Not applicable.
This invention is in the field of data communications, and is more specifically directed to carrier recovery in phase-modulated signals used in such communication.
As is well known in the field, several modulation techniques are now commonly used for the communication of digital signals at high data rates. In general, these modulation techniques are used to encode the communicated digital information into an analog signal by grouping a specified number of bits into a xe2x80x9csymbolxe2x80x9d, and by then modulating a carrier signal according to the digital value of each symbol in the communicated sequence.
One important way in which such modulation is implemented is phase modulation, in which the value of each communicated signal is at least partially encoded by the phase of the symbol relative to the preceding symbol in the serial stream. In phase-shift keying, for example, the relative inter-symbol phase shift fully specifies the symbol value, and as such no amplitude modulation is involved. A common type of phase-shift keying is quadrature-phase-shift-keying (QPSK), where the relative phase shift from symbol-to-symbol is in multiples of 90xc2x0 (hence the quadrature nomenclature). QPSK modulation thus encodes two-bit digital symbol values.
Another type of modulation includes both phase and amplitude modulation, such that each symbol is encoded as the combination of an amplitude value (i.e, one value of a defined set of values) and a relative phase shift (also selected as one of a possible set of defined phase shifts). One type of modulation in this class is referred to as quadrature-amplitude-modulation (QAM). QAM modulation techniques are generally referred to by the number of members in their specified xe2x80x9cconstellationxe2x80x9d of values. For example, 16-QAM refers to a modulation scheme in which the symbol amplitude may occupy one of sixteen possible points in complex space. In modern communication systems, 256-QAM has now become popular for encoding eight-bit digital symbol values (i.e., bytes) into 256 possible points in complex space.
In each of these types of modulation, of course, the modulated signals are communicated at a carrier frequency. The carrier frequency determines the rate at which the digital signal values (symbols) are communicated over the particular physical and logical communication facility, whether implemented by coaxial cable, fiber optics, or twisted-pair wires.
Carrier recovery refers to the processes performed at the receiving end of a modulated signal, by way of which the carrier frequency is eliminated from the incoming signal, and the remaining amplitude and phase information is then rendered available for decoding into the digital values for each symbol. In conventional high-performance digital communications receivers, for example cable modems and the like, this carrier recovery is performed in several stages. Typically a first demodulation operation, also referred to as down-mixing, is performed to reduce the incoming signal into, ideally, a spectrum centered about DC. Realistically, the demodulated signal at this point is a substantially low frequency signal that may be represented as follows:
S(t)ej[2xcfx80xcex94f0t+xcex8]+n
where S(t) corresponds to the exact constellation symbols (and thus is a complex quantity, as including phase information). Because such first stage demodulation is not exactly accurate, however, the demodulated signal generally retains a slight phase error that varies over time. In this representation, xcex80 is a phase error for a given symbol, and xcex94f0 is an error frequency at which this phase error varies over time. The n term refers to random noise present in the input signal. In terms of the complex constellation of possible symbol values, one may consider the first-stage demodulated signal as having a phase error corresponding to a rotation of angle xcex80 of the constellation S(t) from its true position, where the rotation varies over time at error frequency xcex94f0.
Carrier recovery thus also includes a process by way of which the phase errors are eliminated from the demodulated signal, leaving the true complex signal S(t) for decoding. This additional process is often referred to as derotation. A phase-locked loop (PLL) is a commonly used circuit for executing such carrier recovery. As is fundamental in the art, PLLs generally include a phase detection circuit that compares an input signal against the PLL output signal, and that generates an error signal corresponding to the phase difference therebetween; this error signal (typically with high frequency variations filtered out) is then used in modulating the output signal according to the error signal, so that the output signal eventually xe2x80x9clocksxe2x80x9d onto the input signal. The stable output signal, over time, has time-dependent phase error eliminated therefrom, and is thus suitable for decoding.
In modern high-data rate carrier recovery schemes, it has been observed that the phase detection process is of significant importance. One can increase the data rate of a modulated signal by encoding more bits per symbol, thus increasing the number of points in the modulation constellation. This, of course, also results in smaller phase separation between adjacent constellation points, which necessitates accurate phase detection in the carrier recovery processes. Additionally, the gain of the phase correction produced by the phase detector as a function of phase error is also important, not only in providing high-performance carrier recovery, but also in avoiding false lock situations.
