PHASE SHIFT KEYED SIGNALING WITH FORWARD ERROR CORRECTION AND RAMAN AMPLIFICATION
IN OPTICAL WDM LINKS
BACKGROUND
The present invention relates generally to wavelength division multiplexed optical fiber links, and more particularly, to the use of phase shift keyed coherent optical signaling to mitigate the effects of fiber refractive index nonlinearity in optical fiber links.
The most deleterious effects of refractive index nonlinearities are three-fold, and are commonly known as self-phase modulation, cross-phase modulation and four wave mixing. The motivation for mitigating these phenomena is that they lead to two limits on fiber optic link performance. The first is a maximum limit on transmitted power, which leads to a maximum distance between optical amplifiers and/or a maximum distance of transmission for a given optical amplifier spacing. The second is a minimum limit on the frequency spacing between wavelength division multiplexed optical channels, which limits the total number of optical channels within the optical amplifier bandwidth and hence the total aggregate data capacity on a fiber. These are important factors in the overall cost of transmitting information on fiber optic cables greater than 300 kilometers in length.
Attempts to mitigate these three phenomena in conventional on-off keyed wavelength division multiplexed optical fiber links involved replacing existing
inexpensive chromatically dispersive fiber with fiber cable having lessened chromatic dispersion. However, replacement of hundreds of kilometers of fiber cable is expensive. Moreover, although lessened chromatic dispersion minimizes self- and cross-phase modulation, it magnifies the four wave mixing between wavelength division multiplexed channels. Thus, with prior art on-off keyed signaling, mitigation has primarily involved reducing the dispersion of the fiber until the optimum trade off between self- and cross- phase modulation versus four wave mixing is reached.
More specifically, self- and cross-phase modulation and four wave mixing arise from the inherently nonlinear refractive index of the glass optical fiber medium. In other words, the origin of all three of these phenomena is that the refractive index of glass optical fiber varies instantaneously according to the local intensity of the laser light. Prior art on-off keying, which encodes the data through maximal variation of the intensity of the light, by its very nature maximizes this nonlinear action. The nonlinear action distorts on-off keying optical pulse symbols in the following way. The nonlinear action in an optical pulse consists of the pulse itself locally changing the refractive index of the fiber medium in which it is traveling. The peak of the pulse has a different local refractive index than the flanks. The more intense the pulse, the larger the refractive index distortion. Self-phase modulation is defined as the resultant distortion of the optical phase within the pulse caused by its own optical energy. Cross-phase modulation is defined as the distortion of the optical phase within a pulse caused by a coincident pulse from another wavelength division multiplexed channel. The more closely spaced the optical channels, the more severe the cross phase modulation.
The distortion of the optical phase within the pulse due to the nonlinear action broadens the spectral content of the pulse, but does not in and of itself change the temporal pulse shape. Temporal pulse shape change is brought about by the chromatic dispersion of the optical fiber acting more rapidly on the broadened pulse spectrum. Once a pulse has been nonlinearly distorted by this combination of nonlinearity and chromatic dispersion, simple linear chromatic dispersion compensation will not restore it. This accelerated, uncorrectable chromatic dispersion distortion due to pulse spectral broadening places fundamental limits on the distance and optical channel density on prior art on-off keyed fiber links. This is why prior art reduction of the chromatic dispersion of fiber is helpful to reduce self- and cross-phase modulation action in such links. In the hmit of zero chromatic dispersion fiber, there is no change in pulse shape, and hence in zero dispersion on-off keyed links there are no deleterious consequences of self-and cross-phase modulation. However, as mentioned above, use of reduced chromatic dispersion fiber gives rise to four wave mixing, and so, with on-off keying, a compromise value of dispersion must be chosen.
Four wave mixing is classical mixing of the different optical channels due to the nonlinear fiber medium, and will occur regardless of modulation format, even with unmodulated optical carriers. In an equally spaced wavelength division multiplexed system, the mixing products will fall on top of adjacent channels. This effect places limits on launched optical power and optical channel spacing. As mentioned, chromatic dispersion suppresses four wave mixing.
