Abstract:
A transmitter for performing multicarrier modulation comprising a processing unit configured to generate a multicarrier data signal comprising a plurality of subcarriers, wherein each of the plurality of subcarriers represents at least one data bit of a plurality of data bits, select a subset of the subcarriers based on signal quality information about one or more of the subcarriers, construct a kernel signal comprising the subset of subcarriers, and create a digital signal comprising combining the multicarrier data signal and a peak-to-average ratio (PAR) reduction signal based on the kernel signal, wherein a PAR of the digital signal is less than a PAR of the multicarrier data signal.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     Not applicable. 
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not applicable. 
     REFERENCE TO A MICROFICHE APPENDIX 
     Not applicable. 
     BACKGROUND 
     Multicarrier modulation may be used in high-speed communication systems. Multicarrier modulation schemes include Discrete Multi-Tone (DMT) modulation and Orthogonal Frequency Division Multiplexing (OFDM) modulation. DMT modulation may be used in xDSL communication systems over copper in International Telecommunication Union (ITU) standards such as G.992.1 through G.992.5 as well as G.993.1, G.993.2, and G.993.5. DMT modulation is also being considered for G.fast, a standard that is in-progress. OFDM modulation may be used in radio-frequency wireless systems such as Digital Audio Broadcast systems or in wired systems, such as in ITU standard G.hn. 
     Multicarrier signals may experience large peak-to-average signal ratio (PAR) values, where PAR may be a ratio of an instantaneous peak power value to an average power value of a signal. Large PAR values present many challenges in designing multicarrier transceivers. A large PAR may demand large dynamic range for analog circuits and more precision for digital processing. Large dynamic range increases power consumption and cost of digital-to-analog converters (DACs), which may be needed in communication transceivers to convert digital signals into analog signals for transmission on physical media. Large dynamic range for line drivers (LDs) used for power amplification at a DAC output may demand higher voltage supplies and therefore higher power consumption. Consequently, it may be desirable to reduce PAR in multicarrier systems. 
     SUMMARY 
     In a first aspect, the invention includes a transmitter for performing multicarrier modulation comprising a processing unit configured to generate a multicarrier data signal comprising a plurality of subcarriers, wherein each of the plurality of subcarriers represents at least one data bit of a plurality of data bits, select a subset of the subcarriers based on signal quality information about one or more of the subcarriers, construct a kernel signal comprising the subset of subcarriers, and create a digital signal comprising combining the multicarrier data signal and a peak-to-average ratio (PAR) reduction signal based on the kernel signal, wherein a PAR of the digital signal is less than a PAR of the multicarrier data signal. 
     In another aspect, the invention includes a method for reducing a PAR in a multicarrier transmitter comprising generating a multicarrier data signal comprising a plurality of subcarriers, wherein each of the plurality of subcarriers carries at least one data bit, determining one or more locations where an estimated multicarrier data signal exceeds a predetermined threshold value and determining an amplitude of the estimated multicarrier data signal at each location, for each location, scaling a kernel signal based on the amplitude and shifting the kernel signal circularly based on the location to generate a scaled and shifted kernel signal corresponding to each location, if more than one location is determined, combining the scaled and shifted kernel signals to create a combined kernel signal and otherwise setting the combined kernel signal equal to a single scaled and shifted kernel signal, and creating a digital signal comprising combining the combined kernel signal and the multicarrier data signal, wherein a PAR of the digital signal is less than a PAR of the multicarrier data signal, and wherein the kernel signal employs a subset or all of the plurality of subcarriers. 
     In yet another aspect, the invention includes a transmitter for performing multicarrier modulation comprising a processing unit configured to generate a multicarrier data signal comprising a plurality of subcarriers, wherein each of the plurality of subcarriers represents at least one data bit, determine one or more locations where an estimated multicarrier data signal exceeds a predetermined threshold value and determine an amplitude of the estimated multicarrier data signal at each location, for each location, scale a kernel signal based on the amplitude and shift the kernel signal circularly based on the location to generate a scaled and shifted kernel signal corresponding to each location, wherein the kernel signal employs a subset or all of the plurality of subcarriers, if more than one location is determined, combine the scaled and shifted kernel signals to create a combined kernel signal and otherwise setting the combined kernel signal equal to a single scaled and shifted kernel signal, and create a digital signal comprising combining the combined kernel signal and the multicarrier data signal, wherein a PAR of the digital signal is less than a PAR of the multicarrier data signal. 
     These and other features will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts. 
         FIG. 1  shows a Gaussian distribution with a mean value of zero and a standard deviation equal to one. 
         FIG. 2  shows an insertion loss of a typical twisted-pair cable versus frequency for different loop lengths. 
         FIG. 3  shows transmitted signal power level versus loop length for a wireline modem. 
         FIG. 4  shows downstream power spectral density of a transmitted signal and transmitted noise at a transmitter. 
         FIG. 5  shows downstream power spectral density (PSD) of a transmitted signal and a PSD transmitter noise after passing through a channel of length equal to 200 meters (m). 
         FIG. 6  shows downstream power spectral density (PSD) of a transmitted signal and a PSD transmitter noise after passing through a channel of length equal to 400 m. 
         FIG. 7  is a flowchart of an embodiment of a method for constructing a kernel signal. 
         FIG. 8  is a schematic diagram of an embodiment of a discrete multitone (DMT) transceiver. 
         FIG. 9  is a schematic diagram of an embodiment of a DMT transceiver with PAR reduction. 
         FIG. 10  is a schematic diagram of a second embodiment of a DMT transceiver with PAR reduction. 
         FIG. 11  is a schematic diagram of a third embodiment of a DMT transceiver with PAR reduction. 
         FIG. 12  is a schematic diagram of a fourth embodiment of a DMT transceiver with PAR reduction. 
         FIG. 13  illustrates a general-purpose network component. 
     
