Abstract:
A system is disclosed for providing communication across a wireless network. The system includes a transmitter transmitting a modulated signal across a radio channel, wherein the transmitter includes first input means for receiving a primary data signal to be transmitted, second input means for receiving a secondary data signal to be transmitted, a combiner associated with the first and second input means for combining the primary and secondary data signals, and a modulator receiving the combined primary and secondary data signals from the combiner and sequentially developing a modulated signal including a string of phase values with each phase value containing information relative to both the primary and secondary data signals. The system also includes a receiver for receiving the modulated signal, wherein the receiver includes means for separating the received modulated signal into primary and secondary phase values representative of the primary and secondary data signals.

Description:
FIELD OF THE INVENTION 
     The present invention is directed toward an apparatus and method for increasing the effective data rate of a transmitted signal and, more particularly, toward increasing the effective data rate of a phase modulated signal. 
     BACKGROUND OF THE INVENTION 
     The use of multi-level modulation techniques (phase and amplitude) are generally well known. Increasing the level of modulation at a transmitter effectively increases its data rate, i.e., increases the number of bits per symbol that may be transmitted. For instance, π/4-DQPSK (Differential Quadrature Phase Shift Keying) modulation is a well known 2-level modulation technique transmitting two bits per symbol. Another well known modulation technique, 16QAM (Quadrature Amplitude Modulation), is a 4-level modulation technique transmitting four bits per symbol. While the higher level modulations provide higher data rates for the same channel bandwidth, there is a loss in channel sensitivity which may cause distortion under high SNR (Signal-to-Noise Ratio) conditions. Thus, higher level modulations are more reasonable at relatively good channel conditions. 
     Modern telecom modems utilize 256QAM modulation to transmit eight bits per symbol. Thus, noise will have a strong effect on the performance of the transmission link, or data pipeline. Accordingly, in noisy channel conditions the modem will automatically revert to lower modulation techniques that have greater noise immunity. 
     In wireless communication systems, fully linear modulation, such as 16QAM and higher modulation levels, is difficult to design and control. This is particularly due to the large dynamic range of RF (Radio Frequency) links, or channels, present in fully linear modulation. A system using fully linear modulation techniques requires sensitive linear receivers having accurate, dynamic AGC (Automatic Gain Control) amplifiers, transmitters with linear PAs (Power Amplifiers), and other such components. 
     Utilizing PSK (Phase Shift Keying) type modulation enables IF (Intermediate Frequency) limited receivers to be utilized, while providing some level of modulation depth. However, one drawback is that since PSK is phase-only modulation, the second dimension of amplitude modulation available to QAM type modulations is unavailable in PSK modulation. The modulation bits per symbol in phase-only modulation (PSK) is limited by how finely one can space the points of the differential constellation around the unit circle. 
     The four possible phase transitions available in π/4-DQPSK modulation provide a high level of noise immunity. Thus, there is some maneuvering room when it comes to expanding π/4-DQPSK to higher bits per symbol in good channel conditions. If π/4-DQPSK is expanded to include more constellation points, the receiver at the receiving link would need to be notified that a new differential constellation spacing is being transmitted with a higher level of bits per symbol. This would require a full coordination of the transmitting and receiving units. However, when expanding π/4-DQPSK to a higher bits per symbol rate, the issue of AM (Amplitude Modulation) should be considered. As the spacing of the π/4-DQPSK differential constellation grows, so does the chance of phase transitions close to zero level amplitude, which cannot be handled by the transmitter. This limits π/4-DQPSK expansion. 
     The present invention is directed toward overcoming one or more of the above-mentioned problems. 
     SUMMARY OF THE INVENTION 
     A system is disclosed for providing communication across a wireless network. The system includes a transmitter transmitting a modulated signal across a radio channel, wherein the transmitter includes first input means for receiving a primary data signal to be transmitted, second input means for receiving a secondary data signal to be transmitted, a combiner associated with the first and second input means for combining the primary and secondary data signals, and a modulator receiving the combined primary and secondary data signals from the combiner and sequentially developing a modulated signal including a string of phase values with each phase value containing information relative to both the primary and secondary data signals. The system also includes a receiver for receiving the modulated signal, wherein the receiver includes means for separating the received modulated signal into primary and secondary phase values representative of the primary and secondary data signals. 
