PATENT DOCUMENT

Abstract:
A high-speed transmitter and receiver are provided. In one embodiment, a transmitter comprises a baseband processor structured to receive data and to convert the data into a multiplicity of high and low signal values, with each high and low signal value having a first timing interval. A local oscillator generates a clock signal at a second timing interval and a digital circuit combines the high and low signal values with the clock signal to produce a transmission signal directly at a transmission frequency. A receiver is configured to receive the signal. This Abstract is provided for the sole purpose of complying with the Abstract requirement rules that allow a reader to quickly ascertain the subject matter of the disclosure contained herein. This Abstract is submitted with the explicit understanding that it will not be used to interpret or to limit the scope or the meaning of the claims.

Full Description:
This application claims priority under 35 U.S.C. §120 and §121 as a divisional of U.S. patent application Ser. No. 11/055,525, filed Feb. 9, 2005, now U.S. Pat. No. 8,045,935 entitled “High Data Rate Transmitter and Receiver,” which is a continuation-in-part of U.S. patent application Ser. No. 10/010,601, filed Dec. 6, 2001, entitled: “Systems and Methods for Wireless Communication Over a Wide Bandwidth Channel Using a Plurality of Sub-Channels,” now U.S. Pat. No. 7,289,494. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates generally to communications, and more particularly to systems and methods for high data rate communications. 
     2. Background 
     Wireless communication systems are proliferating at the Wide Area Network (WAN), Local Area Network (LAN), and Personal Area Network (PAN) levels. These wireless communication systems use a variety of techniques to allow simultaneous access to multiple users. The most common of these techniques are Frequency Division Multiple Access (FDMA), which assigns specific frequencies to each user, Time Division Multiple Access (TDMA), which assigns particular time slots to each user, and Code Division Multiple Access (CDMA), which assigns specific codes to each user. But these wireless communication systems and various modulation techniques are afflicted by a host of problems that limit the capacity and the quality of service provided to the users. The following paragraphs briefly describe a few of these problems for the purpose of illustration. 
     One problem that can exist in a wireless communication system is multipath interference. Multipath interference, or multipath, occurs because some of the energy in a transmitted wireless signal bounces off of obstacles, such as buildings or mountains, as it travels from source to destination. The obstacles in effect create reflections of the transmitted signal and the more obstacles there are, the more reflections they generate. The reflections then travel along their own transmission paths to the destination (or receiver). The reflections will contain the same information as the original signal; however, because of the differing transmission path lengths, the reflected signals will be out of phase with the original signal. As a result, they will often combine destructively with the original signal in the receiver. This is referred to as fading. To combat fading, current systems typically try to estimate the multipath effects and then compensate for them in the receiver using an equalizer. In practice, however, it is very difficult to achieve effective multipath compensation. 
     A second problem that can affect the operation of wireless communication systems is interference from adjacent communication cells within the system. In FDMA/TDMA systems, this type of interference is prevent through a frequency reuse plan. Under a frequency reuse plan, available communication frequencies are allocated to communication cells within the communication system such that the same frequency will not be used in adjacent cells. Essentially, the available frequencies are split into groups. The number of groups is termed the reuse factor. Then the communication cells are grouped into clusters, each cluster containing the same number of cells as there are frequency groups. Each frequency group is then assigned to a cell in each cluster. Thus, if a frequency reuse factor of 7 is used, for example, then a particular communication frequency will be used only once in every seven communication cells. Thus, in any group of seven communication cells, each cell can only use 1/7 th  of the available frequencies, i.e., each cell is only able to use 1/7 th  of the available bandwidth. 
     In a CDMA communication system, each cell uses the same wideband communication channel. In order to avoid interference with adjacent cells, each communication cell uses a particular set of spread spectrum codes to differentiate communications within the cell from those originating outside of the cell. Thus, CDMA systems preserve the bandwidth in the sense that they avoid reuse planning. But as will be discussed, there are other issues that limit the bandwidth in CDMA systems as well. 
     Thus, in overcoming interference, system bandwidth is often sacrificed. Bandwidth is becoming a very valuable commodity as wireless communication systems continue to expand by adding more and more users. Therefore, trading off bandwidth for system performance is a costly, albeit necessary, proposition that is inherent in all wireless communication systems. 
     The foregoing are just two examples of the types of problems that can affect conventional wireless communication systems. The examples also illustrate that there are many aspects of wireless communication system performance that can be improved through systems and methods that, for example, reduce interference, increase bandwidth, or both. 
     Not only are conventional wireless communication systems effected by problems, such as those described in the preceding paragraphs, but also different types of systems are effected in different ways and to different degrees. Wireless communication systems can be split into three types: 1) line-of-sight systems, which can include point-to-point or point-to-multipoint systems; 2) indoor non-line of sight systems; and 3) outdoor systems such as wireless WANs. Line-of-sight systems are least affected by the problems described above, while indoor systems are more affected, due for example to signals bouncing off of building walls. Outdoor systems are by far the most affected of the three systems. Because these types of problems are limiting factors in the design of wireless transmitters and receivers, such designs must be tailored to the specific types of system in which it will operate. In practice, each type of system implements unique communication standards that address the issues unique to the particular type of system. Even if an indoor system used the same communication protocols and modulation techniques as an outdoor system, for example, the receiver designs would still be different because multipath and other problems are unique to a given type of system and must be addressed with unique solutions. This would not necessarily be the case if cost efficient and effective methodologies can be developed to combat such problems as described above that build in programmability so that a device can be reconfigured for different types of systems and still maintain superior performance. 
     SUMMARY OF THE INVENTION 
     In order to combat the above problems, a high data rate transmitter and receiver are provided. In one embodiment, a transmitter comprises a baseband processor structured to receive data and to convert the data into a multiplicity of high and low signal values, with each high and low signal value having a first timing interval. A local oscillator generates a clock signal at a second timing interval and a digital circuit combines the high and low signal values with the clock signal to produce a transmission signal directly at a transmission frequency. 
     The radio frequency used for transmission may range up to 11 Giga-Hertz, and production of the transmission signal directly at the transmission frequency is possible by use of a high-speed oscillator. 
     A receiver is structured to receive the communication signal, which in one embodiment, may have a fractional bandwidth that may range between approximately 20 percent and approximately 200 percent. The receiver includes a high-speed analog to digital converter configured to directly convert the radio frequency signal into a data signal. 
     These and other features and advantages of the present invention will be appreciated from review of the following Detailed Description of the Preferred Embodiments, along with the accompanying figures in which like reference numerals are used to describe the same, similar or corresponding parts in the several views of the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Preferred embodiments of the present inventions taught herein are illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings, in which: 
         FIG. 1A  is a diagram illustrating an example embodiment of a wideband channel divided into a plurality of sub-channels in accordance with the invention; 
         FIG. 1B  is a diagram illustrating the effects of multipath in a wireless communication system; 
         FIG. 2  is a diagram illustrating another example embodiment of a wideband communication channel divided into a plurality of sub-channels in accordance with the invention; 
         FIG. 3  is a diagram illustrating the application of a roll-off factor to the sub-channels of  FIGS. 1 and 2 ; 
         FIG. 4A  is a diagram illustrating the assignment of sub-channels for a wideband communication channel in accordance with the invention; 
         FIG. 4B  is a diagram illustrating the assignment of time slots for a wideband communication channel in accordance with the invention; 
         FIG. 5  is a diagram illustrating an example embodiment of a wireless communication in accordance with the invention; 
         FIG. 6  is a diagram illustrating the use of synchronization codes in the wireless communication system of  FIG. 5  in accordance with the invention; 
         FIG. 7  is a diagram illustrating a correlator that can be used to correlate synchronization codes in the wireless communication system of  FIG. 5 ; 
         FIG. 8  is a diagram illustrating synchronization code correlation in accordance with the invention; 
         FIG. 9  is a diagram illustrating the cross-correlation properties of synchronization codes configured in accordance with the invention; 
         FIG. 10  is a diagram illustrating another example embodiment of a wireless communication system in accordance with the invention; 
         FIG. 11A  is a diagram illustrating how sub-channels of a wideband communication channel according to the present invention can be grouped in accordance with the present invention; 
         FIG. 11B  is a diagram illustrating the assignment of the groups of sub-channels of  FIG. 11A  in accordance with the invention; 
         FIG. 12  is a diagram illustrating the group assignments of  FIG. 11B  in the time domain; 
         FIG. 13  is a flow chart illustrating the assignment of sub-channels based on SIR measurements in the wireless communication system of  FIG. 10  in accordance with the invention; 
         FIG. 14  is a logical block diagram of an example embodiment of transmitter configured in accordance with the invention; 
         FIG. 15  is a logical block diagram of an example embodiment of a modulator configured in accordance with the present invention for use in the transmitter of  FIG. 14 ; 
         FIG. 16  is a diagram illustrating an example embodiment of a rate controller configured in accordance with the invention for use in the modulator of  FIG. 15 ; 
         FIG. 17  is a diagram illustrating another example embodiment of a rate controller configured in accordance with the invention for use in the modulator of  FIG. 15 ; 
         FIG. 18  is a diagram illustrating an example embodiment of a frequency encoder configured in accordance with the invention for use in the modulator of  FIG. 15 ; 
         FIG. 19  is a logical block diagram of an example embodiment of a TDM/FDM block configured in accordance with the invention for use in the modulator of  FIG. 15 ; 
         FIG. 20  is a logical block diagram of another example embodiment of a TDM/FDM block configured in accordance with the invention for use in the modulator of  FIG. 15 ; 
         FIG. 21  is a logical block diagram of an example embodiment of a frequency shifter configured in accordance with the invention for use in the modulator of  FIG. 15 ; 
         FIG. 22  is a logical block diagram of a receiver configured in accordance with the invention; 
         FIG. 23  is a logical block diagram of an example embodiment of a demodulator configured in accordance with the invention for use in the receiver of  FIG. 22 ; 
         FIG. 24  is a logical block diagram of an example embodiment of an equalizer configured in accordance with the present invention for use in the demodulator of  FIG. 23 ; 
         FIG. 25  is a logical block diagram of an example embodiment of a wireless communication device configured in accordance with the invention; 
         FIG. 26  is an illustration of different communication methods; 
         FIG. 27  is an illustration of two ultra-wideband pulses; 
         FIG. 28  is a chart of ultra-wideband emission limits as established by the Federal Communications Commission on Apr. 22, 2002; 
         FIG. 29  illustrates a transmitter consistent with one embodiment of the present invention; 
         FIG. 30  illustrates a timing diagram of various signals; 
         FIG. 31  illustrates a frame consistent with one embodiment of the present invention; 
         FIG. 32   a  illustrates one embodiment of a digital circuit employed in the transmitter of  FIG. 29 ; 
         FIG. 32   b  illustrates a second embodiment of a digital circuit employed in the transmitter of  FIG. 29 ; 
         FIG. 32   c  illustrates a third embodiment of a digital circuit employed in the transmitter of  FIG. 29 ; 
         FIG. 33  illustrates a data stream consistent with one embodiment of the present invention; 
         FIG. 34  illustrates a receiver consistent with one embodiment of the present invention; 
         FIG. 35  illustrates a schematic of a first portion of a baseband processor employed in the transmitter of  FIG. 29 ; 
         FIG. 36  illustrates a schematic of a second portion of a baseband processor employed in the receiver of  FIG. 34 ; 
         FIG. 37  illustrates one embodiment of a poly-phase filter employed in the baseband processor of  FIG. 36 ; 
         FIG. 38  illustrates another embodiment of a poly-phase filter employed in the baseband processor of  FIG. 36 ; 
         FIG. 39  illustrates another timing diagram of signals consistent with the present invention. 
         FIG. 40  illustrates one embodiment of an equalizer consistent with the present invention; 
         FIG. 41  illustrates an exemplary FEC encoder and exemplary FEC decoder; 
         FIG. 42  illustrates an example FEC encoder configured in accordance with one embodiment of the present invention; 
         FIG. 43  illustrates a FEC encoder configured to generate a code word from input data in accordance with one embodiment; 
         FIG. 44  illustrates the encoder of  FIG. 42  in more detail; 
         FIG. 45  illustrates further detail for the encoder of  FIG. 42 ; 
         FIG. 46  illustrates an example parity node processor that can be included in a decoder in accordance with one embodiment; 
         FIG. 47  illustrates one node of the parity node processor of  FIG. 45 ; 
         FIG. 48  illustrates the parity node processor of  FIG. 45  in more detail; and 
         FIG. 49  illustrates a parity node processor configured in accordance with one embodiment. 
     
    
    
     It will be recognized that some or all of the Figures are schematic representations for purposes of illustration and do not necessarily depict the actual relative sizes or locations of the elements shown. The Figures are provided for the purpose of illustrating one or more embodiments of the invention with the explicit understanding that they will not be used to limit the scope or the meaning of the claims. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     1. Introduction 
     In the following paragraphs, the present invention will be described in detail by way of example with reference to the attached drawings. While this invention is capable of embodiment in many different forms, there is shown in the drawings and will herein be described in detail specific embodiments, with the understanding that the present disclosure is to be considered as an example of the principles of the invention and not intended to limit the invention to the specific embodiments shown and described. That is, throughout this description, the embodiments and examples shown should be considered as exemplars, rather than as limitations on the present invention. As used herein, the “present invention” refers to any one of the embodiments of the invention described herein, and any equivalents. Furthermore, reference to various feature(s) of the “present invention” throughout this document does not mean that all claimed embodiments or methods must include the referenced feature(s). 
     In order to improve wireless communication system performance and allow a single device to move from one type of system to another, while still maintaining superior performance, the systems and methods described herein provide various communication methodologies that enhance performance of transmitters and receivers with regard to various common problems that afflict such systems and that allow the transmitters and/or receivers to be reconfigured for optimal performance in a variety of systems. Accordingly, the systems and methods described herein define a channel access protocol that uses a common wideband communication channel for all communication cells. The wideband channel, however, is then divided into a plurality of sub-channels. Different sub-channels are then assigned to one or more users within each cell. But the base station, or service access point, within each cell transmits one message that occupies the entire bandwidth of the wideband channel. Each user&#39;s communication device receives the entire message, but only decodes those portions of the message that reside in sub-channels assigned to the user. For a point-to-point system, for example, a single user may be assigned all sub-channels and, therefore, has the full wide band channel available to them. In a wireless WAN, on the other hand, the sub-channels may be divided among a plurality of users. 
     In the descriptions of example embodiments that follow, implementation differences, or unique concerns, relating to different types of systems will be pointed out to the extent possible. But it should be understood that the systems and methods described herein are applicable to any type of communication systems. In addition, terms such as communication cell, base station, service access point, etc. are used interchangeably to refer to the common aspects of networks at these different levels. 
     To begin illustrating the advantages of the systems and methods described herein, one can start by looking at the multipath effects for a single wideband communication channel  100  of bandwidth B as shown in  FIG. 1A . Communications sent over channel  100  in a traditional wireless communication system will comprise digital data bits, or symbols, that are encoded and modulated onto a RF carrier that is centered at frequency f c  and occupies bandwidth B. Generally, the width of the symbols (or the symbol duration) T is defined as 1/B. Thus, if the bandwidth B is equal to 100 MHz, then the symbol duration T is defined by the following equation:
 
 T= 1/ B= 1/100 megahertz (MHZ)=10 nanoseconds (ns).   (1)
 
     When a receiver receives the communication, demodulates it, and then decodes it, it will recreate a stream  104  of data symbols  106  as illustrated in  FIG. 1B . But the receiver will also receive multipath versions  108  of the same data stream. Because multipath data streams  108  are delayed in time relative to the data stream  104  by delays d 1 , d 2 , d 3 , and d 4 , for example, they may combine destructively with data stream  104 . 
     A delay spread d s  is defined as the delay from reception of data stream  104  to the reception of the last multipath data stream  108  that interferes with the reception of data stream  104 . Thus, in the example illustrated in  FIG. 1B , the delay spread d s  is equal to delay d 4 . The delay spread d s  will vary for different environments. An environment with a lot of obstacles will create a lot of multipath reflections. Thus, the delay spread d s  will be longer. Experiments have shown that for outdoor WAN type environments, the delay spread d s  can be as long as 20 microseconds. Using the 10 ns symbol duration of equation (1), this translates to 2000 symbols. Thus, with a very large bandwidth, such as 100 MHz, multipath interference can cause a significant amount of interference at the symbol level for which adequate compensation is difficult to achieve. This is true even for indoor environments. For indoor LAN type systems, the delay spread d s  is significantly shorter, typically about 1 microsecond. For a 10 ns symbol duration, this is equivalent to 100 symbols, which is more manageable but still significant. 
     By segmenting the bandwidth B into a plurality of sub-channels  202 , as illustrated in  FIG. 2 , and generating a distinct data stream for each sub-channel, the multipath effect can be reduced to a much more manageable level. For example, if the bandwidth b of each sub-channel  202  is 500 KHz, then the symbol duration is 2 microseconds. Thus, the delay spread d s  for each sub-channel is equivalent to only 10 symbols (outdoor) or half a symbol (indoor). Thus, by breaking up a message that occupies the entire bandwidth B into discrete messages, each occupying the bandwidth b of sub-channels  202 , a very wideband signal that suffers from relatively minor multipath effects is created. 
     Before discussing further features and advantages of using a wideband communication channel segmented into a plurality of sub-channels as described, certain aspects of the sub-channels will be explained in more detail. Referring back to  FIG. 2 , the overall bandwidth B is segmented into N sub-channels center at frequencies f o  to f N−1 . Thus, the sub-channel  202  that is immediately to the right of fc is offset from fc by b/2, where b is the bandwidth of each sub-channel  202 . The next sub-channel  202  is offset by 3b/2, the next by 5b/2, and so on. To the left of fc, each sub-channel  202  is offset by −b/2, −3b/2, −5b/2, etc. 
     Preferably, sub-channels  202  are non-overlapping as this allows each sub-channel to be processed independently in the receiver. To accomplish this, a roll-off factor is preferably applied to the signals in each sub-channel in a pulse-shaping step. The effect of such a pulse-shaping step is illustrated in  FIG. 2  by the non-rectangular shape of the pulses in each sub-channel  202 . Thus, the bandwidth b of each sub-channel can be represented by an equation such as the following:
 
 b =(1 +r )/ T;    (2)
         Where r=the roll-off factor; and
           T=the symbol duration.   
               