    
    
     DETAILED DESCRIPTION 
     It should be understood at the outset that, although an illustrative implementation of one or more embodiments are provided below, the disclosed systems and/or methods may be implemented using any number of techniques, whether currently known or in existence. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary designs and implementations illustrated and described herein, but may be modified within the scope of the appended claims along with their full scope of equivalents. 
     Multicarrier modulations may exhibit large ratios of peak signal value to root-mean-squared (RMS) signal value or large PAR values. A multicarrier modulated signal may be a superposition of many (e.g., hundreds or thousands) subcarriers; i.e., cosines with random amplitude, frequency, and phase. At each instance of time, a multicarrier modulated signal may be a superposition of many random signals. The distribution of such a signal at an instant in time, according to central limit theorem, may tend towards a Gaussian distribution. A Gaussian or Normal distribution may be a well-known bell-shaped distribution where a peak of the signal with this distribution can be much larger than its standard deviation a or RMS value. A probability density function of a Gaussian variable with a standard deviation a and a mean value μ is: 
     
       
         
           
             
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                 ( 
                 x 
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             = 
             
               
                 1 
                 
                   
                     2 
                     ⁢ 
                     π 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       σ 
                       2 
                     
                   
                 
               
               ⁢ 
               
                 ⅇ 
                 
                   - 
                   
                     
                       
                         ( 
                         
                           x 
                           - 
                           μ 
                         
                         ) 
                       
                       2 
                     
                     
                       2 
                       ⁢ 
                       
                         σ 
                         
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       FIG. 1  shows a Gaussian distribution with a mean value of zero and a standard deviation equal to one (also called Standard Normal distribution). Probabilities that a zero-mean Gaussian-distributed signal with a standard deviation a exceeds different threshold levels T re listed in Table 1. 
     
       
         
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Probability that the amplitude of a zero-mean Gaussian 
               
               
                 Threshold T 
                 signal with standard deviation σ exceeds threshold T 
               
               
                   
               
             
             
               
                 T = 1σ 
                 3.173e−01 
               
               
                 T = 2σ 
                 4.550e−02 
               
               
                 T = 3σ 
                 2.700e−03 
               
               
                 T = 4σ 
                 6.334e−05 
               
               
                 T = 5σ 
                 5.733e−07 
               
               
                 T = 5.3σ 
                 1.158e−07 
               
               
                 T = 6σ 
                 1.973e−09 
               
               
                 T = 7σ 
                 2.560e−12 
               
               
                   
               
             
          
         
       
     
