The thesis presents algorithms based on a linear algebraic solution for the identification of the parameters of the FIR system using only higher order statistics when only the output of the system corrupted by additive Gaussian noise is observed. All the traditional parametric methods of estimating the parameters of the system have been based on the 2nd order statistics of the output of the system. These methods suffer from the deficiency that they do not preserve the phase response of the system and hence cannot identify non-minimum phase systems. To circumvent this problem, higher order statistics which preserve the phase characteristics of a process and hence are able to identify a non-minimum phase system and also are insensitive to additive Gaussian noise have been used in recent years. Existing algorithms for the identification of the FIR parameters based on the higher order cumulants use the autocorrelation sequence as well and give erroneous results in the presence of additive colored Gaussian noise. This problem can be overcome by obtaining algorithms which do not utilize the 2nd order statistics. An existing relationship between the 2nd order and any Ith order cumulants is generalized to a relationship between any two arbitrary k, Ith order cumulants. This new relationship is used to obtain new algorithms for FIR system identification which use only cumulants of order > 2 and with no other restriction than the Gaussian nature of the additive noise sequence. Simulation studies are presented to demonstrate the failure of the existing algorithms when the imposed constraints on the 2nd order statistics of the additive noise are violated while the proposed algorithms perform very well and give consistent results. Recently, a new algebraic approach for parameter estimation method denoted the Linear Combination of Slices (LCS) method was proposed and was based on expressing the FIR parameters as a linear combination of the cumulant slices. The rank deficient cumulant matrix S formed in the LCS method can be expressed as a product of matrices which have a certain structure. The orthogonality property of the subspace orthogonal to S and the range space of S has been exploited to obtain a new class of algorithms for the estimation of the parameters of a FIR system. Numerical simulation studies have been carried out to demonstrate the good behaviour of the proposed algorithms. Analytical expressions for the covariance of the estimates of the FIR parameters of the different algorithms presented in the thesis have been obtained and numerical comparison has been done for specific cases. Numerical examples to demonstrate the application of the proposed algorithms for channel equalization in data communication and as an initial solution to the cumulant matching nonlinear optimization methods have been presented.

Το αριθμητικό σύστημα υπολοίπων (RNS) έχει προταθεί ως ένας τρόπος για επιτάχυνση των αριθμητικών πράξεων του πολλαπλασιασμού και της πρόσθεσης. Ένα από τα σημαντικά πλεονεκτήματα της χρήσης του RNS είναι ότι οδηγεί σε κυκλώματα που έχουν το χαρακτηριστικό της χαμηλής κατανάλωσης. Πιο συγκεκριμένα στην παρούσα διατριβή γίνεται μια αναλυτική μελέτη πάνω στην ταχύτητα διεξαγωγής της πράξης του πολλαπλασιασμού και της άθροισης. Ο λόγος που γίνεται αυτό είναι διότι οι εφαρμογές επεξεργασίας σήματος χρησιμοποιούν ιδιαιτέρως τις προαναφερθείσες πράξεις. Επίσης γίνεται μελέτη της ισχύος που καταναλώνεται κατά την επεξεργασία ενός σήματος με τη χρήση των προτεινόμενων αριθμητικών κυκλωμάτων. Ιδιαίτερη έμφαση δίνεται στη χρήση απλών αρχιτεκτονικών τις οποίες μπορούν τα εργαλεία σύνθεσης να διαχειριστούν καλύτερα παράγοντας βέλτιστα κυκλώματα. Τέλος η διατριβή μελετά τα προβλήματα διακύμανσης των παραμέτρων του υλικού που αντιμετωπίζει η σύγχρονη τεχνολογία κατασκευής ολοκληρωμένων κυκλωμάτων. Συγκεκριμένα σε τεχνολογία μικρότερη των 90nm παρατηρείται το φαινόμενο ίδια στοιχεία κυκλώματος να συμπεριφέρονται με διαφορετικό τρόπο. Το φαινόμενο αυτό γίνεται σημαντικά πιο έντονο σε τεχνολογίες κάτω των 45nm. Η παρούσα διατριβή προτείνει λύσεις βασισμένες στην παραλληλία και την ανεξαρτησία των επεξεργαστικών πυρήνων που παρέχει το RNS, για να αντιμετωπίσει το συγκεκριμένο φαινόμενο. / The Residue Number System (RNS) has been proposed as a means to speed up the implementation of multiplication-addition intensive applications, commonly found in DSP. The main benefit of RNS is the inherent parallelism, which has been exploited to build efficient multiply-add structures, and more recently, to design low-power systems. In particular, this dissertation deals with the delay complexity of the multiply-add operation (MAC). The reason for this is that DSP applications are MAC intensive and hence this dissertation proposes solutions to increase the speed of processing. Furthermore, the study of the multiply-add operations is extended to power consumption matters. The dissertation focus on simple architectures such that EDA tools produce efficient in both power and delay, synthesized circuits. Finally the dissertation deals with variability matters that came up as the vlsi technology shrinks below 90nm. Variability becomes unaffordable especially for the 45nm technology node. This dissertation proposes solutions based on parallelism and the independence of the RNS cores to derive variation-tolerant architectures.