Abstract:
Techniques for sending and receiving signals include pre-distorting signals before transmission across a communication path. The signals are pre-distorted as a function of a distortion on the communication path. In one embodiments, transmitter a broadcasts to receiver b and there is also a transmitter b broadcasting to receiver a. This return channel enables both transmitters a and b to have a priori information regarding the transmission medium and path the signal takes. In this way, the nature of the distortion or interference is known to the transmitter, therefore, it pre-distorts the transmitted signal to compensate for the receiver exceeding its capabilities in recovering signal.

Description:
BACKGROUND OF THE INVENTION 
     Radio frequency (RF) receivers are typically more difficult to construct than RF transmitters. This is especially true in broadcast instances. RF receivers should be able to handle various interference issues including same frequency interference and reflections of the transmitted signal, called ghosts. There is typically a finite limit to the amount of interference or poor quality signal that a receiver can handle and still recover the original transmitted signal. 
       FIG. 1  shows a communication system according to the conventional art. The communication system  100  includes a transmitter  110 , a communication path  120 , a receiver  130  and an equalizer  140 . The transmitter  110  transmits a signal [T] across the communication path  120 . The receiver  130  receives a distorted signal [T]*[D] after transmission across the communication path  120 . The equalizer  140  equalizes [D −1 ] the distorted signal [T]*[D]. If the distortion on the communication channel  120  is less than the recovery capability [D −1 ] of the equalizer  140 , the recovered signal will be substantially equal to the transmitted signal [T]. However, if the distortion on the communication channel  120  is greater than the recovery capability of the equalizer  140 , the recovered signal [T′] will not be equal to the transmitted signal [T]. 
     SUMMARY OF THE INVENTION 
     Embodiments of the present technology are directed toward techniques for pre-distorting signals. In one embodiment, a method of sending and receiving signals includes determining the nature of the distortion and/or interference on a communication path. Thereafter, signals to be transmitted on the communication path are pre-distorted as a function of the determined distortion. The pre-distortion may be accomplished using various types of distortion including equalization, multi-path, amplitude, frequency, phase and other well known types. 
     In another embodiment, a system for sending and receiving signals includes one or more devices coupled to one or more communication paths. At least one device includes a transceiver coupled to the communication path and a pre-distortion circuit coupled to the transceiver. The pre-distortion circuit pre-distorts the signals to be transmitted by the transceiver of the given device as a function of the distortion on the communication path. When the signal is transmitted, the distortion on the communication path is at least partially compensated for by the pre-distortion introduced by the pre-distortion circuit. 
     In one embodiment of the present invention, a first transmitter (a) broadcasts to first receiver (b) and there is also a second transmitter (of b) broadcasting to second receiver (of a). This return channel enables both transmitters (a) and (b) to have a priori information regarding the transmission medium and path the signal takes. In this way, the nature of the distortion or interference is known to the transmitter, therefore, it pre-distorts the transmitted signal to compensate for the receiver exceeding its capabilities in recovering signal. This functionality, in accordance with embodiments of the present invention, reduces the complexity of the receiver by placing some of the burden on the transmitter. The back channel enables optimization of the original signal for the current state of the communications channel. The advantageous result is fewer bit errors and/or greater link distances when compared to an identical system without the inventive back channel and pre-distortion under the same environmental factors. 
     In another embodiment, a communication methodology is employed in an asymmetric system where complex modulation can be employed while using equalizers and recovery circuits having only limited complexity. In this embodiment, a training signal is sent from a sink device to a source device using a simple modulation M 1 . The source device, knowing the training signal, determines an equalization D 1   −1  that is able to recover the training signal wherein D 1  is the channel distortion for M 1 . The source then pre-distorts the training signal with the computed D 1   −1  and communicates this back to the sink using a second order modulation M 2 . The sink then knowing the training signal employs a simple equalization circuit to determine another distortion amount D 1 ′ required to recover the training signal from the pre-distorted transmission, where D 1 ′*D 1  equals D 2  (the channel distortion of the M 2  modulated signal). Advantageously, the sink then uses M 1  to transmit back to the source the computed D 1 ′ and upon which the source can compute D 2  since it knows D 1 . Here, the source advantageously uses a simple equalization circuit and simple modulation circuit. Knowing D 2 , the source can use M 2  to communicate large amounts of data to the sink device (as pre-distorted by D 2 ) even though the sink device has a relatively simple equalization circuit and also a simple modulator. Alternatively, the above iterative methodology can be repeated for higher order modulations, e.g., M 3 , etc. Although equalization is described above, this discussion is merely exemplary. This embodiment operates equally well employing other distortion types, e.g., multi-path, amplitude, frequency, phase and other well known types. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the present invention are illustrated by way of example and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which: 
         FIG. 1  shows a block diagram of a conventional communication system. 