     Without the roll-off factor, i.e., b=1/T, the pulse shape would be rectangular in the frequency domain, which corresponds to a (sin x)/x function in the time domain. The time domain signal for a (sin x)/x signal  400  is shown in  FIG. 3  in order to illustrate the problems associated with a rectangular pulse shape and the need to use a roll-off factor. 
     As can be seen, main lobe  402  comprises almost all of signal  400 . But some of the signal also resides in side lobes  404 , which stretch out indefinitely in both directions from main lobe  402 . Side lobes  404  make processing signal  400  much more difficult, which increases the complexity of the receiver. Applying a roll-off factor r, as in equation (2), causes signal  400  to decay faster, reducing the number of side lobes  404 . Thus, increasing the roll-off factor decreases the length of signal  400 , i.e., signal  400  becomes shorter in time. But including the roll-off factor also decreases the available bandwidth in each sub-channel  202 . Therefore, r must be selected so as to reduce the number of side lobes  404  to a sufficient number, e.g., 15, while still maximizing the available bandwidth in each sub-channel  202 . 
     Thus, the overall bandwidth B for communication channel  200  is given by the following equation:
 
 B=N (1 +r )/ T;    (3)
 
or
 
 B=M/T;    (4)
 
Where
 
 M =(1 +r ) N.    (5)
 
     For efficiency purposes related to transmitter design, it is preferable that r is chosen so that M in equation (5) is an integer. Choosing r so that M is an integer allows for more efficient transmitters designs using, for example, Inverse Fast Fourier Transform (IFFT) techniques. Since M=N+N(r), and N is always an integer, this means that r must be chosen so that N(r) is an integer. Generally, it is preferable for r to be between 0.1 and 0.5. Therefore, if N is 16, for example, then 0.5 could be selected for r so that N(r) is an integer. Alternatively, if a value for r is chosen in the above example so that N(r) is not an integer, B can be made slightly wider than M/T to compensate. In this case, it is still preferable that r be chosen so that N(r) is approximately an integer. 
     2. Example Embodiment of a Wireless Communication System 
     With the above in mind,  FIG. 5  illustrates an example communication system  600  comprising a plurality of cells  602  that each use a common wideband communication channel to communicate with communication devices  604  within each cell  602 . The common communication channel is a wideband communication channel as described above. Each communication cell  602  is defined as the coverage area of a base station, or service access point,  606  within the cell. One such base station  606  is shown for illustration in  FIG. 5 . For purposes of this specification and the claims that follow, the term base station will be used generically to refer to a device that provides wireless access to the wireless communication system for a plurality of communication devices, whether the system is a line of sight, indoor, or outdoor system. 
     Because each cell  602  uses the same communication channel, signals in one cell  602  must be distinguishable from signals in adjacent cells  602 . To differentiate signals from one cell  602  to another, adjacent base stations  606  use different synchronization codes according to a code reuse plan. In  FIG. 6 , system  600  uses a synchronization code reuse factor of 4, although the reuse factor can vary depending on the application. 
     Preferably, the synchronization code is periodically inserted into a communication from a base station  606  to a communication device  604  as illustrated in  FIG. 6 . After a predetermined number of data packets  702 , in this case two, the particular synchronization code  704  is inserted into the information being transmitted by each base station  606 . A synchronization code is a sequence of data bits known to both the base station  606  and any communication devices  604  with which it is communicating. The synchronization code allows such a communication device  604  to synchronize its timing to that of base station  606 , which, in turn, allows device  604  to decode the data properly. Thus, in cell  1  (see lightly shaded cells  602  in  FIG. 6 ), for example, synchronization code  1  (SYNC 1 ) is inserted into data stream  706 , which is generated by base station  606  in cell  1 , after every two packets  702 ; in cell  2  SYNC 2  is inserted after every two packets  702 ; in cell  3  SYNC 3  is inserted; and in cell  4  SYNC 4  is inserted. Use of the synchronization codes is discussed in more detail below. In  FIG. 4A , an example wideband communication channel  500  for use in communication system  600  is divided into 16 sub-channels  502 , centered at frequencies f 0  to f 15 . A base station  606  at the center of each communication cell  602  transmits a single packet occupying the whole bandwidth B of wideband channel  500 . Such a packet is illustrated by packet  504  in  FIG. 4B . Packet  504  comprises sub-packets  506  that are encoded with a frequency offset corresponding to one of sub-channels  502 . Sub-packets  506  in effect define available time slots in packet  504 . Similarly, sub-channels  502  can be said to define available frequency bins in communication channel  500 . Therefore, the resources available in communication cell  602  are time slots  506  and frequency bins  502 , which can be assigned to different communication devices  604  within each cell  602 . 
     Thus, for example, frequency bins  502  and time slots  506  can be assigned to 4 different communication devices  604  within a cell  602  as shown in  FIG. 5 . Each communication device  604  receives the entire packet  504 , but only processes those frequency bins  502  and/or timeslots  506  that are assigned to it. Preferably, each device  604  is assigned non-adjacent frequency bins  502 , as in  FIG. 4A . This way, if interference corrupts the information in a portion of communication channel  500 , then the effects are spread across all devices  604  within a cell  602 . Hopefully, by spreading out the effects of interference in this manner the effects are minimized and the entire information sent to each device  604  can still be recreated from the unaffected information received in other frequency bins. For example, if interference, such as fading, corrupted the information in bins f 0 -f 4 , then each user  1 - 4  loses one packet of data. But each user potentially receives three unaffected packets from the other bins assigned to them. Hopefully, the unaffected data in the other three bins provides enough information to recreate the entire message for each user. Thus, frequency diversity can be achieved by assigning non-adjacent bins to each of multiple users. 
     Ensuring that the bins assigned to one user are separated by more than the coherence bandwidth ensures frequency diversity. As discussed above, the coherence bandwidth is approximately equal to 1/d s . For outdoor systems, where ds is typically 1 microsecond, 1/d s =1/1 microsecond=1 Mega Hertz (MHz). Thus, the non-adjacent frequency bands assigned to a user are preferably separated by at least 1 MHz. It is even more preferable, however, if the coherence bandwidth plus some guard band to ensure sufficient frequency diversity separate the non-adjacent bins assigned to each user. For example, it is preferable in certain implementations to ensure that at least 5 times the coherence bandwidth, or 5 MHz in the above example, separates the non-adjacent bins. 
     Another way to provide frequency diversity is to repeat blocks of data in frequency bins assigned to a particular user that are separated by more than the coherence bandwidth. In other words, if 4 sub-channels  202  are assigned to a user, then data block a can be repeated in the first and third sub-channels  202  and data block b can be repeated in the second and fourth sub-channels  202 , provided the sub-channels are sufficiently separated in frequency. In this case, the system can be said to be using a diversity length factor of 2. The system can similarly be configured to implement other diversity lengths, e.g., 3, 4, . . . , l. 
     It should be noted that spatial diversity can also be included depending on the embodiment. Spatial diversity can comprise transmit spatial diversity, receive spatial diversity, or both. In transmit spatial diversity, the transmitter uses a plurality of separate transmitters and a plurality of separate antennas to transmit each message. In other words, each transmitter transmits the same message in parallel. The messages are then received from the transmitters and combined in the receiver. Because the parallel transmissions travel different paths, if one is affected by fading, the others will likely not be affected. Thus, when they are combined in the receiver, the message should be recoverable even if one or more of the other transmission paths experienced severe fading. 
     Receive spatial diversity uses a plurality of separate receivers and a plurality of separate antennas to receive a single message. If an adequate distance separates the antennas, then the transmission path for the signals received by the antennas will be different. Again, this difference in the transmission paths will provide imperviousness to fading when the signals from the receivers are combined. 
     Transmit and receive spatial diversity can also be combined within a system such as system  600  so that two antennas are used to transmit and two antennas are used to receive. Thus, each base station  606  transmitter can include two antennas, for transmit spatial diversity, and each communication device  604  receiver can include two antennas, for receive spatial diversity. If only transmit spatial diversity is implemented in system  600 , then it can be implemented in base stations  606  or in communication devices  604 . Similarly, if only receive spatial diversity is included in system  600 , then it can be implemented in base stations  606  or communication devices  604 . 
     The number of communication devices  604  assigned frequency bins  502  and/or time slots  506  in each cell  602  is preferably programmable in real time. In other words, the resource allocation within a communication cell  602  is preferably programmable in the face of varying external conditions, i.e., multipath or adjacent cell interference, and varying requirements, i.e., bandwidth requirements for various users within the cell. Thus, if user  1  requires the whole bandwidth to download a large video file, for example, then the allocation of bins  502  can be adjust to provide user  1  with more, or even all, of bins  502 . Once user  1  no longer requires such large amounts of bandwidth, the allocation of bins  502  can be readjusted among all of users  1 - 4 . 
     It should also be noted that all of the bins assigned to a particular user can be used for both the forward and reverse link. Alternatively, some bins  502  can be assigned as the forward link and some can be assigned for use on the reverse link, depending on the implementation. 
     To increase capacity, the entire bandwidth B is preferably reused in each communication cell  602 , with each cell  602  being differentiated by a unique synchronization code (see discussion below). Thus, system  600  provides increased immunity to multipath and fading as well as increased bandwidth due to the elimination of frequency reuse requirements. 
     3. Synchronization 
       FIG. 6  illustrates an example embodiment of a synchronization code correlator  800  (shown in  FIG. 7 ). When a device  604  in cell  1  (see  FIG. 5 ), for example, receives an incoming communication from the cell  1  base station  606 , it compares the incoming data with SYNC 1  in correlator  800 . Essentially, the device scans the incoming data trying to correlate the data with the known synchronization code, in this case SYNC 1 . Once correlator  800  matches the incoming data to SYNC 1  it generates a correlation peak  804  at the output. Multipath versions of the data will also generate correlation peaks  806 , although these peaks  806  are generally smaller than correlation peak  804 . The device can then use the correlation peaks to perform channel estimation, which allows the device to adjust for the multipath using an equalizer. Thus, in cell  1 , if correlator  800  receives a data stream comprising SYNC 1 , it will generate correlation peaks  804  and  806 . If, on the other hand, the data stream comprises SYNC 2 , for example, then no peaks will be generated and the device will essentially ignore the incoming communication. 
     Even though a data stream that comprises SYNC 2  will not create any correlation peaks, it can create noise in correlator  800  that can prevent detection of correlation peaks  804  and  806 . Several steps can be taken to prevent this from occurring. One way to minimize the noise created in correlator  800  by signals from adjacent cells  602 , is to configure system  600  so that each base station  606  transmits at the same time. This way, the synchronization codes can preferably be generated in such a manner that only the synchronization codes  704  of adjacent cell data streams, e.g., streams  708 ,  710 , and  712 , as opposed to packets  702  within those streams, will interfere with detection of the correct synchronization code  704 , e.g., SYNC 1 . The synchronization codes can then be further configured to eliminate or reduce the interference. 
     For example, the noise or interference caused by an incorrect synchronization code is a function of the cross correlation of that synchronization code with respect to the correct code. The better the cross correlation between the two, the lower the noise level. When the cross correlation is ideal, then the noise level will be virtually zero as illustrated in  FIG. 8  by noise level  902 . Therefore, a preferred embodiment of system  600  uses synchronization codes that exhibit ideal cross correlation, i.e., zero. Preferably, the ideal cross correlation of the synchronization codes covers a period l that is sufficient to allow accurate detection of multipath  906  as well as multipath correlation peaks  904 . This is important so that accurate channel estimation and equalization can take place. Outside of period l, the noise level  908  goes up, because the data in packets  702  is random and will exhibit low cross correlation with the synchronization code, e.g., SYNC 1 . Preferably, period l is actually slightly longer then the multipath length in order to ensure that the multipath can be detected. 
     a. Synchronization Code Generation 
     Conventional systems use orthogonal codes to achieve cross correlation in correlator  800 . In system  600  for example, SYNC 1 , SYNC 2 , SYNC 3 , and SYNC 4 , corresponding to cells  1 - 4  (see lightly shaded cells  602  of  FIG. 5 ) respectively, will all need to be generated in such a manner that they will have ideal cross correlation with each other. In one embodiment, if the data streams involved comprise high and low data bits, then the value “1” can be assigned to the high data bits and “−1” to the low data bits. Orthogonal data sequences are then those that produce a “0” output when they are exclusively ORed (XORed) together in correlator  800 . The following example illustrates this point for orthogonal sequences 1 and 2: 
     
       
         
           
             
               
                 
                   
                     sequence 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       : 
                     
                   
                 
                 
                   
                     11 
                     - 
                     11 
                   
                 
               
               
                 
                   
                     sequence 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       : 
                     
                   
                 
                 
                   
                     111 
                     - 
                     1 
                   
                 
               
               
                 
                   
                       
                   
                 
                 
                   
                     11 
                     - 
                     1 
                     - 
                     1 
                   
                 
               
             
             = 
             0 
           
         
       
     
     Thus, when the results of XORing each bit pair are added, the result is “0”. 
     But in system  600 , for example, each code must have ideal, or zero, cross correlation with each of the other codes used in adjacent cells  602 . Therefore, in one example embodiment of a method for generating synchronization codes exhibiting the properties described above, the process begins by selecting a “perfect sequence” to be used as the basis for the codes. A perfect sequence is one that when correlated with itself produces a number equal to the number of bits in the sequence. For example: 
     
       
         
           
             
               Perfect 
               ⁢ 
               
                   
               
               ⁢ 
               sequence 
               ⁢ 
               
                   
               
               ⁢ 
               1 
               ⁢ 
               
                 : 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   
                     
                       
                         11 
                         - 
                         11 
                       
                     
                   
                   
                     
                       
                         11 
                         - 
                         11 
                       
                     
                   
                 
                 1111 
               
             
             = 
             4 
           
         
       
     
     But each time a perfect sequence is cyclically shifted by one bit, the new sequence is orthogonal with the original sequence. Thus, for example, if perfect sequence 1 is cyclically shifted by one bit and then correlated with the original, the correlation produces a “0” as in the following example; 
     
       
         
           
             
               Perfect 
               ⁢ 
               
                   
               
               ⁢ 
               sequence 
               ⁢ 
               
                   
               
               ⁢ 
               1 
               ⁢ 
               
                 : 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   
                     
                       
                         11 
                         - 
                         11 
                       
                     
                   
                   
                     
                       
                         111 
                         - 
                         1 
                       
                     
                   
                 
                 
                   11 
                   - 
                   1 
                   - 
                   1 
                 
               
             
             = 
             0 
           
         
       
     
     If the perfect sequence 1 is again cyclically shifted by one bit, and again correlated with the original, then it will produce a “0”. In general, you can cyclically shift a perfect sequence by any number of bits up to its length and correlate the shifted sequence with the original to obtain a “0”. 
     Once a perfect sequence of the correct length is selected, the first synchronization code is preferably generated in one embodiment by repeating the sequence 4 times. Thus, if perfect sequence 1 is being used, then a first synchronization code y would be the following:
 
y=1 1−1 1 1 1−1 1 1 1−1 1 1 1−1 1.
 
     Or in generic form:
 
 y=x (0) x (1) x (2) x (3) x (0) x (1) x (2) x (3) x (0) x (1) x (2) x (3) x (0) x (1) x (2) x (3).
 
     For a sequence of length L:
 
 y=x (0) x (1) . . .  x ( L ) x (0) x (1) . . .  x ( L ) x (0) x (1) . . .  x ( L ) x (0) x (1) . . .  x ( L )
 
     Repeating the perfect sequence allows correlator  800  a better opportunity to detect the synchronization code and allows generation of other uncorrelated frequencies as well. Repeating has the effect of sampling in the frequency domain. This effect is illustrated by the graphs in  FIG. 9 . Thus, in TRACE  1 , which corresponds to synchronization code y, a sample  1002  is generated every fourth sample bin  1000 . Each sample bin is separated by 1/(4L×T), where T is the symbol duration. Thus, in the above example, where L=4, each sample bin is separated by 1/(16×T) in the frequency domain. TRACES  2 - 4  illustrate the next three synchronization codes. As can be seen, the samples for each subsequent synchronization code are shifted by one sample bin relative to the samples for the previous sequence. Therefore, none of the sequences interfere with each other. 
     To generate the subsequent sequences, corresponding to TRACES  2 - 4 , sequence y must be shifted in frequency. This can be accomplished using the following equation:
 
 z   r ( m )= y ( m )*exp( j* 2 *π*r*m /( n*L )),   (5)
 
     for r=1 to L (# of sequences) and m=0 to 4*L−1 (time); and 
     where: Z r (m)=each subsequent sequence;
         y(m)=the first sequence; and   n=the number of times the sequence is repeated.       

