Patent Publication Number: US-8537934-B2

Title: System and method for multi-carrier modulation

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is a continuation of U.S. patent application Ser. No. 09/826,969 filed Apr. 4, 2001, now U.S. Pat. No. 7,010,262, which claims benefit of U.S. Provisional Application No. 60/194,544 filed Apr. 4, 2000, the contents of which is are hereby incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     Multi-carrier modulation (MCM), is widely used in applications requiring the transmission and reception of electromagnetic energy to form a transmission system. Applications can include broadcast receivers such as cellular telephone, wireless data transmission, and point to multi point data transmission systems among others. Increased utilization of a channel in an application is often achieved with multi carrier modulation transmission techniques. In multi-carrier modulation a bit stream, or information sequence, of digital data is broken up into pieces and modulated onto carriers located at different frequencies. Transmission of the electromagnetic energy may be over a transmission line or by electromagnetic radio waves. 
     The design of a transmission system is one of the most complex design tasks in electrical engineering, often requiring expensive circuitry in receiver and transmitter subsystems to achieve a desired performance. Attempting to prevent noise and distortion from interfering with a signal that is being transmitted is typically why high cost circuitry is utilized in a transmission system. 
     However, it would be more cost effective to utilize a differing modulation scheme and construct appropriate low cost circuitry to implement it. Ideally the modulation scheme would allow the appropriate circuitry to be produced inexpensively, and still provide good performance. A common form of distortion is phase noise. Phase noise is characterized by the production of a carrier frequency that is not quite at a desired set frequency, but can deviate randomly from the desired set frequency. Typically the further a possible deviation is from a set carrier frequency, the less likely the deviation is to occur. Phase noise typically becomes worse when inexpensive transmission systems are utilized. Inexpensive frequency conversion components tend to increase phase noise. Thus it would be desirable to provide a modulation system that tends to reduce distortion, while allowing inexpensive circuitry to be utilized. 
     SUMMARY OF THE INVENTION 
     A method of compensating for carrier frequency and phase errors of a received multi-carrier modulated signal. The received multi-carrier signal including modulated carriers for transmitting known data and unmodulated carriers for error correction, comprising, time domain down converting the received multi-carrier signal to base-band to provide a down-converted signal, the down-converted signal including a plurality of modulated carriers for transmitting known data and unmodulated carriers for error correction. Sampling an unmodulated carrier of the down-converted signal to provide received data samples. Providing a reference signal derived from the unmodulated carrier of the down-converted signal. And, estimating phase errors from a phase difference between the unmodulated carrier and the reference signal derived from the unmodulated carrier of the down-converted signal to provide a plurality of received sample phase error estimates for each modulated carrier. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       These and other features and advantages of the present invention will be better understood from the following detailed description read in light of the accompanying drawings, wherein: 
         FIG. 1  is a block diagram of a multi carrier modulation system; 
         FIG. 2   a  is a spectrum of N independent carriers; 
         FIG. 2   b  is a spectrum of multiple independent carriers having modulated signals impressed upon them; 
         FIG. 2   c  illustrates the effects of phase noise on a conventional sine wave; 
         FIG. 3  is a block diagram of an MCM transmitter and receiver that advantageously utilizes training tones, and a training tone tracking circuit in a system that tends to reduce phase noise; 
         FIG. 4  is an illustration of a sinusoidal training tone signal having phase error; 
         FIG. 5  is a block diagram of a second order phase lock loop used as a part of the training tone tracking PLL; 
         FIG. 6  is an alternative embodiment of an MCM receiver having a fast carrier tracking PLL that incorporates a matching delay circuit; 
         FIG. 7   a  is a block diagram of a first embodiment of a phase detector that processes only training tones; 
         FIG. 7   b  is a block diagram of the tone tracking mixers/filters utilized in the phase detector circuit of  FIG. 6 ; 
         FIG. 7   c  is an alternative embodiment of the tone tracking mixer/filter circuit; 
         FIG. 8   a  is a frequency spectrum of an MCM signal comprising data signals impressed with transmitted data and training tones; 
         FIG. 8   b  is a frequency spectrum of the output of the mixer; 
         FIG. 8   c  is a frequency spectrum of a down converted and isolated training tone after low pass filtering; 
         FIG. 9   a  is a diagram of a spectrum that is applied to a tone tracking mixers/filters circuit; 
         FIG. 9   b  is a frequency spectrum of the output of the mixer; 
         FIG. 9   c  is a frequency spectrum of a down converted and isolated training tone after low pass filtering; 
         FIG. 10  is a block diagram of a two pass modulation technique; and 
         FIGS. 11   a ,  11   b , and  11   c  illustrates the processing steps of the third embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The embodiments of the invention presented below utilize tone based carrier tracking, and are useful in any modulation system. Two types of modulation systems are commonly utilized: 1) single carrier modulation, in which an entire information signal is frequency translated to a desired band via a single carrier; and 2) multi-carrier modulation (MCM), in which an information signal, typically including an information sequence of digital data, is subdivided into subsequences. Each subsequence is assigned to one of a set of separate carriers that are individually translated in frequency to a desired band. The subsequences are typically referred to as “bins.” MCM is primarily used in the transmission of digital data. However, analog transmission utilizing this technique is possible. 
     A problem encountered in transmitting a wideband signal that is improved with an MCM is variation in attenuation of the frequencies across the band. Variation in attenuation is characterized by a non-flat frequency response of the channel the information is being transmitted over. Examples of channels are coaxial cables, transmission lines, or the air over which a radio signal is being broadcast. 
     Variations in attenuation across the band are typically responsible for a type of interference called inter-symbol interference (ISI). Reduction in inter-symbol interference is achieved in MCM systems by subdividing a frequency band into individual regions. In this subdivision of the band each region is considered independent of the others. Over each subregion inter-symbol interference is typically reduced from that of a large bandwidth signal, since the attenuation varies less over the smaller band. With this technique, each band appears to have a nearly flat frequency response, thus, the distortion per signal band is typically reduced. 