     Note that a DMT or OFDM signal may be approximated as Gaussian-distributed, and the approximation becomes more accurate as larger numbers of subcarriers are used. 
     There may be a number of techniques to reduce PAR of a multicarrier signal. In one technique, which may be used in low-SNR (signal-to-noise ratio) scenarios in wireless communication, a multicarrier signal may be filtered using a nonlinear phase filter. A nonlinear filter flattens a signal shape slightly thus reducing a signal&#39;s peaks. Another technique uses soft nonlinear compression to reduce signal PAR at the cost of reduced SNR. However, neither of these techniques may yield satisfactory results in multicarrier systems, especially in scenarios in which each subcarrier may carry seven or more bits of information (e.g., at subcarrier SNR higher than 30 decibels (dB)). 
     One technique that may reduce PAR without loss of SNR in data-carrying subcarriers is a tone-reservation technique. In tone reservation, about 5% to 8% of available subcarriers may be reserved to create a signal that may have a peak at a location of a data signal peak but with an opposite sign to reduce or cancel the peak. Reserved tones (or subcarriers) may not be used to transmit data, however. Therefore, tone-reservation techniques penalize data rate to save power and cost. The data rate loss may be about 5% to 8% or more. 
     Tone-reservation techniques attempt to create a dirac-delta-function-like temporal signal, called a kernel signal (or kernel), from the reserved tones to cancel a signal peak without introducing new peaks when combining the kernel with multicarrier signal. However, because only a small percentage of available tones may be reserved for a kernel signal, the kernel signal may not be a good approximation to a dirac-delta function. This may be because a dirac-delta function may require a constant amplitude on all tones in a frequency domain in order to achieve a value of one at one time value (such as time zero) and a value of zero at all other time values in a time domain. Due to inaccurate kernel(s) used in tone-reservation techniques, when multiple signals peaks are present that need to be reduced, the peaks may be located and subtracted one by one in an iterative manner because every time a peak may be located and reduced by a kernel a new peak may be introduced. 
     Tone reservation may not be practical for high bandwidth systems, such as VDSL2 (17.6 megahertz (MHz) or 30 MHz bands) or G.fast because tone reservation may require iterations described above to locate and cancel each signal peak one by one. In each iteration the algorithm needs to determine the peak location and corresponding amplitude in time-domain signal samples. Once the peak amplitude and location is determined, a kernel may need to be scaled and shifted by these amounts for each peak and then combining with the signal. Performing iterations potentially hundreds of times to locate and reduce signal peaks in every DMT symbol for VDSL2 or G.fast may not be practical for implementation. 
     Systems and methods described herein do not reserve any subcarriers separate from subcarriers used to carry data. A kernel signal may be created from subcarriers that may also be used to carry data. 
       FIG. 2  shows an insertion loss of a typical twisted-pair cable versus frequency for different loop lengths. Available bands DS1, DS2, and DS3 for downstream transmission and available bands US1, US2, and US3 for upstream transmission for a VDSL2 30 MHz system are indicated in  FIG. 2 . Three loop lengths of 100 meters (m), 200 m, and 400 m are shown. As shown in  FIG. 2 , an insertion loss of a twisted pair copper cable increases with increasing loop length and frequency. DS3 and US3 bands for downstream and upstream transmission, respectively, in a VDSL2/30 MHz system, may be attenuated more than the other bands. 
       FIG. 3  shows transmitted signal power level versus loop length for a wireline modem. On short loops, insertion loss across frequencies may be small. Therefore, there may be no need to transmit at full power and modems can perform power back-off to both save power and reduce crosstalk to other longer neighboring lines. On long loops, higher frequencies may be attenuated so much that they cannot be used for data transmission. Therefore, modems may transmit at full power on medium range loops and at lower power at short and long loops. 
     As shown in  FIG. 3 , a transmitter performs power backoff up to a first loop length L 1 . At L 1  the transmitter starts transmitting full power until loop length L 2  where higher frequency subcarriers may not be useful and the transmit power reduces from full power. Assuming that a PAR reduction algorithm reduces peak power by an amount represented as R dB, when the transmit power is below (P f −R) dB it is not necessary to run a PAR reduction algorithm. Therefore, a PAR reduction algorithm may be useful between loop length L 0  and L 3 . If L 0  is long enough a PAR reduction algorithm may be employed that may not sacrifice data rate as described below. 
