrum and bandwidth, leading to a transmit waveform that is essentially that of the short pulse in equation (1). That is, nominally white across the operational bandwidth. 
     Receiver 
     UWB transceivers face many of the same problems that narrower band systems do: transceiver clocks are not synchronized; transceiver codes are not synchronized; and clocks are either not exactly at the same frequency, or drift apart as a function of time, temperature, and relative position. The problem of synchronizing the transceiver clocks amounts to finding the unknown time delay that corresponds to the maximum of the correlation.  FIG. 19  illustrates that the correlation peak is exceedingly narrow. This narrowness gives the UWB communications system the ability to operate in the midst of multipath, because the multipath can be resolved. 
     Sliding Correlator DLL (Delay Locked Loop) 
     While we generally do not form the entire correlation function on a single sequence, we can form single terms of it and then slide the position (or lag) of that single term from sequence to sequence. This technique is known as a sliding correlator. We use the sliding correlator for clock acquisition, clock tracking, and data detection. We also use the sliding correlator to scan for the location of the highest signal. This location changes dynamically due to objects moving in the environment, or to motion between the transmitter and receiver, as in mobile applications. A sliding correlator forms inner products—signal multiplication (mixing) followed by integration—of the received signal and the local code at different relative time delays. 
     A simple method of clock acquisition (determining the unknown delay) is to increment the time delay through a code length, while looking for the inner product with the largest absolute value. In spread systems this is often called turning the code wheel. Once the delay is selected, the sign and magnitude of the inner product are used for the bit detection statistic. 
     Clock tracking is implemented with a delay locked loop (DLL). Because the correlation is symmetric, the receiver can use the difference between a leading and lagging inner product to track the transmit clock. When the receiver is synchronized, the difference goes to zero. Otherwise, the difference is positive or negative depending on whether the timing is leading or lagging. 
     Radio Frequency Interference 
     From the perspective of UWB systems, narrowband interference dominates the noise in urban environments. Because the UWB SP signal is “short in time” and “long in frequency” it is highly distinguishable from conventional narrowband signals which are “long in time” and “short in frequency”.  FIG. 20  illustrates the power spectral density at an Alexandria, Va. laboratory. The differences between these signal types are exploited to develop RFI extraction (radio frequency interference) algorithms to improve UWB transmissions. The authors have already developed and demonstrated RFI extraction algorithms that achieve up to 20 dB SNR improvement.  FIGS. 21A-21B  illustrate the results of the developed RFI extraction algorithm on collected data. 
     DETAILED DESCRIPTION 
     In the detailed descriptions we describe the operation of the UWB short pulse transmitter and receiver. Both cases begin with expressions for the key waveforms generated, and then relate their elements to the circuits. 
     Transmitter 
     A block diagram of the transmitter is shown in  FIG. 1 . Its goal is to generate the waveform of equation (11), which was 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           x 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                         
                           
                             d 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           * 
                           
                             h 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           * 
                           
                             s 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ( 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   
                                     N 
                                     d 
                                   
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   d 
                                   k 
                                 
                                 ⁢ 
                                 
                                   δ 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       
                                         kT 
                                         c 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                           * 
                           
                             ( 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 
                                   
                                     N 
                                     c 
                                   
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   h 
                                   n 
                                 
                                 ⁢ 
                                 
                                   δ 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       
                                         T 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                           * 
                           
                             s 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               
                                 N 
                                 d 
                               
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 0 
                               
                               
                                 
                                   N 
                                   c 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 d 
                                 k 
                               
                               ⁢ 
                               
                                 h 
                                 n 
                               
                               ⁢ 
                               
                                 s 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     
                                       T 
                                       n 
                                     
                                     - 
                                     
                                       kT 
                                       c 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     In this formulation, the transmit waveform is defined as the convolution of the data stream d(t) with the code h(t), and the underlying pulse s(t). 
     Data Stream 
     The transmitter receives data from data input  115 . Mathematically, the binary data d(t) are represented by a stream of equispaced impulses, one per data bit, indexed by k.  FIG. 16  is an example for the data d k =[1, 0, 1, 1, 0, 1, 0], as a stream of positive and negative going impulses, one per data bit, where the mapping {0, 1}→{−1,1} has been applied 
     Data Whitening and Differential Encoding 
     There are two special conditions on the data. The first is that the data must be pre-whitened, or scrambled. This means that it has been processed such that its spectrum is nominally flat. The reason for requiring this is that, by the convolution theorem, the spectrum of the transmit signal (13) is the product of the spectrums of the pulse S(ω), the code H(ω), and the data D(ω). That is,
 