One type of conventional phase estimator is referred to in the art as xe2x80x9cpower-type estimatorsxe2x80x9d. Attention in this regard is directed to Lindsey and Simon, Telecommunication Systems Engineering (General Publishing Company, 1973), pp. 71-80. In these systems, the input signal is raised to a significantly high enough power such that phase information is effectively removed, leaving only information concerning phase error. These power-type phase estimators are useful in pure phase-modulated signals (PSK), but are not particularly suited for modulation schemes, such as QAM, in which the possible phases of the data are not evenly distributed, and in which the phase error cannot therefore be readily retrieved.
Another type of conventional phase detection scheme will now be described relative to FIG. 1, in which an example of a conventional carrier recovery circuit is shown. In this example, carrier recovery circuit 2 receives a demodulated input signal of the form:
xxe2x80x2=xejxcex8+n
where x corresponds to the actual signal, where n corresponds to random (Gaussian white) noise, and where xcex8 is the residual phase error to be removed by carrier recovery circuit 2. This input signal is applied to one input of multiplier 4, which applies a phase correction factor exe2x88x92j{circumflex over (xcex8)}. Low-pass loop filter 8 may include some type of summing or integration, particularly in those cases where phase detector 6 generates a phase estimate {circumflex over (xcex8)} in the form of a derivative of a probability function.
According to this conventional phase estimation approach, phase detector 6 operates by effectively maximizing a probability function p(xcex8|xxe2x80x2), and identifying the angle xcex8 that renders this maximum may be considered to be the detected phase error of the input signal xxe2x80x2. After application of Bayes"" Rule, and considering both that the phase angle is independent of the constellation point x and also that the probability distribution of phase error xcex8 is uniform, one may consider the following probability function expression:       log    ⁢          xe2x80x83        ⁢          p      ⁢              (                                            x              xe2x80x2                        |            x                    ,          θ                )              =      K    -                  1                  σ          n          2                    ⁢                        "LeftDoubleBracketingBar"                                    x              xe2x80x2                        -                          x              ⁢                              xe2x80x83                            ⁢                              ⅇ                                  j                  ⁢                                      xe2x80x83                                    ⁢                  θ                                                              "RightDoubleBracketingBar"                2            
where "sgr"n2 is the noise power of the Gaussian noise, and where K is a constant. Expansion of the squared term changes the log of the probability function to:       log    ⁢          xe2x80x83        ⁢          p      ⁡              (                                            x              xe2x80x2                        |            x                    ,          θ                )              =      K    -                            "LeftDoubleBracketingBar"                      x            xe2x80x2                    "RightDoubleBracketingBar"                2                    σ        n        2              -                            "LeftDoubleBracketingBar"          x          "RightDoubleBracketingBar"                2                    σ        n        2              +                  1                  σ          n          2                    ⁢      2      ⁢              xe2x80x83            ⁢      Re      ⁢              {                              x                          xe2x80x2              *                                ⁢          x          ⁢                      xe2x80x83                    ⁢                      ⅇ                          j              ⁢                              xe2x80x83                            ⁢              θ                                      }            
The actual signal value x is, of course, not known a prior, and therefore this probability function is best evaluated as a summation over the entire constellation of x as follows:       log    ⁢          xe2x80x83        ⁢          p      ⁡              (                              x            xe2x80x2                    |          θ                )              =      log    ⁢          xe2x80x83        ⁢                  ∑                  all          ⁢                      xe2x80x83                    ⁢          x                    ⁢              xe2x80x83            ⁢                        p          ⁡                      (                                                            x                  xe2x80x2                                |                θ                            ,              x                        )                          ⁢                  p          ⁡                      (            x            )                              
An exact evaluation of this expression may be considered as:       p    ⁡          (                        x          xe2x80x2                |        θ            )        =            K      ≈        ⁢          xe2x80x83        ⁢          ⅇ              -                                            "LeftDoubleBracketingBar"              x              "RightDoubleBracketingBar"                        2                                σ            n            2                                ⁢                  ∑                  all          ⁢                      xe2x80x83                    ⁢          x                    ⁢              (                              ⅇ                                          -                                                                            "LeftDoubleBracketingBar"                      x                      "RightDoubleBracketingBar"                                        2                                                        σ                    n                    2                                                              +                                                2                  ⁢                                      xe2x80x83                                    ⁢                  Re                  ⁢                                      {                                                                  x                                                  xe2x80x2                          *                                                                    ⁢                      x                      ⁢                                              xe2x80x83                                            ⁢                                              ⅇ                                                  j                          ⁢                                                      xe2x80x83                                                    ⁢                          θ                                                                                      }                                                                    σ                  n                  2                                                              ⁢                      p            ⁡                          (              x              )                                      )            