         FIG. 2  shows a block diagram of a system for transmitting and receiving signals, in accordance with embodiments of the present technology. 
         FIG. 3  shows a flow diagram of a method of transmitting and receiving signals in accordance with embodiments of the present technology. 
         FIG. 4  shows a flow diagram of a method of transmitting and receiving signals in accordance with other embodiments of the present technology. 
         FIG. 5  illustrates a communication methodology in an asymmetric system where complex modulation can be employed while using equalizers and recovery circuits having reduced complexity. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Reference will now be made in detail to the embodiments of the present technology, examples of which are illustrated in the accompanying drawings. While the present technology will be described in conjunction with these embodiments, it will be understood that they are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents, which may be included within the scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present technology, numerous specific details are set forth in order to provide a thorough understanding of the present technology. However, it is understood that the present technology may be practiced without these specific details. In other instances, well-known methods, procedures, components, and circuits have not been described in detail as not to unnecessarily obscure aspects of the present technology. 
     Referring now to  FIG. 2 , an exemplary system for transmitting and receiving signals, in accordance with embodiments of the present technology, is shown. In one embodiment, the system includes a plurality of devices  205  and  225  communicatively coupled by a communication network. A first device  205  may include a transmitter  210 , a receiver  215  and optionally an equalizer  220 . A second device  225  may include a pre-distortion circuit  230 , a transmitter  235 , a receiver  240 , a distortion determination circuit  250  and optionally an equalizer  245 . The first and second devices  205  and  225  transmit and receive signals across one or more communication paths  255  of the communication network. 
     The communication paths may be wired links, wireless links or a combination thereof. In one exemplary implementation, the devices may be consumer electronic devices and the network may be a home multimedia network. In one implementation, the signal may be transmitted at a frequency in the megahertz (MHz) or gigahertz (GHz) range. In an exemplary implementation, the signal may be transmitted at 60 GHz. Operation of the system will be further described with reference to  FIG. 3 , which shows a method of transmitting and receiving signals in accordance with one embodiment of the present technology. 
     With respect to  FIG. 2  and  FIG. 3 , at  305 , a first input signal [T( 1 )] is presented to the transmitter  210  of the first device  205  for transmission. Alternatively, the first input signal [T( 1 )] may be generated internally by the transmitter  21   0 . The first input signal [T( 1 )] may be any signal to be transmitted by the first device  205  across the communication path  255 . In one implementation, the first input signal [T( 1 )] is a training or configuration signal specifically utilized to determine the nature of the distortion or interference on the communication path  255 . In another implementation, the first input signal [T( 1 )] may be a predetermined control signal or general data signal that facilitates the determination of the nature of the distortion or interference on the communication path  255 . For example, the signal may be a predictable control signal transmitted from the first device  205  to the second device  225   
     At  310 , the first input signal [T( 1 )] is transmitted across the communication path  255  by the transmitter  210 . At  315 , the first input signal distorted by channel distortion D( 1 ) due to transmission across the communication path. The transmitted signal is represented here as a convolution product, [T( 1 )]*[D( 1 )], and is received by the receiver  240  of the second device  225 . At  320 , the distortion [D( 1 )] introduced by the communication path  255  is automatically determined by the distortion determination circuit  250  since the training signal T( 1 ) is a known signal. 