 X (ω)= D (ω) H (ω) S (ω).  (14)
 
     Since the code and the pulse are both generated by the transmitter such that H(ω)) and S(ω) are nominally flat over the bandwidth of the system, the spectrum of the output will go as the spectrum of the data. That is, if the spectrum of the data is white over some interval, then the output will be white over that interval. Consider that if the data were constant, say all ones, then d(t) would be a train of unit impulses T c  periodic, resulting in line spectra at frequency bins spaced by ƒ c =1/T c , all the transmit energy would be concentrated at multiples of ƒ c , and the outcome would be interference with any narrowband user at those frequencies. Referring to  FIG. 1 , block  117  applies this data scrambling to the data. It also can apply forward error correction coding (FEC), such as combinations of interleaving, Reed-Solomon block codes, and convolutional codes. Many books are available on the topic of FEC. 
     The second condition is that the data must be differentially encoded. The reason for this constraint is that the transmit waveform is arbitrarily inverted by the environment. The result is that the receiver cannot tell if a non-inverted wavelet or an inverted wavelet was transmitted, but it can tell if two are alike or opposite. Differential encoding allows the receiver to recover the data in that manner. It is applied in block  119 . By employing differential encoding of the data prior to transmission, we can use phase information as well as pulse position to create pulse codes. 
     Digital Codes &amp; Modulation 
     In this system the data are transmitted by biphase modulation of codes rather than modulation of a carrier. Block  111  generates a cyclical stream of pseudo-random bits representing the digital code. Each time the cycle repeats, synch signal  112  triggers differential encoder  119  so that alignment of the data modulation on  120  can occur. Exclusive or gate  114  modulates the digital code on  113  to produce the modulated code sequence on  121 .  FIG. 12  gives an alternative block diagram of a circuit capable of performing the modulation. These circuits produce the data modulated code, independent of the pulse waveform. That is 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           y 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                         
                           
                             d 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           * 
                           
                             h 
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ( 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   = 
                                   0 
                                 
                                 
                                   
                                     N 
                                     d 
                                   
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   d 
                                   k 
                                 
                                 ⁢ 
                                 
                                   δ 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       
                                         kT 
                                         c 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                           * 
                           
                             ( 
                             
                               
                                 ∑ 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 
                                   
                                     N 
                                     c 
                                   
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   h 
                                   n 
                                 
                                 ⁢ 
                                 
                                   δ 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       
                                         T 
                                         n 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ∑ 
                             
                               k 
                               = 
                               0 
                             
                             
                               
                                 N 
                                 d 
                               
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 0 
                               
                               
                                 
                                   N 
                                   c 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 d 
                                 k 
                               
                               ⁢ 
                               
                                 h 
                                 n 
                               
                               ⁢ 
                               
                                 δ 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     
                                       T 
                                       n 
                                     
                                     - 
                                     
                                       kT 
                                       c 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 0 
                               
                               
                                 
                                   N 
                                   d 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 d 
                                 k 
                               
                               ⁢ 
                               
                                 
                                   ∑ 
                                   
                                     n 
                                     = 
                                     0 
                                   
                                   
                                     
                                       N 
                                       c 
                                     
                                     - 
                                     1 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     h 
                                     n 
                                   
                                   ⁢ 
                                   
                                     δ 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         t 
                                         - 
                                         
                                           T 
                                           n 
                                         
                                         - 
                                         
                                           kT 
                                           c 
                                         
                                       
                                       ) 
                                     
                                   
                                   ⁢ 
                                   
                                     d 
                                     k 
                                   
                                 
                               
                             
                           