     Typical electronic systems utilizing an MCM include cable modems, wireless transmission, cellular point to point, cellular point to multi-point transmission, DSL applications, and point to multi-point short-haul television transmission. The embodiments described below are particularly useful in wireless or cable modem applications where a large amount of data is transmitted at high frequencies. Although an MCM is more tolerant to inter-symbol interference, other problems typically arise in using an MCM such as increased sensitivity to phase noise. 
       FIG. 1  is a block diagram of a conventional MCM system. MCM systems typically do not satisfactorily accommodate large amounts of phase noise. Because of the multiple carriers that are present in multi-carrier modulated signals inter carrier interference causes difficulty to removing phase noise by conventional techniques. 
     Phase noise (or phase jitter) typically arises when a signal is translated, or mixed, to a high frequency by utilizing frequency conversion circuitry, such as a mixer, or a “tuner.” The term tuner as used here includes a circuit having a mixer and a local oscillator so that a signal applied to a tuner is converted in frequency. Phase noise is typically added in the mixing process. A local oscillator signal is applied to a local oscillator (LO) port of the mixer to cause the frequency conversion of a signal applied to a radio frequency (RF) port of the mixer. Through the interaction of the signals and the mixer circuitry, the signal that is outputted at an intermediation frequency (IF) output port of the mixer is a replica of the signal applied at the RF input port, but translated in frequency. 
     The frequency conversion circuitry of the tuner has phase noise associated with it that is transferred to the signal during the mixing process. Tuner or mixer phase noise typically arises from an inherent inability of the mixer circuitry to cleanly mix a signal from DC (or a first frequency) to a second frequency. Phase noise typically appears as a jitter or randomness, in the frequencies produced in the tuner. Phase noise is typically high in inexpensive tuners. Thus, inexpensive tuners typically produce large amounts of phase noise that often make an MCM undesirable in low cost applications. 
     The embodiments of tone based carrier tracking systems that are described below will typically allow low cost tuners to be utilized in cost effective MCM systems. Low cost tuners may be utilized by providing compensation circuitry for the phase noise and through manipulation of the signal by utilizing a training tone. Information to manipulate the signal is obtained from one or more training tones and processed in the digital domain utilizing digital signal processing techniques. 
     In an MCM system  102  a conventionally generated digital bit stream, or information sequence,  101  is input to a conventionally constructed an MCM modulator circuit  111 . The output of the multi-carrier modulator circuit  121  is a series of N equally spaced modulated carriers centered about DC. Alternatively unequal spacings may be utilized. Information from the information sequence  101 , or bit stream, is divided into segments, or “BINS”, with each segment encoded onto each of the N independent carriers comprising signal  121 . 
     The output of the MCM modulator  111  is input to a conventionally constructed tuner  103 . Tuner  103  includes a mixer  105  coupled to frequency generator  107  at a first mixer port. The frequency generator  107  produces by conventional means an output frequency fc. The tuner converts a signal applied to a second mixer port to a signal at a third mixer port that is substantially a replica of the signal at the second port, but centered about a different frequency. 
     Conventional circuitry known to those skilled in the art is utilized to construct the tuner. In the embodiment shown fc is equal to 2.4 gHz. In an alternative embodiment, fc is equal to 5 gHz. However, any suitable frequency may be utilized. In the tuner, an output signal  121  of the MCM modulator  111  is upsampled, or upconverted by a conventionally constructed mixer  105  and a coupled to a conventionally constructed frequency source  107  to 2.4 gHz to form a tuner output  115 . 
     Alternatively the MCM modulator output is upconverted by a single tuner such that it is centered about 5 gHz. Alternatively, upconversion of the MCM modulator output is accomplished using multiple tuner stages to achieve a final desired upconversion through in progressive steps. 
     The tuner output  115  is applied to an input of a conventionally constructed bandpass filter  109 . An output of the bandpass filter  117  is a filtered version of the MCM modulator output. Signal  117 , is the signal that is transmitted through a conventional transmission medium  119  such as air or a transmission line. The upconverted signal is captured by a receiver after it is transmitted through the transmission medium. 
     The output of the bandpass filter  109  that has been transmitted through the transmission medium  119  is conventionally down converted by a down conversion tuner  125  in the MCM receiver  123  so that the received signal may be processed by subsequent circuitry. 
     A down conversion tuner  125  includes a conventionally constructed frequency generator  127  outputting a frequency fc that is mixed by a conventionally constructed mixer  129  with the signal received from the output transmission channel  119 , to form down converted output  102 . The output  102  of the down conversion tuner  125  is applied to a conventionally constructed down conversion low pass filter  131 . The output of the down conversion low pass filter forms a down conversion low pass filter output  133 , that appears at low pass filter output  417 . The low pass filter output  133  is similar in its modulation characteristics and carrier frequency location to the MCM modulator output signal  121 . 
     The LPF output signal  417  is input to a conventionally constructed MCM demodulator and FFT circuit  137 . In the MCM demodulator and FFT circuit  137  the data is stripped from the carriers and assigned to bins. The data from the bins is reconstructed into a recovered sequence of digital data at the MCM demodulator output  419 . 
     The conventional sequences of modulation and demodulation described above tend to add considerable amounts of phase noise to the signal that is being modulated and subsequently recovered. A conventional MCM circuit is especially susceptible to phase noise when low cost tuners  103 ,  125  are utilized to lower costs. 
     To understand the distortion mechanisms that produce phase noise that is typically present in the receiver, the individual carriers and the signals impressed upon them in the presence of noise are described in detail, so that the need for a system and method of an MCM, and its operation will be better understood. 
       FIG. 2   a  is a spectrum of N independent carriers  202 ,  204 ,  206 ,  208 ,  210 . In the embodiment shown, each carrier is equally spaced in frequency from the others. However, carriers having an unequal spacing may be utilized. In a multi-carrier system, an independent sequence of information is typically impressed upon each carrier as a modulated signal. 