       FIG. 4  shows a power spectral density (PSD) of a transmitted data signal and a PSD of a transmitter noise signal at a transmitter. A transmitter noise signal may be unintended noise introduced by the transmitter and added to the transmitted data signal.  FIG. 5  shows a PSD of a transmitter data signal and a PSD of a transmitter noise signal after passing through a channel of length equal to 200 m.  FIG. 5  also shows a PSD of a receiver noise signal (or receiver noise) and a PSD of additive white Gaussian noise (AWGN) on the channel. Receiver noise may be a combination of noise sources, including AWGN, amplifier noise, and noise introduced by analog-to-digital converters (ADCs).  FIG. 6  shows a downstream PSD of a transmitted data signal and a PSD of transmitter noise signal after passing through a channel of length equal to 400 m.  FIG. 6  also shows a PSD of receiver noise and a PSD of additive white Gaussian noise (AWGN) on the channel. Note that for 200 m and 400 m loops the transmitter noise signal at a receiver may be well below the receiver noise at many higher frequencies due to the transmitter noise having been attenuated by the channel. This means even if a transmitter SNR at these higher frequencies is degraded, a data rate of a communication system may not be affected. A kernel signal constructed from the tones in these higher frequencies may not affect data rate as long as the tones used to construct the kernel signal are not stronger than a receiver noise. 
     The transmitted signal SNR may be reduced significantly at a receiver on longer loops and at higher frequencies. For example, transmitter SNRs of about 53 dB for DS3 subcarriers may result in receiver SNRs of about 20 dB to 25 dB at higher frequencies after 400 m long line as demonstrated in  FIGS. 4 and 6 . Subcarrier SNRs may be even more degraded if crosstalk from other lines is taken into account (crosstalk is not illustrated in  FIGS. 5 and 6 ). Note that crosstalk coupling may be stronger at higher frequencies than lower frequencies. 
     Consequently, in many loops and under many noise conditions, it may not be necessary to transmit high SNRs in some subcarriers. For example, subcarrier transmit SNR may be reduced by few dB to few tens of dB without affecting the communication link performance. When a transmitter noise at receiver is below a receiver noise level a PAR reduction algorithm as described below may be used. Note that unlike the tone-reservation method described above that limits the PAR reduction tones to about 5% to 8% of the transmitted tones, many more tones may be available. Therefore, the kernel signal may be designed to better approximate a dirac-delta kernel. As an additional benefit, the average energy in each tone may be smaller because the energy of the kernel signal may be distributed over many more tones. By optimizing a design of a kernel signal dependent on the loop length and SNRs for different frequencies, PARs of DMT and/or OFDM signals may be reduced without reserving specific tones for a kernel signal and thus without sacrificing performance. As an additional benefit, because it may now be possible to construct a kernel signal with termporal characteristics closer to a dirac-delta function, the need for iteratively cancelling data signal peaks one by one may be eliminated, as describe further below. All the peaks above a predetermined threshold may be detected once and a combined kernel signal, which may be a superposition of shifted and scaled versions of a kernel signal, may be determined once and all peaks reduced by one summation or subtraction operation without the need for iterations. A combined kernel signal may be viewed as a PAR reduction signal. 
       FIG. 7  is a flowchart of an embodiment of a method for constructing a kernel signal. For the purpose of constructing a kernel signal, tones may be discovered during initial handshake procedures and/or later during channel discover and training phases. Tones may be selected that have significantly lower received SNR as compared to the transmitted SNR. 
     In step  710 , a channel sounding signal may be transmitted. A channel sounding signal may use a same set of subcarriers as used for data signals. In step  720 , the transmitted channel sounding signal may be received, and channel quality for all subcarriers may be determined. Channel quality may be an estimate of subcarrier SNR, for example. Channel quality measurements for various subcarriers may be fed back to a transmitter in step  720 . In step  730 , signal quality measurements may be received at the transmitter. The transmitter may determine which subcarriers have a signal quality below a threshold and designate these subcarriers as subcarriers to be used to construct a kernel signal, referred to as kernel signal subcarriers. Some or all the subcarriers may be kernel signal subcarriers. Further, kernel signal subcarriers may be determined during a handshake phase or later during channel discover and training phases. In step  740 , a kernel signal may be constructed using kernel signal subcarriers to approximate a dirac-delta function. One way to construct a kernel signal may be to set a value of kernel signal subcarriers to a same value in a frequency domain with a value of all other subcarriers that are not kernel signal subcarriers to zero in a frequency domain. The larger number of kernel signal subcarriers used the better the kernel signal approximates a dirac-delta function. A kernel may be constructed on the fly or a number of kernels may be constructed and stored in advance and the appropriate one selected and loaded after a channel analysis and exchange phase. Finally, another embodiment may determine signal quality based on predictions at the transmitter. The predictions may be based on initial handshake information exchanged between two modems. 
       FIG. 8  is a schematic diagram of an embodiment of a DMT transceiver  800 . OFDM transceivers may be similar, but DMT transceivers are used for illustrative purposes. DMT transceiver  800  comprises a transmit path comprising a channel coder  802 , serial-to-parallel (S/P) converter  804 , signal mapper  806 , inverse fast Fourier transform (IFFT) modulator block  808 , parallel-to-serial (P/S) converter  810 , time domain processing block  812 , upsampler  814 , digital-to-analog converter (DAC)  816 , programmable attenuator  818 , low pass filter  820 , line driver (LD)  822 , and hybrid circuit  830  configured as shown in  FIG. 8 . Information bits to be transmitted may be scrambled by an scrambler block (not shown in the figure) and then may be encoded by a channel coder  802 . A S/P converter  804  may pick an appropriate number of encoded bits to be mapped into each subcarrier by a mapper  806 . Mapper  806  may include a trellis encoder. Mapped bits may create a complex frequency-domain digital signal at an IFFT modulator  808  input. The IFFT modulator  808  may convert the accumulation of mapped complex digital signals in frequency domain into an accumulation of real (in case of DMT) or complex (in case of OFDM) time-domain signal. A P/S converter  810  prepares the time-domain signal for serial processing. 