     The above-described system transparently increases the effective transmitted data rate using phase modulation techniques. The existing infrastructure and hardware available in a π/4-DQPSK communication system are utilized with little change in software. The system is particularly useful in relative good channel conditions and increases the perceived usefulness of communication systems utilizing π/4-DQPSK modulation techniques. 
     In one form, the first input means includes a first impulse stream encoder receiving the primary data signal and generating a first impulse stream representative thereof. The second input means includes a second impulse stream encoder receiving the secondary data signal and generating a second impulse stream representative thereof. 
     In another form, the second impulse stream encoder receives an information signal from the first impulse stream encoder indicative of the phase transition in the primary data signal. The second impulse stream generated by the second impulse stream encoder represents a modification of the phase transition in the primary data signal. 
     In another form, the combiner includes a summer summing the first and second impulse streams. 
     In another form, the modulated signal includes a DQPSK signal. 
     In another form, the modulator includes an IQ modulator. 
     In another form, the separating means includes first determining means for determining the primary phase values from the received modulated signal, and second determining means responsive to the first determining means for determining the secondary phase values from the received modulated signal. 
     In yet another form, the first determining means includes a phase differentiator determining differences between successive phase values in the received modulated signal, the differences including the primary phase values, and a first converter converting the primary phase values into an approximation of the primary data signal. The second determining means includes a second converter converting the approximated primary data signal into converted phase values, and a subtractor subtracting the primary phase values from the converted phase values to generate the secondary phase values. 
     In still another form, the second determining means further includes a third converter converting the secondary phase values into an approximation of the secondary data signal. 
     A method of communication across a wireless network is also provided. The method includes the steps of transmitting a modulated signal across a radio channel, the modulated signal including a string of phase values with each phase value containing information relative to primary and secondary data signals, receiving the modulated signal, and separating the received modulated signal into primary and secondary phase values representative of the primary and secondary data signals. 
     In one form, the step of transmitting a modulated signal across a radio channel includes the steps of receiving the primary data signal to be transmitted, receiving the secondary data signal to be transmitted, combining the primary and secondary data signals, modulating the combined primary and secondary data signals to sequentially develop the modulated signal, and transmitting the modulated signal across the radio channel. 
     In another form, the step of transmitting a modulated signal across a radio channel further includes the steps of generating a first impulse stream representative of the primary data signal, and generating a second impulse stream representative of the secondary data signal. The step of combining the primary and secondary data signals includes the step of combining the first and second impulse streams. 
     In another form, the step of combining the first and second impulse streams includes the step of summing the first and second impulse streams together. 
     In another form, the modulated signal includes a DQPSK signal. 
     In another form, the step of separating the received modulated signal into primary and secondary phase values representative of the primary and secondary data signals includes the steps of determining the primary phase values from the received modulated signal, and determining, responsive to the primary phase value determination, the secondary phase values from the received modulated signal. 
     In yet another form, the step of determining the primary phase values from the received modulated signal includes the steps of determining differences between successive phase values in the received modulated signal, the differences including the primary phase values, and converting the primary phase values into an approximation of the primary data signal. The step of determining, responsive to the primary phase value determination, the secondary phase values from the received demodulated signal includes the steps of converting the approximated primary data signal into converted phase values, and subtracting the primary phase values from the converted phase values to generate the secondary phase values. 
     In still another form, the step of determining, responsive to the primary phase value determination, the secondary phase values from the received modulated signal further includes the step of converting the secondary phase values into an approximation of the secondary data signal. 
     It is an object of the present invention to increase the effective transmitted data rate in a communication system using phase modulation techniques. 
     It is a further object of the present invention to increase the effective transmitted data rate in a π/4-DQPSK communication system. 
     It is a further object of the present invention to transparently increase the effective transmitted data rate in a π/4-DQPSK communication system. 
     It is a further object of the present invention to increase the effective transmitted data rate in a π/4-DQPSK communication system utilizing the existing infrastructure and hardware, with little change in software. 
     It is still a further object of the present invention to increase the perceived usefulness of π/4-DQPSK communication systems. 
     It is yet a further object of the present invention to increase the effective transmitted data rate in π/4-DQPSK communication systems in relatively good channel conditions. 