       FIG. 2   b  is a spectrum of multiple independent carriers having modulated signals impressed upon them. The N independent modulated signals  209 ,  211 ,  213 ,  215 ,  217  make up a multi-carrier modulated signal. Subsequence of a data stream are typically modulated or impressed upon each carrier. The carrier signals  202 ,  204 ,  206 ,  208 ,  210  shown are substantially equal in all characteristics, but offset in frequency. The tuners ( 103  and  125  of  FIG. 1 ) typically contribute phase noise to each of the carrier signals  202 ,  204 ,  206 ,  208 ,  210  and the signals  209 ,  211 ,  213 ,  215  and  217 , that are modulated upon the carriers respectively, when they are down converted, and/or when they are upconverted. The phase noise interferes with a series of signals  209 ,  211 ,  213 ,  215 ,  217  modulated on the carrier when it is desired to remove the carriers and demodulate the information stream. 
     In the frequency domain, phase noise typically appears as uncertainty in the location of the carrier frequencies  202 ,  204 ,  206 ,  208 ,  210 . When examined in the time domain, phase modulation, and the uncertainly in frequency it produces appears as an imperfectly formed sine wave. 
       FIG. 2   c  illustrates the effects of phase noise on a conventional sine wave. As shown, a sine wave  203  that produces a frequency f, is affected by phase noise. In any given cycle  204  a sine wave may arrive late at its zero crossing  205 , rather than being on time at the zero crossing  206 . The late arrival causes a lower frequency f low  to be produced at that instant. Whereas in the next, or some other cycle, the sine wave  203  may start early in crossing the zero crossing  207 , causing a frequency f High  to be produced at that instant that is higher than would normally be produced  208 . The sine wave is thus phase modulated such that a beginning or ending phase is introduced into the sine wave causing the zero crossing time to be expanded  205  or contracted  207 . 
     When viewed in the frequency domain, the probability of not obtaining a frequency that is exactly the desired frequency can be seen in a spectrum of unmodulated carriers. Most of the time the frequency generated tends to be produced correctly at the desired frequency. When viewing a frequency spectrum of a pure carrier on an instrument, such as a spectrum analyzer, most of the time a heavy line appears at the desired location indicating the carrier being measured. However, when viewing a typical carrier, an envelope, that is not part of a modulated signal, typically appears at the base of the signal. The envelope is indicative of the signal&#39;s “jittering” about the desired frequency. As distance in frequency from the desired carrier increases, the amplitude of the envelope typically decreases, indicating reduced probability of the frequency occurring farther from the carrier. 
     Each time a sine wave undergoes the mixing process, such as in the transmitter tuner ( 103  of  FIG. 1 ), or the receiver tuner ( 125  of  FIG. 1 ), phase noise tends to be added. Phase noise introduced by tuners typically causes the purity of the signal generated to degrade. When low cost tuners, often having relaxed phase noise specifications, are used phase noise typically worsens. 
     Phase noise tends to interfere with a signal when it is demodulated tending to cause degradation and possibly a loss of data. 
     In the embodiments of the invention that will be presented, a training tone tracking PLL is added to track, calculate and compensate for phase noise. In the frequency domain, the frequency spectrum tends to be cleaned up such that a series of sinusoidal signals having a frequency closer to that which is desired tends to be produced. 
     A current trend in circuit design is the increasing use of digital signal processing techniques (DSP) in implementing circuit designs. DSP is rapidly tending to replace the more conventional analog design techniques. Phase distortion, or phase errors, typically arise in analog circuitry such as IF and RF tuners. Single carrier techniques typically utilizes a DSP technique of processing decision data in order to combat phase distortion. Decision data refers to the estimated value of a transmitted data sequence or symbol, based on received data. There are two problems with using decision data in a multi-carrier system. 
     First, decision data is typically only available after a received analog signal is sampled and transformed into a digital signal that is suitable for processing with DSP circuit techniques. However, the transformation process tends to distort phase error information needed to compensate for phase errors. 
     Second, decision data is generated at a symbol rate present in the DSP system. The symbol rate in a multi-carrier system as compared to a symbol rate used in a single carrier system is typically N times slower for N sub-carriers. A faster rate is typically needed to make the existing phase error compensation techniques produce satisfactory results by providing a sufficiently fast rate for tracking the errors typically present. Thus, it is desirable to compensate for phase noise in the time domain prior to a conversion of the signal into the frequency domain. Time domain compensation for phase errors tends to avoid the distortion encountered after conversion to a frequency-domain signal. Also, in the time domain a much faster MCM sample rate may be utilized to track the phase errors. Typical MCM sample rates tend to be one hundred to one thousand times faster than typical symbol rates. A system that utilizes one or more training tones and a training tone tracking circuit tends to reduce phase distortion and advantageously utilize the MCM sample rate. 
       FIG. 3  is a block diagram of an MCM transmitter and receiver that advantageously utilizes training tones, and a training tone tracking circuit  420  in a system  302  that tends to reduce phase noise. A training tone tracking circuit  420  accepts an input signal  417  and splits the signal into a first signal, and a second signal. The first signal is applied to a first input port of a mixer  407 . The second signal is applied to a training tone tracking PLL  135 . An output of the training tone tracking PLL  135  is applied to a second input port of the mixer  407 . An output  104  of the mixer  407  is coupled to an MCM demodulator and FFT  137 . Input  417  of the training tone tracking PLL  135  is coupled as described in  FIG. 1 . The remainder of the circuitry of  FIG. 3  is identical to the circuitry described in  FIG. 1 . 
     In the time domain, phase jitter of the signal is tracked by comparing it to a known standard. The signal being tracked is the one that is applied to the first input port of the mixer  407 . The known standard is provided by the output of the training tone tracking PLL  135 . The known standard is typically created by purifying the signal that is being applied to the first input port of the mixer  407 . The output of mixer  407  is a “phase error free” MCM signal. 
     At any zero crossing, the amount of phase jitter, or phase error, present is known by comparison made in mixer  407 . By applying the negative of the measured phase jitter to the signal being recovered, the phase jitter tends to be removed from a signal that will be demodulated later. 
     The training tone tracking PLL  135  circuitry deduces what the phase noise is at any given instant and applies its negative to the received signal such that the phase noise tends to be canceled. The error in phase is recovered from a received signal, and its negative is applied to the received signal at a later time such that phase noise tends to be reduced. 