     A time-domain processing block  812  may perform insertion of a cyclic prefix and a suffix as well as transmit windowing and filtering. The processed time-domain signal then may be up-sampled (or interpolated) in an upsampler block  814  before being provided to a DAC  816  to convert a digital signal into an analog signal. The analog signal may be transmitted using an analog transmitter or analog portion of the multicarrier transmitter. The analog portion may comprise a programmable attenuator  818 , low pass filter  820 , LD  822 , and hybrid circuit  830  arranged as shown in  FIG. 8 . The analog signal may be attenuated by a programmable attenuator  818  and filtered by a low pass filter  820 . Further, the analog signal may be amplified by a LD  822 . A hybrid circuit  830  that may be used in a frequency-division-duplex (FDD) wireline system. The role of a hybrid circuit  830  may be to separate transmit and received paths of the transceiver. In a transmit direction hybrid circuit  830  passes the transmitted signal into the line and blocks the transmitted signal being passed into a receive path. Alternatively, when transceiver  800  is acting as a receiver, the hybrid circuit  830  blocks a received signal from getting into a transmit path. 
     DMT transceiver  800  comprises a receive path configured to receive signals from a line. In addition to hybrid circuit  830  described earlier, the DMT transceiver receive path comprises a low pass filter  840 , a programmable gain amplifier (PGA)  842 , an analog-to-digital converter (ADC)  844 , time domain processing block  846 , S/P converter  848 , a fast Fourier transform (FFT) block  850 , a frequency domain equalizer (FEQ)  852 , a demapper block  854 , a P/S converter  856 , and a channel decoder  858  configured as shown in  FIG. 8 . The received signal may pass through a low-pass filter LPF  840 , then may be amplified by a PGA  842  and next converted to a digital signal by an ADC  844 . The digital signal may be processed by a time domain processing block  846  before converted to a parallel signal by a S/P converter  848  and provided to FFT block  850 . FFT block  850  may act as a demodulator and with the help of FEQ  852  attempts to recover a transmitted frequency domain signal. A demapper  854  may convert the signal into data bits. The demapper  854  may include a Viterbi decoder if a trellis encoder is used at the transmitter. The data bits may be then converted to serial bits or bytes by a P/S converter  856  and further processed by channel decoder  858  to correct errors that may have been introduced in the line by noise and other disturbances. Channel decoder  858  output then may be provided to a descrambler (not shown) to convert received data bits to information bits. 
     DMT transceiver  800  may be used to construct one or more kernel signals using the methods described previously. For example, transceiver  800  may perform steps  710 ,  730 , and  740 . Another transceiver, which may be similar to transceiver  800 , may be paired with the transceiver  800  to perform step  720 . One or more kernel signals may be employed in a PAR reduction algorithm. 
     A PAR reduction algorithm may run at a transmitter, such as transceiver  800 . A PAR reduction algorithm may employ a time-domain signal at an IFFT output, such as an output of IFFT block  808  in  FIG. 8 , to determine a location and amplitude of signal values exceeding a predetermined threshold value T. Then a position and amplitude of a kernel signal may be adjusted such that when added to a data signal will reduce the data signal peak below threshold T. There may be more than one peak exceeding threshold T. If a kernel signal is similar enough to a dirac-delta function in the time domain there may be no need for iterations to reduce peaks and all signal peaks may be reduced by a combined kernel signal, which may be a superposition of an original kernel scaled and shifted (circularly) by each peak&#39;s amplitude and location, respectively. 
       FIG. 9  is a schematic diagram of an embodiment of a DMT transceiver  900  with PAR reduction. DMT transceiver  900  may use one or more kernel signals that were constructed using methods described previously. The DMT transceiver  900  comprises a main data transmit path comprising a channel coder  902 , S/P converter  904 , signal mapper  906 , IFFT block  908 , P/S converter  910 , upsampler  914 , time domain processing block  916 , DAC  918 , programmable attenuator  920 , low pass filter  922 , line driver  924 , and hybrid circuit  926  configured as shown in  FIG. 9 . These elements may be similar to those described earlier for DMT transceiver  800 . 
     In addition to the above elements in a transmit path, DMT transceiver  900  comprises additional elements for PAR reduction in a PAR reduction path. Namely, DMT transceiver  900  further comprises IFFT block  960 , P/S converter  962 , upsampler  964 , a low pass filter  966 , peak detector  968 , kernel signal storage  970 , and combined kernel builder  972  configured as shown in  FIG. 9 . Also, a delay block  912  may be introduced on a main path to account for delays due to a PAR reduction algorithm. The PAR of a signal may increase after upsampling and conversion to an analog domain. Thus, it may be desirable that a PAR reduction algorithm operates at higher sampling rate than the minimum size IFFT output sampling rate. Hence, upsampling block  964  may be employed to upsample a signal used for PAR reduction. 