     Other aspects, objects and advantages of the present invention can be obtained from a study of the application, the drawings, and the appended claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a differential constellation diagram of the symbols utilized in a π/4-DQPSK communication system; 
     FIG. 2 is a differential constellation diagram of the symbols included in the primary and secondary channel transitions in an enhanced π/4-DQPSK communication system according to the present invention; 
     FIG. 3 is a block diagram of a transmitter utilized in the enhanced π/4-DQPSK communication system according to the present invention; and 
     FIG. 4 is a block diagram of a receiver utilized in the enhanced π/4-DQPSK communication system of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     FIG. 1 illustrates the differential constellation diagram utilized in a conventional π/4-DQPSK modulator. As previously described, π/4-DQPSK modulation is a 2-level modulation technique transmitting two bits per symbol. A π/4-DQPSK modulator receives a stream of bits, two bits at a time, i.e., one symbol at a time, and responds to each bit pair by generating a two-component output signal specifying one of eight points A-H equally spaced about a circle, shown dotted at  10 , in the complex plane defined by real (I) and imaginary (Q) axes. The phase of each point A-H represents a different phase with respect to a carrier on which the output signal is modulated. Each of the four possible 2-bit combinations results in a different one of four (2 2 ) possible shifts from the previous phase, namely, ±π/4 and ±π/4. Accordingly, the output of a π/4-DQPSK modulator depends not only on its current 2-bit input, but also on the state of its previous output. 
     As FIG. 1 shows, if the symbol generated at a given time represents an even multiple of π/4 (states A, C, E or G), the subsequent symbol can represent only an odd multiple of π/4 (states B, D, F or H). The same is true of all odd multiples of π/4. If the phase that results from one symbol in the bit stream is an odd multiple of π/4 (states B, D, F or H), the phase resulting from the subsequent symbol will be an even multiple of π/4 (states A, C, E or G). 
     As an example, assume that the current symbol is at state A, representing a phase angle of  0  radians. The subsequent symbol can represent only an odd multiple of π/4. That is, from state A, phase transitions can only occur to states B (π/4), D (3π/4), F (-3π/4) or H (-π/4). Assume that the phase transitioned to state B. Then, the next symbol subsequent to state B, can represent only an even multiple of π/4. Thus, from state B, phase transitions can only occur to states C (π/2), E (π), G (-π/2) or A ( 0 ). The phase transitions occur throughout the bit stream. 
     FIG. 2 shows a differential constellation of the enhanced π/4-DQPSK modulation technique according to the present invention, illustrating the primary and secondary phase (or channel) transitions. The primary phase transitions occur between states A-H and are the phase transitions which occur in conventional π/4-DQPSK modulation as previously described with respect to FIG.  1 . 
     The secondary phase transitions are illustrated as “X&#39;s” around the primary phase transitions A-H. For convenience, secondary channel transitions are only illustrated at states B, D, F and H in FIG.  2 . The primary phase transitions contain the bulk of the phase information, while the secondary phase transitions contain smaller amounts of phase information used to adjust or modify the primary phase transition. An understanding of the different constellation shown in FIG. 2 will become apparent as the transmitter and receiver according to the present invention are described below. 
     FIG. 3 is a block diagram of a transmitter, shown generally at  12 , according to the present invention. The transmitter  12  includes an enhanced π/4-DQPSK modulator  14 . In such an arrangement, a signal (voice, data, etc.) is applied to the transmitter  12  front-end circuitry (not shown), which digitizes the signal, performs various levels of encoding and framing of the resultant raw digitized signal, and produces a resultant output as a stream of bits. These are illustrated in FIG. 3 as primary  16  and secondary  18  bit streams, respectively. The primary bit stream  16  is input to an impulse stream encoder  20  which generates a complex signal as a series of impulses on a line  21  representative of the primary bit stream  16 . The secondary bit stream  18  is also input to an impulse stream encoder  22 , which generates a complex signal as a series of impulses on a line  23  representative of the secondary bit stream  18 . However, the series of impulses on the line  23  produced by the impulse stream encoder  22  is dependent on the series of impulses on the line  21  produced by the impulse stream encoder  20 , via the next state info signal  24  produced by the impulse stream encoder  20  and received by the impulse stream encoder  22 . The next state info signal  24  contains information regarding the primary phase transition. 