                         
                         , 
                         
                           
                             h 
                             n 
                           
                           ∈ 
                           
                             { 
                             
                               
                                 - 
                                 1 
                               
                               , 
                               1 
                             
                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     which says that for each bit, d k , of the data stream, a pulse code h(t) is generated, and the entire code is then multiplied by d k . The effect is to either invert, or not invert, the code h(t) depending on whether d k  was a −1 or 1 respectively. Much of the code generation and modulation is processed digitally. In these circuits modulo 2 addition (exclusive nor) replaces traditional multiplication, and {1, −1} are mapped to {1,0}.  FIG. 16  illustrates a data stream. 
     The coefficients h n  of the digital code are binary sequences of 1&#39;s and 0&#39;s occurring at times T n  relative to the start of the code. A sample 7 length code is shown in  FIG. 17 . In this case the coefficients are equispaced, say T p  seconds apart, thus T n =nT p .  FIG. 18  illustrates the data modulated code that results from applying equation (15) to the data and code of  FIGS. 16 and 17 . 
     Referring to the block diagram in  FIG. 12 , and equation (15), the coefficients of the code are stored in memory  40  and addressed by counter  30 . The counter generates the code index n, and counts from 0 to N c −1, the length of the code. The counter is incremented once for each coefficient of the code, at intervals of T n  seconds. Following each increment of counter  30  the corresponding coefficient is emitted from the memory to line  13 . 
     In equation (15), one code word is applied to each data bit. These are synchronized by parallel to serial register  10  and word counter  42 . When counter  30  completes the count for a single code word it asserts line  41  which signals register  10  to output one bit. When line  41  is asserted it also signals word counter  42  to advanced the count of data bits shifted out. This counter is programmed to count to N i , the width in bits of a data word (whitened and differentially encoded). When the counter has been advanced N i  times, it asserts line  12  which signals register  10  to load another data word. It is also possible to compute the code coefficients on the fly, for example, with a linear feedback shift registers. 
     Referring to  FIG. 1 , the coefficients of the code and the bits of the data are presented to exclusive or (XOR) gate  114 , which produces y(t), the code modulated data, that is presented to the pulse forming network on line  121 . Switch  107 , responds to the modulated code  121  to selectively output a positive (non-inverted) or negative (inverted) wavelet onto  108 . Positive wavelet generator  103 , and negative wavelet generator  104  produce a wavelet in response to an xmit clock signal  102 . The shape of the wavelet is selected by a wavelet shape selector signal. 
     Pulse Forming &amp; Pulse Modulation 
     Circuits for generating short pulses include: avalanche transistors; step recovery diodes (SRD) in comb filter circuits; and high speed discrete logic and transistors. The present system generates short pulses using circuits built from discrete logic gates and passive delay lines.  FIG. 3  shows a simplified diagram of a differential ECL implementation that generates a wavelet approximating the first derivative of a Gaussian.  FIG. 4  shows a timing diagram for  FIG. 3 .  FIG. 7  is a block level diagram of a wavelet generator with selectable wave-shape.  FIG. 8  shows a timing diagram for  FIG. 7  with the switches selected to produce the second derivative of a Gaussian. Switch  784  applies the data modulated code on  786  to select the polarity of the transmitted wavelet. Switches  736 ,  738 , and  737  are driven to select the zero, first, or second derivative of a Gaussian. In the block diagram of  FIG. 7  signal is delayed by different line lengths into ports A( 712 ) and B( 714 ) of AND gate  716 . The timing diagrams shown in  FIGS. 4 and 8  show idealized waveforms for clarity. The actual rise and fall times of the devices, however, produce the “filtered” output waveforms shown. Typically, the transmitter and receiver wavelet functions are not identical. Instead, the shape of the wavelet used in the receiver is typically the derivative or Hilbert transform of the shape used in the transmitter. 
     As shown in  FIG. 3 , the wavelet generator includes a clock  300 , an amplifier  304 , an inverter  306 , a line  308 , a line  310 , an AND gate  316 , an amplifier  320 , an inverter  322 , a line  324 , a line  326 , an amplifier  332 , an amplifier  334 , an inverter  336 , an inverter  338 , a summer  348 , a summer  350 , and a switch  356 . 
     As shown in  FIGS. 3 and 4 , the signal  302  is output from the clock  300 , the signal  312  is output from the line  310 , the signal  314  is output from the line  308 , the signal  318  is output from the AND gate  316 , the signal  340  is output from the amplifier  332 , the signal  342  is output from the amplifier  334 , the signal  129  is output from the inverter  336 , the signal  346  is output from the inverter  338 , the signal  352  is output from the summer  348 , the signal  354  is output from the summer  350 , and the signal  360  is output from the switch  356 . The signal  358  controls the switch  356 . 
     As shown in  FIG. 7 , the wavelet generator includes a clock  700 , an amplifier  704 , an inverter  706 , a line  710 , an AND gate  716 , an amplifier  720 , an inverter  722 , an amplifier  724 , an inverter  726 , a line  728 , a line  734 , a switch  736 , a switch  738 , a switch  737 , an amplifier  748 , an amplifier  750 , an amplifier  752 , an amplifier  756 , an inverter  758 , an inverter  759 , an inverter  760 , an inverter  762 , a summer  778 , a summer  780 , and a switch  784 . 
     As shown in  FIGS. 7 and 8 , the signal  702  is output from the clock  700 , the signal  712  is output from the line  710 , the signal  714  is output from a line L +X, the signal  718  is output from the AND gate  716 , the signal  764  is output from the amplifier  748 , the signal  766  is output from the amplifier  750 , the signal  768  is output from the amplifier  752 , the signal  770  is output from the amplifier  756 , the signal  772  is output from the inverter  758 , the signal  774  is output from the inverter  759 , the signal  776  is output from the inverter  760 , the signal  777  is output from the inverter  762 , the signal  781  is output from the summer  778 , the signal  782  is output from the summer  780 , and the signal  788  is output from the switch  784 . The signal  786  controls the switch  784 . 
       FIG. 31  is an exemplary wavelet generator circuit according to the present invention.  FIG. 33  is another exemplary wavelet generator circuit according to the present invention. 
     Analog Codes 
     Unique to the present invention is the ability to concatenate codes and allow implementations of the two codes in different technology. Referring to  FIG. 1 , analog code  109  is implemented extremely wide bandwidth microwave components which do not have the limitations of semiconductor technologies. Therefore, the present invention can generate codes composed of both digital and analog parts. The digital, h d (t), and analog, h a (t), codes are given by 
     