     It will be understood that multiplying by an exp(j2π(r*m/N)) factor, where N is equal to the number of times the sequence is repeated n multiplied by the length of the underlying perfect sequence L, in the time domain results in a shift in the frequency domain. Equation (5) results in the desired shift as illustrated in  FIG. 9  for each of synchronization codes  2 - 4 , relative to synchronization code  1 . The final step in generating each synchronization code is to append the copies of the last M samples, where M is the length of the multipath, to the front of each code. This is done to make the convolution with the multipath cyclic and to allow easier detection of the multipath. 
     It should be noted that synchronization codes can be generated from more than one perfect sequence using the same methodology. For example, a perfect sequence can be generated and repeated four times and then a second perfect sequence can be generated and repeated four times to get a n factor equal to eight. The resulting sequence can then be shifted as described above to create the synchronization codes. 
     b. Signal Measurements Using Synchronization Codes 
     Therefore, when a communication device is at the edge of a cell, it will receive signals from multiple base stations and, therefore, will be decoding several synchronization codes at the same time. This can be illustrated with the help of  FIG. 10 , which illustrates another example embodiment of a wireless communication system  1100  comprising communication cells  1102 ,  1104 , and  1106  as well as communication device  1108 , which is in communication with base station  1110  of cell  1102  but also receiving communication from base stations  1112  and  1114  of cells  1104  and  1106 , respectively. 
     If communications from base station  1110  comprise synchronization code SYNC 1  and communications from base station  1112  and  1114  comprise SYNC 2  and SYNC 3  respectively, then device  1108  will effectively receive the sum of these three synchronization codes. This is because, as explained above, base stations  1110 ,  1112 , and  1114  are configured to transmit at the same time. Also, the synchronization codes arrive at device  1108  at almost the same time because they are generated in accordance with the description above. 
     Again as described above, the synchronization codes SYNC 1 , SYNC 2 , and SYNC 3  exhibit ideal cross correlation. Therefore, when device  1108  correlates the sum x of codes SYNC 1 , SYNC 2 , and SYNC 3 , the latter two will not interfere with proper detection of SYNC 1  by device  1108 . Importantly, the sum x can also be used to determine important signal characteristics, because the sum x is equal to the sum of the synchronization code signal in accordance with the following equation:
 
x=SYNC1+SYNC2+SYNC3.   (6)
 
     Therefore, when SYNC 1  is removed, the sum of SYNC 2  and SYNC 3  is left, as shown in the following:
 
 x −SYNC1=SYNC2+SYNC3.   (7)
 