     The impulse stream encoder  20  determines the phase transition from the present primary state to the next primary state. For instance, referring to FIG. 2, if the primary phase transition occurred between states A (present state) and state D (next state), the impulse stream encoder  20  would add 3π/4 to the present state A to transition to the next state D. The next state info signal  24  essentially informs the impulse stream encoder  22  of the amount of angular movement in the primary phase transition, along with the state transition information, e.g., state transition from state A to state D. This information is utilized by the impulse stream encoder  22  to determine the secondary phase transition to arrive at one of the sub-states (X&#39;s) around the primary phase transition. The impulse stream encoder  22  will shift the primary phase transition (+3π/4) a predetermined amount of radians to arrive at the secondary phase transition. Both the primary and secondary transitions can be viewed as moving from a reference point to a next point in the differential plane of FIG. 2 defined by the real (I) and imaginary (Q) axes. An example of illustrating operation is provided below. 
     Referring to FIGS. 2 and 3, assume the primary bit stream  16  represents the digitized bits “001101 . . . ” and the secondary bit stream  18  represents the digitized bits “011011 . . . ”. Since π/4-DQPSK modulation is a 2-level modulation technique, two bits are represented in each DQPSK symbol. The impulse stream encoder  20  receives the first two bits of the primary bit stream  16 , namely, “00”. Assume further that the present state is state A, indicated as the active state in FIG.  2 . Receiving bits “00” at the impulse stream encoder  20  represents a primary phase transition of 45° to state B. (For clarity purposes, phase transitions will hereafter be referred to in terms of degrees rather than radians.) The resulting impulse stream  21  output by the impulse stream encoder  20  will reflect this phase transition. 
     Transitioning from state A to state B can be viewed as simply adding 45° to state A to transition to state B. This addition of 45°, along with state transition information in the form of the present to next state transition, is represented on the next state info signal  24  input to the impulse stream encoder  22 . The impulse stream encoder  22  receives the first two bits of the secondary bit stream  16 , namely, “01”. By knowing the phase (+45°) and state (A to B) transitions of the primary channel, via next state info signal  24 , and knowing a priori the bit representations of the secondary phase transitions, the impulse stream encoder  22  is able to generate the impulse stream  23  representing a modification of the primary phase transition, i.e., the secondary phase transition. 
     The impulse stream encoder  22  is programmed with the secondary phase transition spread and also with the bits represented by each secondary state within the spread. For example, assume that the secondary spread is 10°, then the secondary states would occur around the primary states A-H at ±10° intervals, with the number of secondary states limited by the number of bits per symbol increase associated with the secondary channel. 
     As shown in FIG. 2, increasing the data rate by two bits per symbol, results in four secondary states surrounding each primary state A-H. If a 10° secondary spread is assumed, one bit allocation scheme might be as follows: +20° represents 00; +10° represents 01; −10° represents  1 ; and −20° represents  11 . Of course, other bit allocation schemes and/or phase spreads may be utilized without departing from the spirit and scope of the present invention. Further, while the secondary channel is being described herein as adding two bits per symbol, three, four, five, etc. bits per symbol can be added by the secondary channel on top of the existing two bits per symbol of the primary channel. For instance, if the secondary channel added three bits per symbol, eight (2 3 ) secondary states would surround each primary state A-H in FIG.  2 . The number of bits per symbol added by the secondary channel and the secondary phase spread are limited by zero level transitions. 
     The impulse stream encoder  22  knows, via next state info signal  24 , that the primary phase transition is +45° (state A to state B). The impulse stream encoder  22  also knows that the first two bits of the secondary bit stream “01” represent a secondary phase transition of +10°. In order to represent “01” in the secondary phase transition, the impulse stream encoder  22  has to add 10° to the primary phase transition of 45° (state B). Thus, the impulse stream on the line  23  output by the impulse stream encoder  22  represents such addition/subtraction. The impulse streams on lines  21 ,  23  are summed at a summation block  26  producing a complex signal on a line  27  representative of the modified DQPSK phase transition illustrated by arrow  28  in FIG.  2 . The operation of the impulse stream encoders  20 , 22  is primarily done via lookup tables. 