Therefore, it is an objective of the present invention to provide for the use of phase shift keyed coherent optical signaling, in combination with inexpensive unmodified chromatic dispersion fiber to permit simultaneous reduction of self- and cross- phase modulation and four wave mixing. It is a further objective of the present invention to provide for the use of phase shift keyed coherent optical signaling, in combination with inexpensive unmodified chromatic dispersion fiber, to permit higher transmitted power and increased transmission distance, and allow tighter spacing between wavelength division multiplexed channels. It is another objective of the present invention to provide for the use of phase shift keyed coherent optical signaling, in combination with inexpensive unmodified chromatic dispersion fiber, to reduce the cost of the fiber link and increase the aggregate data transmission capacity per fiber. It is yet another objective of the present invention to provide for the use of forward error correction encoding of transmitted data and Raman amplification of the fiber to extend the phase shift keyed link length.
SUMMARY OF THE INVENTION
To accomplish the above and other objectives, the present invention uses phase shift keyed coherent optical signaling to mitigate self- and cross-phase modulation, and dispersive fiber to mitigate four wave mixing. The present invention uses phase shift keyed coherent optical signaling, in combination with inexpensive unmodified chromatic dispersion fiber (having a dispersion coefficient approximately 17 ps/(nm x km)), to simultaneously reduce self- and cross-phase modulation and four wave mixing. This permits higher transmitted power and increased transmission distance through the fiber link. This also allows tighter spacing between wavelength division multiplexed channels in the fiber link. This also reduces the cost of the fiber link and increases the aggregate data transmission capacity per fiber. Also, the present invention uses forward error correction encoding of the data and Raman amplification of the fiber to extend the phase shift keyed link length. Phase shift keying in accordance with the principles of the present invention mitigates self- and cross-phase modulation. In contrast to on-off keying, phase-shift keying presents a locally constant, uninterrupted optical intensity envelope to the fiber.
The nonlinear action therefore simply yields an altered but locally constant refractive index. Because there is no variation in optical intensity, phase-shift keying ideally results in no self- and cross-phase modulation. Rather, the nonlinear action yields a simple constant optical phase shift that causes no harm to a phase-shift keyed format. Therefore, the dispersion of the fiber need not be reduced, and four wave mixing remains suppressed. This results in higher limits on optical channel power, and thus improved overall link length. It also results in reduced allowable wavelength division multiplexed channel spacing. In fact, in new links, it may be advantageous to install increased chromatic dispersion fiber (> 17 ps/(nm x km)) to suppress four wave mixing further. This would allow even higher optical power and narrower optical channel spacing. In summary, unlike on-off keying, phase shift keying obviates the fiber dispersion value compromise.
Many formats of electrical information may be transmitted by means of phase shift modulation, including analog, binary phase shift keying, quaternary phase shift keying, and higher orders of phase shift keying. These formats all have a constant optical intensity envelope, and thus benefit from the present invention. Of particular interest is quaternary phase shift keying (QPSK) which, as is well known, doubles the spectral efficiency of data transmission versus binary signaling with no optical signal to noise ratio penalty. Also, the narrower optical spectrum of quaternary phase shift keying is less susceptible to chromatic dispersion and polarization mode dispersion than binary signaling. Also, narrower optical channel spacing allows reduction of the total optical wavelength division multiplexed spectrum width, which reduces stimulated Raman scattering. The electronics of a quaternary phase shift keying transmitter need operate at only half the speed of a binary transmitter to achieve the same aggregate bit rate. The present invention also provides for a novel coherent quaternary phase shift keying optical demodulator that incorporates a novel 90 degree optical hybrid.
8-ary phase shift keying and 16-ary phase shift keying formats may be used to trade optical signal-to-noise ratio for even further optical spectral efficiency and reduction in speed of electronics. The optical spectral bandwidth of the quaternary, 8-ary and 16-ary phase shift keyed forinats may also be further compacted by shaping their electronic baseband low pass spectra. For the quaternary case in particular, the commonly known staggered quaternary phase shift keyed, minimum shift keyed, and quaternary advance retard keyed formats are of interest. Of particular interest are the staggered quaternary phase shift keyed and minimum shift keyed formats as they would aid in keeping the launched optical signal power envelope effectively constant even for very narrow optical spectral width requirements.
Unlike on-off keying, a coherent link preserves the phase of the data spectrum. Therefore the receiver may incorporate electrical chromatic dispersion compensation and electrical wavelength division multiplexed channel crosstalk cancellation.
