In this thesis, we compute the distance spectrum for non-causal generating signals and compare the different spectrum effects for different non-causal systems. The non-causal system is the system which the present output is determined by the future and the past. The distance spectrum is the list of the difference measures of any two signals and search through all the possible event paths by trellis as much as possible. We use the method of the line difference to compute the distance spectrum of non-causal generating signal systems by defining the line and the line difference to find the distance for every pair of signals. Using this method, we have computed the distance spectrum for non-causal generating signals. Finally, we compare the different spectrums for different non-causal systems of different coefficients.

In this thesis, the target tracking problem with input estimation is investigated. The estimation performance of the optimum decoding based smoothing algorithm and a target tracking scheme based on the Kalman filter is compared by performing simulations. The advantages and the disadvantages of these algorithms are presented.

In coherent receivers, the effect of the multipath fading channel on the transmitted signal must be estimated to recover the transmitted data. In this thesis, the channel phase and data estimation problems are investigated in a transmitted data sequence when the channel is modeled as slowly fading, frequency non-selective channel. Channel phase estimation in a transmitted data sequence is investigated and data estimation is obtained in a symbol-by-symbol MAP receiver that is designed for minimum symbol error probability criterion. The channel phase is quantized in an interval of interest, the trellis diagram is constructed and Viterbi decoding algorithm is applied that uses the phase transition and observation models for channel phase estimation. The optimum coherent and noncoherent detectors for binary orthogonal and PSK signals are derived and the modulated signals in a sequence are detected in symbol-by-symbol MAP receivers.Simulation results have shown that the performance of the receiver with phase estimation is between the performance of the optimum coherent and noncoherent receiver.

Chaotically modulated signals are used in various engineering areas such as communication systems, signal processing applications, automatic control systems. Because chaotically modulated signal sequences are broadband and noise-like signals, they are used to carry binary signals especially in secure communication systems. In this thesis, a target tracking problem under interference at chaotic communication systems is investigated. Simulating the chaotic communication system, noise-like signal sequences are generated to carry binary signals. These signal sequences are affected by Gaussian channel noise and interference while passing through the communication channel. At the receiver side, target tracking is performed using Optimum Decoding Based Smoothing Algorithm. The estimation performances of optimum decoding based smoothing algorithm at one dimensional chaotic systems and nonlinear chaotic algorithm map are presented and compared with the performance of the Extended Kalman Filter application.

In this thesis, Optimum Decoding-based Smoothing Algorithm (ODSA) is applied to well-known Discrete Lotka-Volterra Model. The performance of the algorithm is investigated for various parameters by simulations. Moreover, ODSA is compared with the SIR Particle Filter Algorithm. The advantages and disadvantages of the both algorithms are presented.