Disclosure of Invention
The embodiment of the invention provides a long-distance single-span optical transmission method and a system, which are used for improving the transmission distance and capacity of an ultra-long-distance single-span optical communication system and improving the pumping calculation and adjustment efficiency of the system.
In one aspect, a method for long-distance single-span optical transmission is provided, which is characterized by comprising the following steps:
constructing a digital model based on the parameters of the optical transmission system, wherein the digital model is used for determining the corresponding relation between the signal-to-noise ratio of the tail end output spectrum and the required pumping power;
Inputting a target output spectrum signal-to-noise ratio into the digital model and acquiring predicted pumping power based on the corresponding relation;
And iteratively adjusting the actual tail end output spectrum signal-to-noise ratio of the optical transmission system based on the difference value of the predicted pump power and the actual pump power to optimize the digital model.
In some embodiments, the constructing a digital model based on the optical transmission system parameters includes the steps of:
determining the corresponding relation between the signal-to-noise ratio of the tail end output spectrum and the required pumping power based on a Raman power coupling equation, a remote pump transmission equation and a Gaussian noise model;
Training the digital model based on the measured end output spectral signal-to-noise ratio and the actual input pump power to optimize the correspondence.
In some embodiments, the determining the correspondence between the end output spectrum signal-to-noise ratio and the required pump power based on the raman power coupling equation, the remote pump transmission equation, and the gaussian noise model includes the steps of:
calculating the gain and noise of each channel by adopting a Raman power coupling equation;
calculating the gain and noise of each channel by adopting a remote pump transmission equation;
the gaussian noise model is used to calculate the channel noise and the end output spectral signal-to-noise ratio is calculated by amplifying the spontaneous emission noise and the nonlinear noise.
In some embodiments, the calculating the gain and noise of each channel using the raman power coupling equation includes:
calculating the gain and noise of each channel based on a first formula:
Where α sigi denotes the loss coefficient of the ith channel of the signal in the fiber, P sigi (z) denotes the power of the ith channel at position z, C R(fpj,fsigi) denotes the raman coupling coefficient between the pump at frequency f pj and the signal at frequency f sigi, P p1j (z) is the raman amplifier pump power at the originating end, and P 3j (z) is the raman amplifier pump power at the receiving end.
In some embodiments, the calculating the gain and noise of each channel using the remote pump transmission equation includes the steps of:
Calculating the gain and noise of each channel based on a second formula, wherein the second formula is as follows:
Where μ k denotes the direction of light transmission, μ k =1 denotes the forward direction, μ k = -1 denotes the backward direction, σ ek denotes the emission cross-section coefficient, mhv kΔvk is the contribution of spontaneous radiation caused by the upper level particle number n 2 to P k, m denotes the mode number, v k is the bandwidth of amplified spontaneous radiation effects, σ ak denotes the absorption cross-section coefficient, Representing the normalized intensity distribution function of the beam, r andRepresenting the cross-sectional coordinates of the erbium fiber, P k (z) represents the optical power along the length of the fiber at z in the fiber amplifier.
In some embodiments, the calculating noise of each channel using a gaussian noise model and calculating the end output spectral signal-to-noise ratio by amplifying spontaneous emission noise and nonlinear noise includes the steps of:
calculating the end output spectral signal-to-noise ratio based on a third formula comprising:
Wherein SNR i represents the signal-to-noise ratio of the ith channel, P ASE is the amplified spontaneous emission noise power, eta n is the nonlinear crosstalk coefficient, P si is the signal power, G (f) is the power spectral density of nonlinear crosstalk, f i is the center frequency of the ith channel, phi is an intermediate variable, gamma is the nonlinear coefficient, beta 2 is the group velocity dispersion parameter, beta 3 is the slope of the group velocity dispersion parameter, Is normalized signal power distribution, B ch is signal bandwidth, G (v+f i) is V is frequency integral sign, G Tx is input signal power spectral density,As an intermediate variable, the number of the variables,Is the transmission distance.