Finally, when the dominant source of link optical noise is optical amplifier amplified spontaneous emission, coherent binary phase shift keying and quaternaiy phase shift keying have been shown to theoretically have a 3 dB smaller optical signal- to-noise power requirement than incoherent on-off keying. Therefore, relative to prior art incoherent on-off keying, the binary and quaternary phase shift keyed formats employed in the present invention allow even longer fiber lengths between optical amplifiers and longer total link length than only the mitigation of fiber nonhnearity suggests.
BRIEF DESCRIPTION OF THE DRAWINGS
The various features and advantages of the present invention may be more readily understood with reference to the following detailed description taken in conjunction with the accompanying drawing, wherein like reference numerals designate like structural elements, and in which:
Figs. 1 and la illustrate an exemplary wavelength division multiplexed fiber optic link in accordance with the principles of the present invention; Fig. 2 illustrates how the constellation points of an 8-ary phase shift keyed constellation may be partitioned into two quaternary phase shift keyed constellations that are each less subject to symbol error; and
Fig. 3 illustrates an exemplary embodiment of a four phase coherent optical Costas loop demodulator, for demodulating a quaternary phase shift key data format; and
Fig. 3a illustrates a prior art optical 90 degree hybrid for use in coherent optical demodulators;
Fig. 3b illustrates an exemplary fiber coupler based optical 90 degree optical hybrid in accordance with the principles of the present invention; and Fig. 4 illustrates an exemplary method in accordance with the principles of the present invention.
DETAILED DESCRIPTION
Referring to the drawing figures, Figs. 1 and la illustrate an exemplary wavelength division multiplexed fiber optic link 10 in accordance with the principles of the present invention. The wavelength division multiplexed fiber optic link comprises a
phase shift keyed coherent transmitter 20 and receiver 30 coupled together by way of a periodically optically amplified fiber link 40.
The phase shift keyed coherent transmitter 20 comprises a plurality of forward error correction encoders 21 that each receive a separate electronic data waveform (Dl, D2, ... , DN) for transmission over the optically amplified fiber link 40. Because, unlike on-off keying, phase shift keying transmits a constellation of data symbols, multilevel forward error correcting codes which partition the constellation into sub-constellations with larger Euclidean distance between the symbol points are of particular interest. Fig. 2 illustrates this point with an 8-ary constellation. A multi-level forward error correcting code may be used that virtually partitions the illustrated 8-ary phase shift keyed constellation into two quadrature phase shift keyed constellations, symbolically differentiated in Fig. 2 by triangles and squares. This scheme effectively approaches 4- ary bit error rates while transmitting the data capacity of an 8-ary constellation.
Each forward error correction code encoder 21 is in series with a phase shift keyed (PSK) optical modulator 23. Each of a plurality of lasers LI, L2, ... LN produce respective optical wavelengths Wl, W2, ... WN is uniquely coupled to one of a plurality of optical phase shift keyed modulators 23 whose respective output beams are each modulated with a forward error correction encoded data waveform. The forward error correcting code encoders 21 may encode in a block code format, including but not limited to Reed-Solomon, Bose-Chaudhuri-Hocquenghem (BCH), Hairrming and Golay formats, or a product code format, a turbo code format, a convolutional code format, a lattice code, or a Hamming code based turbo product code.
According to the system optical spectral width and optical signal to noise ratio requirements, the phase shift keyed modulators 23 may encode the data using the commonly known quaternary phase shift keyed, 8-ary phase shift keyed, 16-ary phase shift keyed, staggered quaternary phase shift keyed, minimum shift keyed, and quaternary advance retard keyed formats. Of particular interest are the staggered quaternary phase shift keyed and minimum shift keyed formats as they would aid in keeping the launched optical signal power envelope effectively constant even for veiy narrow optical spectral width requirements.
To achieve the required high power, narrow linewidth performance with a solid state construction, the lasers LI, L2, ... LN may be either distributed feedback semiconductor or distributed feedback fiber lasers. Outputs of each of the phase shift keyed (PSK) modulators 23 are input to a wavelength division multiplexing (WDM) multiplexer 24 that combines the phase shift keyed modulated outputs of the phase shift keyed modulators 23 for transmission over the optically amplified fiber link 40.