For a uniform probabilty distribution of symbol values x over an N-point constellation, one may consider the sum as follows:             ∑              all        ⁢                  xe2x80x83                ⁢        x              ⁢          xe2x80x83        ⁢          p      ⁡              (        x        )              =      1    N  
which renders the desired probability function of xxe2x80x2 given xcex8 to the following:       p    ⁡          (                        x          xe2x80x2                |        θ            )        =            K      ≈        ⁢          xe2x80x83        ⁢                  ∑                  all          ⁢                      xe2x80x83                    ⁢          x                    ⁢                        ⅇ                      -                                          "LeftDoubleBracketingBar"                x                "RightDoubleBracketingBar"                            2                                      ⁢                  ⅇ                      2            ⁢                          xe2x80x83                        ⁢            Re            ⁢                          {                                                x                                      xe2x80x2                    *                                                  ⁢                x                ⁢                                  xe2x80x83                                ⁢                                  ⅇ                                      j                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                              }                                          
According to this approach, this expression is typically evaluated by way of various estimations of the probability function p(xxe2x80x2|xcex8), primarily due to computational complexity. Furthermore, determination of the maximum of the probability function p(xxe2x80x2|xcex8) is conventionally made by estimating the derivative f the probability function p(xxe2x80x2|xcex8), with the understanding that the derivative of a function is zero at a maximum. One example of such an estimate of the probability function p(xxe2x80x2|xcex8), as used in conventional decision directed phase estimation processes carried out by phase detector 6 in carrier recovery circuit 2 of FIG. 1, utilizes a Taylor series expansion of the probability function. This and other conventional estimates are suitable for non-amplitude modulated signals, such as QPSK modulation. However, these estimates generally introduce significant error into QAM signals, particularly in cases where the number N of constellation values becomes large, such as 64 or 256.
A well-known measure of the effectiveness of carrier recovery is the so-called S curve. The S curve plots the phase correction signal output of the phase detector circuit (e.g., phase detector 6 of FIG. 1) as a function of phase error. Typically, because the curve passes through the origin of the plot (zero phase error resulting in a null correction signal), and increases in magnitude with increasing phase error (and of the same polarity as the error), this plot is ideally sinusoidal for realistic circuitry, hence the name S-curve. For typical examples of carrier recovery circuits such as those illustrated in FIG. 1, particularly in the case where estimations are made of the probability function, as described above, the S-curves are far from ideal. FIG. 2 is an example of an S-curve for a conventional decision-directed carrier recovery circuit such as shown in FIG. 1 and described above, for a 64 QAM modulation scheme. As evident from FIG. 2, the phase correction signal is quite well-behaved at very small phase errors, but rapidly drops off at somewhat larger phase errors. In addition, false zero points FZ are present in the S curve, indicating that certain non-zero phase errors may also produce a null correction signal, locking phase error into the recovered signal.
It is therefore an object of the present invention to provide a carrier recovery circuit and method that provides highly accurate phase detection for amplitude and phase modulated signals.
It is a further object of the present invention to provide such a circuit and method that may be readily implemented by way of modern digital signal processor technology.
It is a further object of the present invention to provide such a circuit and method in which an extract form of the probability function derivative is used in phase detection.
It is a further object of the present invention to provide such a circuit and method that is useful for high bandwidth applications such as cable modems.
Other objects and advantages of the present invention will be apparent to those or ordinary skill in the art having reference to the following specification together with its drawings.
The present invention may be implemented into a carrier recovery circuit in which phase detection is carried out by way of generation of a derivative of a probability function. According to the present invention, the evaluation of this derivative is performed by summing a complex operator over at least a portion of the possible points in the modulation constellation. The resulting derivative signal corresponds to the phase error then detected by the phase detector and, after filtering and integration, is applied as a phase correction to the input signal. Evaluation of the derivative signal preferably utilizes an increased estimate of random noise power, for stability in the correction S curve. The derivative probability function may also be evaluated by summing only small magnitude constellation points, for computational efficiency. According to another alternative implementation of the present invention, a Taylor series estimate is used in connection with QAM or other amplitude-modulated signals.