       
         
           
             
               
                 
                   
                     
                       
                         h 
                         d 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           m 
                           = 
                           0 
                         
                         
                           M 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           g 
                           m 
                         
                         ⁢ 
                         
                           δ 
                           ⁡ 
                           
                             ( 
                             
                               t 
                               - 
                               
                                 T 
                                 m 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   , 
                   
                     
                       
                         h 
                         a 
                       
                       ⁡ 
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           q 
                           = 
                           0 
                         
                         
                           Q 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           a 
                           q 
                         
                         ⁢ 
                         
                           δ 
                           ⁡ 
                           
                             ( 
                             
                               t 
                               - 
                               
                                 T 
                                 q 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   , 
                   
                     g 
                     m 
                   
                   , 
                   
                     
                       a 
                       q 
                     
                     ∈ 
                     
                       
                         { 
                         
                           
                             - 
                             1 
                           
                           , 
                           1 
                         
                         } 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The effect on the formulation of equation (15) is to replace h(t) with the concatenated code 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           h 
                           ⁡ 
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                         
                           
                             
                               h 
                               a 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                           * 
                           
                             
                               h 
                               d 
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ( 
                             
                               
                                 ∑ 
                                 
                                   m 
                                   = 
                                   0 
                                 
                                 
                                   M 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   g 
                                   m 
                                 
                                 ⁢ 
                                 
                                   δ 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       
                                         T 
                                         m 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                           * 
                           
                             ( 
                             
                               
                                 ∑ 
                                 
                                   q 
                                   = 
                                   0 
                                 
                                 
                                   Q 
                                   - 
                                   1 
                                 
                               
                               ⁢ 
                               
                                 
                                   a 
                                   q 
                                 
                                 ⁢ 
                                 
                                   δ 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       - 
                                       
                                         T 
                                         q 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             ∑ 
                             
                               m 
                               = 
                               0 
                             
                             
                               M 
                               - 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 q 
                                 = 
                                 0 
                               
                               
                                 Q 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 a 
                                 q 
                               
                               ⁢ 
                               
                                 g 
                                 m 
                               
                               ⁢ 
                               
                                 δ 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     t 
                                     - 
                                     
