Blind Adaptive Channel Equalization for QAM Source Signals

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Blind adaptive equalizers are key receiver components in high performance, high density, digital communications systems. In less than fifteen years since the conception of blind adaptive equalization, various algorithms, frequently tailored to a particular source constellation class, have been proposed, implemented, tested and installed. Convergence, despite an arbitrarily poor initialization, to a parameterization with nearly optimum achievable performance is a seemingly desirable attribute of an acceptable blind adaptive equalizer algorithm, or of any parameter adaptive system for that matter. Apparently no blind adaptive algorithm for a finite-impulse-response equalizer is known to exist that can promise this, even for an idealized situation with perfect recovery capability and the simplest digital source of plus and minus ones. yet, no theorem proves that such a globally convergent algorithm does not exist, even in an idealized setting. Indeed, the available literature pertinent to this issue leaves a mixed impression due to some (seemingly) contradictory claims. The research addresses this existence question, at least among the class of schemes with memoryless error functions which subsumes the most popular blind adaptive equalizers currently in use. Within the proscribed class of applications and algorithms that do not posses admissibility (i.e., global asymptotic optimality), the severity of the practical consequences of this inadmissibility will be investigated by examining the geometry of the associated error surface. For schemes lacking global asymptotic optimality, the utility of equalizer parameter initialization schemes will also be investigated. Finally, the potential for admissibility of "new" schemes that are outside the class established which lacks global asymptotic optimality will be investigated, e.g., adaptive algorithms that utilize error functions with memory.