     In an embodiment of the method for reducing phase noise in a received signal, a training tone is utilized to facilitate measurement of the phase noise. The training tone is placed at a convenient frequency location within the N independent signals previously described. The amplitude of the training tone is typically larger than that of the N signals present. 
     The training tone typically has no signal modulated into it. Due to the lack of modulation, the zero crossings of the training tone are clearly defined since uncertainty in the zero crossing caused by the information sequence encoded onto the training tone is not present. A period T of the training signal is known, and at the end of each period T, the training tone is sampled at a point in time where the zero crossings should occur. A non-zero value obtained every T seconds provides an indication of the phase error at that instant in time that phase error was caused by the frequency conversion process. 
       FIG. 4  is an illustration of a sinusoidal training tone signal having phase error associated with it. Phase errors  305 ,  307  are typically measured in degrees. Phase error is the amount that the distorted sine wave differs from a desired undistorted sine wave having zero crossings at 0, 180, and 360 degrees. Alternatively, a time period T  303  may be used to mark the desired zero crossing points. For an unmodulated sine wave utilized as a training tone, the exact phase error introduced by the modulation and demodulation circuitry is measured. Next, the phase error information is utilized to create a signal having reduced phase error. 
     By measuring the phase error in the training tone at each calculated zero crossing, the phase error is determined. The negative of the phase error is applied to each of the N independent signals carrying information from the information sequence such that the phase distortion tends to be reduced. This is possible, even though the N independent signals are present at frequencies differing from that of the training tone because the phase distortion introduced at any one given frequency in a given cycle tends to be the same at all frequencies. 
     If a training tone that is similar in amplitude to the N independent signals is utilized, noise tends to be present on the training tone, interfering with accurate measurement of phase deviation of the training tone signal. In an alternative embodiment in which the training tone is equal to or slightly greater than the N independent signals in amplitude, the training tone signal is first bandpass filtered to remove noise from the training tone. 
     In an alternative embodiment, multiple training tones are utilized. In the alternative embodiment, every 8th tone is a training tone. In a further alternative embodiment, every 16th tone is a training tone. Equivalent training tones may be spaced as desired among a series of N independent signal carrying tones. This technique tends to reduce the noise of the training tone phase estimate. 
     In the alternative embodiments utilizing multiple training tones, phase information is obtained from each training tone and averaged to determine an average phase deviation at a particular instant in time. Thus, each phase estimate from each training tone will have a certain amount of noise present. The noise in each training tone is not correlated. Thus, for an embodiment having two training tones, the signal power in the phase error estimates adds coherently to four times the signal power in each phase error sample. However, since the noise power is uncorrelated, it does not sum coherently like the phase estimate, and only a doubling of the noise power is present. Thus, a 3 db gain is achieved by utilizing two training tones. In alternative embodiments, a 3 db gain is realized each time the number of training tones present is doubled. 
       FIG. 5  is a block diagram of a second order phase lock loop used as a part of the training tone tracking PLL ( 135  of  FIG. 3 ). The second order PLL is used as a carrier tracking PLL to reconstruct a training tone as it was transmitted, without phase error. The second order PLL is conventionally constructed utilizing components known to those skilled in the art. A signal f c  is input to a phase detector  401 . Also, a second input to phase detector  401  is a signal f ref . The output of phase detector  401  is input to a loop filter  403 . An output of loop filter  403  is an input to a frequency synthesizer  405 . The output of frequency synthesizer  405  forms the signal f ref  that is the phase detector  401  input and a mixer  407  input e −jφ(t) . 
     The phase lock loop is often used to purify a signal without appreciatively changing the signal. The purpose of the PLL in this application is to match an internally generated signal f ref  to a received signal f c =S n e jφ(t) . The purpose of the PLL is to produce a clean signal that is substituted for the received signal f c . Typically an incoming signal, such as f c , that is being replaced possesses one or more undesirable properties such as jitter, phase noise or other undesirable properties. The signal f ref  that is internally generated based on f c  tends to have the desirable property of being a smooth signal matched in frequency and phase with the input signal f c . Thus, f ref  tends to be a clean replica of f c . 
     The second order PLL inherently has the ability to match phase and frequency of an incoming signal in the generated signal f ref . Phase detector  401  instantaneously provides an indication of the phase difference between incoming signal f c  and reference signal f ref . The output of the phase detector is a phase error estimate (φ error ) 
     The phase error estimate φ error  is the difference between the phases of f ref  and f c . The phase error is applied to a conventionally constructed loop filter  403 . The loop filter  403  is a first order loop filter having a proportional term K lin  and an integrator term INT. Thus the phase errors build up in the loop filter to provide a control word (CW) output from the loop filter  403 . The control word CW output is applied to an input of a conventionally constructed frequency synthesizer  405 . 
     The second order structure allows the production of a zero frequency error with a zero phase error reproduction of f c . The frequency synthesizer  405  generates as an output f ref  that is applied to the phase detector  401  and is also designated e −jφ(t)  and coupled to a mixer  407 . 
     The carrier tracking PLL  135  of  FIG. 5  provides circuitry which typically allows phase compensation to be achieved. The carrier tracking phase lock loop is used to track the training tone phase noise error and provide an estimate of phase noise. 
     Returning to  FIG. 3 , the input  417  to the training tone tracking PLL, ( 135  of  FIG. 3 ), consists of a series of modulated carriers centered about base band  133 . The carriers are not clean, a certain amount of phase noise or phase jitter is present on each of the down converted carriers. In the MCM demodulator and FFT ( 137  of  FIG. 3 ), the instantaneous phase error determined by examining the training tone(s) will be subtracted from each of the N sampled carriers that makes up the N independent signals. The subtraction produces a series of N independent signals impressed on equally spaced carriers at the output  104  of the training tone tracking circuit  420 . The carriers are relatively free of phase noise or jitter. Mathematically the process is as follows: A series of k training tones are inserted into a MCM signal. The training tones are represented as:
 