In some embodiments, the iterative adjustment of the actual end output spectral signal-to-noise ratio of the optical transmission system based on the difference between the predicted pump power and the actual pump power to optimize the digital model includes the steps of:
calculating the root mean square error of the predicted pump power and the actual pump power;
If the root mean square error does not meet the target precision, calculating a signal gain required by the optical transmission system based on the root mean square error and adjusting an actual tail end output spectrum signal-to-noise ratio of the optical transmission system based on the signal gain;
and taking the adjusted actual tail end output spectrum signal-to-noise ratio as the input of the digital model, and calculating new predicted pump power and corresponding new root mean square error until the new root mean square error meets the target precision.
In some embodiments, the root mean square error is calculated based on a fourth formula:
wherein RMSE is the root mean square error, P pi,GPR is the predicted pump power, P pi is the actual pump power, and m is the number of pumps.
In another aspect, there is also provided a long-distance single-span optical transmission system, which includes:
An automatic adjustment system for interacting with an optical transmission system, the automatic adjustment system comprising:
The digital model construction module is used for constructing a digital model according to the parameters of the optical transmission system, and the digital model is used for determining the corresponding relation between the tail end output spectrum and the required pumping power;
the prediction output module is used for inputting a target output spectrum into the digital model and acquiring predicted pumping power based on the corresponding relation;
and the automatic adjustment module is used for iteratively adjusting the actual tail end output spectrum signal-to-noise ratio of the optical transmission system based on the difference value of the predicted pump power and the actual pump power so as to optimize the digital model.
In some embodiments, the optical transmission system is further included, and from an transmitting end to a receiving end of the optical signal, the optical transmission system includes:
The system comprises a signal transmitting unit, a transmitting end optical amplifier, a forward second-order Raman amplifier, a forward remote pump gain unit, a backward Raman amplifier, a receiving end optical amplifier, a wave separator and a signal receiving unit;
the forward remote pump gain unit is connected with the forward second-order pump emission unit, and the forward second-order pump emission unit is used for providing pump light for the forward remote pump gain unit through the pump optical fiber;
the backward remote pump gain unit is connected with the backward second-order pump emission unit, and the backward second-order pump emission unit provides pump light for the backward remote pump gain unit through the pump optical fiber.
The embodiment of the invention provides a long-distance single-span optical transmission method and a system. According to the long-distance single-span optical transmission method provided by the embodiment of the invention, a digital model acting on the system is calculated and constructed according to the parameters of the optical transmission system, and the pump optical power is predicted and regulated through the digital model, so that the OSNR spectrum of an output signal is changed. The digital modeling and the automatic pump adjustment technology are combined, so that the Raman pump and the remote pump can be quickly and accurately adjusted, and the automatic equalization of the OSNR (Optical Signal Noise Ratio, optical signal to noise ratio) can be intelligently realized. On the other hand, in the system provided by the embodiment of the invention, the optical transmission system structure of the second-order Raman and the second-order remote pump is adopted, so that the system has a lower equivalent noise coefficient and a higher system Q factor while realizing higher gain, can reduce transmission noise, improve signal to noise ratio, and simultaneously provides a pumping signal with higher power for the remote pump unit.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, an embodiment of the present invention provides a long-distance single-span optical transmission method, which is characterized by comprising the steps of:
s100, constructing a digital model based on parameters of an optical transmission system, wherein the digital model is used for determining the corresponding relation between the signal-to-noise ratio of an output spectrum of the tail end and required pumping power;
s200, inputting a target output spectrum signal-to-noise ratio into the digital model and acquiring predicted pumping power based on the corresponding relation;
And S300, iteratively adjusting the signal-to-noise ratio of the actual tail end output spectrum of the optical transmission system based on the difference value of the predicted pump power and the actual pump power so as to optimize the digital model.
It should be noted that the optical transmission system parameters in S100 may include raman amplifier parameters, remote pump parameters, device insertion loss, optical fiber parameters, etc., where the raman amplifier parameters include a wavelength-dependent insertion loss spectrum, a pump center wavelength, and a maximum pump power of each pump, etc., the remote pump parameters include a wavelength-dependent insertion loss spectrum, a pump center wavelength, a maximum pump power of each pump, etc., the optical fiber parameters include a wavelength-dependent insertion loss spectrum of the transmission optical fiber, a raman gain coefficient, a pump optical wavelength-dependent insertion loss spectrum of the pump optical fiber, etc.;
According to the embodiment of the invention, a digital model acting on the system is calculated and constructed according to the parameters of the optical transmission system, and the pump light power is predicted and regulated through the digital model, so that the OSNR spectrum of the output signal is changed. The digital modeling and the automatic pump adjustment technology are combined, so that the Raman pump and the remote pump can be quickly and accurately adjusted, and the automatic equalization of the OSNR (Optical Signal Noise Ratio, optical signal to noise ratio) can be intelligently realized.