                                       T 
                                       q 
                                     
                                     - 
                                     
                                       T 
                                       m 
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     The system can be operated with either digital only or analog only codes. The purpose of the analog code is to generate waveforms whose pulses occur faster than can be processed digitally. A replica of the analog code replaces each pulse of the digitally generated code on a fine time scale. Good codes for the analog section have low autocorrelation sidelobes, like Barker codes. The reason for this is that the sidelobe structure of the concatenated code will contain all combinations of the main and side lobes of the component codes. 
       FIG. 10  shows a very simplified block level diagram of a circuit for generating an analog code.  FIG. 11  shows the timing diagram associated with it. The digitally modulated code of wavelet pulses from signal  1000  are input to splitter  1002 . The present implementation employs passive power splitters, alternatives depending on cost, size, and power, include resistive dividers and active networks. The line lengths L 1  to L 4  on  1004  thru  1010  at the outputs of the power splitter are selected to delay the pulses in time. In order to generate the delays T n  in (b) of the figure, the required line lengths are
   L   n   =nε   r   T   d , n=1, . . . ,4 
     where ε r  is the propagation velocity in the media and delays of multiples of T d  were required. In general, the delays are not restricted to be common multiples. All the pulses in time slots that are not inverted are summed together in power combiner  1016  to generate a first sum  1040 , and all pulses in time slots that are to be inverted are summed together in power combiner  1020  to generate a second sum  1012 . The pulses to be inverted  1012  are subtracted from the non-inverted set by hybrid  1060 , and the difference is output on signal  1080 . 
     Referring to  FIG. 1 , prior to final amplification and transmission the signal may be bandpass filtered by  122  in, to suppress energy in frequency bands out of the operational band of the receiver. The output signal can also be notched filtered by  124  to remove energy from other narrowband signals as appropriate. Another strategy to create notches in the output spectrum is to design the codes h(t) such that the undesirable frequencies are attenuated in the pulse code p(t)=s(t)*h(t). Amplifier  126  drives antenna  128  to broadcast the sequence of wavelets. 
       FIG. 25  shows an embodiment of a programmable dispersive-analog-code using couplers and a lattice structure that allows the transmission lines to be implemented on a printed circuit board. The line lengths follow a binary length formula to minimize line lengths.  FIG. 26  shows an embodiment of a programmable dispersive-analog-code using inverting amplifiers instead of a hybrid coupler to obtain programmable polarity.  FIG. 30  shows an embodiment of a programmable dispersive-analog-code using a tapped transmission line and an active network suitable for integrating in a monolithic integrated circuit.  FIG. 9  shows an embodiment for switching a common antenna between the transmitter and the receiver, and sharing the same dispersive analog code hardware, even when the dispersive analog code construction is directional. This feature is important when amplifiers are buried in the structure of the programmable dispersive-analog-code. 
       FIG. 27  shows an embodiment of a programmable dispersive-analog-code using a tapped transmission line and an active network suitable for integrating in a monolithic integrated circuit.  FIG. 32  is an exemplary receiver circuit according to the present invention.  FIG. 34  shows an embodiment of a programmable dispersive-analog code generator. 
     Receiver 
     The receiver implements a sliding correlator delay locked loop specialized to short pulse waveforms, as illustrated in the block level diagrams of  FIGS. 2A-2B  and  FIGS. 29A-29B . The difference between the two is where the analog code is inserted. In  FIGS. 2A-2B , the analog code affects the wavelet sequence going into the “lo-port” of the mixer/multiplier correlators. In  FIGS. 29A-29B  the analog code is used as a compressive matched filter. Whereas the analog code in the transmitter spreads a single pulse to a sequence of pulses, the receive analog code does the reverse, and compresses the sequence of pulses back into a single pulse. 
     The receiver has two main operating modes (1) acquisition and (2) tracking and detection. Below is a description of the sliding correlator DLL implemented in the present system. The appendix contains detailed schematics of the acquisition, tracking, and detection circuits. 
     Receiver Input Stage 
       FIG. 13  is a more detailed block level diagram of the delay locked loop (DLL) circuit employed in the present system. After amplification, filtering, and optional RFI extraction, the received signal is input to the DLL. Splitter  400  separates the received signal into three copies, which are each delayed a different amount. The prototype uses line lengths of L+Y, L−Y, and L, to form lead, lag and on-time signals for the DLL. These line length differences lead to time delays that, during acquisition, are selected to place the on-time signal at the maximum of the pulse code autocorrelation function, and the lead and lag terms symmetrically before and after it. 
     What might be referred to as the “local oscillator” is, in this case, the code of receive wavelets on line  10   r . Unique to the UWB high-speed communications system, this signal is different from the transmit waveform to account for the transmission effects of the antennas. It is generated similarly to the transmit system, except the data line is driven to a logic low state. To improve noise discrimination, bandpass and notch filtering consistent with any applied by the transmitter can also be applied to signal  10   r . The effect is to improve the match of the filter. 