     The energy computed from the sum (SYNC 2 +SYNC 3 ) is equal to the noise or interference seen by device  1108 . Since the purpose of correlating the synchronization code in device  1106  is to extract the energy in SYNC  1 , device  1108  also has the energy in the signal from base station  1110 , i.e., the energy represented by SYNC 1 . Therefore, device  1106  can use the energy of SYNC 1  and of (SYNC 2 +SYNC 3 ) to perform a signal-to-interference measurement for the communication channel over which it is communicating with base station  1110 . The result of the measurement is preferably a signal-to-interference ratio (SIR). The SIR measurement can then be communicated back to base station  1110  for purposes that will be discussed below. 
     The ideal cross correlation of the synchronization codes, also allows device  1108  to perform extremely accurate determinations of the Channel Impulse Response (CIR), or channel estimation, from the correlation produced by correlator  800 . This allows for highly accurate equalization using low cost, low complexity equalizers, thus overcoming a significant draw back of conventional systems. 
     4. Sub-Channel Assignments 
     As mentioned, the SIR as determined by device  1108  can be communicated back to base station  1110  for use in the assignment of channels  502 . In one embodiment, due to the fact that each sub-channel  502  is processed independently, the SIR for each sub-channel  502  can be measured and communicated back to base station  1110 . In such an embodiment, therefore, sub-channels  502  can be divided into groups and a SIR measurement for each group can be sent to base station  1110 . This is illustrated in  FIG. 11A , which shows a wideband communication channel  1200  segmented into sub-channels f 0  to f 15 . Sub-channels f 0  to f 15  are then grouped into 8 groups G 1  to G 8 . Thus, in one embodiment, device  1108  and base station  1110  communicate over a channel such as channel  1200 . 
     Sub-channels in the same group are preferably separated by as many sub-channels as possible to ensure diversity. In  FIG. 11A  for example, sub-channels within the same group are 7 sub-channels apart, e.g., group G 1  comprises f 0  and f 8 . Device  1102  reports a SIR measurement for each of the groups G 1  to G 8 . These SIR measurements are preferably compared with a threshold value to detemine which sub-channels groups are useable by device  1108 . This comparison can occur in device  1108  or base station  1110 . If it occurs in device  1108 , then device  1108  can simply report to base station  1110  which sub-channels groups are useable by device  1108 . 
     SIR reporting will be simultaneously occurring for a plurality of devices within cell  1102 . Thus,  FIG. 11B  illustrates the situation where two communication devices corresponding to User  1  and User  2  report SIR levels above the threshold for groups G 1 , G 3 , G 5 , and G 7 . Base station  1110  preferably then assigns sub-channel groups to User  1  and User  2  based on the SIR reporting as illustrated in  FIG. 11B . When assigning the “good” sub-channel groups to User  1  and User  2 , base station  1110  also preferably assigns them based on the principles of frequency diversity. In  FIG. 11B , therefore, User  1  and User  2  are alternately assigned every other “good” sub-channel. 
     The assignment of sub-channels in the frequency domain is equivalent to the assignment of time slots in the time domain. Therefore, as illustrated in  FIG. 12 , two users, User  1  and User  2 , receive packet  1302  transmitted over communication channel  1200 .  FIG. 12  also illustrated the sub-channel assignment of  FIG. 11B . While  FIGS. 11 and 12  illustrate sub-channel/time slot assignment based on SIR for two users, the principles illustrated can be extended for any number of users. Thus, a packet within cell  1102  can be received by 3 or more users. Although, as the number of available sub-channels is reduced due to high SIR, so is the available bandwidth. In other words, as available channels are reduced, the number of users that can gain access to communication channel  1200  is also reduced. 
     Poor SIR can be caused for a variety of reasons, but frequently it results from a device at the edge of a cell receiving communication signals from adjacent cells. Because each cell is using the same bandwidth B, the adjacent cell signals will eventually raise the noise level and degrade SIR for certain sub-channels. In certain embodiments, therefore, sub-channel assignment can be coordinated between cells, such as cells  1102 ,  1104 , and  1106  in  FIG. 10 , in order to prevent interference from adjacent cells. 
     Thus, if communication device  1108  is near the edge of cell  1102 , and device  1118  is near the edge of cell  1106 , then the two can interfere with each other. As a result, the SIR measurements that device  1108  and  1118  report back to base stations  1110  and  1114 , respectively, will indicate that the interference level is too high. Base station  1110  can then be configured to assign only the odd groups, i.e., G 1 , G 3 , G 5 , etc., to device  1108 , while base station  1114  can be configured to assign the even groups to device  1118 . The two devices  1108  and  1118  will then not interfere with each other due to the coordinated assignment of sub-channel groups. 
     Assigning the sub-channels in this manner reduces the overall bandwidth available to devices  1108  and  1118 , respectively. In this case the bandwidth is reduced by a factor of two. But it should be remembered that devices operating closer to each base station  1110  and  1114 , respectively, will still be able to use all channels if needed. Thus, it is only devices, such as device  1108 , that are near the edge of a cell that will have the available bandwidth reduced. Contrast this with a CDMA system, for example, in which the bandwidth for all users is reduced, due to the spreading techniques used in such systems, by approximately a factor of 10 at all times. It can be seen, therefore, that the systems and methods for wireless communication over a wide bandwidth channel using a plurality of sub-channels not only improves the quality of service, but can also increase the available bandwidth significantly. 
     When there are three devices  1108 ,  1118 , and  1116  near the edge of their respective adjacent cells  1102 ,  1104 , and  1106 , the sub-channels can be divided by three. Thus, device  1108 , for example, can be assigned groups G 1 , G 4 , etc., device  1118  can be assigned groups G 2 , G 5 , etc., and device  1116  can be assigned groups G 3 , G 6 , etc. In this case the available bandwidth for these devices, i.e., devices near the edges of cells  1102 ,  1104 , and  1106 , is reduced by a factor of 3, but this is still better than a CDMA system, for example. 
     The manner in which such a coordinated assignment of sub-channels can work is illustrated by the flow chart in  FIG. 13 . First in step  1402 , a communication device, such as device  1108 , reports the SIR for all sub-channel groups G 1  to G 8 . The SIRs reported are then compared, in step  1404 , to a threshold to determine if the SIR is sufficiently low for each group. Alternatively, device  1108  can make the determination and simply report which groups are above or below the SIR threshold. If the SIR levels are good for each group, then base station  1110  can make each group available to device  1108 , in step  1406 . Periodically, device  1108  preferably measures the SIR level and updates base station  1110  in case the SIR as deteriorated. For example, device  1108  may move from near the center of cell  1102  toward the edge, where interference from an adjacent cell may affect the SIR for device  1108 . 
     If the comparison in step  1404  reveals that the SIR levels are not good, then base station  1110  can be preprogrammed to assign either the odd groups or the even groups only to device  1108 , which it will do in step  1408 . Device  1108  then reports the SIR measurements for the odd or even groups it is assigned in step  1410 , and they are again compared to a SIR threshold in step  1412 . 
     It is assumed that the poor SIR level is due to the fact that device  1108  is operating at the edge of cell  1102  and is therefore being interfered with by a device such as device  1118 . But device  1108  will be interfering with device  1118  at the same time. Therefore, the assignment of odd or even groups in step  1408  preferably corresponds with the assignment of the opposite groups to device  1118 , by base station  1114 . Accordingly, when device  1108  reports the SIR measurements for whichever groups, odd or even, are assigned to it, the comparison in step  1410  should reveal that the SIR levels are now below the threshold level. Thus, base station  1110  makes the assigned groups available to device  1108  in step  1414 . Again, device  1108  preferably periodically updates the SIR measurements by returning to step  1402 . 
     It is possible for the comparison of step  1410  to reveal that the SIR levels are still above the threshold, which should indicate that a third device, e.g., device  1116  is still interfering with device  1108 . In this case, base station  1110  can be preprogrammed to assign every third group to device  1108  in step  1416 . This should correspond with the corresponding assignments of non-interfering channels to devices  1118  and  1116  by base stations  1114  and  1112 , respectively. Thus, device  1108  should be able to operate on the sub-channel groups assigned, i.e., G 1 , G 4 , etc., without undue interference. Again, device  1108  preferably periodically updates the SIR measurements by returning to step  1402 . Optionally, a third comparison step (not shown) can be implemented after step  1416 , to ensure that the groups assigned to device  1408  posses an adequate SIR level for proper operation. Moreover, if there are more adjacent cells, i.e., if it is possible for devices in a 4 th  or even a 5 th  adjacent cell to interfere with device  1108 , then the process of  FIG. 13  would continue and the sub-channel groups would be divided even further to ensure adequate SIR levels on the sub-channels assigned to device  1108 . 
     Even though the process of  FIG. 13  reduces the bandwidth available to devices at the edge of cells  1102 ,  1104 , and  1106 , the SIR measurements can be used in such a manner as to increase the data rate and therefore restore or even increase bandwidth. To accomplish this, the transmitters and receivers used in base stations  1102 ,  1104 , and  1106 , and in devices in communication therewith, e.g., devices  1108 ,  1114 , and  1116  respectively, must be capable of dynamically changing the symbol mapping schemes used for some or all of the sub-channel. For example, in some embodiments, the symbol mapping scheme can be dynamically changed among BPSK, QPSK, 8PSK, 16QAM, 32QAM, etc. As the symbol mapping scheme moves higher, i.e., toward 32QAM, the SIR level required for proper operation moves higher, i.e., less and less interference can be withstood. Therefore, once the SIR levels are determined for each group, the base station, e.g., base station  1110 , can then determine what symbol mapping scheme can be supported for each sub-channel group and can change the modulation scheme accordingly. Device  1108  must also change the symbol mapping scheme to correspond to that of the base stations. The change can be effected for all groups uniformly, or it can be effected for individual groups. Moreover, the symbol mapping scheme can be changed on just the forward link, just the reverse link, or both, depending on the embodiment. 
     Thus, by maintaining the capability to dynamically assign sub-channels and to dynamically change the symbol mapping scheme used for assigned sub-channels, the systems and methods described herein provide the ability to maintain higher available bandwidths with higher performance levels than conventional systems. To fully realize the benefits described, however, the systems and methods described thus far must be capable of implementation in a cost effect and convenient manner. Moreover, the implementation must include reconfigurability so that a single device can move between different types of communication systems and still maintain optimum performance in accordance with the systems and methods described herein. The following descriptions detail example high level embodiments of hardware implementations configured to operate in accordance with the systems and methods described herein in such a manner as to provide the capability just described above. 
     5. Sample Transmitter Embodiments 
       FIG. 14  is logical block diagram illustrating an example embodiment of a transmitter  1500  configured for wireless communication in accordance with the systems and methods described above. The transmitter could, for example be within a base station, e.g., base station  606 , or within a communication device, such as device  604 . Transmitter  1500  is provided to illustrate logical components that can be included in a transmitter configured in accordance with the systems and methods described herein. It is not intended to limit the systems and methods for wireless communication over a wide bandwidth channel using a plurality of sub-channels to any particular transmitter configuration or any particular wireless communication system. 
     With this in mind, it can be seen that transmitter  1500  comprises a serial-to-parallel converter  1504  configured to receive a serial data stream  1502  comprising a data rate R. Serial-to-parallel converter  1504  converts data stream  1502  into N parallel data streams  1504 , where N is the number of sub-channels  202 . It should be noted that while the discussion that follows assumes that a single serial data stream is used, more than one serial data stream can also be used if required or desired. In any case, the data rate of each parallel data stream  1504  is then R/N. Each data stream  1504  is then sent to a scrambler, encoder, and interleaver block  1506 . Scrambling, encoding, and interleaving are common techniques implemented in many wireless communication transmitters and help to provide robust, secure communication. Examples of these techniques will be briefly explained for illustrative purposes. 
     Scrambling breaks up the data to be transmitted in an effort to smooth out the spectral density of the transmitted data. For example, if the data comprises a long string of “1”s, there will be a spike in the spectral density. This spike can cause greater interference within the wireless communication system. By breaking up the data, the spectral density can be smoothed out to avoid any such peaks. Often, scrambling is achieved by XORing the data with a random sequence. 
     Encoding, or coding, the parallel bit streams  1504  can, for example, provide Forward Error Correction (FEC). The purpose of FEC is to improve the capacity of a communication channel by adding some carefully designed redundant information to the data being transmitted through the channel. The process of adding this redundant information is known as channel coding. Convolutional coding and block coding are the two major forms of channel coding. Convolutional codes operate on serial data, one or a few bits at a time. Block codes operate on relatively large (typically, up to a couple of hundred bytes) message blocks. There are a variety of useful convolutional and block codes, and a variety of algorithms for decoding the received coded information sequences to recover the original data. For example, convolutional encoding or turbo coding with Viterbi decoding is a FEC technique that is particularly suited to a channel in which the transmitted signal is corrupted mainly by additive white gaussian noise (AWGN) or even a channel that simply experiences fading. 
     Convolutional codes are usually described using two parameters: the code rate and the constraint length. The code rate, k/n, is expressed as a ratio of the number of bits into the convolutional encoder (k) to the number of channel symbols (n) output by the convolutional encoder in a given encoder cycle. A common code rate is ½, which means that 2 symbols are produced for every 1-bit input into the coder. The constraint length parameter, K, denotes the “length” of the convolutional encoder, i.e. how many k-bit stages are available to feed the combinatorial logic that produces the output symbols. Closely related to K is the parameter m, which indicates how many encoder cycles an input bit is retained and used for encoding after it first appears at the input to the convolutional encoder. The m parameter can be thought of as the memory length of the encoder. 
     Interleaving is used to reduce the effects of fading. Interleaving mixes up the order of the data so that if a fade interferes with a portion of the transmitted signal, the overall message will not be effected. This is because once the message is de-interleaved and decoded in the receiver, the data lost will comprise non-contiguous portions of the overall message. In other words, the fade will interfere with a contiguous portion of the interleaved message, but when the message is de-interleaved, the interfered with portion is spread throughout the overall message. Using techniques such as FEC, the missing information can then be filled in, or the impact of the lost data may just be negligible. 
     After blocks  1506 , each parallel data stream  1504  is sent to symbol mappers  1508 . Symbol mappers  1508  apply the requisite symbol mapping, e.g., BPSK, QPSK, etc., to each parallel data stream  1504 . Symbol mappers  1508  are preferably programmable so that the modulation applied to parallel data streams can be changed, for example, in response to the SIR reported for each sub-channel  202 . It is also preferable, that each symbol mapper  1508  be separately programmable so that the optimum symbol mapping scheme for each sub-channel can be selected and applied to each parallel data stream  1504 . 
     After symbol mappers  1508 , parallel data streams  1504  are sent to modulators  1510 . Important aspects and features of example embodiments of modulators  1510  are described below. After modulators  1510 , parallel data streams  1504  are sent to summer  1512 , which is configured to sum the parallel data streams and thereby generate a single serial data stream  1518  comprising each of the individually processed parallel data streams  1504 . Serial data stream  1518  is then sent to radio module  1512 , where it is modulated with an RF carrier, amplified, and transmitted via antenna  1516  according to known techniques. 
     The transmitted signal occupies the entire bandwidth B of communication channel  100  and comprises each of the discrete parallel data streams  1504  encoded onto their respective sub-channels  102  within bandwidth B. Encoding parallel data streams  1504  onto the appropriate sub-channels  102  requires that each parallel data stream  1504  be shifted in frequency by an appropriate offset. This is achieved in modulator  1510 . 
       FIG. 15  is a logical block diagram of an example embodiment of a modulator  1600  in accordance with the systems and methods described herein. Importantly, modulator  1600  takes parallel data streams  1602  performs Time Division Modulation (TDM) or Frequency Division Modulation (FDM) on each data stream  1602 , filters them using filters  1612 , and then shifts each data stream in frequency using frequency shifter  1614  so that they occupy the appropriate sub-channel. Filters  1612  apply the required pulse shaping, i.e., they apply the roll-off factor described in section  1 . The frequency shifted parallel data streams  1602  are then summed and transmitted. Modulator  1600  can also include rate controller  1604 , frequency encoder  1606 , and interpolators  1610 . All of the components shown in  FIG. 15  are described in more detail in the following paragraphs and in conjunction with  FIGS. 16-22 . 
       FIG. 16  illustrates one example embodiment of a rate controller  1700  in accordance with the systems and methods described herein. Rate control  1700  is used to control the data rate of each parallel data stream  1602 . In rate controller  1700 , the data rate is halved by repeating data streams d( 0 ) to d( 7 ), for example, producing streams a( 0 ) to a( 15 ) in which a( 0 ) is the same as a( 8 ), a( 1 ) is the same as a( 9 ), etc.  FIG. 16  also illustrates that the effect of repeating the data streams in this manner is to take the data streams that are encoded onto the first 8 sub-channels  1702 , and duplicate them on the next 8 sub-channels  1702 . As can be seen, 7 sub-channels separate sub-channels  1702  comprising the same, or duplicate, data streams. Thus, if fading effects one sub-channel  1702 , for example, the other sub-channels  1702  carrying the same data will likely not be effected, i.e., there is frequency diversity between the duplicate data streams. So by sacrificing data rate, in this case half the data rate, more robust transmission is achieved. Moreover, the robustness provided by duplicating the data streams d( 0 ) to d( 7 ) can be further enhanced by applying scrambling to the duplicated data streams via scramblers  1708 . 
     It should be noted that the data rate can be reduced by more than half, e.g., by four or more. Alternatively, the data rate can also be reduced by an amount other than half. For example if information from n data stream is encoded onto m sub-channels, where m&gt;n. Thus, to decrease the rate by ⅔, information from one data stream can be encoded on a first sub-channel, information from a second data stream can be encoded on a second data channel, and the sum or difference of the two data streams can be encoded on a third channel. In which case, proper scaling will need to be applied to the power in the third channel. Otherwise, for example, the power in the third channel can be twice the power in the first two. 
     Preferably, rate controller  1700  is programmable so that the data rate can be changed responsive to certain operational factors. For example, if the SIR reported for sub-channels  1702  is low, then rate controller  1700  can be programmed to provide more robust transmission via repetition to ensure that no data is lost due to interference. Additionally, different types of wireless communication system, e.g., indoor, outdoor, line-of-sight, may require varying degrees of robustness. Thus, rate controller  1700  can be adjusted to provide the minimum required robustness for the particular type of communication system. This type of programmability not only ensures robust communication, it can also be used to allow a single device to move between communication systems and maintain superior performance. 
       FIG. 17  illustrates an alternative example embodiment of a rate controller  1800  in accordance with the systems and methods described. In rate controller  1800  the data rate is increased instead of decreased. This is accomplished using serial-to-parallel converters  1802  to convert each data streams d( 0 ) to d( 15 ), for example, into two data streams. Delay circuits  1804  then delay one of the two data streams generated by each serial-to-parallel converter  1802  by ½ a symbol. Thus, data streams d( 0 ) to d( 15 ) are transformed into data streams a( 0 ) to a( 31 ). The data streams generated by a particular serial-to-parallel converter  1802  and associate delay circuit  1804  must then be summed and encoded onto the appropriate sub-channel. For example, data streams a( 0 ) and a( 1 ) must be summed and encoded onto the first sub-channel. Preferably, the data streams are summed subsequent to each data stream being pulsed shaped by a filter  1612 . 
     Thus, rate controller  1604  is preferably programmable so that the data rate can be increased, as in rate controller  1800 , or decreased, as in rate controller  1700 , as required by a particular type of wireless communication system, or as required by the communication channel conditions or sub-channel conditions. In the event that the data rate is increased, filters  1612  are also preferably programmable so that they can be configured to apply pulse shapping to data streams a( 0 ) to a( 31 ), for example, and then sum the appropriate streams to generate the appropriate number of parallel data streams to send to frequency shifter  1614 . 
     The advantage of increasing the data rate in the manner illustrated in  FIG. 17  is that higher symbol mapping rates can essentially be achieved, without changing the symbol mapping used in symbol mappers  1508 . Once the data streams are summed, the summed streams are shifted in frequency so that they reside in the appropriate sub-channel. But because the number of bits per each symbol has been doubled, the symbol mapping rate has been doubled. Thus, for example, a 4QAM symbol mapping can be converted to a 16QAM symbol mapping, even if the SIR is too high for 16QAM symbol mapping to otherwise be applied. In other words, programming rate controller  1800  to increase the data rate in the manner illustrated in  FIG. 17  can increase the symbol mapping even when channel conditions would otherwise not allow it, which in turn can allow a communication device to maintain adequate or even superior performance regardless of the type of communication system. 
     The draw back to increasing the data rate as illustrated in  FIG. 17  is that interference is increased, as is receiver complexity. The former is due to the increased amount of data. The latter is due to the fact that each symbol cannot be processed independently because of the ½ symbol overlap. Thus, these concerns must be balanced against the increase symbol mapping ability when implementing a rate controller such as rate controller  1800 . 
       FIG. 18  illustrates one example embodiment of a frequency encoder  1900  in accordance with the systems and methods described herein. Similar to rate encoding, frequency encoding is preferably used to provide increased communication robustness. In frequency encoder  1900  the sum or difference of multiple data streams are encoded onto each sub-channel. This is accomplished using adders  1902  to sum data streams d( 0 ) to d( 7 ) with data streams d( 8 ) to d( 15 ), respectively, while adders  1904  subtract data streams d( 0 ) to d( 7 ) from data streams d( 8 ) to d( 15 ), respectively, as shown. Thus, data streams a( 0 ) to a( 15 ) generated by adders  1902  and  1904  comprise information related to more than one data streams d( 0 ) to d( 15 ). For example, a( 0 ) comprises the sum of d( 0 ) and d( 8 ), i.e., d( 0 )+d( 8 ), while a( 8 ) comprises d( 8 )−d( 0 ). Therefore, if either a( 0 ) or a( 8 ) is not received due to fading, for example, then both of data streams d( 0 ) and d( 8 ) can still be retrieved from data stream a( 8 ). 
     Essentially, the relationship between data stream d( 0 ) to d( 15 ) and a( 0 ) to a( 15 ) is a matrix relationship. Thus, if the receiver knows the correct matrix to apply, it can recover the sums and differences of d( 0 ) to d( 15 ) from a( 0 ) to a( 15 ). Preferably, frequency encoder  1900  is programmable, so that it can be enabled and disabled in order to provided robustness when required. Preferable, adders  1902  and  1904  are programmable also so that different matrices can be applied to d( 0 ) to d( 15 ). 
     After frequency encoding, if it is included, data streams  1602  are sent to TDM/FDM blocks  1608 . TDM/FDM blocks  1608  perform TDM or FDM on the data streams as required by the particular embodiment.  FIG. 19  illustrates an example embodiment of a TDM/FDM block  2000  configured to perform TDM on a data stream. TDM/FDM block  2000  is provided to illustrate the logical components that can be included in a TDM/FDM block configured to perform TDM on a data stream. Depending on the actual implementation, some of the logical components may or may not be included. TDM/FDM block  2000  comprises a sub-block repeater  2002 , a sub-block scrambler  2004 , a sub-block terminator  2006 , a sub-block repeater  2008 , and a sync inserter  2010 . 