The fiber link 40 is periodic in nature, and is identical to that typically used with prior art on-off keying. Each period is a 30- 150 km length of optical fiber 41 coupled to a two-stage erbium doped optical fiber amplifier (EDFA). There may be a Raman amplifying laser 42 coupled into the fiber before the first-stage erbium doped fiber amplifier to lessen the fiber loss. The two-stage optical amplifier comprises a low noise optical preamplifier 43 and a high power booster amplifier 45. Disposed between the first and second stage erbium doped fiber amplifiers 43, 45 is a chromatic dispersion compensation module (DCM) 44. The gains of the respective amplifiers 42, 43, 45 are such that the total link period has unity gain. An optical link may include many such periods totaling thousands of kilometers.
As discussed above, both self- and cross-phase modulation are due to the nonhnearity with optical power of the propagation constant of the fiber 41. Prior art on- off keyed pulses maximize optical power variation and hence maximize distortion due to this nonlineaiϊty. This limits the maximum launched optical power, which limits the length of the link. The coherent phase shift keyed modulation format used in the present invention transmits a constant optical power envelope which is minimally distorted by self- and cross-phase modulation, even in common high dispersion characteristic fiber 41. The high dispersion characteristic fiber 41 also suppresses four wave mixing. This simultaneous mitigation of self-phase modulation, cross-phase modulation and four wave mixing allows higher optical power to be transmitted, and hence allows a longer length fiber optic link 40. Additionally, suppression of four wave mixing allows for narrower wavelength division multiplexed channel spacing which results in more total capacity per fiber link 40.
Positioning of the chromatic dispersion compensator 44 will now be discussed. Positioning the dispersion compensation module 44 between the optical preamplifier 43 and booster amplifier 45 is a preferred configuration for minimizing optical noise. For this reason, the dispersion compensator in prior art on-off keyed links is positioned in this way. Fortunately, this position is also ideal for the phase shift keyed signaling employed by the present invention. This is because, although the phase shift keyed signal launched into the fiber link 40 has a constant envelope, if the fiber 41 is chromatically dispersive, the envelope will not remain constant.
This may be understood by the following qualitative description of how the optical envelope of the phase-shift keyed signal changes as it propagates down the periodically amplified fiber link 40. At start, the signal will be very close to the ideal constant envelope of the phase shift keyed format. As the signal propagates down a fiber segment 41, the fiber chromatic dispersion produces increasing differential phase distortion within the phase shift keyed optical signal spectrum. In terms of the optical
intensity envelope, this manifests itself as an evolving intensity modulation. In other words, chromatically dispersive fiber is a phase modulation to amplitude modulation converter. This evolving intensity modulation is, like on-off keyed signals, subject to distortion by the fiber nonhnearity. However, as the signal travels, it is also subject to inherent optical fiber loss, so as the phase-to-amplitude modulation conversion evolves, the signal is simultaneously attenuated. Depending on launch power levels, symbol rate and fiber dispersion magnitude, this loss can be rapid enough such that the absolute power fluctuation in the envelope will remain insignificant as far as the fiber nonhnearity is concerned. The quaternary phase shift keyed, 8-ary and 16-ary phase shift keyed modulation formats employed in the present invention are much less susceptible to this phase-to-amplitude modulation conversion and its attendant nonlinear effects than is binary signaling. This is because the quaternary phase shift keying and 8-ary and 16-ary phase shift keyed optical spectra are half as wide or less than binary phase shift keying, and chromatic dispersion causes at most half as much differential spectrum phase distortion.
Given that the nonhnearity may be neglected, at the end of a link period, the chromatic dispersion compensation module 44 restores the original optical spectrum phase and thus the original constant optical envelope. Importantly, it does so immediately before the booster optical amplifier 45 increases the optical signal power back into the nonlinear region. Thus, the chromatic dispersion compensator in prior art on-off keying links is positioned to minimize optical noise. However, coincidentally this position is also such that the ideal phase shift keyed constant optical amplitude envelope is restored in the peak power regions immediately after amplification where fiber nonhnearity is most significant. As mentioned above, natural fiber attenuation subsequently reduces the signal rapidly enough so that the evolving phase-to-amplitude modulation conversion due to chromatic dispersion does not result in significant nonlinear action.