     In accordance with embodiments of the present invention, the nature of the distortion or interference may then be used to pre-distort signals transmitted from the second device  225  to the first device  205  or optionally vice-versa. For example, the pre-distortion circuit  230  of the second device  225  may receive a second signal [T( 2 )], for transmission to device  205  at  325 . At  330 , the second signal [T( 2 )] is pre-distorted by [D( 1 ) −1 ] at the pre-distortion circuit  230 . The pre-distortion [D( 1 ) −1 ] is a function of the distortion on the communication path  255  determined at process  320 . At  335 , the transmitter  235  in the second device  225  transmits the pre-distorted signal [T( 2 )]*[D( 1 ) −1 ] across the communication path  255  which introduces a determined amount of distortion [D( 2 )]. The distortion [D( 2 )] from the communication path  255  and the pre-distortion [D( 1 ) −1 ] introduced by the pre-distortion circuit  230  of the second device  225  produce convolved distortion [D( 2 )]*[D( 1 ) −1 ]. If this convolution product=1, the recovered signal T( 2 ) will be correct and the pre-distortion introduced by device  225  enables recovery of signal T( 2 ) at device  205 . 
     At  340 , the receiver  215  in the first device  205  receives the pre-distorted signal [T( 2 )]*[D( 1 ) −1 ] further distorted by [D( 2 )] after transmission across the communication path  255 . If the product of [D( 2 )]*[D( 1 ) −1 ]≠1 at  345 , the equalizer  220  in the first device equalizes, or performs some amount of signal recovery on the pre-distorted signal further distorted [T( 2 )]*[D( 1 ) −1 ]*[D( 2 )] by transmission across the communication path to recover the second signal [T( 2 )]. The convolved distortion [D( 2 )]*[D( 1 ) −1 ] is recoverable by the equalization function [D(n) −1 ] of the equalizer  220 . At  350 , the recovered second signal [T( 2 )] is output by the equalizer  220  for use by other circuits of the first device  205 . It is appreciated that equalization is discussed herein as an example of a signal recovery process that may be employed. However, this embodiment operates equally well employing other forms of signal recovery, e.g., multi-path, amplitude, frequency, phase and other well known types and is therefore not limited to equalization. 
     It is appreciated that the equalizer  220  may be a separate circuit or integral to the receiver  215 . It is also appreciated that in some instances, the pre-distortion applied by the pre-distortion circuit  230  may eliminate the need for an equalizer  220  when the nature of the distortion and/or interference on the communication path  255  can be fully compensated for by the pre-distortion circuit  230 . However, in other implementations, the amount of pre-distortion applied by the pre-distortion circuit  230  does not fully compensate for the distortion on the communication path  255 . Instead, the amount of pre-distortion applied is selected so that the distortion introduced by the communication path  255  is recoverable by the receiver  215  and/or equalizer  220  while reducing the complexity of the receiver  215  and/or equalizer  220 . Furthermore, it is appreciated that the devices may be implemented using separate receivers and transmitters or the transmitter and receivers circuits may be implemented as an integral transceiver. It is also appreciated that the receiver and transmitter and optionally the equalizer, distortion determination circuit and/or pre-distortion circuit may be implemented as integral sub-circuits of the device or an internal or external peripheral of the device, such as a network interface card. 
     In one embodiment, a given application may only need pre-distortion for communication in one direction. For example, a DTV may only transmit control signals requiring a relatively low transmission rate to one or more content sources such as a set top box (STB). However, in the other direction, the set top box transmits a large amount of image data that requires a high transmission rate, which may experience high bit error rates when the distortion and/or interference on the communication path  255  is greater than a particular level. Therefore, implementing pre-distortion in the set top box may be sufficient for such a configuration. In other embodiments it may be desirable to implement pre-distortion in both devices. Therefore, the first device  205  may also include a distortion determination circuit  260  and a pre-distortion circuit  265  in the first device  205  for determining the distortion [D( 1 )] introduced by the communication path  255  and pre-distorting signals transmitted by the first device  205 . Likewise, the second device  225  may include an equalizer  245  to recover pre-distorted signals transmitted by the first device  205 . 
     Referring now to  FIG. 4 , a method of transmitting and receiving signals, in accordance with other embodiments of the present technology, is shown. The system implementing the method of  FIG. 4  may be the communications system of  FIG. 2 , for instance. At least one transmitter, e.g., of device  205  contains a distortion determination circuit  260  and a pre-distortion circuit  265 . A back channel exists between the transmitter  235  of device  225  and the receiver  215  of device  205 . 