     The PAR of a signal that is reduced in a digital domain may increase in an analog domain after the LPF  922 . For this reason, the LPF  922  may need to be modeled and taken into account when performing PAR reduction to make sure that the PAR remains below a target PAR at LPF  922  output. Digital LPF  966  models analog low pass filtering effects, such as LPF  922 . An output of digital LPF  966  may be considered an estimate of a data signal in which analog effects may be taken into account. 
     The peak detector  968  attempts to detect where peaks exceeding a threshold T occur in the transmitted signal. Kernel signal storage  970  stores one or more kernel signals. The kernel signals may have been constructed by DMT transceiver  900  using methods described earlier, such as the method described with respect to  FIG. 7 . Each kernel signal may employ one or more subcarriers employed by DMT transceiver  900  for data transmission. 
     Combined kernel builder  972  may use inputs from peak detector  968  and kernel signal storage  970  to construct a combined kernel signal, which may be viewed as a PAR reduction signal. For example, if M peaks are detected, where M is an integer, M kernel signals may be combined (or superimposed) to create a combined kernel signal, one kernel signal corresponding to each peak. The M kernel signals may be scaled and circularly shifted versions of one kernel signal, wherein the scaling and circular shift may depend on the peak amplitude and location, respectively, being addressed. There may be only one peak, in which case M equals one, and the combined kernel signal or PAR reduction signal may comprise only one shifted and scaled kernel signal. 
     Generally, a combined kernel signal may be subtracted from a data signal in a time domain or a frequency domain. Because the number of tones used to construct a combined kernel signal may be large, it may not be efficient to build the combined kernel signal in a frequency domain. Thus, it may be preferable to construct the combined kernel signal and subtract it from a data signal in a time domain, as demonstrated in DMT transceiver  900 , where the data signal (i.e., signal at the output of upsampler  914 ) may be added to the combined kernel signal (i.e., signal at output of combined kernel builder  972 ). A net effect is that the PAR value of a data signal may be higher than the data signal combined with the combined kernel signal. 
     The DMT transceiver  900  comprises a received signal path similar to the DMT transceiver  800  and configured to receive signals from a line. That is, the DMT transceiver  900  receive path comprises a low pass filter  930 , a PGA  932 , an ADC  934 , time domain processing block  936 , S/P converter  938 , a FFT block  940 , a FEQ  942 , a demapper block  944 , a P/S converter  946 , and a channel decoder  948  configured as shown in  FIG. 9 . 
       FIG. 10  is a schematic diagram of a second embodiment of a DMT transceiver with PAR reduction. The DMT transceiver  1000  comprises a main transmit path comprising a channel coder  1002 , S/P converter  1004 , signal mapper  1006 , IFFT block  1008 , P/S converter  1010 , delay block  1012 , upsampler  1014 , time domain processing block  1016 , DAC  1018 , programmable attenuator  1020 , low pass filter  1022 , line driver  1024 , and hybrid circuit  1026  configured as shown in  FIG. 10 . These elements may be similar to those described earlier for DMT transceiver  900 . 
     In addition to the elements in a main transmit path described above, DMT transceiver  1000  comprises additional elements for PAR reduction in a transmit path. Namely, DMT transceiver  1000  further comprises IFFT block  1060 , P/S converter  1062 , low pass filter  1064 , peak detector  1066 , kernel signal storage  1068 , and a combined kernel builder  1070  configured as shown in  FIG. 10 . In the DMT transceiver  1000  a PAR reduction algorithm may run at higher sampling rate than the minimum IFFT output sampling rate by using a higher IFFT size by N times, where N is an integer. This approach is reflected in DMT transceiver  1000  by the IFFT block  1060 , which uses a higher IFFT size by N times. This approach is different than that taken in DMT transceiver  900 , which employed an upsampler  964  to increase the sampling rate of the PAR algorithm. The P/S converter  1062 , low pass filter  1064 , peak detector  1066 , kernel storage block  1068 , and combined kernel signal builder  1070  are similar to those elements of the same name described above for DMT transceiver  900 . 
     The DMT transceiver  1000  comprises a received signal path similar to the DMT transceiver  900  and configured to receive signals from a line. That is, the DMT transceiver  1000  receive path comprises a low pass filter  1030 , a PGA  1032 , an ADC  1034 , time domain processing block  1036 , S/P converter  1038 , a FFT block  1040 , a FEQ  1042 , a demapper block  1044 , a P/S converter  1046 , and a channel decoder  1048  configured as shown in  FIG. 10 . 
     Because the number of tones used to construct a kernel signal may be large, it may not be efficient to construct the combined kernel in a frequency domain and it may be preferred that the combined kernel be both constructed and subtracted from a data signal in a time domain, as in  FIGS. 9 and 10 . However, it may be necessary for a speed of an interface between a digital portion, such as a digital chip, and an analog portion, such as an analog chip, to be kept relatively low, to save power and cost, in which case a combined kernel signal may be constructed and subtracted from a data signal in a frequency domain, as in  FIGS. 11 and 12  below In this case up-sampling (i.e., interpolation), while a digital operation, will be performed inside the analog chip. The analog chip is a part of the Analog Processing shown in  FIGS. 8-12 . 