     Sub-block repeater  2002  is configured to receive a sub-block of data, such as block  2012  comprising bits a( 0 ) to a( 3 ) for example. Sub-block repeater is then configured to repeat block  2012  to provide repetition, which in turn leads to more robust communication. Thus, sub-block repeater  2002  generates block  2014 , which comprises 2 blocks  2012 . Sub-block scrambler  2004  is then configured to receive block  2014  and to scramble it, thus generating block  2016 . One method of scrambling can be to invert half of block  2014  as illustrated in block  2016 . But other scrambling methods can also be implemented depending on the embodiment. 
     Sub-block terminator  2006  takes block  2016  generated by sub-block scrambler  2004  and adds a termination block  2034  to the front of block  2016  to form block  2018 . Termination block  2034  ensures that each block can be processed independently in the receiver. Without termination block  2034 , some blocks may be delayed due to multipath, for example, and they would therefore overlap part of the next block of data. But by including termination block  2034 , the delayed block can be prevented from overlapping any of the actual data in the next block. 
     Termination block  2034  can be a cyclic prefix termination  2036 . A cyclic prefix termination  2036  simply repeats the last few symbols of block  2018 . Thus, for example, if cyclic prefix termination  2036  is three symbols long, then it would simply repeat the last three symbols of block  2018 . Alternatively, termination block  2034  can comprise a sequence of symbols that are known to both the transmitter and receiver. The selection of what type of block termination  2034  to use can impact what type of equalizer is used in the receiver. Therefore, receiver complexity and choice of equalizers must be considered when determining what type of termination block  2034  to use in TDM/FDM block  2000 . 
     After sub-block terminator  2006 , TDM/FDM block  2000  can include a sub-block repeater  2008  configured to perform a second block repetition step in which block  2018  is repeated to form block  2020 . In certain embodiments, sub-block repeater can be configured to perform a second block scrambling step as well. After sub-block repeater  2008 , if included, TDM/FDM block  2000  comprises a sync inserter  210  configured to periodically insert an appropriate synchronization code  2032  after a predetermined number of blocks  2020  and/or to insert known symbols into each block. The purpose of synchronization code  2032  is discussed in section  3 . 
       FIG. 20 , on the other hand, illustrates an example embodiment of a TDM/FDM block  2100  configured for FDM, which comprises sub-block repeater  2102 , sub-block scrambler  2104 , block coder  2106 , sub-block transformer  2108 , sub-block terminator  2110 , and sync inserter  2112 . As with TDM/FDM block  2000 , sub-block repeater  2102  repeats block  2114  and generates block  2116 . Sub-block scrambler then scrambles block  2116 , generating block  2118 . Sub-block coder  2106  takes block  2118  and codes it, generating block  2120 . Coding block correlates the data symbols together and generates symbols b. This requires joint demodulation in the receiver, which is more robust but also more complex. Sub-block transformer  2108  then performs a transformation on block  2120 , generating block  2122 . Preferably, the transformation is an IFFT of block  2120 , which allows for more efficient equalizers to be used in the receiver. Next, sub-block terminator  2110  terminates block  2122 , generating block  2124  and sync inserter  2112  periodically inserts a synchronization code  2126  after a certain number of blocks  2124  and/or insert known symbols into each block. Preferably, sub-block terminator  2110  only uses cyclic prefix termination as described above. Again this allows for more efficient receiver designs. 
     TDM/FDM block  2100  is provided to illustrate the logical components that can be included in a TDM/FDM block configured to perform FDM on a data stream. Depending on the actual implementation, some of the logical components may or may not be included. Moreover, TDM/FDM block  2000  and  2100  are preferably programmable so that the appropriate logical components can be included as required by a particular implementation. This allows a device that incorporates one of blocks  2000  or  2100  to move between different systems with different requirements. Further, it is preferable that TDM/FDM block  1608  in  FIG. 15  be programmable so that it can be programmed to perform TDM, such as described in conjunction with block  2000 , or FDM, such as described in conjunction with block  2100 , as required by a particular communication system. 
     After TDM/FDM blocks  1608 , in  FIG. 15 , the parallel data streams are preferably passed to interpolators  1610 . 
     After Interpolators  1610 , the parallel data streams are passed to filters  1612 , which apply the pulse shapping described in conjunction with the roll-off factor of equation (2) in section  1 . Then the parallel data streams are sent to frequency shifter  1614 , which is configured to shift each parallel data stream by the frequency offset associated with the sub-channel to which the particular parallel data stream is associated. 
       FIG. 21  illustrates an example embodiment of a frequency shifter  2200  in accordance with the systems and methods described herein. As can be seen, frequency shifter  2200  comprises multipliers  2202  configured to multiply each parallel data stream by the appropriate exponential to achieve the required frequency shift. Each exponential is of the form: exp(j2πf c nT/rM), where c is the corresponding sub-channel, e.g., c=0 to N−1, and n is time. Preferably, frequency shifter  1614  in  FIG. 5  is programmable so that various channel/sub-channel configurations can be accommodated for various different systems. Alternatively, an IFFT block can replace shifter  1614  and filtering can be done after the IFFT block. This type of implementation can be more efficient depending on the implementation. 
     After the parallel data streams are shifted, they are summed, e.g., in summer  1512  of  FIG. 14 . The summed data stream is then transmitted using the entire bandwidth B of the communication channel being used. But the transmitted data stream also comprises each of the parallel data streams shifted in frequency such that they occupy the appropriate sub-channel. Thus, each sub-channel may be assigned to one user, or each sub-channel may carry a data stream intended for different users. The assignment of sub-channels is described in section  3   b . Regardless of how the sub-channels are assigned, however, each user will receive the entire bandwidth, comprising all the sub-channels, but will only decode those sub-channels assigned to the user. 
     6. Sample Receiver Embodiments 
       FIG. 22  illustrates an example embodiment of a receiver  2300  that can be configured in accordance with the present invention. Receiver  2300  comprises an antenna  2302  configured to receive a message transmitted by a transmitter, such as transmitter  1500 . Thus, antenna  2302  is configured to receive a wide band message comprising the entire bandwidth B of a wide band channel that is divided into sub-channels of bandwidth b. As described above, the wide band message comprises a plurality of messages each encoded onto each of a corresponding sub-channel. All of the sub-channels may or may not be assigned to a device that includes receiver  2300 ; Therefore, receiver  2300  may or may not be required to decode all of the sub-channels. 
     After the message is received by antenna  2300 , it is sent to radio receiver  2304 , which is configured to remove the carrier associated with the wide band communication channel and extract a baseband signal comprising the data stream transmitted by the transmitter. The baseband signal is then sent to correlator  2306  and demodulator  2308 . Correlator  2306  is configured to correlated with a synchronization code inserted in the data stream as described in section  3 . It is also preferably configured to perform SIR and multipath estimations as described in section  3 ( b ). Demodulator  2308  is configured to extract the parallel data streams from each sub-channel assigned to the device comprising receiver  2300  and to generate a single data stream therefrom. 
       FIG. 23  illustrates an example embodiment of a demodulator  2400  in accordance with the systems and methods described herein. Demodulator  2402  comprises a frequency shifter  2402 , which is configured to apply a frequency offset to the baseband data stream so that parallel data streams comprising the baseband data stream can be independently processed in receiver  2400 . Thus, the output of frequency shifter  2402  is a plurality of parallel data streams, which are then preferably filtered by filters  2404 . Filters  2404  apply a filter to each parallel data stream that corresponds to the pulse shape applied in the transmitter, e.g., transmitter  1500 . Alternatively, an IFFT block can replace shifter  1614  and filtering can be done after the IFFT block. This type of implementation can be more efficient depending on the implementation. 
     Next, receiver  2400  preferably includes decimators  2406  configured to decimate the data rate of the parallel bit streams. Sampling at higher rates helps to ensure accurate recreation of the data. But the higher the data rate, the larger and more complex equalizer  2408  becomes. Thus, the sampling rate, and therefore the number of samples, can be reduced by decimators  2406  to an adequate level that allows for a smaller and less costly equalizer  2408 . 
     Equalizer  2408  is configured to reduce the effects of multipath in receiver  2300 . Its operation will be discussed more fully below. After equalizer  2408 , the parallel data streams are sent to de-scrambler, decoder, and de-interleaver  2410 , which perform the opposite operations of scrambler, encoder, and interleaver  1506  so as to reproduce the original data generated in the transmitter. The parallel data streams are then sent to parallel to serial converter  2412 , which generates a single serial data stream from the parallel data streams. 
     Equalizer  2408  uses the multipath estimates provided by correlator  2306  to equalize the effects of multipath in receiver  2300 . In one embodiment, equalizer  2408  comprises Single-In Single-Out (SISO) equalizers operating on each parallel data stream in demodulator  2400 . In this case, each SISO equalizer comprising equalizer  2408  receives a single input and generates a single equalized output. Alternatively, each equalizer can be a Multiple-In Multiple-Out (MIMO) or a Multiple-In Single-Out (MISO) equalizer. Multiple inputs can be required for example, when a frequency encoder or rate controller, such as frequency encoder  1900 , is included in the transmitter. Because frequency encoder  1900  encodes information from more than one parallel data stream onto each sub-channel, each equalizers comprising equalizer  2408  need to equalize more than one sub-channel. Thus, for example, if a parallel data stream in demodulator  2400  comprises d( 1 )+d( 8 ), then equalizer  2408  will need to equalize both d( 1 ) and d( 8 ) together. Equalizer  2408  can then generate a single output corresponding to d( 1 ) or d( 8 ) (MISO) or it can generate both d( 1 ) and d( 8 ) (MIMO). 
     Equalizer  2408  can also be a time domain equalizer (TDE) or a frequency domain equalizer (FDE) depending on the embodiment. Generally, equalizer  2408  is a TDE if the modulator in the transmitter performs TDM on the parallel data streams, and a FDE if the modulator performs FDM. But equalizer  2408  can be an FDE even if TDM is used in the transmitter. Therefore, the preferred equalizer type should be taken into consideration when deciding what type of block termination to use in the transmitter. Because of power requirements, it is often preferable to use FDM on the forward link and TDM on the reverse link in a wireless communication system. 
     As with transmitter  1500 , the various components comprising demodulator  2400  are preferably programmable, so that a single device can operate in a plurality of different systems and still maintain superior performance, which is a primary advantage of the systems and methods described herein. Accordingly, the above discussion provides systems and methods for implementing a channel access protocol that allows the transmitter and receiver hardware to be reprogrammed slightly depending on the communication system. 
     Thus, when a device moves from one system to another, it preferably reconfigures the hardware, i.e. transmitter and receiver, as required and switches to a protocol stack corresponding to the new system. An important part of reconfiguring the receiver is reconfiguring, or programming, the equalizer because multipath is a main problem for each type of system. The multipath, however, varies depending on the type of system, which previously has meant that a different equalizer is required for different types of communication systems. The channel access protocol described in the preceding sections, however, allows for equalizers to be used that need only be reconfigured slightly for operation in various systems. 
     a. Sample Equalizer Embodiment 
       FIG. 24  illustrates an example embodiment of a receiver  2500  illustrating one way to configure equalizers  2506  in accordance with the systems and methods described herein. Before discussing the configuration of receiver  2500 , it should be noted that one way to configure equalizers  2506  is to simply include one equalizer per channel (for the systems and methods described herein, a channel is the equivalent of a sub-channel as described above). A correlator, such as correlator  2306  ( FIG. 22 ), can then provide equalizers  2506  with an estimate of the number, amplitude, and phase of any multipaths present, up to some maximum number. This is also known as the Channel Impulse Response (CIR). The maximum number of multipaths is determined based on design criteria for a particular implementation. The more multipaths included in the CIR the more path diversity the receiver has and the more robust communication in the system will be. Path diversity is discussed a little more fully below. 
     If there is one equalizer  2506  per channel, the CIR is preferably provided directly to equalizers  2506  from the correlator (not shown). If such a correlator configuration is used, then equalizers  2506  can be run at a slow rate, but the overall equalization process is relatively fast. For systems with a relatively small number of channels, such a configuration is therefore preferable. The problem, however, is that there is large variances in the number of channels used in different types of communication systems. For example, an outdoor system can have has many as 256 channels. This would require 256 equalizers  2506 , which would make the receiver design too complex and costly. Thus, for systems with a lot of channels, the configuration illustrated in  FIG. 25  is preferable. In receiver  2500 , multiple channels share each equalizer  2506 . For example, each equalizer can be shared by 4 channels, e.g., Ch 1 -Ch 4 , Ch 5 -Ch 8 , etc., as illustrated in  FIG. 25 . In which case, receiver  2500  preferably comprises a memory  2502  configured to store information arriving on each channel. 
     Memory  2502  is preferably divided into sub-sections  2504 , which are each configured to store information for a particular subset of channels. Information for each channel in each subset is then alternately sent to the appropriate equalizer  2506 , which equalizes the information based on the CIR provided for that channel. In this case, each equalizer must run much faster than it would if there was simply one equalizer per channel. For example, equalizers  2506  would need to run 4 or more times as fast in order to effectively equalize 4 channels as opposed to 1. In addition, extra memory  2502  is required to buffer the channel information. But overall, the complexity of receiver  2500  is reduced, because there are fewer equalizers. This should also lower the overall cost to implement receiver  2500 . 
     Preferably, memory  2502  and the number of channels that are sent to a particular equalizer is programmable. In this way, receiver  2500  can be reconfigured for the most optimum operation for a given system. Thus, if receiver  2500  were moved from an outdoor system to an indoor system with fewer channels, then receiver  2500  can preferably be reconfigured so that there are fewer, even as few as 1, channel per equalizer. The rate at which equalizers  2506  are run is also preferably programmable such that equalizers  2506  can be run at the optimum rate for the number of channels being equalized. 
     In addition, if each equalizer  2506  is equalizing multiple channels, then the CIR for those multiple paths must alternately be provided to each equalizer  2506 . Preferably, therefore, a memory (not shown) is also included to buffer the CIR information for each channel. The appropriate CIR information is then sent to each equalizer from the CIR memory (not shown) when the corresponding channel information is being equalized. The CIR memory (not shown) is also preferably programmable to ensure optimum operation regardless of what type of system receiver  2500  is operating in. 
     Returning to the issue of path diversity, the number of paths used by equalizers  2506  must account for the delay spread d s  in the system. For example, if the system is an outdoor system operating in the 5 Giga Hertz (GHz) range, the communication channel can comprise a bandwidth of 125 Mega Hertz (MHz), e.g., the channel can extend from 5.725 GHz to 5.85 GHz. If the channel is divided into 512 sub-channels with a roll-off factor r of 0.125, then each subchannel will have a bandwidth of approximately 215 kilohertz (KHz), which provides approximately a 4.6 microsecond symbol duration. Since the worstcase delay spread d s  is 20 microseconds, the number of paths used by equalizers  2504  can be set to a maximum of 5. Thus, there would be a first path P 1  at zero microseconds, a second path P 2  at 4.6 microseconds, a third path P 3  at 9.2 microseconds, a fourth path P 4  at 13.8 microseconds, and fifth path P 5  at 18.4 microseconds, which is close to the delay spread d s . In another embodiment, a sixth path can be included so as to completely cover the delay spread d s ; however, 20 microseconds is the worst case. In fact, a delay spread d s  of 3 microseconds is a more typical value. In most instances, therefore, the delay spread d s  will actually be shorter and an extra path is not needed. Alternatively, fewer sub-channels can be used, thus providing a larger symbol duration, instead of using an extra path. But again, this would typically not be needed. 
     As explained above, equalizers  2506  are preferably configurable so that they can be reconfigured for various communication systems. Thus, for example, the number of paths used must be sufficient regardless of the type of communication system. But this is also dependent on the number of sub-channels used. If, for example, receiver  2500  went from operating in the above described outdoor system to an indoor system, where the delay spread d s  is on the order of 1 microsecond, then receiver  2500  can preferably be reconfigured for 32 sub-channels and 5 paths. Assuming the same overall bandwidth of 125 MHz, the bandwidth of each sub-channel is approximately 4 MHz and the symbol duration is approximately 250 nanoseconds. 
     Therefore, there will be a first path P 1  at zero microseconds and subsequent paths P 2  to P 5  at 250 ns, 500 ns, 750 ns, and 1 microsecond, respectively. Thus, the delay spread ds should be covered for the indoor environment. Again, the 1 microsecond delay spread d s  is worst case so the 1 microsecond delay spread d s  provided in the above example will often be more than is actually required. This is preferable, however, for indoor systems, because it can allow operation to extend outside of the inside environment, e.g., just outside the building in which the inside environment operates. For campus style environments, where a user is likely to be traveling between buildings, this can be advantageous. 
     7. Sample Embodiment of a Wireless Communication device 
       FIG. 25  illustrates an example embodiment of a wireless communication device in accordance with the systems and methods described herein. Device  2600  is, for example, a portable communication device configured for operation in a plurality of indoor and outdoor communication systems. Thus, device  2600  comprises an antenna  2602  for transmitting and receiving wireless communication signals over a wireless communication channel  2618 . Duplexor  2604 , or switch, can be included so that transmitter  2606  and receiver  2608  can both use antenna  2602 , while being isolated from each other. Duplexors, or switches used for this purpose, are well known and will not be explained herein. 
     Transmitter  2606  is a configurable transmitter configured to implement the channel access protocol described above. Thus, transmitter  2606  is capable of transmitting and encoding a wideband communication signal comprising a plurality of sub-channels. Moreover, transmitter  2606  is configured such that the various sub-components that comprise transmitter  2606  can be reconfigured, or programmed, as described in section  5 . Similarly, receiver  2608  is configured to implement the channel access protocol described above and is, therefore, also configured such that the various sub-components comprising receiver  2608  can be reconfigured, or reprogrammed, as described in section  6 . 
     Transmitter  2606  and receiver  2608  are interfaced with processor  2610 , which can comprise various processing, controller, and/or Digital Signal Processing (DSP) circuits. Processor  2610  controls the operation of device  2600  including encoding signals to be transmitted by transmitter  2606  and decoding signals received by receiver  2608 . Device  2610  can also include memory  2612 , which can be configured to store operating instructions, e.g., firmware/software, used by processor  2610  to control the operation of device  2600 . 
     Processor  2610  is also preferably configured to reprogram transmitter  2606  and receiver  2608  via control interfaces  2614  and  2616 , respectively, as required by the wireless communication system in which device  2600  is operating. Thus, for example, device  2600  can be configured to periodically ascertain the availability is a preferred communication system. If the system is detected, then processor  2610  can be configured to load the corresponding operating instruction from memory  2612  and reconfigure transmitter  2606  and receiver  2608  for operation in the preferred system. 
     For example, it may preferable for device  2600  to switch to an indoor wireless LAN if it is available. So device  2600  may be operating in a wireless WAN where no wireless LAN is available, while periodically searching for the availability of an appropriate wireless LAN. Once the wireless LAN is detected, processor  2610  will load the operating instructions, e.g., the appropriate protocol stack, for the wireless LAN environment and will reprogram transmitter  2606  and receiver  2608  accordingly. In this manner, device  2600  can move from one type of communication system to another, while maintaining superior performance. 
     It should be noted that a base station configured in accordance with the systems and methods herein will operate in a similar manner as device  2600 ; however, because the base station does not move from one type of system to another, there is generally no need to configure processor  2610  to reconfigure transmitter  2606  and receiver  2608  for operation in accordance with the operating instruction for a different type of system. But processor  2610  can still be configured to reconfigure, or reprogram the sub-components of transmitter  2606  and/or receiver  2608  as required by the operating conditions within the system as reported by communication devices in communication with the base station. Moreover, such a base station can be configured in accordance with the systems and methods described herein to implement more than one mode of operation. In which case, controller  2610  can be configured to reprogram transmitter  2606  and receiver  2608  to implement the appropriate mode of operation. 
     8. High Data Rate Transmitter and Receiver 
     Referring now to  FIGS. 26-49 , additional embodiments of the present invention are illustrated. The embodiments described below may contain some of the features and functionality as described above. 
     The embodiments of the present invention discussed below employ ultra-wideband communication technology. Referring to  FIGS. 26 and 27 , impulse type ultra-wideband (UWB) communication employs discrete pulses of electromagnetic energy that are emitted at, for example, nanosecond or picosecond intervals (generally tens of picoseconds to a few nanoseconds in duration). For this reason, ultra-wideband is often called “impulse radio.” That is, the UWB pulses may be transmitted without modulation onto a sine wave, or a sinusoidal carrier, in contrast with conventional carrier wave communication technology. This type of UWB generally requires neither an assigned frequency nor a power amplifier. 
     An example of a conventional carrier wave communication technology is illustrated in  FIG. 26 . IEEE 802.11a is a wireless local area network (LAN) protocol, which transmits a sinusoidal radio frequency signal at a 5 GHz center frequency, with a radio frequency spread of about 5 MHz. As defined herein, a carrier wave is an electromagnetic wave of a specified frequency and amplitude that is emitted by a radio transmitter in order to carry information. The 802.11 protocol is an example of a carrier wave communication technology. The carrier wave comprises a substantially continuous sinusoidal waveform having a specific narrow radio frequency (5 MHz) that has a duration that may range from seconds to minutes. 
     In contrast, an ultra-wideband (UWB) pulse may have a 2.0 GHz center frequency, with a frequency spread of approximately 4 GHz, as shown in  FIG. 27 , which illustrates two typical UWB pulses.  FIG. 27  illustrates that the shorter the UWB pulse in time, the broader the spread of its frequency spectrum. This is because bandwidth is inversely proportional to the time duration of the pulse. A 600-picosecond UWB pulse can have about a 1.8 GHz center frequency, with a frequency spread of approximately 1.6 GHz and a 300-picosecond UWB pulse can have about a 3 GHz center frequency, with a frequency spread of approximately 3.3 GHz. Thus, UWB pulses generally do not operate within a specific frequency, as shown in  FIG. 26 . Either of the pulses shown in  FIG. 27  may be frequency shifted, for example, by using heterodyning, to have essentially the same bandwidth but centered at any desired frequency. And because UWB pulses are spread across an extremely wide frequency range, UWB communication systems allow communications at very high data rates, such as 100 megabits per second or greater. 
     Several different methods of ultra-wideband (UWB) communications have been proposed. For wireless UWB communications in the United States, all of these methods must meet the constraints recently established by the Federal Communications Commission (FCC) in their Report and Order issued Apr. 22, 2002 (ET Docket 98-153). Currently, the FCC is allowing limited UWB communications, but as UWB systems are deployed, and additional experience with this new technology is gained, the FCC may revise its current limits and allow for expanded use of UWB communication technology. 
     The FCC April 22 Report and Order requires that UWB pulses, or signals occupy greater than 20% fractional bandwidth or 500 megahertz, whichever is smaller. Fractional bandwidth is defined as 2 times the difference between the high and low 10 dB cutoff frequencies divided by the sum of the high and low 10 dB cutoff frequencies. Specifically, the fractional bandwidth equation is: 
     