     The complex output of the summation block  26  on the line  27  is input to one or more conventional raised cosine filters  30 , generally having a very consistent impulse response. The complex filtered signal on line  31  is fed to a conventional IQ, or Quadrature, modulator  32  which modulates a carrier  34  primarily with the generated phase information representative of the primary  16  and secondary  18  bit streams. The phase modulated signal  36  is transmitted over the air by the transmitter  12  via antenna  38 . 
     In this manner, the effective transmission rate of the transmitter  12  can be doubled. For instance, if the transmitter  12  is transmitting data packets  0 - 10 , conventionally the transmitter would send the first data packet in slot  0 , wait for an acknowledgement from the receiver, send the next data packet in slot  1 , wait for an acknowledgement from the receiver, send the next data packet in slot  2 , wait for an acknowledgement from the receiver, etc. By utilizing the above-described secondary channel transitions, the transmitter  12  can simultaneously send the primary channel transition in slot  0  and the secondary channel transition, representing the next data packet, in slot  1 . If an acknowledgement is received from the receiver indicating that both slots were received, the transmitter  12  knows that the receiver is receiving the secondary channel and the data rate of the transmitter  12  has been effectively doubled. This would require the implementation of some type of ACK/NACK (Acknowledge/Not Acknowledge) protocol to let the transmitter know whether the secondary channel transitions are being demodulated. RSSI (Received Signal Strength Information) levels, or some other means, could be used as well. 
     FIG. 4 illustrates a receiver, shown generally at  40 , according to the present invention. The receiver  40  includes a demodulator  42  receiving the transmitted signal  36  via an antenna  44 . A phase differentiator, or differential phase extractor,  46  measures the differential phase in the received/demodulated signal on line  48 . The differential phase output by the differential phase extractor  46  is received by a phase to bit converter  50  which converts the measured differential phase into a string of primary channel bits. The string of bits output by the phase to bit converter  50  is input to a bit to phase converter  52 , which converts the primary channel bits into a relative phase. A summation block  54  subtracts the relative phase from the measured differential phase. The output of the summation block  54  is fed to a phase to bit converter  56  which converts the resulting phase values to a string of secondary channel bits. Detailed operation of the receiver  40  is provided below. 
     The demodulator  42  receives the transmitted signal  36  and essentially extracts only the phase information present on the modulated carrier of the transmitted signal. The phase information is output by the demodulator  42  as a series of symbols on the line  48 . The series of symbols on the line  48  are input to the differential phase extractor  46  which extracts the differential phase over a period of one symbol. Essentially, the differential phase extractor  46  extracts the phase at the beginning and at the end of a symbol, and determines the difference. 
     The output of the differential phase extractor  46  is fed to a sync control  58  which determines if there is a sequence of phase transitions that represent a sync word. The sync control  58  enables the acquisition of initial phase, initial frequency offset, and symbol/frame timing, which are necessary for demodulation. After syncing is complete, the receiver  40  essentially knows the precise point at which the transmitted data begins, and can begin demodulating. 
     The output of the differential phase extractor  46  is also input to the phase to bit converter  50  which takes the phase difference determined by the differential phase extractor  46  and maps it to two bits. The phase to bit converter  50  maps the phase differences to the primary channel bits. As an example, referring to FIG.  2  and assuming that the secondary channel transitions are not present, assume that the present state is state A and the differential phase extractor determined a phase difference of 45°. A phase transition of 45° indicates a transition to state B. The phase to bit converter  50  maps the phase transition of 45° to state B and outputs “00” as the primary channel bits. Similarly, a phase transition of 135° indicates a transition to state D. The phase to bit converter  50  maps the phase difference of 135° and outputs “01” as the corresponding primary channel bits. 
     However, since the primary phase transitions have been adjusted to accommodate secondary channel bits, the differential phase extractor  46  will determine phase differences not equal to the phase differences associated with the primary channel transitions A-H. Accordingly, the phase to bit converter  50  must be able to accommodate the adjustments made to the primary phase transition by the secondary channel. Depending on the spread of the secondary channel, ranges can be set around the primary transitions A-H wherein if a differential phase is determined that falls within a particular range, it will be mapped by the phase to bit converter  50  to the primary transition associated with that particular range. 
     For example, a primary phase transition from state A to state B may be defined as occurring within the range of 10°−80°, 5°−85°, 0°−90°, etc. Thus, if the phase to bit converter  50  receives any phase difference within that range, it outputs “00” as the primary channel bits. Similar ranges may be utilized for the other primary phase transitions. 