TT=TrainingTones= e   j2πkn/N  
         where: k=0, 8, 16 . . . 1016       

     Each carrier is identically modulated by the tuner: 
     
       
         
           
             
               
                 
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             φ RAND =a normal distribution random variable 
             α=a leakage factor
 
Phase error is determined by demodulating the training tone:
 
TT= e   j2π(kn/N+φ(t))  
 
Phase error=TT e   −j2π(kn/N)   =e   j2π(kn/N)  
 
Phase error= e   jφ(t) =Phase Angle
 
The phase errors of all tones after demodulation are combined.
 
For straight combining:
 
           
         
       
    
               Phase   ⁢           ⁢   Error     =       1     (   NumberofTrainingTones   )       ⁢     ∑     TT   ⁢           ⁢     ⅇ       -   j     ⁢           ⁢   2   ⁢           ⁢   π   ⁢           ⁢     (     kn   /   N     )                     
A set of k carriers having a signal impressed upon them without distortion is represented by:
 
[ S ( n ), S ( n+ 1), S ( n+ 2) . . .  S ( n+k )]
 
The k signals with phase noise added are represented as follows:
 
[ S ( n ) e   jφ(n)   ,S ( n+ 1) e   jφ(n+1)   ,S ( n+ 2) e   jφ(n+2)    . . . S ( n+k ) e   jφ(n+k) ]
 
     Next, the phase noise contribution which is identical to the phase noise of the k signals with phase noise is removed from the pilot tone. Therefore, the negative of the phase noise of the pilot is taken. The phase noise term is multiplied ( 407  of  FIG. 5 ) with a distorted input signal S(n)e jφ(t) . 
     The resulting product  104  output to the MCM demodulator  137  is the undistorted message signals S(n), since the exponentials cancel. 
       FIG. 6  is an alternative embodiment of an MCM receiver having a fast carrier tracking PLL that incorporates a matching delay circuit. A training tone tracking PLL typically has time delay associated with its operation. A PLL having a large delay tends to have a much narrower bandwidth than a PLL having a small amount of delay. Delay tends to be removed from the training tone tracking PLL by matching the delay of the carrier tracking PLL with a matching delay circuit  413 . 
     Utilizing a matching delay circuit, the overall training tone tracking PLL is implemented such that a minimum delay appears to be present. Thus, a one delay PLL, which is the minimum delay that may be obtained for a phase lock loop is achieved. Other than the addition of matching delay circuit  413 , the carrier tracking PLL, described in this embodiment, functions as previously described. 
     The circuit is configured as previously described in  FIG. 5 . However, in  FIG. 6  a matching delay circuit  413  has been inserted in the line coupling the output of the time domain filtering/down conversion circuit  418  and the multiplier input  407 . 
     The phase detector  401  of  FIGS. 5 and 6  is responsible for developing an accurate phase error estimate. Three embodiments suitable for a phase detector design are presented in the following text. 
     A first embodiment of a phase detector  401  processes training tones, a second embodiment of a phase detector relies on a combination of training tones and modulated data signals, and a third embodiment of a phase detector utilizes data signals only. 
       FIG. 7   a  is a block diagram of an the first embodiment of a phase detector  401  that processes only training tones. The embodiment shown is utilized in the phase detector  401  shown in  FIG. 5 . The first embodiment of the phase detector  401  is capable of processing a MCM signal that employs training tones. The phase error is estimated from the phase difference of a received data sample x(n), and a reference signal f(n). Reference signal f(n) is derived from the training tone. A training tone is defined as known data that is transmitted in a sub channel. Here the training tones are a series of carriers interspersed throughout an MCM signal. 
     Input  601  is simultaneously coupled to phase error circuits  607 ,  609  and  611 . Input  601  is coupled to a first mixer port of mixer  613  in each block  607 ,  609 ,  611 . A second mixer port is coupled to a sinusoidal signal e j2π0n/N , e j2π kn/N , e j2π(N-8) n/N , of blocks  607 ,  609  and  611  respectively. A mixer output in each block  607 ,  609 ,  611 . The mixer supplies an output coupled to an input port of a second mixer  650 . In the embodiment shown a second mixer input port of mixer  650  is supplied with decision data TT(k). In an alternative embodiment the second mixer port of mixer  650  is supplied with a conjugate of the training tone, x(k). An output of mixer  650  is applied to a conventionally constructed low pass filter  501 . An output of low pass filter  501  is applied to an input of a conventionally constructed channel compensation circuit  503 . An output of channel compensation circuit  503  is applied to an input of a conventionally constructed arc tangent circuit  505 . An output of arc tangent circuit  505  is coupled to an input of the summing junction  605 . The connections described above for block  607  are identically repeated in blocks  609  and  611  for tones at f=k and f=N−8 respectively. 
     Summing junction  605  includes an output  603  that consists of a signal representative of a phase. Input  603  is applied to a conventionally constructed complex exponential block input. An output of the complex exponential block  550  is a signal e jφ(t)  a complex value. Thus, a phase is input and a complex value phasor is output from block  550 . The output of complex exponential block  550  is applied to an input of a mixer  551 . Mixer  551  is conventionally constructed as known to those skilled in the art. A second mixer input to mixer  551  supplies a signal f ref  previously generated as shown in  FIG. 5 . 
     An output of mixer  551  is applied to a conventionally constructed phase angle calculation circuit  411 . An output of a phase angle calculation circuit  411  consists of a signal output φ error . 
       FIG. 7   b  is a block diagram of the tone tracking mixers/filters  409  utilized in the phase detector circuit of  FIG. 6 . The circuitry disposed between input  601  and summing junction  605  is identical to that previously described in  FIG. 7   a . However, the output of summing junction  605  in  FIG. 7   b  the phase output  603  is converted to a complex phasor in block  550  as previously described to form output  651 . 
       FIG. 7   c  is an alternative embodiment of the tone tracking mixer/filter circuit  409 . In the embodiment shown an input  601  is simultaneously applied to phase error circuits for tones at f=0, f=k and f=N−8, 607, 609, 611 respectively. In the present embodiment blocks  607 ,  609  and  611  have been simplified. Each block  607 ,  609 ,  611  is identically constructed. Thus, the circuit connections in block  607  are described and are representative of the other remaining blocks. 
     In block  607  a mixer  613  is configured as previously described. However, an output of mixer  613  is coupled directly to a conventionally constructed channel compensation circuit  503 . An output of channel compensation circuit  503  is coupled directly to a summing junction  605 . Note in the above circuit block that the low pass filter previously described and the arc tangent circuit previously described have been omitted. 
     The low pass filter is cascaded at the output  603  of the summing junction  605 . Output  603  is coupled to an input of low pass filter  501 . A low pass filter output is coupled to an input of an arc tangent circuit  505 . An output of arc tangent circuit  505  forms the output  651 . 
       FIG. 8   a - c  are diagrams illustrating the construction and operation of the tone tracking mixers/filters ( 409  of  FIG. 7   b ) for processing a MCM signal including training tones. 
       FIG. 8   a  is a frequency spectrum  700  of an MCM signal comprising data signals  701  impressed with transmitted data and training tones  703 . In the embodiment shown the training tones are present every eighth tone and are of greater amplitude than the data signals. However, in alternative embodiments the amplitude of the training tones may be equal to the amplitude of the data signals or an arbitrary amplitude relative to the data signals. The frequency spectrum  700  is applied to a first input port of a mixer ( 613  of  FIG. 7   a ), where the desired training tone is mixed down to DC, or an IF frequency, by a complex sinusoid signal applied at a second mixer port as known to those skilled in the art. Down conversion of the eighth training tone is explained as an example. The remaining training tones are similarly processed. 
     Down conversions of the sixteenth, twenty-forth, thirty-second, fortieth, forty-eighth, and fifty-sixth training tones to DC is accomplished by selecting an appropriate signal to be applied to the second mixer port of the respective phase error circuits ( 607 ,  609 ,  611  of  FIG. 7   a ). The respective mixer outputs are applied to their respective low pass filter inputs. 
       FIG. 8   b  is a frequency spectrum  705  of the output of the mixer ( 613  of  FIG. 7   a ). The desired tone has been conventionally down converted to DC and the spectrum is applied to the input of a low pass filter ( 501  of  FIG. 7   a ). 
       FIG. 8   c  is a frequency spectrum  710  of a down converted and isolated training tone after low pass filtering. The frequency spectrum  705  has been applied to a conventionally constructed low pass filter ( 501  of  FIG. 7   a ) to produce spectrum  710  at the low pass filter output. Note that at the output  710  a residual signal level of the data signals that were adjacent to the training tone remain due to typical limitations of the filters. 
     The output of the low pass filter is the phase error for the training tone being examined. The signals produced by the circuitry of  FIG. 8  are processed as described below. 
     An estimate of the received sample phase at each training tone frequency, k, is obtained by implementing a DSP circuit of the following equation:
 