       
         
           
             
               Fractional 
               ⁢ 
               
                   
               
               ⁢ 
               Bandwidth 
             
             = 
             
               2 
               ⁢ 
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       f 
                       h 
                     
                     - 
                     
                       f 
                       l 
                     
                   
                 
                 
                   
                     f 
                     h 
                   
                   + 
                   
                     f 
                     
                       l 
                       ⁢ 
                       
                           
                       
                     
                   
                 
               
             
           
         
       
     
     where f h  is the high 10 dB cutoff frequency, and f l  is the low 10 dB cutoff frequency. 
     Stated differently, fractional bandwidth is the percentage of a signal&#39;s center frequency that the signal occupies. For example, a signal having a center frequency of 10 MHz, and a bandwidth of 2 MHz (i.e., from 9 to 11 MHz), has a 20% fractional bandwidth. That is, center frequency, f c =(f h +f l )/2 
       FIG. 28  illustrates the ultra-wideband emission limits for indoor systems mandated by the April 22 Report and Order. The Report and Order constrains UWB communications to the frequency spectrum between 3.1 GHz and 10.6 GHz, with intentional emissions to not exceed −41.3 dBm/MHz. The report and order also established emission limits for hand held UWB systems, vehicular radar systems, medical imaging systems, surveillance systems, through-wall imaging systems, ground penetrating radar and other UWB systems. It will be appreciated that the invention described herein may be employed indoors, and/or outdoors, and may be fixed, and/or mobile, and may employ either a wireless or wire media for a communication channel. 
     Generally, in the case of wireless communications, a multiplicity of UWB pulses may be transmitted at relatively low power density (milliwatts per megahertz). However, an alternative UWB communication system, located outside the United States, may transmit at a higher power density. For example, UWB pulses may be transmitted between 30 dBm to −50 dBm. 
     UWB pulses, however, transmitted through many wire media will not interfere with wireless radio frequency transmissions. Therefore, the power (sampled at a single frequency) of UWB pulses transmitted though wire media may range from about +30 dBm to about −140 dBm. The FCC&#39;s April 22 Report and Order does not apply to communications through wire media. 
     Communication standards committees associated with the International Institute of Electrical and Electronics Engineers (IEEE) are considering a number of ultra-wideband (UWB) wireless communication methods that meet the constraints established by the FCC. One UWB communication method may transmit UWB pulses that occupy 500 MHz bands within the 7.5 GHz FCC allocation (from 3.1 GHz to 10.6 GHz). In one embodiment of this communication method, UWB pulses have about a 2-nanosecond duration, which corresponds to about a 500 MHz bandwidth. The center frequency of the UWB pulses can be varied to place them wherever desired within the 7.5 GHz allocation. In another embodiment of this communication method, an Inverse Fast Fourier Transform (IFFT) is performed on parallel data to produce 122 carriers, each approximately 4.125 MHz wide. In this embodiment, also known as Orthogonal Frequency Division Multiplexing (OFDM), the resultant UWB pulse, or signal is approximately 506 MHz wide, and has approximately 242-nanosecond duration. It meets the FCC rules for UWB communications because it is an aggregation of many relatively narrow band carriers rather than because of the duration of each pulse. 
     Another UWB communication method being evaluated by the IEEE standards committees comprises transmitting discrete UWB pulses that occupy greater than 500 MHz of frequency spectrum. For example, in one embodiment of this communication method, UWB pulse durations may vary from 2 nanoseconds, which occupies about 500 MHz, to about 133 picoseconds, which occupies about 7.5 GHz of bandwidth. That is, a single UWB pulse may occupy substantially all of the entire allocation for communications (from 3.1 GHz to 10.6 GHz). 
     Yet another UWB communication method being evaluated by the IEEE standards committees comprises transmitting a sequence of pulses that may be approximately 0.7 nanoseconds or less in duration, and at a chipping rate of approximately 1.4 giga pulses per second. The pulses are modulated using a Direct-Sequence modulation technique, and is called DS-UWB. Operation in two bands is contemplated, with one band is centered near 4 GHz with a 1.4 GHz wide signal, while the second band is centered near 8 GHz, with a 2.8 GHz wide UWB signal. Operation may occur at either or both of the UWB bands. Data rates between about 28 Megabits/second to as much as 1,320 Megabits/second are contemplated. 
     Another method of UWB communications comprises transmitting a modulated continuous carrier wave where the frequency occupied by the transmitted signal occupies more than the required 20 percent fractional bandwidth. In this method the continuous carrier wave may be modulated in a time period that creates the frequency band occupancy. For example, if a 4 GHz carrier is modulated using binary phase shift keying (BPSK) with data time periods of 750 picoseconds, the resultant signal may occupy 1.3 GHz of bandwidth around a center frequency of 4 GHz. In this example, the fractional bandwidth is approximately 32.5%. This signal would be considered UWB under the FCC regulation discussed above. 
     Thus, described above are four different methods of ultra-wideband (UWB) communication. It will be appreciated that the present invention may be employed by any of the above-described UWB methods, or others yet to be developed. 
     Referring now to  FIG. 29 , which illustrates a block diagram of a transmitter  5210  consistent with one embodiment of the present invention. In this embodiment data  5110  of interest may be provided to data interface  5040 . A number of data interfaces  5040  are known in the art and can be used to practice the current invention. The data interface  5040  may include an industry standard such as a Universal Serial Bus (USB) standard interface, an IEEE 1394 standard interface, a Peripheral Component Interconnect standard (PCI), a Peripheral Component Interconnect Express (PCI-Express) standard, a MILSPEC-1760 standard, and a MILSPEC-1553 standard. Non-industry standard interfaces may also be employed and the present invention is not limited with respect to the type of data interface  5040  used. Data  5110  is sent from data interface  5040  to the Medium Access Controller (MAC)  5030 . The MAC  5030  performs a number of functions on the data  5110  to form a plurality of frames  5100 . 
     As illustrated in  FIG. 31 , a data frame  5100  comprises a medium access control header  5120 , a data section  5110 , a source ID, a destination ID, a rate field  5130 , and in some embodiments may include a Cyclical Redundancy Check  5115  (CRC) appended to the end of the frame  5100 . Referring back to  FIG. 29 , the data frames  5100  are then sent to a baseband processor  5020 , which performs a number of functions (described below) and produces baseband frame  5050 , illustrated in  FIG. 33 . 
     A “frame” as defined herein, whether a data frame  5100 , a baseband frame  5050 , or another type of “frame,” may include many different constructions and arrangements. Generally, a “frame” usually consists of a representation of the original data to be transmitted (generally comprising a specified number of bits, or binary digits), together with other bits that may be used for error detection or control. A “frame” may also include routing information, such as a source address, a destination address, and other information. A “frame” may be of different lengths, and contain variable amounts of data. It will be appreciated that the construction of baseband frame  5050  and data frame  5100  may vary without exceeding the scope of the present invention. 
     For example, additional bits in a “frame” may be used for routing (possibly in the form of an address field), synchronization, overhead information not directly associated with the original data, a frame check sequence, and a cyclic redundancy check (CRC), among others. CRC is an error detection algorithm that is known in the art of communications. One embodiment of a CRC may be described as follows. Given a data section  5110  having bits of length “k,” the transmitter  5210  generates an n-bit sequence, known as the Frame Check Sequence (FCS) such that by appending the FCS to the data section  5110 , the resulting data section  5110  has a length k+n. The FCS is calculated in such a way that when a receiver divides the received resulting data section  5110  by a predetermined number there is no remainder. If no remainder is found the data section  5110  is assumed to be error free. 
       FIG. 33  illustrates the baseband frame  5050  produced by the baseband processor  5020 . The baseband frame  5050  comprises a physical layer header  5180 , the medium access control header  5120  and a number of data packets  5200 . Each data packet  5200  includes a code block  5190 , which is used by the receiver  5220  (shown in  FIG. 34 ) for synchronization of the packet  5200 . Additionally, the baseband frame  5050  may include the FCS used to decode the CRC as described above. Physical layer header  5180  may comprise a number of synchronization code blocks  5190  which are used by the receiver  5220  to synchronize its timing reference to the timing reference of the transmitter  5210 . 
     Generally, synchronization is used to obtain a fixed relationship among corresponding significant instants of two or more signals. Put differently, synchronization (also known as frame synchronization, frame alignment, or framing) is used by a receiver to lock onto an incoming frame so that it may receive the data contained in the frame. Generally, the receiver synchronizes its time base, or reference to the time base of the transmitter. 
     For example, a “frame synchronization pattern,” generally comprising a recurring pattern of bits, is transmitted that enables the receiver to align its clock, or time reference with the transmitter&#39;s time reference (i.e., synchronization). Repetition of the bit pattern helps ensure that the receiver will have an opportunity to “lock” in on the timing of the incoming signal. 
     In one embodiment of the present invention, the synchronization code blocks  5190  are comprised of 256 bit Golay codes. In another embodiment, one or more of the Golay codes may be inverse Golay codes. It will be appreciated that other types of synchronization codes, comprised of other bit sizes, may be employed by the present invention. One feature of the present invention is that upon reception of the synchronization sequence, the receiver may adjust its time base, its frequency base, and a setting of an automatic gain control amplifier (not shown). 
     Returning to  FIG. 29 , the baseband frame  5050  is then sent from the baseband processor  5020  to modulator  5420 , which contains a digital circuit  5080  and local oscillator  5090 . Modulator  5420  performs modulation of the baseband frame  5050 , which includes representations of individual data bits, into a transmission signal  5070 . That is, the baseband processor  5020  outputs a signal comprised of high and low signal values, each having a time duration, or time base T 0 , shown in  FIG. 30 , which represent the data comprising the baseband frame  5050 . 
     The local oscillator  5090  generates a clock signal  5060  at a time base T 1 , illustrated in  FIG. 30 . In one embodiment of the present invention local oscillator  5090  may be a voltage controlled oscillator. As mentioned above, the signal values representing the baseband frame  5050  are at a time base T 0 . Using the clock signal  5060 , the digital circuit  5080  modulates, or changes the signal values representing the baseband frame  5050 . In the illustrated embodiment, the type of modulation is phase modulation. 
     As shown in  FIG. 30 , the inverse of the clock signal time base T 1  is the center frequency of the transmission signal  5070 . That is, 1/T 1 =center frequency. It will be appreciated that virtually any center frequency can be employed by the present invention. For example, the local oscillator  5090  may generate a clock signal  5060  with a time base T 1  of 250 picoseconds. In this example, the digital circuit  5080  produces a transmission signal  5070  that would be centered at 4 Giga-Hertz (GHz), which is the inverse of 250 picoseconds. The inverse of the baseband frame  5050  signal values (time base T 0 ) controls the amount of occupied bandwidth around the center frequency of the transmission signal  5070 . In the above example, if the time base T 0  of the baseband frame  5050  signal values is 750 picoseconds, the transmission signal would occupy 1.3 GHz of bandwidth, around a 4 GHz center frequency. In this case the bandwidth (i.e., amount of radio frequency spectrum) occupied would extend from approximately 3.33 GHz to approximately 4.66 GHz. The fractional bandwidth of this signal, calculated by the formula given above, would be approximately 33.25%. Thus, this transmission signal  5070  would be considered UWB under the current FCC definition because its fractional bandwidth exceeds 20%. 
     In another example, the clock signal  5060  time base T 1  may be approximately  133  picoseconds and the time base T 0  of the baseband frame  5050  signal values may be approximately 146 picoseconds. The transmission signal  5070  in this case would have a center frequency of 6.85 GHz and the signal would occupy 7.5 GHz of bandwidth around the center frequency. In this example, the transmission signal  5070  would occupy the entire available UWB spectrum from 3.1 GHz to 10.6 GHz. It would have a fractional bandwidth of approximately 110% and would be considered UWB. In yet another example, a clock signal time base T 1  of approximately 2 nanoseconds with a time base T 0  of the baseband frame  5050  signal values of approximately 5300 picoseconds yields a transmission signal  5070  that occupies 500 MHz of bandwidth located around a center frequency of 3.35 GHz. The fractional bandwidth of this exemplary transmission signal  5070  is only approximately 15%. While this signal does not meet the current UWB definition in terms of fractional bandwidth, it is still considered UWB since it occupies the required minimum of 500 MHz of bandwidth. In yet another example, a clock signal  5060  time base T 1  may be approximately 100 picoseconds and the time base T 0  of the baseband frame  5050  signal values may be 200 picoseconds. In this example, the transmission signal  5070  would occupy 10 GHz of bandwidth around a center frequency of 5 GHz. The bandwidth occupied by this transmission signal  5070  would extend from Direct Current at zero Hertz up to 10 GHz. This signal would occupy a fractional bandwidth of approximately 200%. Under the current UWB definition this signal would be a UWB signal but under the current FCC regulations would not be allowed for wireless transmission as a portion of the signal would be below the FCC mandated 3.1 GHz frequency boundary. 
     One feature of the present invention is that by generating a clock signal at the desired center frequency used for transmission, the present invention does not need to employ a mixer to position the signal at the transmission frequency. As discussed above, the present invention can generate a signal anywhere within (or outside of) the FCC mandated UWB radio frequency band by using a high-speed clock signal at the desired frequency. This feature reduces the overall cost and complexity of the device. In one embodiment, the high-speed clock is a 10.6 Giga-Hertz (GHz) clock, but it will be appreciated that other clocks, such as 4 GHz, 8 GHz, 12 GHz, and others may be employed by the present invention. 
     Several embodiments of digital circuit  5080  are illustrated in  FIGS. 32   a ,  32   b , and  32   c . One feature of the digital circuits  5080  discussed below is that they directly generate the transmission signal, without mixing, or up-converting the signal to the radio frequency used for transmission. 
     Referring to  FIG. 32   a , the locally generated clock  5060  and the baseband frame  5050  signal values are the inputs to an “exclusive or” function or gate. As is known in the art, and shown in TABLE I, an “exclusive or” (XOR) gate performs the following function: 
     
       
         
               
               
               
             
           
               
                 TABLE I 
               
               
                   
               
               
                 Input: 
                 Input: 
                 Output: 
               
               
                 Signal values 5050 
                 Clock 5060 
                 Transmission Signal 5070 
               
               
                   
               
             
             
               
                 0 
                 0 
                 0 
               
               
                 0 
                 1 
                 1 
               
               
                 1 
                 0 
                 1 
               
               
                 1 
                 1 
                 0 
               
               
                   
               
             
          
         
       
     
     As illustrated in  FIG. 30 , during time periods where signal values, or baseband data  5050  has a “low” value, the “high” values in clock  5060  will cause the transmission signal  5070  to be “high.” During time periods where the signal values  5050  are “low,” the “low” values will result in a “low” in the transmission signal  5070 . Put differently, during “low” signal value  5050  time periods T 0 , the transmission signal  5070  mirrors the clock  5060 . During time periods T 0  where signal values  5050  have a “high” value, the “high” values in clock  5060  result in “low” values in the transmission signal  5070 . Additionally during “high” signal value  5050  time periods, the “low” clock  5060  values result in a “high” transmission signal  5070 . In other words, during “high” signal values  5050  time periods, the inverse of clock  5060  becomes the transmission signal  5070 . In this manner the signal values  5050  modulate the phase of the transmission signal  5070 . 
     In an alternate embodiment of digital circuit  5080 , illustrated in  FIG. 32   b , signal values  5050  and clock  5060  are inputs into an “and” gate. Additionally, the inverse of clock  5060  and signal values  5050  are inputs into another “and” gate. Combiner  5160  may then passively combine the outputs of the two “and” gates, or functions. As is known in the art, and shown in TABLE II, an “and” gate performs the following logical function: 
     
       
         
               
               
               
             
           
               
                 TABLE II 
               
               
                   
               
               
                 Input: 
                 Input: 
                 Output: 
               
               
                 Signal values 5050 
                 Clock 5060 
                 Transmission Signal 5070 
               
               
                   
               
             
             
               
                 0 
                 0 
                 0 
               
               
                 0 
                 1 
                 0 
               
               
                 1 
                 0 
                 0 
               
               
                 1 
                 1 
                 1 
               
               
                   
               
             
          
         
       
     
     In a like manner, and as illustrated in  FIG. 38 , during time periods T 0  where the signal values  5050  are high, the output of the “and” gate  5150   a  follows the clock  5060 . When the signal values  5050  are low, the output of “and” gate  5150  is “low”. The inverse of signal values  5050  and the inverse of clock  5060  are inputs to “and” gate  5150   b . During time periods where the signal values  5050  are low, the inverse of signal values are “high.” During this time period the transmission signal  5070  becomes the inverse of the clock  5060 . The two outputs from “and” gates  5150   a  and  5150   b  may then be combined by combiner  5160  to produce transmission signal  5070 . In like manner to the “exclusive or” implementation described above, the phase of the clock  5060  is modulated by the signal values  5050  to become transmission signal  5070 . It should be noted that the transmission signal  5070  generated by the embodiment in  FIG. 32   a  has an inverse phase relationship to the transmission signal generated by the embodiment shown in  FIG. 32   b . Either circuit may be modified by one with skill in the art to produce the other signal. 
     Yet another embodiment of digital circuit  5080  is illustrated in  FIG. 32   c . This embodiment can produce either of the transmission signals  5070  shown in  FIG. 30  and  FIG. 38 , by reversing the inputs of clock  5060  and its inverse. In this embodiment, a 2:1 multiplexer  5170  is used to generate a transmission signal  5070 . The clock  5060  and its inverse are connected to the multiplexer  5170 . The signal values  5050  from the baseband frame are connected to the control S 0 . When the signal value  5050  has a low value, the signal present at input  0 , clock  5060 , is passed to the output transmission signal  5070 . When the signal value  5050  has a “high” value, the signal present at input  1 , inverse clock  5060 , is passed to the output. In this manner, the clock  5060  is phase modulated by signal values  5050  to produce transmission signal  5070 . 
     Many spread spectrum communications technologies are known in the art of communications. Generally, data to be transmitted is multiplied by a chipping code, where the time period of the code is referred to as a chip, or chip duration. The chipping code usually has a shorter duration time period than the signal value used to represent the data. Stated otherwise, the chip duration is usually shorter than the data symbol, or signal value duration. The resulting signal is a signal that occupies the bandwith of the chipping signal and carries the data signal. This bandwidth can be expressed as the inverse of the chip duration. The ratio of chips per data symbol is commonly referred to as the spreading factor. The process of multiplying the data signal by the chipping code is generally referred to as spreading the signal. In like manner, the process in a receiver of recovering the data signal from a spread signal may be referred to as de-spreading. In conventional spread spectrum communications systems, the spread signal is then multiplied by a carrier wave to place the signal at the radio frequency used for transmission. In some communication systems, orthogonal codes are used to enable a multiple access scheme, where multiple users can communicate simultaneously. 
     The spreading factor introduces generally unwanted overhead into a communications system. For example, a data symbol could be transmitted without spreading. In this case, a spreading factor of 1 is employed, implying the data has not been spread. When using a spreading factor of 256 the same data symbol would be 256 times larger than the same symbol using a spreading factor of 1. For example, if a spreading factor of 1 is used to send 1 bit of data, then 1 bit is transmitted. If a spreading factor of 256 is employed, then 256 bits are used to transmit 1 bit of data. So, as the spreading factor increases, the amount of data transmitted decreases. 
     One advantage of spreading the signal with a chipping code is that a receiver may use the entire chipping code to recover the signal. This process is commonly referred to as processing gain. Processing gain, expressed in dB, assists the receiver in detection of the signal, which increases communication reliability. Another advantage of spreading with a chipping code, is that when orthogonal codes are employed in different networks, the users in one network will not intercept the signals of the users in other networks. 
     In one embodiment of the present invention, the transmission signal  5070  is spread by a chipping code or code block  5190 , shown in  FIG. 33 . In one embodiment, portions of the transmission signal  5070  have a different spreading factor. For example, the physical layer header  5180  may have a spreading factor of  256  where the medium access control header  5120  may have a spreading factor of 64. In another embodiment of the present invention, the packets  5200  may have a spreading factor that is dynamically controlled by the medium access controller  5030  that inserts the chosen spreading factor in rate field  5130  of the medium access control header  5120 . 
     In this fashion, the spreading factor may be dynamically adjusted to accommodate a changing communication environment. For example, if the distance the transmission signal  5070  must travel increases, the spreading factor may also increase, so that a receiver can recover the signal. Or, in a communication environment that is conducive to multipath, the spreading factor may also be increased. Alternatively, when the communication environment is favorable to communications, the spreading factor may be reduced, thereby increasing the rate at which data is transmitted. 
     Referring now to  FIG. 35 , which illustrates some functions performed by baseband processor  5020 . Frames  5100  are received from the medium access controller  5030  by the baseband processor  5020 . The rate field  5130  in the medium access control header  5120  is evaluated to determine the data rate for the packets  5200 . Based on the rate field  5130 , FEC encoder  5300  applies a FEC (forward error correction, discussed below) encoding level to the data frame  5100 . For example, in one embodiment shown in TABLE III, the baseband processor  5020  uses the rate field  5130  to set the FEC encoding and/or the spreading factor. It will be appreciated that different spreading factors, and/or FEC encoding levels may be employed by the present invention. 
     
       
         
               
               
               
             
               
               
               
             
           
               
                 TABLE III 
               
               
                   
               
               
                 Rate Field 5130 
                 FEC Encoding 
                 Spreading 
               
               
                 Value 
                 Level 
                 Factor 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 0 
                 1 
                 1 
               
               
                 1 
                 ¾ 
                 1 
               
               
                 2 
                 ½ 
                 1 
               
               
                 3 
                 1 
                 2 
               
               
                 4 
                 ¾ 
                 2 
               
               
                 5 
                 ½ 
                 2 
               
               
                 6 
                 1 
                 4 
               
               
                 7 
                 ¾ 
                 4 
               
               
                 8 
                 ½ 
                 4 
               
               
                 9 
                 1 
                 8 
               
               
                 10 
                 ¾ 
                 8 
               
               
                 11 
                 ½ 
                 8 
               
               
                 12 
                 1 
                 16 
               
               
                 13 
                 ¾ 
                 16 
               
               
                 14 
                 ½ 
                 16 
               
               
                 15 
                 1 
                 32 
               
               
                 16 
                 ¾ 
                 32 
               
               
                 17 
                 ½ 
                 32 
               
               
                 18 
                 1 
                 64 
               
               
                 19 
                 ¾ 
                 64 
               
               
                 20 
                 ½ 
                 64 
               
               
                 21 
                 1 
                 128 
               
               
                 22 
                 ¾ 
                 128 
               
               
                 23 
                 ½ 
                 128 
               
               
                 24 
                 1 
                 256 
               
               
                 25 
                 ¾ 
                 256 
               
               
                 26 
                 ½ 
                 256 
               
               
                   
               
             
          
         
       
     