In a specific embodiment, for the optical transmission system as shown in fig. 2, the 0SNR of each channel in the input spectrum in the optical transmission system can be obtained, the wavelength-dependent insertion loss spectrum, the pump center wavelength and the maximum pump power of each pump of the raman amplifier 1 and the raman amplifier 2, the wavelength-dependent insertion loss spectrum, the pump center wavelength and the maximum pump power of each pump of the pump emission unit 1 and the pump emission unit 2, the wavelength-dependent insertion loss spectrum and the raman gain coefficient of the transmission optical fiber 1 and the transmission optical fiber 2, the wavelength-dependent insertion loss spectrum of the pump optical fiber 1 and the pump optical fiber 2;
The required parameters include, but are not limited to, raman amplifier 1 input signal power P sig, pump power P p1,Pp2,Pp3,Pp4, system insertion loss Att 1, VOA attenuation value Att 2 of optical amplifier 2, fiber parameters (length L eff, loss coefficient α s, and raman coupling coefficient C R).
In some embodiments, constructing a digital model based on the optical transmission system parameters in S100 includes the steps of:
S110, determining the corresponding relation between the signal-to-noise ratio of the tail end output spectrum and required pumping power based on a Raman power coupling equation, a remote pump transmission equation and a Gaussian noise model;
And S120, training the digital model based on the actual measured tail end output spectrum signal-to-noise ratio and the actual input pump power to optimize the corresponding relation.
It will be appreciated that in S120, initial values of corresponding super parameters are set according to the kernel function of step S110, thereby determining an a priori model of the digital model. The method comprises the steps of obtaining optimal super parameters through training a priori model, further determining a posterior model, namely a final digital model, predicting input of a test set by using the digital model (the input is actual output spectrum OSNR, a prediction result is required pumping power), obtaining distribution of predicted output points, namely mean value and covariance with uncertainty expression capability, comparing the predicted output of the test set with the actual output, calculating corresponding root mean square error and average absolute error, and analyzing and evaluating the predicted performance of the digital model.
Further, S110 includes the steps of:
S111, calculating gain and noise of each channel by adopting a Raman power coupling equation;
s112, calculating the gain and noise of each channel by adopting a remote pump transmission equation;
S113, calculating noise of each channel by using a Gaussian noise model and calculating the signal-to-noise ratio of the tail end output spectrum by amplifying spontaneous emission noise and nonlinear noise.
Preferably, the gain and noise of each channel are calculated based on a first formula in S111, and the first formula is:
Where α sigi denotes the loss coefficient of the ith channel of the signal in the fiber, P sigi (z) denotes the power of the ith channel at position z, C R(fpj,fsigi) denotes the raman coupling coefficient between the pump at frequency f pj and the signal at frequency f sigi, P p1j (z) is the raman amplifier pump power at the originating end, and P 3j (z) is the raman amplifier pump power at the receiving end.
Preferably, the gain and noise of each channel are calculated based on a second formula in S112, and the second formula is:
Where μ k denotes the direction of light transmission, μ k =1 denotes the forward direction, μ k = -1 denotes the backward direction, σ ek denotes the emission cross-section coefficient, mhv kΔvk is the contribution of spontaneous radiation caused by the upper level particle number n 2 to P k, m denotes the mode number, v k is the bandwidth of amplified spontaneous radiation effects, σ ak denotes the absorption cross-section coefficient, Representing the normalized intensity distribution function of the beam, r andRepresenting the cross-sectional coordinates of the erbium fiber, P k (z) represents the optical power along the length of the fiber at z in the fiber amplifier.