       FIG. 11  is a schematic diagram of a third embodiment of a DMT transceiver with PAR reduction. In this embodiment, a combined kernel signal may be constructed and subtracted from a data signal in a frequency domain as described below. The DMT transceiver  1100  comprises a main transmit path comprising a channel coder  1102 , S/P converter  1104 , signal mapper  1106 , delay block  1108 , IFFT block  1110 , P/S converter  1112 , time domain processing block  1114 , upsampler  1116 , DAC  1118 , programmable attenuator  1120 , low pass filter  1122 , line driver  1124 , and hybrid circuit  1126  configured as shown in  FIG. 11 . These elements may be similar to those described earlier for DMT transceiver  1000 . 
     In addition to the elements in a transmit path described above, DMT transceiver  1100  comprises additional elements for PAR reduction in a transmit path. Namely, DMT transceiver  1100  further comprises IFFT block  1160 , P/S converter  1162 , upsampler  1164 , low pass filter  1166 , peak detector  1168 , kernel signal storage  1170 , and a combined kernel builder  1172  configured as shown in  FIG. 11 . The IFFT block  1160 , P/S converter  1162 , upsampler  1164 , low pass filter  1166 , peak detector  1168 , and kernel signal storage  1170  are similar to those elements of the same name described above for DMT transceiver  900 . One difference between DMT transceiver  1100  and the DMT transceivers described earlier may be that the combined kernel builder  1172  outputs a combined kernel signal in a frequency domain, rather than a time domain. The combined kernel signal may then be subtracted from a data signal in the frequency domain. 
     The DMT transceiver  1100  comprises a received signal path similar to the DMT transceiver  1000  and configured to receive signals from a line. That is, the DMT transceiver  1100  receive path comprises a low pass filter  1130 , a PGA  1132 , an ADC  1134 , time domain processing block  1136 , S/P converter  1138 , a FFT block  1140 , a FEQ  1142 , a demapper block  1144 , a P/S converter  1146 , and a channel decoder  1148  configured as shown in  FIG. 11 . 
       FIG. 12  is a schematic diagram of a fourth embodiment of a DMT transceiver with PAR reduction. In the DMT transceiver  1200  a PAR reduction algorithm may run at higher sampling rate than the minimum IFFT output sampling rate using larger size IFFT, and the combined kernel may be constructed and subtracted in a frequency domain as described below. The DMT transceiver  1200  comprises a main transmit path comprising a channel coder  1202 , S/P converter  1204 , signal mapper  1206 , delay block  1208 , IFFT block  1210 , P/S converter  1212 , time domain processing block  1214 , upsampler  1216 , DAC  1218 , programmable attenuator  1220 , low pass filter  1222 , line driver  1224 , and hybrid circuit  1226  configured as shown in  FIG. 12 . These elements may be similar to those described earlier for DMT transceiver  1100 . 
     In addition to the elements in a transmit path described above, DMT transceiver  1200  comprises additional elements for PAR reduction in a transmit path. Namely, DMT transceiver  1200  further comprises IFFT block  1260 , P/S converter  1262 , low pass filter  1264 , peak detector  1266 , kernel signal storage  1268 , and a combined kernel builder  1270  configured as shown in  FIG. 12 . The combined kernel builder  1270  may be similar to the combined kernel builder  1172  described above for DMT transceiver  1170 . For example, combined kernel builder  1270  outputs a combined kernel signal in a frequency domain. IFFT block  1260  may be similar to IFFT block  1060  described above for DMT transceiver  1000 . For example, IFFT block  1260  uses a higher FFT size by N times to increase the sampling rate of the PAR algorithm. 
     The DMT transceiver  1200  comprises a received signal path similar to the DMT transceiver  1100  and configured to receive signals from a line. That is, the DMT transceiver  1200  receive path comprises a low pass filter  1230 , a PGA  1232 , an ADC  1234 , time domain processing block  1236 , S/P converter  1238 , a FFT block  1240 , a FEQ  1242 , a demapper block  1244 , a P/S converter  1246 , and a channel decoder  1248  configured as shown in  FIG. 12 . 
     In  FIGS. 9 and 10 , a main data signal path may use a smaller IFFT followed by upsampling (i.e., interpolates) and then performing time-domain processing before sending the signal to a DAC. In  FIGS. 11 and 12 , a main data signal path may use a smaller IFFT, followed by time-domain processing, and then upsampling before sending the signal to a DAC for reasons discussed previously. Alternatively, a main data path may use oversampling using a larger size IFFT. If a larger size IFFT is used on a main data path, the IFFT block on a main data path of each of  FIGS. 9-12  may be replaced by NxIFFT to indicate a larger size IFFT by N times, and the upsampler block, such as upsampler  914 , may be eliminated or have its upsampling ratio decreased depending on the value of N. In many applications, N may equal to two. The upsampling rate may depend on the IFFT output sampling rate and the DAC&#39;s operating rate. 
