Communications systems often employ adaptive equalization to compensate for the distortion effects of changing channel conditions and disturbances on the signal transmission channel. The equalization process, for example, may estimate the transfer function of the transmission channel and apply the inverse of the transfer function to the received signal so as to reduce or eliminate distortion effects.
Channel equalization typically employs filters that remove amplitude and phase distortions resulting from a frequency dependent time variant response of the transmission channel, for example, to thereby provide improved symbol detection capability. The channel equalization may remove baseband intersymbol interference (ISI) caused by transmission channel disturbances, including the low pass filtering effect of the transmission channel. ISI may cause the value of a given symbol to be distorted by the values of preceding and following symbols, and essentially represents symbol “ghosts” because ISI may include advanced and delayed symbols with respect to a reference symbol location in a given decision region.
An adaptive equalizer may be viewed as a digital filter with an adaptive response to compensate for channel distortions. Several well-known algorithms are available for adapting the filter coefficients and thereby the filter response to converge the equalizer.
Significant effort has been spent enhancing adaptation algorithms for use in data transmission, whether over communication systems or from storage mediums. Such adaptation algorithms typically are employed to compensate for distortions introduced into the signals by the transmission medium through which the signals have traveled. Such transmission mediums might comprise, for example, optical networks, wireless networks, standard public switch telephone networks, or even storage media where the signals have been stored and transmitted through interfaces to a user.
In all of these situations, the media through which the signal is transmitted or in which the media is stored may, in fact, affect the contents of the signal. Accordingly, equalization systems are generally employed to place the signal as nearly as possible in its original form. However, because the exact nature of this distortion as to which the signal is subjected to may not be known at the receiving end, the structure and methods employed to equalize the received signals necessarily involve certain assumptions.
Typically, the techniques for enhancing the adaptation algorithms focus on the value of the signal at the time the signal is sampled in discrete time implementations. However, very limited effort has been spent with respect to continuous time adaptation for continuous time delay line equalizers.
One technique which has been used to adapt the feedforward equalizer to compensate for signal distortion due to the transmission or storage media is known as discrete time least mean square based adaptation. A typical continuous time least mean square (“LMS”) based adaptation is applied to the feedforward equalizer followed by decision feedback. This technique can be expressed as:
                                          c            i                    ⁡                      (            t            )                          =                              ∫            0            t                    ⁢                      μ            ·                          e              ⁡                              (                τ                )                                      ·                                          s                i                            ⁡                              (                τ                )                                      ·                          ⅆ              τ                                                          (        1        )            where:                μ is an adaptation parameter;        ci denotes the ith tap either feed forward or feedback;        si(τ) denotes the sampled input signal appropriately time aligned as applied to the ith tap; and        e(τ) denotes an error signal, such as the difference between the output of a timing control circuit and a feedback signal.One problem with this form of the adaptation is “coefficient drift” associated with decision-directed fractionally spaced equalizers. For decision-directed equalizers, “coefficient drift” can be a serious problem for a number of reasons. For example, the coefficient vector c with coefficients ci satisfying the above equation can be c or −c. Furthermore, with enough taps, the feedforward equalizer coefficient vector can be shifted either left or right (i.e., the effective group delay change of the feedforward equalizer) with the same performance.        
The generic coefficient-update equation in continuous time LMSE equalizers can be given as follows:
                                                        c              i                        ⁡                          (              t              )                                +                      T            ⁢                          ⅆ                              ⅆ                t                                      ⁢                                          c                i                            ⁡                              (                t                )                                                    =                              β            ⁢                                                  ⁢                                          c                i                            ⁡                              (                t                )                                              +                      μ            ·                          e              ⁡                              (                t                )                                      ·                                          s                i                            ⁡                              (                t                )                                                                        (        2        )            where T is the time-constant parameter, μ is the adaptation gain parameter and β is the leakage parameter. Note that when β=1 (representing no leakage), the equation simplifies to the previous integral equation. The coefficient-drift problem can be minimized with tap-leakage.
In general, a significant challenge within a communication system (e.g., a telecommunication network or a data retrieval system) has been the application of channel parameter measurement and performance monitoring techniques. These techniques are desired to assist with maintenance of the communication system and/or quality of service and possibly provide fault detection and isolation.
For example, the techniques may be utilized to provide relevant information or take remedial action during set-up or provide system optimization to enhance throughput, reliability, and/or monitor the health within the communication system on a real-time basis. It may also be important to have a measure of the quality of the signal to prevent any degradation in the quality of service through any path of the communication system.
Thus, adaptively changing the coefficients allows the system to compensate for the various changes in the signal, such as discussed above. Adaptive coefficient generators may be used to provide appropriate coefficients to a feedforward or feedback filter or equalizer. The adaptive coefficient generators changes the coefficients based on an input signal, such as an information or data signal s(t), and an error signal, which may be an iterative feedback error signal e(t). However, for LMS adaptation of coefficients, input signals s(t) and e(t) are ideally uncorrelated, i.e., the average value of the product is zero at the converged state, with optimal coefficients s(t) and e(t) uncorrelated. This would require infinite effective loop gain and hence translate to infinite gain requirement for the coefficient adaptation block. The high gain requirement poses a very severe constraint, e.g., resulting from mismatches in differential circuit topologies. Nominally identical devices suffer from random mismatches, and the problem worsens with the scaling of CMOS technology.
One possible way for correcting offsets is to use digital-to-analog converters (DACs). But, high device offsets, along with high gain, increases the range and resolution requirement of the DAC. Note that offsets need to be corrected at the power-up of the IC only, as in continuous-time mode, there is no way to distinguish between the adapted coefficient and the offset.
Accordingly, it would be desirable to have systems and methods for adaptively generating coefficients for continuous time equalizers that overcome the disadvantages of the prior art as discussed, such as generating coefficients with high adaptation loop gain and requisite time-constant, mitigating offsets, and maintaining closed-loop stability.