     Similar to the received signal, the local code on  10   r  is split into three copies by  402 , however, here the line lengths and path delays are kept identical to the mixers  320 ,  390 , and  392 . The reason for this is to allow the lead, lag, and ontime inner products formed by the mixers and gated integrators to all operate with the same control signals. 
     Acquisition Process 
     The acquisition process amounts to finding the time delay that maximizes the inner product of the ontime signal and the local code. Received signal  300  is delayed through  312 , the ontime delay, and input to the RF port of mixer  390 , while the local code is applied to the LO port of the mixer. The resulting product is the on-time IF signal input to gated integrator  380 . Integrate control signal  403  to the integrator is synchronized by controller  500  such that the integration begins when the local code arrives at the integrator input. When the local code ends, controller  500  issues an encode command to analog to digital converter  370  on control line  404 . This completes the formation of the inner product, whose value is now present on digital lines  405 . The dump signal to integrator  380  is activated by controller  500 , clearing the integrated value and preparing the integrator for the next inner product. The gated integrators may be constructed using a ping-pong technique to allow continuous time gated integration.  FIG. 28  is a block diagram showing an implementation of a continuous time integrator. 
     The digitized value of the on-time inner product is input to controller  500  on lines  405 . At the beginning of the acquisition process, the controller stores this value. The controller then issues an advance command to phase delay circuit  520 , and increments its count of the number of advances that have been applied. It also stores the number of advances that correspond to the inner product just collected. 
     The effect of delay circuit  520  is to slide, in time, the local code relative to the received signal.  FIG. 14  and  FIG. 15  give block level diagrams of circuits capable of sliding the clock. The circuit of  FIG. 14  operates by increasing or decreasing the frequency of the reference oscillator a short time in order to slide the phase of the clock.  FIG. 15  operates by directly programming a delay term. Both change the start time of the codes generated by circuits implementing  FIG. 12 . 
     Controller  500  continues to advance the phase and collect inner products, and their associated advance counts, for the on-time term. Each inner product formed is compared against the last stored. If it is greater, it replaces it, and its advance count is noted. When the total amount of time the local code has been slid equals the duration of a single code, we say the code wheel has been turned. After some number of turns of the code wheel, the acquisition process is halted. The unknown phase between the transmitter and receiver oscillators and codes is taken to be the delay of the maximum on-time inner product found. At this point the system switches to a tracking and detection mode. 
       FIG. 22  shows an embodiment for jittering the clock using a jitter code stored in RAM.  FIG. 23  shows an embodiment for jittering the clock using a linear feedback shift register.  FIG. 24  shows an alternate embodiment for jittering using a ciphered data sequence. 
     Tracking &amp; Detection Process 
     Lead and lag inner products, similar to the ontime term, are formed by delays  310  and  311 , and mixers  320  and  392  respectively. Blocks  330  and  333  complete the integration of these terms. These are synchronized with the local code by controller  500  in the same manner as the ontime term. After the inner products have been formed, circuits  340  and  342  take their absolute value. The difference of these terms is formed by summer  350 , and is digitized by analog to digital convert  360  on encode command  407  from the controller. The timing of the encode command is such that the difference of the lead and lag inner products has had sufficient time to propagate through to the A/D. 
     The lead and lag terms are formed at symmetric time delays before and after the ontime term. Because the correlation function is also symmetric, these values will be equal when the local code is synchronized with the received signal. If the controller detects a non-zero value it will advance or retard the phase in order to zero the error. As a means of improving the signal to noise ratio of the error term, many of these may be summed together before making an advance or retard decision. 
     Detection is performed by a window comparison on the ontime inner product. Values greater than zero map to a one, those less than zero map to a zero. An erasure zone may be added as well. The detected data is differentially decoded, whitening decoded, and forward error corrected. 
     Referring to  FIGS. 2A-2B , a “search” channel, shown blocks  262  through  270 , is used to continually scan for multipath signals which may be stronger than the one (or several) being used. In the event that a stronger correlation peak is found by  234 , then the main channel, or an auxiliary rake channel, can be moved to track the larger peak via phase delay  241  or  280 . This operation allows the system to operate in dynamic multipath conditions. 
     A first rake channel is used to track the second strongest signal so that the next strongest correlation can be added to the main channel signal. This summation is the first term in a time domain RAKE filter that takes advantage of multipath to improve the BER performance. Although  FIGS. 2A-2B  show only one rake channel, it is the intent that several rake channels would operate simultaneously.