 RPHI ( k )=Lowpass Filter(( e   2πjk/n ×( n ))complex-conjugate(TT( k ))
 
where RPHI(k) is the received sample phase at frequency k, and n is summed over n=0 . . . N−1, and TT(k) is the known training tone value for frequency k. RPHI(k) is the signal that is output from the low pass filters ( 501  of  FIG. 7   a ).
 
     Returning to  FIG. 7   a , the channel compensation circuit  503  includes an input that is coupled to the output of the low pass filter  501 . In practically implemented MCM systems, the received sample phase errors are distorted by the effect of a communication channel. Compensation for the received sample phase errors contained in each channel is provided. Compensation requires the channel estimate to be known at each of the training tone frequencies, k. Using empirically derived or calculated channel information, channel compensation can be applied to the received sample phase errors as follows:
 
CC —   PHI ( k )= RPHI ( k )/CE( k ),
 
where CC_PHI(k) is the channel compensated sample phase error at frequency k, and CE(k) is the channel estimate for frequency k. The result is the output of the channel compensation circuit  503 .
 
     The arctangent circuit  505  is coupled to the output of the channel compensation circuit  503 . Each of the received sample phase errors output from the channel compensation circuit is represented as a complex phasor. To convert these phasors to a phase angle it is necessary to compute the inverse tangent of each CC_PHI(k) by utilizing a DSP implementation of the following function:
 
Angle —   PHI ( k )=arctangent[CC —   PHI ( k )]
 
     In practice, adequate accuracy tends to be obtained and it is typically preferable to approximate the phase angle as:
 
Angle —   PHI ( k )=imaginary part[CC —   PHI ( k )]
 
     The result of the process described above is the signal appearing at the output of ARCTAN circuit  505 . 
     Each sample phase angle is derived from each of a plurality of training tones applied to a plurality of phase error circuits  607 ,  609 ,  611 . Three phase error circuits  607 ,  609 ,  611  to process the training tones are shown. However, any number of phase error circuits may be utilized. 
     At summing junction  605  a total received sample phase error estimate is produced by adding each of the received sample phase angles. The total received sample phase error is given by the following equation:
 
 PHI =Σ[Angle —   PHI ( k )]
 
where k is a set of indices for all training tones. The indices define the ordinal position of the training tones in the MCM signal. The result of this equation is output  603 .
 
       FIG. 7   c  is an alternative embodiment a more efficient process described by the equation below, and implemented with conventionally constructed circuitry utilizing conventional DSP techniques, is theoretically identical to the equation above, but tends to be more computationally efficient. 
     