     The output of the phase to bit converter  50  is routed to the bit to phase converter  52  which determines the appropriate phase transition from the primary bits. For example, if the primary bits output by the phase to bit converter  50  are “00”, the bit to phase converter  52  would map the primary bits to the corresponding primary channel transition of 45°. Essentially, the bit to phase converter  52  maps the primary bits to the associated primary channel transition, regardless of the phase difference actually determined by the differential phase extractor  46 . 
     In our previous example, the primary channel transition was 45° (state A to state B), and the secondary channel transition was +10°, resulting in a modified phase transition of 55° as shown by arrow  28  in FIG.  2 . Thus, the output of the differential phase extractor  46  would be 55°; the modified phase transition transmitted on signal  36  across the radio channel. This value should fall within an appropriate range set at the phase to bit converter  50 , and is mapped by the phase to bit converter  50  to primary bits “00” which are output as the primary channel bits. The primary bits “00” are fed to the bit to phase converter  52 , which maps them to the primary channel transition of 45°, which is output by the bit to phase converter  52 . 
     The outputs of the differential phase extractor  46  and the bit to phase converter  52  are fed to the summation block  54 , which subtracts the phase value output by the bit to phase converter  52  from the differential phase value determined by the differential phase extractor  46 . In the above example, the summation block  54  performs the operation 55°−45°=10°. 
     The output of the summation block  54 , 10° in the previous example, is fed to the phase to bit converter  56 . The phase to bit converter  56  maps the phase output by the summation block  54  to the secondary channel bits. The phase to bit converter  56  knows a priori the secondary channel spread and the secondary bits associated therewith. The phase to bit converter  56  also receives a state info signal  60  from the phase to bit converter  50 . The state info signal  60  basically tells the phase to bit converter  56  the primary phase transition. By knowing the primary phase transition, the phase to bit converter  56  is able to map the phase values output by the summation block  54  to the secondary bit stream. 
     For instance, referring to FIGS. 2 and 4 in the above example, the state info signal  60  informs the phase to bit converter  56  that the primary phase transition was 45°, namely, from state A to state B. The phase to bit converter  56 , upon receiving a +10° signal from the summation block  54 , maps +10° to the secondary bits “01” which are output as the secondary channel bits. Similarly, if the phase to bit converter  56  would have received a +20° value, it would have mapped phase value to secondary bits “00”. It follows that a −10° value would be mapped to secondary bits “10”, and a −20° value would mapped to secondary bits “11”. The primary and secondary channel bits are then fed to a data modem, a vocoder, a control device, or any other device at the receiving end. 
     It should be noted that the phase values described above will not be exact due to internal component tolerances and external noise and other factors affecting the transmitted signal. However, such fluctuations are common and can be taken into account in system/component design. 
     If the secondary spread is made small, precise phase value measurements are necessary in order to determine the secondary channel transitions. If this is the case, some form of adaptive equalization may be required at the receiver end in order to remove the effects ISI (Intersymbol Interference) on the transmitted signal. ISI is generally caused by the IF filters at the receiving end, and may need to be removed if accurate phase measurement is required. 
     In addition, fading may cause fluctuations in the transmitted signal. If the fluctuation is fast it usually means that a magnitude notch, i.e., a dip in the signal, is present. Otherwise, the phase is probably moving slow relative to the transmitted symbol rate. If the magnitude of the transmitted signal is drastically changing, then both the primary and secondary channels will suffer. In that case the overall bit rate of both the primary and secondary channels would have the same basic BER (Bit Error Rate). 
     Single root raised cosine filters may be used in place of the raised cosine filter at the transmitter. However, both the transmitter and the receiver would require a single root raised cosine filter. Adaptive equalizers may also need to be added for the detection of smaller phase values. At the receiver, the root raised cosine filter would need to placed at the base band signal. 
     Transparent detection of the secondary channel presumes that some FEC (Forward Error Correction) or other coding is used to verify the success or failure of detection. Non-transparent detection of the secondary bits would not require this sensing and would be done by simply transmitting raw bits indicating transmission of the secondary channel. 
     While the invention has been described with particular reference to the drawings, it should be understood that various modifications could be made without departing from the spirit and scope of the present invention.