In phase modulated links, the above described nonlinear action resulting from phase to amplitude modulation conversion imposes an upper limit on the combination of optical launch power and the amount of fiber dispersion that may be introduced to suppress four wave mixing. Higher dispersion results in faster phase to amplitude modulation conversion, thus larger absolute optical power envelope variation, and more nonlinear action. Full optimization of the phase shift keyed format involves a trade between launched power, symbol rate and fiber dispersion value. Note that on-off keying results in maximum relative optical power variation at the peak power region after the booster optical amplifier 45 and hence maximizes harmful fiber nonlinear action, while phase shift keying does the opposite.
The last length of fiber 46 is coupled into a front end of the coherent receiver 30. The front end of the receiver 30 comprises either an optical power splitter 31 or a wavelength division demultiplexing optical filter 32. The optical power splitter 31 is used if access to all channels by any single demodulator 33 is desired, or if optical channel spacing is closer than can be resolved by available demultiplexing filters. The wavelength division demultiplexing optical filter 32 is used in case conservation of individual optical channel power is the dominant consideration. In either case, the front end of the receiver 30 splits the received signal into a plurality of signals. Each of these signals is then coupled to a coherent optical demodulator 33. If the optical power splitter 31 is used, temperature tuning of the local oscillator laser described below may be used to tune the receiver to any incoming wavelength division multiplexed optical carrier.
A wavelength division multiplexing (WDM) demultiplexer 37 in series with an array of optical power splitters 38 may also be used as the receiver front end. The WDM demultiplexer 37 first splits the incoming optical spectrum into optical subbands, each containing several optical carriers. Each optical subband is then input into an optical power splitter 38, which outputs a copy of the subband to each of several tunable coherent optical demodulators 33. In the figure four optical WDM subbands are shown as an example. This method gives a compromise between optical power conservation and receiver tunability
The electrical data signal output of each demodulator 33 is coupled to an electronic filter 34 to remove undesired spectral elements from adjacent wavelength division multiplexed channels. The electronic output of each filter 34 is coupled into an equalizer 35 to compensate for channel nonidealities. Finally, if forward error correc- tion is utilized, the data is sent through a forward error correction decoder 36 to restore the originally transmitted data, Dl, D2, ..., DN.
Fig. 3 illustrates an exemplary embodiment of a four phase coherent optical Costas loop demodulator 50. In Fig. 1, this optical demodulator 50 fulfills the function of each coherent optical demodulator 33 used in the fiber optic link 10 shown in Fig. 1. The quaternary phase shift keyed modulated optical input (Iopt) and the local oscillator output (LO) of a high power, narrow linewidth local laser 52 are input into a 90 degree optical hybrid 51. Two configurations of the 90 degree optical hybrid are schematically illustrated in Figs. 3a and 3b. Fig. 3a illustrates the prior art optical hybrid, while Fig. 3b illustrates an exemplary fiber coupler based optical 90 degree optical hybrid in accordance with the principles of the present invention that provides better performance and is easier to construct.
The function of the 90 degree optical hybrid is to combine Iopt and the phase locked optical local oscillator LO to produce two pairs of outputs. The pairs are labeled A, A' and B, B' in Figs. 3a and 3b. The difference between the first and second pairs is that the LO is shifted 90 degrees relative in phase to the input signal. The halves of a pair differ in that the optical beat frequency between the Iopt and LO is of opposite phase.
The functionality of the prior art hybrid is achieved using free space optical components and is illustrated in Fig. 3a. The polarization of the incoming LO is oriented so that it has linear optical polarization at 45 degrees to the principal axes of the quarter wave plate. Thus the action of the quarter wave plate 104 results in the LO light being equally divided into two polarization components with a 90 optical phase difference aligned with the quarter wave plate principal axes (circular polarization). The input signal Iopt is processed through a polarization controller 101 to linearly polarize it such that, upon combination with the LO in the 50/50 beam splitter, Iopt is divided into equal parts along the LO polarization components.
A 50/50 beam splitter cube 102 combines the Iopt and LO signals, resulting in one polarization containing Iopt + 0 degrees relative phase LO, and the perpendicular polarization containing Iopt + 90 degrees relative phase LO. However, the two outputs of the beamsplitter cube 102 will naturally have beat signals that are 180 degrees out of phase with each other. These beat signals correspond to the I and Q data spectra. Next the two polarization beam splitters 103 with principal axes aligned to those of the quarter wave plate 104 split the light into the four desired components (A, A', B, B') shown in Fig. 3 a.