     Encoding for Forward Error Correction (FEC) is a process by which redundancy is added to the data to be transmitted. With the additional redundancy the receiver may then attempt to detect and correct errors in the received data. An initial step in a FEC algorithm is to encode the data with additional bits. There are a number of FEC encoding algorithms. Of significant importance in communications are block codes and convolutional codes. Both types of encoding algorithms transform the original data set into a coded sequence of larger size. This increased size can yield a decrease in performance of information throughput for a particular data rate but may enable a more robust communication link. In convolutional encoding the coded sequence depends not only on the current data bits being encoded but also on one or more previous data bits. In convolutional coding the encoding is performed on a continuous basis. In block encoding a distinct block of data bits is encoded by a code. The FEC encoding level, otherwise known as the coding efficiency is a ratio of the original data to the encoded data. In other words, a FEC encoding level of ½ implies a 50% overhead or redundancy has been added to the data (50% more bits). Likewise, a ¾ FEC encoding level includes a 25% overhead. A FEC encoding level of 1 means that no additional bits have been added to the data. Other encoding rates are known in the art of communications and may be used. Those encoding levels include ⅛ th  rate encoding, ¼ rate encoding, ⅜ th  rate encoding ½ rate encoding, ⅝ th  rate encoding, ⅞ th  rate encoding, and ¾ rate encoding. 
     Referring again to  FIG. 35 , after the FEC encoder  5300  has encoded the data, the data is then passed on to the interleaver  5310 . Interleaving is a process by which the order of the bits to be transmitted is changed. One purpose of interleaving bits or a block of bits is to improve a communications systems&#39; noise immunity. For example, if bits from different portions of the data frame  5100  are interleaved, or mixed into a packet  5200  and that packet is corrupted by noise, or other factors during transmission, the impact of the corrupted packet is distributed across multiple areas of the data. This reduces the number of potential errors in any contiguous block of data, thereby increasing the probability that a receiver can correct the corrupted data. 
     After the data is been interleaved, the data is forwarded to scrambler  5320 . Scrambling the data reduces the probability of having long strings of similar data bits. Long strings of similar data bits may alter the distribution of transmitted power, known as the Power Spectral Density (PSD), within the spectrum. In many cases it is advantageous to have the effect of the data on the PSD be minimal. In those instances the effect of data should be random, or white, within the spectrum. A number of scrambling algorithms are known in the art and may be used to practice this embodiment of the invention. 
     The data is then sent to the spreader  5430 . Depending on the information in the rate field  5130  a spreading factor is applied to the data. As discussed above, the spreading factor may change based on the contents of the rate field  5130 . 
     The spread data is then sent to the packetizer  5340  where it is broken into discrete blocks appropriate for each packet  5200 . The synchronization generator  5350  generates synchronization code blocks  5190  for each packet. The header generator  5330  generates and forms the physical layer header  5180 . The physical layer header  5180  is then appended onto the medium access control header  5120 . A completed baseband frame  5050  is then forwarded to the modulator  5420 . It will be appreciated that the data processing order described above may be changed, and that other processing steps may be added or subtracted. 
     An exemplary receiver  5220  is depicted in  FIG. 34 . In one embodiment, an RF signal is received from the communication media (wire or wireless) by the RF front end  5010 . The RF front end  5010  sends the received signal to an analog-to-digital converter (ADC)  5230 . The ADC  5230  may be a 1-bit ADC, a 2-bit ADC, a 3-bit ADC, a 4-bit ADC, a 5-bit ADC, a 6-bit ADC, a 7-bit ADC or an 8-bit ADC. Other bit densities for ADCs are known in the art of communications and may be used to practice the invention. Additionally, a number of ADC architectures are known in the art and may be used to practice the invention but will not be discussed here. In one embodiment of the present invention ADC  5230  is a 1-bit sigma delta ADC. In this embodiment, ADC  5230  samples the RF signal and creates a serial data signal. The serial data signal is sent to baseband processor  5020  which converts, or reassembles the packets  5200  from the serial data signal into data frames  5110  which are sent to the medium access controller  5030 . The medium access controller converts the data frames  5110  into data  5100 , which is sent to a data interface  5040 . Data interface  5040  may comprise a number of different data interfaces as described above. 
     RF front end  5010  may comprise a number of components including one or more antennas for communications in a wireless media, or coupling circuits for communication using wire media. The baseband processor  5020 , as illustrated in  FIG. 36 , may comprise a poly-phase filter  5240 , a de-spreader  5250 , a channel impulse response detector  5260 , a channel matched filter  5410 , a de-scrambler  5270 , a de-interleaver  5280  and a FEC decoder  5290 . 
     In one embodiment RF front end  5010  may comprise two or more receive antennas (not shown). In this embodiment the receive antennas are separated by a physical distance from each other that approximates at least one wavelength of the center frequency of the signal the receiver is designed to receive. The wavelength is calculated by dividing the speed of light by the frequency. For example, a communication signal with a 4 GHz center frequency has a wavelength of approximately 7.5 cm. By separating multiple receive antennas by this distance, the receiver has a better chance of determining which received signal is a direct path signal and which is a multi-path signal. Additionally, the multiple receive antennas provide additional energy collection which may be used to detect the communication signal. 
     Two embodiments of poly-phase filter  5240  are illustrated in  FIGS. 37 and 38 . One function of the poly-phase filter  5240  is to down-convert the serial data signal into two lower frequency signals. The two signals are commonly referred to as In-phase (I) and Quadrature (Q). This conversion is accomplished by multiplying the serial data signal by a complex sinusoid. Since the serial data signal is discrete (having been sampled) the complex sinusoid is discrete samples of a sinusoid. The real and imaginary parts of a complex sinusoid may be calculated and stored in a look-up table  5400 . The serial data signal is split into two parallel signals by serial to parallel converter  5360 . Serial to parallel converter  5360  merely outputs alternate samples onto each output. Multipliers  5370  multiply the samples by real and imaginary coefficients that represent the complex sinusoid. In the embodiment illustrated in  FIG. 37 , the resultant product signals are filtered by filters  5380 . In one embodiment, filters  5380  are low-pass finite impulse response (FIR) filters. FIR filters are known in the art of signal processing and will not be discussed herein. It will be appreciated that other types of filters may be employed by the present invention. Decimators  5390  then decimate the filtered signals. Decimation is a process by which a number of samples are discarded. In the embodiment illustrated in  FIG. 38 , decimation occurs prior to filtering the signals. 
     Returning to  FIG. 36 , the poly-phase filter sends the resultant signal to the de-spreader  5250 . The process of de-spreading the signal involves correlating the signal with a synchronization code block. If the received signal contains the same, or an inverse of the synchronization code block, the de-spreader finds a strong correlation, either positive or negative. The synchronization code block may then be removed and replaced by a value. The de-spreader  5250  then sends the signal to the channel impulse response detector  5260  and the channel matched filter  5410 . 
     One feature of the present invention is that it provides an adaptive matched filter system that can rapidly adjust to changing communication conditions. A wireless communication channel is generally characterized as a multipath fading channel, which includes multipath signals that cause intersymbol interference. A conventional matched filter includes an estimated model of the communication channel, which is used to aid the matched filter in obtaining the strongest possible signal. However, when the estimated model does not accurately reflect the actual communication channel, the signal may be poorly recovered leading to a poor signal-to-noise ratio (SNR). A degraded SNR may result in an increased bit-error-rate (BER), or may reduce the effective range of the communication system. 
     In the present invention, a channel impulse response detector  5260  is employed to provide a real-time analysis of the actual communication channel to the channel matched filter  5410 . During the detection of the physical layer header  5180 , the channel impulse response detector  5260  measures the communication channel impulse response by “listening” for correlations at a number of time periods. Generally, the impulse response is detected from the time period in which strong correlations are found with the codes contained within the physical layer header  5180  and code blocks  5190  (in packets  5200 ). A number of codes are known in the art, but exemplary codes may include Golay, Walsh and perfect code sequences. 
     In the presence of multipath signal components, the de-spreader  5250  may correlate on delayed or multipath copies of the intended signal. Because of different propagation path lengths, multipath copies may show up at the receiver  5220  at a different time period than the intended signal. In this situation, the channel impulse response detector  5260  provides the time of arrival and strength of the multipath copies to the channel matched filter  5410 . The channel matched filter  5410  may then sum the received energy within the multipath copies to provide a stronger signal strength. In this way, the actual communication channel characteristics are determined and used to obtain the strongest possible signal. 
     Referring to  FIG. 36 , the channel matched filter  5410  may also include an equalization capability, or function. Generally, the goal of equalization is to provide as accurate an estimate of the original data as possible. This “estimated” data can then be forwarded to subsequent processing blocks, such as the forward error correction (FEC) decoder  5290 . One function of the FEC is to detect and correct errors in the estimated data. If errors are detected, various remedial measures are performed. These measures will be discussed below in connection with the FEC decoder  5290 . 
     The channel matched filter  5410  includes a simplified decision feedback equalization (DFE) function. The multipath copies of previous signals may arrive at a time when receiver  5220  is processing a current signal. In this case the received signal may be made up of the intended signal and a number of multipath copies of previous signals. For example, the data signal may comprise the sum of 2 or more autocorrelation functions. In one case, the data signal may comprise the sum of 64 autocorrelation functions, or alternatively, the data signal may comprise the sum of 32, 128 or other sums of autocorrelation functions. As a result:
 
 Z   n =( A   0   ×d   n )+( A   1   ×d   n−2 )+( A   2   ×d   n−1 )+( A   1   * ×d   n+1 )+( A   2   *×d   n+2 )   (8)
         Where: A 1 * and A 2 * are the complex conjugates of A 1  and A 2 .       

     In this example the last four terms in equation (8) are what is known as Inter Symbol Interference (ISI) or Inter Chip Interference (ICI). In some cases where the symbol is substantially longer than the chip duration the interference may be intra-symbol. The first term is the data. So, in this example, a current data sample, or decision, actually depends on the current sample as well as two past samples and two future samples. Obtaining the two past samples should not drive the complexity of the equalizer; however, obtaining two future samples does increase complexity. 
     Accordingly, in one embodiment of equalizer of the present invention, the two future samples are ignored. In this embodiment, a “hard” estimation is employed. This is in contrast with most conventional equalizers, which often depend on “soft” decisions. The output from the hard decision is used to obtain the past two samples, which are multiplied by the associated amplitude factors A 1  and A 2  and combined. As shown in  FIG. 40 , the A 1  and A 2  and other amplitude factors are represented by g L,L . The coefficients g L,L  are determined from the channel estimations. In one embodiment, the amplitude factors are supplied to the channel matched filter  5410  from the channel impulse response detector  5260  during processing of the physical layer header  5180  and during the processing of each packet  5200 . 
     Thus, the DFE converts the following:
 
 Z   0 =( A 0 ×d 0)+( A 1 ×d 1)+( A 2 ×d 2)   (9)
 
     Which becomes:
 
 Z   0 −[( A 1 ×d 1)+( A 2 ×d 2)]=( A 0 ×d 0)   (10)
 
     The output of the DFE can then be passed onward for further processing. A general implementation of DFE is an iterative process that significantly reduces the ISI or ICI. Further, the DFE may include a parity check, or the like, in order to detect errors. If there are no errors, then there is no reason to feedback the data and perform the iteration. 
     As shown in  FIG. 36 , in one embodiment, the channel matched filter  5410  then sends the signal to de-scrambler  5270 . In an embodiment where the transmitter  5210  scrambled the data, de-scrambler  5270  de-scrambles the data. The de-scrambler sends the de-scrambled data to the de-interleaver  5280 . In an embodiment where transmitter  5210  interleaved the data, de-interleaver  280  de-interleaves the data. FEC decoder  5290  detects and corrects errors in the recovered data  5110 . A number of decoding algorithms are known in the art and may be used to practice the invention. In one embodiment the FEC decoding algorithm is a low density parity check (LDPC) algorithm. 
     There are a number of error control methods known in the art of communications. Generally speaking, error control comprises two methods, error detection and error correction. In most error detection algorithms, the received data is merely checked for error. If errors are found, the transmitter may be notified and the data may be retransmitted. In error correction algorithms, the receiver attempts to correct detected errors. In one class of algorithms, known as Forward Error Correction (FEC), extra bits are transmitted with the data that can be used by the receiver to detect and correct errors in the data that was received. Depending on the implementation, the receiver can then ask that the data be re-sent if too many errors are detected. 
     Accordingly, as can be seen in  FIG. 41 , an FEC encoder  3202  adds bits to an input data stream  3204  to create an output data stream  3206  that necessarily requires a higher data rate due to the added bits. In the example of  FIG. 32 , FEC encoder  3202  is a ½ rate FEC encoder, which means that for every input bit d n , FEC encoder  3202  adds a bit that can be used to detect errors when data stream  3206  is decoded. As discussed above other rate encoders, such as full rate, or ¾ rate encoders may be employed by the present invention. Thus, in the case of a ½ rate FEC encoder, data rate of output  3206  is twice that of input  3204 . Data stream  3206  can then be modulated and transmitted to a receiver. In the receiver, an FEC decoder  3208  can be used to remove the extra bits and detect errors in the original data. Thus, FEC decoder  3208  should match FEC encoder  3202 , i.e., FEC decoder  3208  should be a ½ rate FEC decoder, in the above example. 
     A problem with conventional FEC encoders and decoders is that the data rates can be too high for conventional technology. This can be especially true, for example, in an ultra-wideband application, where the data rates can be extremely high. One way to overcome this problem in accordance with the systems and methods described herein is illustrated in  FIG. 42 , which depicts a portion of a transmitter chain  3300 . In the example of  FIG. 33 , a data stream  3302 , with a data rate (R) is first split into a plurality of parallel data streams  3306  in serial to parallel converter  3304 , each with a lower data rate (R/n) where n is the number of parallel data streams  3306 . The parallel data streams  3306  can then be encoded using a plurality of FEC encoders. Here two encoders  3308  and  3310  are illustrated. Thus, each of FEC encoders  3308  and  3310  can, depending on the implementation, encode half as much data and operate at a lower speed than required in a conventional system. More generally, FEC encoders  3308  and  3310  can be configured to assist each other with FEC encoding and reduce the overall load on each FEC encoder in the system. This, of course, requires some coordination, or message passing, between the two FEC encoders. 
     The outputs of FEC encoders  3308  and  3310  can then, for example, be passed through parallel to serial converters  3312  and  3314  and combined via combiner  3316  into a single data stream with FEC encoding. The single data stream can then be optional filtered and/or pulse shaped before being modulated an transmitted, e.g., via optional block  3318 , 
     In another example embodiment, of an FEC encoder configured in accordance with the systems and methods described herein, a code word is generated from an input data word by adding parity bits to the data word as illustrated in  FIG. 43 . In this example embodiment, FEC encoder  3402 , referred to as a Low Density Parity Check (LDPC) encoder, takes data word  3404  and generates output code word  3406 . As can be seen, the data word and code word are illustrated in matrix form. Thus, for example, the data word is a matrix comprising p m +d k  rows and 1 column. 
     LDPC is an error correction algorithm where the data to be sent is encoded by a generator matrix and decoded by a parity matrix. Derivation of the two matrices is seen below in equation 12. The FEC encoder  3402 , a “K” length block of data {right arrow over (d)} K×1  is multiplied by the generator matrix G N×K  which produces a “N” length block {right arrow over (C)} N×1  where N&gt;K. The additional length is attributed to the overhead described above. The parity matrix may represent a connection of two types of nodes in the decoder. The locations of 1&#39;s in the matrix represent the connection of the two types of nodes. 
     The decoding of the block on receipt is usually an iterative process by which the first type of node may calculate information related to the probability of the bit under consideration being a 1 or a 0. In some cases this probability may be expressed as a “log likelihood ratio” or mathematically: 
               l   ⁡     (   c   )       =     ln   ⁡     [       Pr   ⁡     (       c   i     =     0   |   y       )         Pr   ⁡     (       c   i     =     1   |   y       )         ]             
where In is the natural log, the numerator is the probability that the bit c i  is a zero and the denominator is the probability it is a 1. This information is passed to the other type of nodes specified by the parity check matrix, who perform a similar calculation based on the information received from each of the first type of node. The second type of node then sends its calculation to each of the first type of nodes it is connected to. This process continues until it is stopped or reaches some figure of merit in its result. Since each node is connected to a number of nodes of the other type, each iteration improves the probability calculation at each node.
 
     In one embodiment of an LDPC  3402 , the code word can be generated using a generator matrix as illustrated by the following equation:
 
 {right arrow over (C)}   N×1   =G   N×K   *{right arrow over (d)}   K×1    (11)
         where: G N×K  is the Generator Matrix
           N=M+k;   R=k/N;   if R=½, then M=k.   
               

     The generator matrix can, in turn, be generated from an identify matrix and a parity check matrix as illustrated in the following equation:
 
G=[I; P]  (12)
         where: I=the identity matrix; and
           P=the parity matrix.   
               

