| We appeal to the estimator-correlator philosophy of detection and estimation to develop a unified decision theory of equalization for digital communication over linear, time invariant, dispersive propagation media obscured by additive foreign interference. Our theory constructively introduces a fundamental principle for efficiently trading system complexity for improved performance while, more generically, establishes the role and raison d' etre of a synthetic point of view which might be coined the canonic theory of equalization. Our methodology differs drastically from what is customary in the field of network synthesis for optimal and suboptimal discrimination of noisy time-dispersed digital signals. Though it is likelihood based, our structural considerations are generally carried out directly in the continuous time-domain. Our generic goal is to obtain approximate likelihood-ratio rearrangements with practical significance for the optimal, in the minimum per-block (OBBD) error probability sense, Bayesian demodulator. Upon adopting the estimator-correlator realization of the OBBD, we are led to a synthesis triptych, with the selection of the estimator playing the leading role in center stage, and the interpretation of the resulting approximate likelihood-ratio in terms of physically realizable network elements and effective performance as important supporting characters.;This point of view is pursued in Chapters 2 & 3 on the basis of the generalized likelihood-ratio test (GLRT) and the standard likelihood-ratio test (SLRT). It is well-understood that receivers exhibiting optimal performance characteristics are highly nonlinear simply because they fully exploit the discrete nature of intersymbol interference. Our development assumes that the intersymbol interference is only partially discrete, and succeeds in bringing into sharp focus a natural connection of the GLRT to suboptimal receiver structures that yield complete or partial suppression of intersymbol interference, while concurrently establishing an intimate relationship of the SLRT to variants of the latter that minimize approximately the block error probability.;The growing conviction that a canonic theory of equalization could only arise from deeper understanding and generalization of the above sampled-data estimator-correlator interpretation led to the programme of theoretical research reported in Chapters 4 & 6. Our generic contribution in these chapters is a general procedure of configuring explicit estimator-correlator receiver realizations that can be constructively determined by the channel and noise characteristics.;Our specific contribution is the synthesis of an estimator-correlator receiver which is of considerable interest, inasmuch as it forms the basis for a whole new class of canonic receiver architectures. (Abstract shortened by UMI.). |