       
         
           
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     Phase error estimate=PD(n)=arctan[RPHI] approximated by imaginary [RPHI]. 
     Continuing with  FIG. 7   a , the circuitry for carrying out the processes described above is accomplished by utilizing conventional analog and digital signal processing techniques. 
     Input  601  includes a series of tones centered about a baseband frequency that are applied simultaneously to a plurality of phase error circuits  607 ,  609 ,  611 . The phase error circuits are dedicated to processing a tone at f=0, f=k, and a tone at f=N−8, respectively where N is the total number of carriers present. The outputs of each of the plurality of phase error circuits are coupled to a conventionally constructed summing junction  605 . The summing junction  605  includes an output  603 . 
     Each of the phase error circuits  607 ,  609 ,  611  includes a mixer  613  having a first input coupled to input  601 , a second mixer  613  input. A mixer output is coupled to an input on a conventionally constructed low pass filter  501 . The low pass filter  501  includes an output coupled to an input of a conventionally constructed channel compensation circuit  503 . 
     The channel compensation circuit  503  includes an output coupled to an input of an arc tangent circuit  505 . The arc tangent circuit  505  includes an output coupled to the summing junction  605 . The arc tangent circuit is conventionally constructed and performs the function of computing the arc tangent of a signal applied to it. 
     The second mixer input to the mixer  613  in the “phase error circuit for a tone at f=0”,  607  is a sinusoidal signal e j2π0n/N . The second mixer input for the mixer  613  in the “phase error circuit for a tone at f=k”,  609  is a sinusoidal signal e j2πkn/N . The second mixer input of the mixer  613  in the “phase error circuit for a tone at f=N−8”,  611  is the sinusoidal signal e j2π(N-8)n/N . 
     Training tones of different frequencies that are included in input signal  601  are applied to the phase detector  401 . Each of the training tones is separated by simultaneously applying the input signal  601  to all of the mixers  613 . Each mixer in each phase error circuit  607 ,  609 ,  613  has a second input frequency that mixes the training tone of interest to DC. The DC signal representative of each training tone is low pass filtered leaving only a DC representation of the desired training tone. With this technique, phase and frequency offset are corrected. 
     At each training tone frequency there often tends to be frequency specific distortion present on the training tone. In an embodiment of the invention at each training tone present, an amplitude adjustment, and a phase adjustment may be generated to compensate for the channel. 
     Based on the transmission characteristics of channel, the signal without phase noise is still expected to have a differing amplitude and phase attributable to the channel that the signal is being transmitted through. Thus, at the output of the channel compensation circuits  503 , a signal having no phase noise would have a value of zero. A non-zero value at the output of the channel compensation circuit indicates the presence of phase noise. 
     The signal output from the channel compensation circuit  503  is applied to an arc tangent circuit  505  where the arc tangent of the output of the channel compensation circuit is calculated. The channel compensation circuit output is a complex-valued signal, and by performing an arc tangent processing, the output of the arc tangent circuit provides the phase. 
     The output of the summer  605  provides a coherently summed phase error that is applied to a mixer ( 421  of  FIG. 6 ) LO port. 
     Returning to  FIG. 6 , an IF port of each mixer  421  is coupled to a conventionally constructed phase angle calculation circuit  411 . An output of the phase angle calculation circuit  411  is coupled to an input of a conventionally constructed loop filter  403 . An output of loop filter  403  is coupled to an input of a conventionally constructed frequency synthesizer  405 . An output of the frequency synthesizer  405  is coupled to an RF port of mixer  421 . 
     The output of frequency synthesizer  405  is also coupled to an RF input port of conventionally constructed mixer  407 . An LO port of mixer  407  is coupled to an output of a conventionally constructed matching delay circuit  413 . An input of matching delay circuit  413  is coupled to input  417 . Input  417  is also coupled to tone tracking mixers/filters  409 . An output of tone tracking mixers/filters  409  is coupled to an input of mixer  421 . 
     An IF output of the mixer  407  is coupled to a frequency domain processing (FFT)  415 . The output of frequency domain processing (FFT) forms output  419 . 
     In the embodiment just described above, training tones are present every 8th tone in the evenly spaced multi-tone spectrum. Phase estimates were thus calculated every 8th tone of the end independent signals present at the input as follows: 
       FIGS. 9   a - 9   c  is a block diagram of the first embodiment of the phase detector and the processing of training tones alone, in which data signals near the training tone have been deleted. Recall that in  FIG. 8   c  the signal remaining after low pass filtering  710  by the low pass filter ( 501  of  FIG. 7   a ) included residual data signals with the desired training tone. 
     Residual signals are due to limitations of the low pass filter  501 . The skirts of the low pass filter  501  are typically not sharp enough to eliminate interference caused by the adjacent data signals. The residual data signals show up as noise interfering with a desired signal&#39;s reception. In the embodiment shown the transmitted signal is modified at the transmitter ( 113  of  FIG. 3 ) such that data signals adjacent to training tones are nulled or zeroed so that they are not used. Removing data signals adjacent to the training tones improves the effectiveness of the low pass filtering in separating phase information of the training tone from system noise. 
     Equivalently a subset of training tones including only some of the training tones utilized may have adjacent data signals zeroed. In the subsequent receiver circuitry only the training tones with adjacent zero data signals are used for carrier frequency/phase error compensation. 
       FIG. 9   a  is a diagram of a spectrum  800  that is applied to a tone tracking mixers/filters circuit ( 409  of  FIG. 7   b ). A series of data carriers impressed with data  806  have training tones  805 ,  803  interspersed among them. A subset of the training tones  805  have adjacent data carrying channels  801  suppressed. 
       FIG. 9   b  is a frequency spectrum  810  of the output of the mixer ( 613  of  FIG. 7   a ) in which a spectrum from which data signals adjacent training tones have been eliminated. In the example shown the eighth training tone has been down converted to DC, or zero frequency. The down converted spectrum  810  is applied to a low pass filter ( 501  of  FIG. 7   a ). 
       FIG. 9   c  is a frequency spectrum  815  of a down converted and isolated training tone after low pass filtering. The frequency spectrum  810  has been applied to a conventionally constructed low pass filter ( 501  of  FIG. 5 ) to produce spectrum  815  at the low pass filter output. Note that the residual signal level of the adjacent data signals shown in  FIG. 8   c  are not present in this spectrum. 
     A second embodiment of a phase detector utilizes a combination of training tones and data information to make data decisions (in addition to training tone information, when available) for carrier frequency/phase tracking. A signal input to such a receiver may or may not have training tones associated with it. The advantages of using data information is that the technique can be used for MCM systems that do not employ training tones and the power of coherent addition of phase information from independent subchannels is further emphasized. 
     When using data tones for carrier frequency/phase tracking a typical obstacle is that the data information is not known at the receiver until after a frequency domain transformation has been performed. Frequency and phase information is not available at a time when the MCM signal is still a time-domain signal and deriving the carrier frequency/phase compensation would be straightforward. 
     A two-pass approach is used to process the MCM signal utilizing a combination of training tones and data information to derive frequency and phase information. First, a received MCM signal is demodulated using either conventional MCM techniques (where no carrier tracking is performed). In an alternative embodiment, on the first pass the signal may be demodulated using a variation of a training tone driven carrier-tracking loop. The primary goal of the first pass is to determine MCM data decisions, x(k). These data decisions may be compromised by carrier frequency/phase errors, and therefore some incorrect decisions may be included, which are stored in a 1 MCM block memory delay for time domain data. 
     On the second pass, the originally received data is again demodulated. However, on this pass, carrier tracking is performed using a data directed technique. The data directed techniques use exactly the same mathematics described for the first embodiment, except that phase estimates of the received signal are obtained for every sub-channel frequency that contains a data signal in addition to training tone signals. Each crrier is stripped of modulation in the second pass before the phase comparison is made. The phase estimates are compared with the expected phase and the phase errors are coherently combined. Coherent combination of phase errors is accomplished using decision data, x(k), obtained from the first pass to replace TT(k) (for each k where TT(k) is not available). 
     An improvement in performance is typically observed when training tones are spaced away from information carrying tones. In an embodiment, gaps are left just near training tones that are utilized for determination of phase error estimation. By eliminating training tones, hardware simplification is realized by eliminating one channel typically dedicated to the processing of one training tone. 
     In the third alternative embodiment, tones carrying data are used as training tones. Training tones without modulated data waste power since the carrier carries no information. In order to satisfactorily use a data tone as a training tone, first the transmitted data must be deduced from the data tone that will potentially serve as a training tone. 
     First an entire block of data is demodulated. All of the data values are determined to reconstruct the transmitted data stream. 
     The recovered data stream is then re-modulated onto a set of carriers. The re-modulated information allows the originally transmitted tones to be recovered without the modulated data. Thus, every single information tone may be treated as a training tone because the carrier has been separated from the data stream. The third embodiment of a phase detector utilizes data information only. 
       FIG. 10  is a block diagram of a two pass modulation technique. Multi-carrier data is segmented into blocks of data. A block of data is passed through a receiver to provide initial correction of phase noise and to provide one collected block of decision data. 
     The output of the receiver is stored in a one MCM block memory delay decision data block. The block of stored data represents the best estimate of which data was actually transmitted. In addition an entire set of input data is stored in a one MCM block memory delay block. The data stored in unmodulated data that is applied to a second replicated receiver. 
     The output of the one MCM block memory delay is input to a second receiver where it is processed as previously described. The second pass utilizes decision data to drive a tone tracking PLL disposed in the second receiver. The output of the one MCM block memory delay consists of in signals that are applied to the tone tracking mixers/filters  409  at each training tone input to mixer  650 . The method shown in  FIG. 10  advantageously allows data from every bin to be utilized to develop the training tone estimate. All bins instead of N/8 bins may be utilized to develop phase estimates. Thus a 3 dB improvement for every doubling of the number of bins being utilized is obtained. In the embodiment described a combination of training tones and modulation data may be utilized to produce a phase error estimate. Alternatively, training tones are not needed in this embodiment to produce a phase error estimate. 
       FIGS. 11   a ,  11   b  and  11   c  illustrates the processing steps of the third embodiment. “Known” information, either in the form of training tones or data decisions, may be used to construct a re-modulated signal. The re-modulated signal is constructed to contain all information except that of the tone of interest. The re-modulated signal is then subtracted from the total MCM signal, to remove unrelated information from the tone of interest. Phase angle estimation may then be performed on the “cleaned” tone. 
     First a technique is used whereby the data decisions are determined, such as was explained for the second embodiment above. It is desired to determine the phase error at an arbitrary frequency k. We may construct a complementary re-modulated signal that contains the entire MCM signal, except for the signal at tone k, as follows:
 