     Regarding  FIG. 4 , at  405 , there is a first input signal [T( 1 )] to be transmitted by the first device  205  across the communication path  255 . The first signal [T( 1 )] is pre-distorted by [D( 1 )] by the pre-distortion circuit  265 , at  410 . The first input signal [T( 1 )] may be distorted based upon the nature of the distortion or interference on the communication path  255  as previously determined by the distortion determination circuit  260  during receipt of a previous signal (e.g., during process  460  described below). At  415 , the pre-distorted signal [T( 1 )]*[D( 1 ) −1 ] is transmitted by the transmitter  210  across the communication path  255 . 
     At  420 , the receiver  240  of the second device  225  receives the pre-distorted signal [T( 1 )]*[D( 1 ) −1 ] further distorted by [D( 1 )] after transmission across the communication path  255 . The received pre-distorted signal is represented as[[T( 1 )]*[D( 1 ) −1 ]]*D( 1 ). At  425 , the equalizer  245  of the second device  225  equalizes the received pre-distorted signal by D( 1 ) −1  to recover the first signal [T( 1 )]. At  430 , the recovered signal [T( 1 )] is output from the equalizer  245  for use by other circuits of the second device  225 . In addition, the distortion determination circuit  250  determines the distortion [D( 1 )] on the communication path  255 , at  435 . The distortion [D( 1 )] may be used by the pre-distortion circuit  230  to pre-distort signals (e.g., during process  445  described below). It is appreciated that equalization is discussed herein as an example of a signal recovery process that may be employed. However, this embodiment operates equally well employing other forms of signal recovery, e.g., multi-path, amplitude, frequency, phase and other well known types and is therefore not limited to equalization. 
     At  440 , there is a second input signal [T( 2 )] to be transmitted by the second device  225  across the communication path  255  to device  205 . The second signal [T( 2 )] is pre-distorted [D( 1 ) −1 ] by the pre-distortion circuit  230 , at  445 . The second input signal [T( 2 )] may be distorted based upon the nature of the distortion or interference on the communication path  255  as determined by the distortion determination circuit  230  during receipt of a previous signal (e.g., during process  435  described above). At  450 , the pre-distorted signal [T( 2 )]*[D( 1 ) −1 ] is transmitted by the transmitter  235  across the communication path  255 . 
     At  455 , the receiver  215  in the first device  205  receives the pre-distorted signal [T( 2 )]*[D( 1 ) −1 ] further distorted by [D( 2 )] after transmission across the communication path  255 . At  460 , the equalizer  220  equalizes the received pre-distorted signal [[T( 2 )]*[D( 1 ) −1 ]]*[D( 2 )] to recover the first signal [T( 2 )]. At  465 , the recovered signal [T( 2 )] is output from the equalizer  220  for use by other circuits of the first device  205 . In addition, the distortion determination circuit  260  determines the distortion [D( 1 )] on the communication path  255 . The nature of the distortion or interference determined by the distortion determination circuit  260  is used at process  410  to apply an appropriate amount of pre-distortion [D( 1 ) −1 ]. Again, the distortion [D( 1 )] on the communication path  255  may be determined for each signal received by the receiver  215  or periodically when the distortion changes over time. In another implementation, the distortion can be determined during a setup stage or when a parameter such as bit error rate (BER) exceeds a predetermined level when the distortion does not regularly fluctuate. 
     The above described embodiments are intended for use when the distortion on the communication path  255  is substantially the same when signals are transmitted from the first device  205  to the second device  225  and from the second device  225  to the first device  205 . However, in other circumstances the distortion on the communication path is not the same in both directions between two devices and may also differ between different devices. Therefore, in another embodiment (as shown in  FIG. 5 ), data indicating the distortion determined at process  435  is transmitted from the second device  225  back to the first device  205  and used by the pre-distortion circuit  260  of the first device  205  to pre-distort the signal (T( 1 )) transmitted from the first device  205  to the second device  225  at process  410 . Similarly, data indicating the distortion determined at process  470  is transmitted from the first device  205  back to the second device and used by the pre-distortion circuit  230  of the second device  225  to pre-distort the signal (T( 2 )) at process  445 . 