Preferably, the end output spectral signal-to-noise ratio is calculated in S113 based on a third formula, and the third formula includes:
Wherein SNR i represents the signal-to-noise ratio of the ith channel, P ASE is the amplified spontaneous emission noise power, eta n is the nonlinear crosstalk coefficient, P si is the signal power, G (f) is the power spectral density of nonlinear crosstalk, f i is the center frequency of the ith channel, phi is an intermediate variable, gamma is the nonlinear coefficient, beta 2 is the group velocity dispersion parameter, beta 3 is the slope of the group velocity dispersion parameter, Is normalized signal power distribution, B ch is signal bandwidth, G (v+f i) is v is frequency integral sign, G Tx is input signal power spectral density,As an intermediate variable, the number of the variables,Is the transmission distance.
In some embodiments, S300 further comprises the steps of:
S310, calculating the root mean square error of the predicted pump power and the actual pump power;
S320, if the root mean square error does not meet the target precision, calculating a signal gain required by the optical transmission system based on the root mean square error and adjusting the actual tail end output spectrum signal-to-noise ratio of the optical transmission system based on the signal gain;
s330, taking the adjusted actual tail end output spectrum signal-to-noise ratio as the input of the digital model and calculating new predicted pump power and corresponding new root mean square error until the new root mean square error meets the target precision.
Preferably, in S310, the root mean square error may be calculated based on a fourth formula, and the fourth formula is:
wherein RMSE is the root mean square error, P pi,GPR is the predicted pump power, P pi is the actual pump power, and m is the number of pumps.
In some embodiments, the gain is adjusted using a gradient descent method, and the minimum value of the root mean square error is solved in a direction to reduce the root mean square error or below a given value. Each time the iterative adjustment is performed, the SNR of the output spectrum 0 is corrected to change along the direction in which the root mean square error between the predicted pump power and the actual pump power becomes smaller, and the iterative adjustment process can be expressed as follows:
Wherein k is the iteration number, lambda k is the iteration step length, a proper initial value OSNR k (k=0) is selected, the target precision is epsilon, when RMSEk-RMSE k+1 is smaller than epsilon, iteration adjustment is stopped, and the root mean square error at the moment is considered to meet the preset condition.
As shown in fig. 4, the embodiment of the present invention further provides a long-distance single-span optical transmission system, which includes an automatic adjustment system interacting with the optical transmission system, the automatic adjustment system including:
The digital model construction module is used for constructing a digital model according to the parameters of the optical transmission system, and the digital model is used for determining the corresponding relation between the tail end output spectrum and the required pumping power;
the prediction output module is used for inputting a target output spectrum into the digital model and acquiring predicted pumping power based on the corresponding relation;
and the automatic adjustment module is used for iteratively adjusting the actual tail end output spectrum signal-to-noise ratio of the optical transmission system based on the difference value of the predicted pump power and the actual pump power so as to optimize the digital model.
In some embodiments, the digital model construction module is further configured to determine a correspondence between the end output spectral signal-to-noise ratio and the required pump power based on a raman power coupling equation, a remote pump transmission equation, and a gaussian noise model, and train the digital model to optimize the correspondence based on an actual measured end output spectral signal-to-noise ratio and an actual input pump power.
In some embodiments, the digital model building block is further configured to calculate the gain and noise for each channel using a raman power coupling equation, calculate the gain and noise for each channel using a telecump transmission equation, calculate each channel noise using a gaussian noise model, and calculate the terminal output spectral signal-to-noise ratio by amplifying the spontaneous emission noise and the nonlinear noise.
In some embodiments, the digital model building module is further configured to calculate a gain and noise of each channel based on a first formula, where the first formula is:
Where α sigi denotes the loss coefficient of the ith channel of the signal in the fiber, P sigi (z) denotes the power of the ith channel at position z, C R(fpj,fsigi) denotes the raman coupling coefficient between the pump at frequency f pj and the signal at frequency f sigi, P p1j (z) is the raman amplifier pump power at the originating end, and P 3j (z) is the raman amplifier pump power at the receiving end.
In some embodiments, the digital model building module is further configured to calculate a gain and noise of each channel based on a second formula, where the second formula is:
Where μ k denotes the direction of light transmission, μ k =1 denotes the forward direction, μ k = -1 denotes the backward direction, σ ek denotes the emission cross-section coefficient, mhv kΔvk is the contribution of spontaneous radiation caused by the upper level particle number n 2 to P k, m denotes the mode number, v k is the bandwidth of amplified spontaneous radiation effects, σ ak denotes the absorption cross-section coefficient, Representing the normalized intensity distribution function of the beam, r andRepresenting the cross-sectional coordinates of the erbium fiber, P k (z) represents the optical power along the length of the fiber at z in the fiber amplifier.