     Alternatively, a parity matrix H can be used to generate the code word C according to the following:
 
 H   M×N   *{right arrow over (C)}   N×1 ={right arrow over (0)} M×1    (13)
 
     The parity matrix H can then be defined as:
 
 H   M×N   =[H   P   M×M   H   D   M×K ]  (14)
 
     Accordingly, and dropping the subscripts for simplicity: 
     
       
         
           
             
               
                 
                   
                     
                       
                         [ 
                         
                           
                             H 
                             P 
                           
                           ⁢ 
                           
                             H 
                             D 
                           
                         
                         ] 
                       
                       * 
                       
                         [ 
                         
                           
                             P 
                             ⇀ 
                           
                           
                             d 
                             ⇀ 
                           
                         
                         ] 
                       
                     
                     = 
                     0 
                   
                   , 
                   or 
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ( 
                       
                         
                           H 
                           P 
                         
                         * 
                         
                           P 
                           ⇀ 
                         
                       
                       ) 
                     
                     + 
                     
                       ( 
                       
                         
                           H 
                           D 
                         
                         * 
                         
                           d 
                           ⇀ 
                         
                       
                       ) 
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The goal now is to solve for {right arrow over (P)}, since {right arrow over (d)} is known, i.e., it is the input data. To facilitate finding {right arrow over (P)} in one embodiment, H P  is configured as a dual diagonal matrix with M rows and M columns. Dual diagonal matrices are well known and will not be described here; however and exemplary one is illustrated by the following: 
     
       
         
           
             
               
                 
                   
                     H 
                     P 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           1 
                         
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           1 
                         
                         
                           1 
                         
                         
                           0 
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                         
                           1 
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                         
                           … 
                         
                         
                           
                               
                           
                         
                       
                       
                         
                           
                               
                           
                         
                         
                           
                               
                           
                         
                         
                           
                               
                           
                         
                         
                           
                               
                           
                         
                         
                           
                               
                           
                         
                         
                           1 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           … 
                         
                         
                           0 
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Further, H D  can, depending on the embodiment, be formed from a matrix of matrices. In one embodiment, this matrix of matrices is itself block cyclic. For example, in one embodiment, 4 matrices A, B, C and D can be used as in the following: 
     
       
         
           
             
               
                 
                   
                     H 
                     D 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           A 
                         
                         
                           B 
                         
                         
                           C 
                         
                         
                           D 
                         
                       
                       
                         
                           B 
                         
                         
                           C 
                         
                         
                           D 
                         
                         
                           A 
                         
                       
                       
                         
                           C 
                         
                         
                           D 
                         
                         
                           A 
                         
                         
                           B 
                         
                       
                       
                         
                           D 
                         
                         
                           A 
                         
                         
                           B 
                         
                         
                           C 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Here, each of the matrices A, B, C, and-D will have k/4 rows and k/4 columns. 
     Thus, an encoder and decoder configured in accordance with the systems and methods described herein can be optimized for a dual diagonal H P  and a block cyclic H D , as explained below. Many methods can be used to generate matrices A, B, C, and D consistent with the systems and methods described herein. One example method, however, will be described in the following paragraphs. This example method will assume, for the time being, that k=16 and therefore k/4=4. Then an identity matrix I can be used, such as the following: 
     
       
         
           
             
               
                 
                   I 
                   = 
                   
                     [ 
                     
                       
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Each of matrices A, B, C, and D can then be generated from this identity matrix I. For example, a permutation vector, in this example of length 4, can then be used to generate A. Of course, other methods for generating matrices A, B, C, and D can be used consistently with the systems and methods described herein. Thus, the matrix A can, e.g., have the following form, once an appropriate permutation vector is used to modify identity matrix I: 
     
       
         
           
             
               
                 
                   A 
                   = 
                   
                     [ 
                     
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                       
                       
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     Basically, as can be seen, a permutation vector can be used to shift the positions of the 1&#39;s in identity matrix I. In one embodiment, a single permutation matrix can be required. Once the first matrix A is generated using the single permutation vector, then the other matrices B, C, and D can be generated by shifting matrix A. For example, in one embodiment, each subsequent matrices B, C, and D is generated by shifting the previous matrix, starting with A, by 90°. Thus, B would be as follows: 
     
       
         
           
             
               
                 
                   B 
                   = 
                   
                     [ 
                     
                       
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                       
                       
                         
                           0 
                         
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     But as can be seen, in the example embodiment for generating matrices A, B, C, and D described above, each row has only a single 1. 
     In one embodiment, Galois Field algebra (GF(2)) can be used to define the following equations for use in solving for {right arrow over (P)}:
 
1+1=0;
 
1−1=0;
 
1+0=1;
 
0+1=1;
 
0+1=1; and
 
0−1=−1=1.   (22)
 
     Thus, even results are equal to 0, while odd results are equal to 1. 
     Now returning to the equation at issue:
 
( H   P   *{right arrow over (P)} )+( H   D   *{right arrow over (d)} )=0   (23)
 
     This can be rewritten as:
 
( H   P   *{right arrow over (P)} )=−( H   D   *{right arrow over (d)} )   (24)
 
     But using the equations (22), −1=1, therefore:
 
( H   P   *{right arrow over (P)} )=( H   D   *{right arrow over (d)} )   (25)
 
     In one embodiment, the following equation can be used:
 
( H   D   *{right arrow over (d)} )= {right arrow over (u)}   (26)
 
Accordingly:
 
( H   P   *{right arrow over (P)} )= {right arrow over (u)}   (27)
 
     Equation (27) can be implemented effectively if {right arrow over (u)} can be generated efficiently. In one embodiment, based on the examples above, if k=6, then {right arrow over (u)} can be determined as follows: 
     
       
         
           
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             1 
                           
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                           
                             1 
                           
                           
                             0 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                           
                             1 
                           
                           
                             0 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                           
                             1 
                           
                         
                         
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             0 
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                     * 
                     
                       [ 
                       
                         
                           
                             
                               p 
                               5 
                             
                           
                         
                         
                           
                             
                               p 
                               4 
                             
                           
                         
                         
                           
                             
                               p 
                               3 
                             
                           
                         
                         
                           
                             
                               p 
                               2 
                             
                           
                         
                         
                           
                             
                               p 
                               1 
                             
                           
                         
                         
                           
                             
                               p 
                               0 
                             
                           
                         
                       
                       ] 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             u 
                             5 
                           
                         
                       
                       
                         
                           
                             u 
                             4 
                           
                         
                       
                       
                         
                           
                             u 
                             3 
                           
                         
                       
                       
                         
                           
                             u 
                             2 
                           
                         
                       
                       
                         
                           
                             u 
                             1 
                           
                         
                       
                       
                         
                           
                             u 
                             0 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     This will result in the following equations:
 
p 0 =u 0 ;
 
 p   1   +p   0   =u   1 ;
 
 p   2   +p   1   =u   2 ;
 
 p   3   +p   2   =u   3 ;
 
 p   4   +p   3   =u   4 ;
 
 p   5   +p   4   =u   5 ;   (29)
 
     The equations of (29) define the following general equation:
 
 p   n   =u   n   −p   n−1    (30)
 
     This equation then suggests a configuration for an LDPC encoder  3402 , such as that illustrated in  FIG. 44 . As can be seen, the {right arrow over (u)} values are fed into Exclusive-OR (XOR)  3502 , the output of which is fed through a delay  3504  and back to the other input of XOR  3502 . A remaining issue, however, is the generation of the {right arrow over (u)} terms. In other words, the equation (H P *{right arrow over (P)})={right arrow over (u)} as implemented by block  3506  should also be done in the most efficient manner possible. 
     In the example above, H D  was partitioned in 4s, therefore {right arrow over (d)} should also be partitioned by 4 as illustrated in the following: 
     
       
         
           
             
               
                 
                   
                     u 
                     ⇀ 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             A 
                           
                           
                             B 
                           
                           
                             C 
                           
                           
                             D 
                           
                         
                         
                           
                             D 
                           
                           
                             A 
                           
                           
                             B 
                           
                           
                             C 
                           
                         
                         
                           
                             C 
                           
                           
                             D 
                           
                           
                             A 
                           
                           
                             B 
                           
                         
                         
                           
                             B 
                           
                           
                             C 
                           
                           
                             D 
                           
                           
                             A 
                           
                         
                       
                       ] 
                     
                     * 
                     
                       [ 
                       
                         
                           
                             
                               
                                 d 
                                 ⇀ 
                               
                               A 
                             
                           
                         
                         
                           
                             
                               
                                 d 
                                 ⇀ 
                               
                               B 
                             
                           
                         
                         
                           
                             
                               
                                 d 
                                 ⇀ 
                               
                               C 
                             
                           
                         
                         
                           
                             
                               
                                 d 
                                 ⇀ 
                               
                               D 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
           
         
       
     
     The above equation can be implemented efficiently, for example, using a circuit such as the example circuit illustrated in  FIG. 45 . The circuit of  FIG. 45  is generalized for the situation where k=128; however, it will be appreciated that the example embodiments described herein are not limited to any particular lengths or configurations. As can be seen, the circuit of  FIG. 45  uses a bank of cyclic shift registers  3606  to implement {right arrow over (d)}. The outputs of shift registers  3606  can then be passed to a plurality XORs  3602  as shown. Thus, XORs  3602  collect the appropriate outputs from shift registers  3606  in order to generate the {right arrow over (u)} terms. 
     But since it is known, in the examples above, that the output of each cyclic shift register will only have one 1, due to the fact that A, B, C, and D have only one 1 in each row, the outputs of cyclic shift registers  3606  can be rearranged and fixed so that, e.g., the first outputs of each go to the first XOR  3602 , the second outputs go to the second XOR  3602 , etc. Accordingly, efficient fixed connections  3608  can be used to reduce the complexity of LDPC  3402 . The {right arrow over (u)} terms can then be registered and fed to XOR  3502  as illustrated. 
     Accordingly, if everything is segmented by 4&#39;s as illustrated in the above examples, then the cyclic shift registers  3606  can be shifted k/4 times. On each clock cycle, k/4 of the solution would be generated, such that it takes k/4 cycles to get the entire solution. This can result in a highly parallel encoder, such as that illustrated in  FIG. 36 , for high-speed operation. The result can also be a low cost encoder, because the hardware can be reduced to ¼th that required by conventional circuits through the reuse of the components. 
     The LDPC encoder of  FIG. 44  can, therefore, be used to generate code word C, which can be modulated and transmitted. But the receiver will receive C corrupted by noise as illustrated in the following:
 
 {right arrow over (x)} =(1−2 {right arrow over (C)} )+(noise)   (32)
 
     The job of the decoder is then to extract {right arrow over (d)} from the signal represented by equation 32. In one embodiment, this can be accomplished by making soft decisions as to the value of {right arrow over (x)} and combining it with hard decisions related to the sign {right arrow over (x)} such that {right arrow over (d)} can then be accurately determined. The soft decisions can be based on a multilevel possibility. For example, if 4 bits are used in 2&#39;s complement, then you can have up to 16 levels. In one embodiment, the levels can, for example, be from −8 to 7. Alternatively, using offset 2&#39;s complement, the levels can be from −7.5 to 7.5. An advantage of the later is that the levels are not biased, e.g., toward the negative. An advantage of the former, however, is that it includes the level 0. Of course, any level scheme can be used as long as it allows for accurate determinations of {right arrow over (d)}. 
     The levels can be used to determine the probabilities of the value of {right arrow over (x)} and ultimately {right arrow over (d)}. For example, if the level determined for {right arrow over (x)} is 7 or 7.5, then the decoder can be configured to see this as a high probability that the value is 1. If the level is −8 or −7.5, then this can be seen as a high probability that the value is −1. 
     Parity check equations can then be generated from the following: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           1 
                         
                         
                           1 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           1 
                         
                         
                           1 
                         
                         
                           0 
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                         
                           1 
                         
                         
                           … 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           1 
                         
                         
                           … 
                         
                         
                           
                               
                           
                         
                       
                       
                         
                           
                               
                           
                         
                         
                           
                               
                           
                         
                         
                           
                               
                           
                         
                         
                           
                               
                           
                         
                         
                           
                               
                           
                         
                         
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                           … 
                         
                         
                           0 
                         
                         
                           1 
                         
                       
                     
                     ] 
                   
                   * 
                   
                     
                       [ 
                       
                         
                           
                             A 
                           
                           
                             B 
                           
                           
                             C 
                           
                           
                             D 
                           
                         
                         
                           
                             B 
                           
                           
                             C 
                           
                           
                             D 
                           
                           
                             A 
                           
                         
                         
                           
                             C 
                           
                           
                             D 
                           
                           
                             A 
                           
                           
                             B 
                           
                         
                         
                           
                             D 
                           
                           
                             A 
                           
                           
                             B 
                           
                           
                             C 
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               x 
                               0 
                             
                           
                         
                         
                           
                             
                               x 
                               1 
                             
                           
                         
                         
                           
                             
                               x 
                               2 
                             
                           
                         
                         
                           
                             
                                 
                             
                           
                         
                         
                           
                             
                               x 
                               
                                 n 
                                 - 
                                 1 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
     This will produce a set of parity equations in which, based on the examples above, there will be 6 terms, except in the last one, because there is exactly one 1 in each row of A, B, C, and D. The first of these parity equations would then, e.g., look like the following, based on the above examples:
 
 S   0   =x   0   +x   1   +x   2   +x   3   +x   4   +x   5    (34)
 
     Then, if S o =+1, then the operation can be viewed as passing. If, on the other hand, it is −1, then it can be viewed as a failure. A parity node processor  3702  can be used to implement equation 34, as illustrated by the example embodiment depicted in  FIG. 46 . Message passing algorithms can be used to allow each such node  3702  to make final estimations. 
       FIG. 48  is a diagram illustrating and example embodiment in which a plurality of parity node processors  3702  are configured in accordance with the systems and methods described herein. Thus, each node  3702  receives information as to what the values x 0 , x 1 , . . . x N  are believed to be. A given node  3702  can then process this information and produce estimates as to what the node believes the output of the other nodes should be and feed this information back in such a manner that the subsequent input to the other nodes is modified. It should be noted, therefore, that in such an embodiment, a node does not produce information to be fedback to its own input related to what it believes its own output should be. 
     This is illustrated in  FIG. 47  for a single node processor at time=0. As can be seen, information for each bit is provided to node  3702 , which processes the information and produces information related to what it determines each bit should be. These inputs and outputs can be referred to as edges (E). Each output edge is fedback to the relevant input bit. The node processors  3702  will, therefore, comprise storage to store the information being fed to it and processed as required. As a result, both storage and routing overheads can become excessive. 
     For example, when information related to bit x 0  is fed to node S 0 , the information from each other node related to x 0  is also added into the information provided to s 0 . This is illustrated by the following:
 
 x   0   +E   1+1 ( s   1→x   0 )+ E   1+1 ( S   2   →x   0 )+  (35)
 
     Again, as mentioned above, in this embodiment, the edge produce by node S 0  is not fed back to bit x 0 . 
       FIG. 49  is a diagram illustrating an example decoder  4000  that can be configured to reduce storage and routing overhead in accordance with one embodiment of the systems and methods described herein. The basic premise behind decoder  4000  is that all the edges produced form parity node processor  4002  can be added and then the last edge for each node, produced by that node, can be subtracted out. Thus, on the right hand side of  FIG. 49 , a given row can be updated for all edges and then shifted in shift registers  4004 . The appropriate edge can then be subtracted out for each row using the data provided from registers  4014 , as opposed to doing each row, storing the result and updating it with information from other nodes. 
     It should be noted that the output of shift registers  4004  can be rearranged and fixed to reduce routing overhead. It should also be noted that this process provides an approximation of the correct data; however, the results converge and ultimately provide the same answer. On the left hand side of decoder  4000 , each shift register  4008  gets information from only two nodes  3702 , e.g., via registers  4010  and  4012 . 
     One feature of the present invention is that it may be used to increase the bandwidth of wireless networks or networks that employ wired media. The present invention can be used to transmit ultra-wideband signals across any type of wired media. For example, the wired media can include optical fiber ribbon, fiber optic cable, single mode fiber optic cable, multi-mode fiber optic cable, plenum wire, PVC wire, and coaxial cable. 
     In addition, the wired media can include twisted-pair wiring, whether shielded or unshielded. Twisted-pair wire may consist of “pairs” of color-coded wires. Common sizes of twisted-pair wire are 2 pair, 3 pair, 4 pair, 25 pair, 50 pair and 100 pair. Twisted-pair wire is commonly used for telephone and computer networks. It comes in ratings ranging from category 1 to category 7. Twisted-pair wiring also is available unshielded. That is, the wiring does not have a foil or other type of wrapping around the group of conductors within the jacket. This type of wiring is most commonly used for wiring for voice and data networks. The foregoing list of wired media is meant to be exemplary, and not exclusive. 
     As described above, the present invention can provide additional bandwidth to enable the transmission of large amounts of data over an existing wired media network, whether the wired media network is a Internet service provider, cable television provider, or a computer network located in a business or university. The additional bandwidth can allow consumers to receive the high speed Internet access, interactive video and other features that are bandwidth intensive. 
     The present invention may be employed in any type of network, be it wireless, wire, or a mix of wire media and wireless components. That is, a network may use both wire media, such as coaxial cable, and wireless devices, such as satellites, or cellular antennas. As defined herein, a network is a group of points or nodes connected by communication paths. The communication paths may use wires or they may be wireless. A network as defined herein can interconnect with other networks and contain sub-networks. A network as defined herein can be characterized in terms of a spatial distance, for example, such as a local area network (LAN), a personal area network (PAN), a metropolitan area network (MAN), a wide area network (WAN), and a wireless personal area network (WPAN), among others. A network as defined herein can also be characterized by the type of data transmission technology used by the network, such as, for example, a Transmission Control Protocol/Internet Protocol (TCP/IP) network, a Systems Network Architecture network, among others. A network as defined herein can also be characterized by whether it carries voice, data, or both kinds of signals. A network as defined herein may also be characterized by users of the network, such as, for example, users of a public switched telephone network (PSTN) or other type of public network, and private networks (such as within a single room or home), among others. A network as defined herein can also be characterized by the usual nature of its connections, for example, a dial-up network, a switched network, a dedicated network, and a non-switched network, among others. A network as defined herein can also be characterized by the types of physical links that it employs, for example, optical fiber, coaxial cable, a mix of both, unshielded twisted pair, and shielded twisted pair, among others. The present invention may be employed in any type of wireless network, such as a wireless PAN, LAN, MAN, or WAN. In addition, the present invention may be employed in wire media, as the present invention dramatically increases the bandwidth of conventional networks that employ wire media, yet it can be inexpensively deployed without extensive modification to the existing wire media network. 
     One feature of the present invention is that it has a data rate and quality of service high enough to support multiple video streams. For example, one embodiment of the present invention may provide a communication channel having a data rate of 1.3 gigabits per second. This high data rate is particularly useful in hand held security devices. Such systems can provide dramatically improved national security. For example, current airport security systems involve large, stationary equipment that scans luggage and passengers. However, an individual may pass through a security checkpoint without being scanned or checked for identification. At most commercial airports it may be exceedingly difficult to locate the individual using current methods and equipment. In most cases the security personnel are relying on a verbal description of the individual, which may be inaccurate. Under current regulatory guidelines the terminal must be closed, emptied of passengers and manually searched. 
     With the data rates provided by the present invention, security camera access points throughout the airport may transmit one or more channels of streaming video directly to video viewers carried by security personnel, thereby allowing the search to be conducted in a more efficient manner. The data rates of conventional wireless communication systems cannot support multiple video streams, and therefore cannot provide the features and functionality of the present invention. 
     Thus, it is seen that systems and methods of providing a high speed transmitter and receiver are provided. One skilled in the art will appreciate that the present invention can be practiced by other than the above-described embodiments, which are presented in this description for purposes of illustration and not of limitation. The specification and drawings are not intended to limit the exclusionary scope of this patent document. It is noted that various equivalents for the particular embodiments discussed in this description may practice the invention as well. That is, while the present invention has been described in conjunction with specific embodiments, it is evident that many alternatives, modifications, permutations and variations will become apparent to those of ordinary skill in the art in light of the foregoing description. Accordingly, it is intended that the present invention embrace all such alternatives, modifications and variations as fall within the scope of the appended claims. The fact that a product, process or method exhibits differences from one or more of the above-described exemplary embodiments does not mean that the product or process is outside the scope (literal scope and/or other legally-recognized scope) of the following claims.