     In another embodiment, a signal is transmitted from the first device  205  to the second device  225 . The signal is re-transmitted (e.g., reflected back) by the second device  205  to the first device  225  pre-distorted [D( 1 ) −1 ] by the second device  225  as a verification that the pre-distortion substantially compensates for the distortion introduced by the communication path  255 . In yet another embodiment, an iterative method might include using simple robust training signals that gradually increase in complexity while pre-distortion and equalization circuits keep correcting such that a complex modulation scheme (e.g., conveying higher data rates) can be possible with the dual efforts of the pre-distortion circuits and equalizer, see  FIG. 5 . The training signal may be known signal transmitted from one device to the other periodically. In one instance, for example, frames of data sent from one device to the other are aggregated into “superframes.” Each frame may have its own forward error correction (FEC). Each superframe may have training data in the header with which to generate the current instantaneous multipath distortion for the given path. Therefore, the inverse distortion factor may be determined from the expected payload [T( 1 )] *[D( 1 )]. The inverse distortion factor [D( 1 ) −1 ] can be sent back to the other device to be used as the pre-distortion [D( 1 ) −1 ]. 
     In one implementation, the channel frequency response is determined. The inverse of the channel frequency response may then be used by the pre-distortion circuit  430  to pre-distort signals. In another implementation, the amount of pre-distortion applied by the pre-distortion circuit  430  may be a function of the impulse response of the communication path  445 . The distortion [D( 1 )] on the communication path  445  may be determined for each signal received by the transceiver  435 , or periodically. In other implementations, the distortion can be determined during a setup stage or based on a parameter, such as when a bit error rate (BER) exceeds a predetermined level. 
     The signals are pre-distorted so that the distortion does not exceed the capabilities of the receiver at the other end of the channel. The techniques advantageously reduce the complexity of the receiver by placing some of the burden (e.g., circuit complexity) on the transmitter. The back channel can be exploited to compensate the original signal for the current state of the communication channel. This can result in improved performance, such as fewer bit errors and/or greater link distances, when compared to substantially similar systems without the pre-distortion modulation under substantially the same environmental factors. Accordingly, embodiments of the present technology advantageously reduce the complexity of the conventional communication interface. The reduced complexity typically translates to reduced die size of the integrated circuit implementing the communication interface and therefore may also lower the cost of the integrated circuit. 
       FIG. 5  illustrates a communication methodology in an asymmetric system where complex modulation can be employed while using equalizers and recovery circuits having only reduced complexity. The asymmetric system includes a source device  510  and a sink device  515 . The source  510  is capable of pre-distortion and equalization. The source also advantageously supports multiple modulations from simple to complex (e.g., M 1 , M 2 , M 3 , . . . , Mn) and also supports a simple demodulation for reduced complexity. In one embodiment, M 1  may be BPSK modulation and M 2  may be QPSK modulation and M 3  may be 16 QAM modulation, however, any of a number of well known modulation techniques can be used. 
     The sink device  515  has only minimal equalization capability but supports multiple demodulations, from simple to complex (e.g., M 1   −1 , M 2   −1 , M 3   −1 , . . . , Mn −1 ). The sink  515  also supports a simple modulation scheme (e.g., M 1 ) for the return channel back to the source  510  and may support more complex modulations optionally. The asymmetric system is advantageous in that: 1) a simple equalizer is required of the sink device  515 , 2) a simple modulator is required of the sink device  515  and 3) a simple equalizer and demodulator are required of the source device  5   10 . It is appreciated that pre-distortion functionality as described below is performed in the digital domain in accordance with embodiments of the present invention. 
     It is appreciated that equalization is discussed herein as an example of a signal recovery process that may be employed. However, this embodiment operates equally well employing other forms of signal recovery, e.g., multi-path, amplitude, frequency, phase and other well known types and is therefore not limited to equalization. 