     For kernel signals constructed with temporal characteristics closer to a dirac-delta function, as described herein, the need for iteratively cancelling data signal peaks one by one may be eliminated. All the peaks above a predetermined threshold may be detected once and a combined kernel signal, which is a superposition of shifted and scaled version of a kernel signal, may be found at once and all peaks reduced without a need for iteration. Thus, the methods and systems disclosed herein may significantly reduce the amount of processing needed for PAR reduction and thus make PAR reduction more practical for high-speed communication systems. 
       FIG. 13  illustrates a general-purpose network component  1300  suitable for implementing one or more embodiments of the components disclosed herein. The network component  1300  includes a processor  1302  that is in communication with memory devices including secondary storage  1304 , read only memory (ROM)  1306 , random access memory (RAM)  1308 , input/output (I/O) devices  1310 , and network connectivity devices  1312 . The processor  1302  may be implemented as one or more CPU chips and may include one or more digital signal processing chips (or digital signal processors). The processor  1302  may comprise all or part of digital portions of DMT transceivers  900 ,  1000 ,  1100 , and  1200  and may be configured to implement at least some of the steps of the method  700 . The processor  1302  may comprise general purpose hardware, such as a central processing unit (CPU), that is configured to couple to a processing unit, which may comprise special purpose hardware, such as filters and IFFT components, that comprise digital portions on DMT transceivers  900 ,  1000 ,  1100 , and  1200 . Alternatively, a processing unit may comprise a processor, such as processor  1302 . The I/O device  1310  may include an analog chip and additional analog processing components. 
     The secondary storage  1304  is typically comprised of one or more disk drives or tape drives and is used for non-volatile storage of data and as an over-flow data storage device if RAM  1308  is not large enough to hold all working data. Secondary storage  1304  may be used to store programs that are loaded into RAM  1308  when such programs are selected for execution. The ROM  1306  is used to store instructions and perhaps data that are read during program execution. ROM  1306  is a non-volatile memory device that typically has a small memory capacity relative to the larger memory capacity of secondary storage  1304 . The RAM  1308  is used to store volatile data and perhaps to store instructions. Access to both ROM  1306  and RAM  1308  is typically faster than to secondary storage  1304 . 
     At least one embodiment is disclosed and variations, combinations, and/or modifications of the embodiment(s) and/or features of the embodiment(s) made by a person having ordinary skill in the art are within the scope of the disclosure. Alternative embodiments that result from combining, integrating, and/or omitting features of the embodiment(s) are also within the scope of the disclosure. Where numerical ranges or limitations are expressly stated, such express ranges or limitations may be understood to include iterative ranges or limitations of like magnitude falling within the expressly stated ranges or limitations (e.g., from about 1 to about 10 includes, 2, 3, 4, etc.; greater than 0.10 includes 0.11, 0.12, 0.13, etc.). For example, whenever a numerical range with a lower limit, R l , and an upper limit, R u , is disclosed, any number falling within the range is specifically disclosed. In particular, the following numbers within the range are specifically disclosed: R=R l +k*(R u −R l ), wherein k is a variable ranging from 1 percent to 100 percent with a 1 percent increment, i.e., k is 1 percent, 2 percent, 3 percent, 4 percent, 5 percent, . . . , 50 percent, 51 percent, 52 percent, . . . , 95 percent, 96 percent, 97 percent, 98 percent, 99 percent, or 100 percent. Moreover, any numerical range defined by two R numbers as defined in the above is also specifically disclosed. Use of the term “optionally” with respect to any element of a claim means that the element is required, or alternatively, the element is not required, both alternatives being within the scope of the claim. Use of broader terms such as comprises, includes, and having may be understood to provide support for narrower terms such as consisting of, consisting essentially of, and comprised substantially of. Accordingly, the scope of protection is not limited by the description set out above but is defined by the claims that follow, that scope including all equivalents of the subject matter of the claims. Each and every claim is incorporated as further disclosure into the specification and the claims are embodiment(s) of the present disclosure. The discussion of a reference in the disclosure is not an admission that it is prior art, especially any reference that has a publication date after the priority date of this application. The disclosure of all patents, patent applications, and publications cited in the disclosure are hereby incorporated by reference, to the extent that they provide exemplary, procedural, or other details supplementary to the disclosure. 
     While several embodiments have been provided in the present disclosure, it may be understood that the disclosed systems and methods might be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted, or not implemented. 
     In addition, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, modules, techniques, or methods without departing from the scope of the present disclosure. Other items shown or discussed as coupled or directly coupled or communicating with each other may be indirectly coupled or communicating through some interface, device, or intermediate component whether electrically, mechanically, or otherwise. Other examples of changes, substitutions, and alterations are ascertainable by one skilled in the art and may be made without departing from the spirit and scope disclosed herein.