Fig. 3b illustrates the novel 90 degree hybrid in accordance with the present invention which incorporates a 50/50 (3 dB) fiber coupler 107 instead of a beamsplitter cube 102. A fiber coupler provides the same relative beat frequency phase inversion at the outputs. However, the fiber coupler is by nature a better coherent coupler than the beamsplitter cube 102. Coherent combination of the Iopt and LO beams by means of a beamsplitter cube 102 implies very good collimation out of the Iopt and LO fibers leading to the 90 degree optical hybrid, and perfect alignment of the axes of the beamsplitter cube 102 to perfectly perpendicular signal and LO beams. Also, the beamsplitting surface of the beamsplitting cube 102 must be flat to within a few percent of the optical wavelength. Any deviation results in rapidly diminished response of the demodulator and I and Q crosstalk. These mechanical constraints make such a 90 degree hybrid difficult to manufacture in quantity as tedious custom alignment of the optical elements of each device is necessary.
Using the fiber coupler gives excellent coherent combination in a controlled waveguide environment. The fiber pigtails into and out of the 3 dB fiber coupler 107 may cause a change in the polarization state, but this can be pre- and post-compensated for by polarization controllers 105, 106, 109 to give the proper orientation leading into the polarizing beam splitters 108. As long as the 3 dB coupler pigtails are kept short, fairly straight and rigidly fixed, it is anticipated that the polarization controller 109 (which compensates for the differences between the two output fibers) is not necessary.
Each output pair of the 90 degree optical hybrid 51 are input into one of two balanced photodiode pahs 53 which act as optical mixers. The balanced photodiodes subtract the two components of each pair 53, thus yielding the desired beat signal while canceling out the LO and any noise associated with it. The beat signals are the in-phase and quadrature data signals I, Q. In principle, the DC photocurrent is zero, but non- idealities can cause a small DC current which is removed by the AC coupled low noise amplifiers 54. The amplified in-phase and quadrature data signals are low pass filtered 55 to remove undesired remnants of adj acent wavelength division multiplexed optical channels to produce I and Q data.
The data waveform is split into two branches. The data in the through branch of each waveform is put through a decision threshold 56 which amplifies the data symbols to a full magnitude positive or negative value according to whether the data symbol voltage is above or below the maximum likelihood decision voltage threshold. The function of the decision threshold 56 is to add the required nonhnearity to the feedback loop. This component may not be required if the mixers 57 are driven sufficiently in nonlinear operation.
Copies of the data are electrically cross-multiplied in mixers 57, and a sum 58 of the mixing products is produced. This sum corresponds to the phase error of the LO to the input signal Iopt optical carrier. This error signal is low pass filtered 59 and used to adjust the laser current 60 and hence the frequency of the local laser 52 to maintain phase lock. The temperature of the laser is controlled 61 and may be varied to tune the distributed feedback laser 52 to a particular input optical wavelength. Fig. 4 illustrates an exemplary optical signaling method 70 in accordance with the principles of the present invention. The exemplary optical signaling method 70 comprises the following steps.
Data in a plurality of data channels that are to be transmitted over an optically amplified fiber link are encoded 71 with a forward error correction code. The encoded data is then impressed upon optical cairiers by means of phase shift key modulation 72, such as by using an individual plurality of lasers each in series with an electro-optic
phase modulator, for example. The respective phase shift keyed modulated signals are then wavelength division multiplexed 73.
The wavelength division multiplexed signals are transmitted over a Raman amplified optical fiber 74, amplified 75, processed 76 to compensate for chromatic dispersion, and amplified 77 a second time. The previous four steps (74-77) are repeated 78 a predetermined number of times to achieve a desired total optical fiber link length.
The signals transmitted over the fiber link are separated 79 into a plurality of data channels. The signals in each of the data channels are coherently optically demodulated 80 to produce the forward error correction encoded data for the respective channels. This data is then processed 81 through a forward error correction decoder to reproduce the original data for the respective channels.
Thus, systems and methods that use phase shift keyed coherent optical signaling to mitigate the effects of fiber refractive index nonhnearity in wavelength division multiplexed optical fiber links have been disclosed. It is to be understood that the above-described embodiments are merely illustrative of some of the many specific embodiments that represent applications of the principles of the present invention. Clearly, numerous and other arrangements can be readily devised by those skilled in the art without departing from the scope of the invention.