     In accordance with  FIG. 5 , the sink device  515  sends a training signal or data packet T( 1 ) to the source device  510  using a simple modulation M 1   520 . The training signal is known to the source device  5   10 . The transmit signal is represented at  525  as [T( 1 )*M 1 ]*D 1  where D 1  is the distortion of the communication channel as seen using modulation M 1 . Channel distortion can have phase, amplitude and multipath distortion characteristics which may all be non-linear. Herein, a distortion description, Dx, is valid for a single type of modulation, Mx, but may not be accurate for more advanced modulations, e.g., M(x+1). The source device  510  receives the signal  525  and equalizes the signal and demodulates the signal until the known training data packet T( 1 ) is recovered at  527 . Since the source device  510  knows the modulation M 1  used, the equalizer is varied in a feedback loop fashion until the known training signal T( 1 ) is recovered. When recovered, the equalizer located a good first order approximation of the channel distortion, or D 1   −1 . This first order approximation is good enough for the simple modulation M 1 . 
     The source  510  then sends “known” training signal or data packet T( 1 ) using a more complex modulation M 2   530  to the sink  515  and using pre-distortion D 1   −1  at  532 . That is, the signal transmitted by the source  510  is pre-distorted by D 1   −1 . This transmission is also distorted by channel distortion D 2  when recovered by the sink device  515 . The sink device  515  equalizes this slightly by D 1 ′ until the training signal is recovered at  534 . The equalization performed at this point is not complex because the transmitted signal at  532  was pre-distorted already by D 1   −1  at the source device, where D 1   −1  is good enough to recover a signal modulated by M I but not enough for M 2 . It is noted that D 2 =D 1 *D 1 ′. This equalization characteristic is advantageous for the sink  515  because a less complex equalizer can be used since only D 1 ′ −1  is employed, rather than D 2   −1 . 
     At this point, the sink device  515  communicates D 1 ′ to the source device  510  using the simple modulation M 1 . Specifically, the sink device uses simple modulation M 1  to transmit D 1 ′ to the source device at  536 . This transmission  536  experiences channel distortion D 1 . The source device  510  already knows the channel distortion approximation D 1   −1  and the modulation scheme M 1 , so the data packet D 1 ′ is readily recovered at  538 . Since the source device knows D 1 ′ and D 1 , it can advantageously compute D 2 , a second order approximation of the channel distortion for modulation M 2 . Source  510  now sends T( 1 ) again by transmission  542  but using a more complex modulation scheme, M 3   540 , with the transmitted signal pre-distorted by the second order pre-distortion, D 2   −1 . The sink  515  again has to equalize the recovered signal slightly because the D 2   −1  pre-distortion is good enough for M 2 , but not quite good enough for M 3 . Equalization continues until the training signal is recovered at  544 . This leads to distortion approximation D 2 ′(D 3 =D 2 *D 2 ′). Again, the sink  515  sends back to the source  510  (using M 1 ) the additional equalization T(D 2 ′) necessary to decode T( 1 ) when modulated with M 3 . This is shown as  546 . 
     The source device  510  already knows the channel distortion approximation D 1   −1  and the modulation scheme Ml, so the data packet D 2 ′ is readily recovered at  538 . Since the source device knows D 2 ′ and D 2 , it can advantageously compute D 3 , a third order approximation of the channel distortion for M 3 . This third order channel distortion D 3  can be used by the source device  510  to communicate large amounts of data to the sink device  515  using pre-distortion D 3   −1  and modulation M 3 , as shown in general terms by transmission  560 ,  565  and  570 . The above process is iterative, as shown in general terms by transmission  550  and  560 , with each group of communications providing for more complex modulation while using limited equalization. The number of iterations is variable depending on the modulation required and the particular number of iterations shown in  FIG. 5  is exemplary. 
     A result of the communication methodology of  FIG. 5  is complex modulation and the corresponding complex pre-distortion that allows the receive side to use little or no signal recovery, e.g., equalization in the above example. Circuit complexity is generally linked to modulation complexity and the degree of channel distortion that is expected. However, by simplifying the receiver side embodiments of the present invention reduce the number of necessary bits in the analog to digital converter circuits which in turn reduces power consumption. 
     High speed analog circuitry has fewer accurate models, and is more difficult. Therefore, embodiments as shown in  FIG. 5  allow the use of increasingly complex modulation schemes while not requiring a large/complex equalization circuit in the sink device  515 . 
     The foregoing descriptions of specific embodiments of the present technology have been presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed, and obviously many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the present technology and its practical application, to thereby enable others skilled in the art to best utilize the present technology and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the Claims appended hereto and their equivalents.