Remod_sig —   k ( n )=[Σ e   2πkn/N   X ( m )]
 
where Remod_sig_k(n) is the complementary re-modulated signal for frequency k, and m is summed over m=0 . . . N−1, where m does not equal k.
 
     The re-modulated signal is subtracted where m from the total received MCM signal, to yield a signal that is very good estimate of the signal at frequency k.
 
Est_sig —   k ( n )= MCM ( n )−Remod_sig —   k ( n )
 
where Est_sig_k(n) is the estimate signal at frequency k.
 
     The phase angle estimate at frequency k is determined by appropriately processing Est_sig_k (low-pass filtering, channel compensation and arctangent calculation) as described in the first embodiment. This can be performed at all frequencies (re-computing Est_sig_k for each frequency), and the phase angles coherently summed. 
     The technique described in this section may be performed without training tones if data decisions are made available. The techniques may also be employed without data tones, if training tones are available. 
     Each tone typically contributes interference to its neighboring tone. This interference is termed inter-carrier interference (ICI). 
     Multiple techniques are available for an MCM. If perfect band pass filters were available, no inter carrier interference would occur. However, in practically realizable bandpass filters, a transition band is present. Instead of bandpass filtering, a FFT of a data sequence is taken. The spectrum taken appears as a sinx/x, or sync response. In the digital domain, the nulls of the sync function are arranged such that the nulls fall on the location of the nearest neighboring signal that is be present. If the phase noise or frequency error is present, the neighboring signals will not fall exactly on the nulls of the sync function, and there will be interference. Thus, the interference arises due to the fact that a perfect spectral line is not present for each carrier. It is desirable to eliminate ICI. 
     The entire sequence of data is demodulated. The original information sequence is recovered. Next, a re-modulation of the entire signal is performed. Re-modulation of the signal would result in filling of all frequency bins available. In this embodiment, we are interested in one frequency bin. 
     A modified MCM modulator is used to regenerate the data sequence with the additional property of having the carrier of interest eliminated from the sequence. The original sequence has the re-constructed sequence subtracted from it. The resultant signal is a desired training tone signal without the interference of the other carriers. The process is repeated utilizing multiple MCM modulators for each carrier sought to be recovered. The phase information is extracted from a carrier recovered in this manner and then applied to the training tone tracking PLL for recovery of phase information.