In some embodiments, the digital model building module is further configured to calculate an end output spectral signal-to-noise ratio based on a third formula, and the third formula comprises:
Wherein SNR i represents the signal-to-noise ratio of the ith channel, P ASE is the amplified spontaneous emission noise power, eta n is the nonlinear crosstalk coefficient, P si is the signal power, G (f) is the power spectral density of nonlinear crosstalk, f i is the center frequency of the ith channel, phi is an intermediate variable, gamma is the nonlinear coefficient, beta 2 is the group velocity dispersion parameter, beta 3 is the slope of the group velocity dispersion parameter, Is normalized signal power distribution, B ch is signal bandwidth, G (v+f i) is v is frequency integral sign, G Tx is input signal power spectral density,As an intermediate variable, the number of the variables,Is the transmission distance.
In some embodiments, the automatic adjustment module is further configured to calculate a root mean square error of the predicted pump power and the actual pump power, calculate a signal gain required by the optical transmission system based on the root mean square error and adjust an actual end output spectral signal-to-noise ratio of the optical transmission system based on the signal gain if the root mean square error does not meet a target accuracy, take the adjusted actual end output spectral signal-to-noise ratio as an input of the digital model, and calculate a new predicted pump power and a new root mean square error corresponding to the new root mean square error until the new root mean square error meets the target accuracy.
Preferably, the automatic adjustment module further calculates the root mean square error based on a fourth formula, and the fourth formula is:
wherein RMSE is the root mean square error, P pi,GPR is the predicted pump power, P pi is the actual pump power, and m is the number of pumps.
As shown in fig. 2, the long-distance single-span optical transmission system provided by the present invention further includes an optical transmission system, and from a transmitting end to a receiving end of an optical signal, the optical transmission system includes:
The system comprises a signal transmitting unit, a transmitting end optical amplifier, a forward second-order Raman amplifier, a forward remote pump gain unit, a backward Raman amplifier, a receiving end optical amplifier, a wave separator and a signal receiving unit;
the forward remote pump gain unit is connected with the forward second-order pump emission unit, and the forward second-order pump emission unit is used for providing pump light for the forward remote pump gain unit through the pump optical fiber;
the backward remote pump gain unit is connected with the backward second-order pump emission unit, and the backward second-order pump emission unit provides pump light for the backward remote pump gain unit through the pump optical fiber.
It can be understood that the optical transmission system provided by the embodiment of the invention is an ultra-low loss and high power transmission system applicable to ultra-long-distance submarine cable single span. The signal transmitting unit and the signal receiving unit complete the signal receiving and transmitting function, the transmitting end optical amplifier and the forward second-order Raman amplifier complete the signal amplifying function and the signal pre-emphasis, the forward second-order pumping transmitting unit provides pumping light for the forward remote pump gain unit through the pumping optical fiber, the backward second-order pumping transmitting unit provides pumping light for the backward remote pump gain unit through the pumping optical fiber, and the transmission signal reaches the backward second-order Raman amplifier and the receiving end optical amplifier after being amplified twice by the forward remote pump gain unit and the backward remote pump gain unit and reaches the signal receiving unit after being subjected to the wave splitter, so that the signal receiving and transmitting are completed. The system comprises a remote pump gain unit, a second-order Raman, a second-order remote pump and a second-order remote pump, wherein the transmission optical fiber and the pumping optical fiber used for system networking can be selected from low-loss large-effective-area optical fibers and are used for reducing transmission loss and prolonging transmission distance, the second-order Raman is used for improving signal gain and reducing noise index, and the second-order remote pump is used for providing high-power pumping signals to the remote pump gain unit.
Preferably, the optical signal transmitting device comprises a signal transmitting unit, a combiner, a dispersion compensating unit, a transmitting optical amplifier, a forward second-order Raman amplifier, a forward remote pump gain unit, a backward Raman amplifier, a receiving optical amplifier, a wave splitter and a signal receiving unit in sequence from the transmitting end to the receiving end of the optical signal. The optical transmission system also comprises a front pumping system and a rear pumping system which are respectively composed of a forward second-order pumping emission unit and a backward second-order pumping emission unit. Wherein the dispersion compensation unit is used for performing dispersion compensation on the signal.
In a specific embodiment, the unidirectional schematic structure of the optical transmission system is shown in fig. 2, and the unidirectional schematic structure sequentially comprises a signal transmitting unit, a combiner, a dispersion compensating unit, an optical amplifier 1, a raman amplifier 1, a transmission optical fiber 1, a remote pump gain unit 1, a transmission optical fiber 2, a remote pump gain unit 2, a transmission optical fiber 3, a raman amplifier 2, an optical amplifier 2, a demultiplexer and a signal receiving unit from sending to receiving of an optical signal. The ultra-long-distance submarine cable single-span transmission system also comprises a front pumping system and a rear pumping system which are respectively composed of a pumping transmitting unit 1, a pumping optical fiber 1, a pumping transmitting unit 2 and a pumping optical fiber 2.
The signal transmitting unit and the signal receiving unit complete the signal receiving and transmitting function, and the speed of the receiving and transmitting module can be 10Gbit/s, 40Gbit/s, 100Gbit/s, 200Gbit/s and 400Gbit/s; the wave combiner is arranged behind the transmitting unit and is used for combining the optical signals of the plurality of channels; the optical amplifier 1 uses an erbium-doped fiber amplifier (Erbium Doped Fiber Amplifier, abbreviated as EDFA) and is arranged behind the dispersion compensation unit for carrying out first-stage amplification on the combined wave signal.
The raman amplifier 1 uses a second-order raman, and is disposed after the optical amplifier 1, for re-amplifying the composite signal.
The remote pump gain unit 1 is arranged at the tail end of the transmission optical fiber 1, the signal receiving end of the remote pump gain unit is connected with the signal output end of the Raman amplifier 1 through the transmission optical fiber 1, the pump receiving end of the remote pump gain unit is connected with the pump transmitting unit 1 through the pump optical fiber 1, and the signal output end of the remote pump gain unit is connected with the remote pump gain unit 2 through the transmission optical fiber 2;
the remote pump gain unit 2 is arranged at the tail end of the transmission optical fiber 2, the signal receiving end of the remote pump gain unit is connected with the signal output end of the remote pump gain unit 1 through the transmission optical fiber 2, the pump receiving end of the remote pump gain unit is connected with the pump transmitting unit 2 through the pump optical fiber 2, and the signal output end of the remote pump gain unit is connected with the signal input end of the Raman amplifier 2 through the transmission optical fiber 3;
the optical amplifier 2 uses EDFA, is set up in the signal output end of the Raman amplifier 2;
the demultiplexer is arranged at the signal output end of the optical amplifier 2 and is used for dividing the composite signal and then sending the composite signal to the corresponding signal receiving unit for processing.
The second-order remote pump is used by the pump transmitting unit 1 and is positioned at the transmitting station, and the output end of the second-order remote pump is connected with the pump optical fiber 1;
The transmission fibers 1,2,3 use g.654 type fibers for transmitting signal light, and the pump fibers 1,2 use g.654 type fibers for transmitting pump light.
According to the embodiment of the invention, the ultra-low loss large effective area optical fiber is used, so that the attenuation of the optical fiber is reduced, more incoming optical power can be received, and the signal transmission distance can be effectively increased. The second-order Raman has lower equivalent noise coefficient and higher system Q factor while realizing higher gain, and can reduce transmission noise and improve signal-to-noise ratio. The second-order remote pump can provide a pumping signal with higher power for the remote pump unit.
Those of ordinary skill in the art will appreciate that all or some of the steps, systems, functional modules/units in the apparatus, and methods disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof. In a hardware implementation, the division between functional modules/units mentioned in the above description does not necessarily correspond to the division of physical components, for example, one physical component may have a plurality of functions, or one function or step may be cooperatively performed by several physical components. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on computer-readable storage media, which may include computer-readable storage media (or non-transitory media) and communication media (or transitory media).
It should be noted that in the present invention, relational terms such as "first" and "second" and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises an element.
The foregoing is only a specific embodiment of the invention to enable those skilled in the art to understand or practice the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.