In this work wireless communication systems with multiple co-channel signals present at the receiver are considered. One of the major challenges in the development of such systems is the computational complexity required for the detection of the transmitted signals. This thesis addresses this problem and develops reduced complexity algorithms for the detection of multiple co-channel signals in receivers with multiple antennas. The signals are transmitted from either a single user employing multiple transmit antennas, from multiple users or in the most general case by a mixture of the two. The receiver is assumed to be overloaded in that the number of transmitted signals exceeds the number of receive antennas. Joint Maximum Likelihood (JML) is the optimum detection algorithm which has exponential complexity in the number of signals. As a result, detection of the signals of interest at the receiver is challenging and infeasible in most practical systems. The thesis presents a framework for the detection of multiple co-channel signals in overloaded receivers. It proposes receiver structures and two list-based signal detection algorithms that allow for complexity reduction compared to the optimum detector while being able to maintain near optimum performance. Complexity savings are achieved by first employing a linear preprocessor at the receiver to reduce the effect of Co-Channel Interference (CCI) and second, by using a detection algorithm that searches only over a subspace of the transmitted symbols. Both algorithms use iterative processing to extract ordered lists of the most likely transmit symbols. Soft information can be obtained from the detector output list and can then be used by error control decoders. The first algorithm named Parallel Detection with Interference Estimation (PD-IE) considers the Additive White Gaussian Noise (AWGN) channel. It relies on a spatially reduced search over subsets of the transmitted symbols in combination with CCI estimation. Computational complexity under overload is lower than that of JML. Performance results show that PD-IE achieves near optimum performance in receivers with Uniform Circular Array (UCA) and Uniform Linear Array (ULA) antenna geometries. The second algorithm is referred to as List Group Search (LGS) detection. It is applied to overloaded receivers that operate in frequency-flat multipath fading channels. The List Group Search (LGS) detection algorithm forms multiple groups of the transmitted symbols over which an exhaustive search is performed. Simulation results show that LGS detection provides good complexity-performance tradeoffs under overload. A union bound for group-wise and list-based group-wise symbol detectors is also derived. It provides an approximation to the error performance of such detectors without the need for simulation. Moreover, the bound can be used to determine some detection parameters and tradeoffs. Results show that the bound is tight in the high Signal to Interference and Noise Ratio (SINR) region.

Multitarget tracking in the presence of false alarm is a difficult problem to consider. The objective of multitarget tracking is to estimate the number of targets and their states recursively from available observations. At any given time, targets can be born, die and spawn from already existing targets. Sensors can detect these targets with a defined threshold, where normally the observation is influenced by false alarm. Also if the targets are with low signal to noise ratio (SNR) then the targets may not be detected. The Random Finite Set (RFS) filters can be used to solve such multitarget problem efficiently. Specially, one of the best and most widely used RFS based filter is the Probability Hypothesis Density (PHD) filter. The PHD filter approximates the posterior probability density function (PDF) by the first order moment only, where the targets SNR assumed to be much higher. The PHD filter supports targets die, born, spawn and missed-detection by using the well known implementations including Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and Gaussian Mixture Probability Hypothesis Density (GM-PHD) methods. The SMC-PHD filter suffers from the well known degeneracy problems while GM-PHD filter may not be suitable for nonlinear and non-Gaussian target tracking problems. It is desirable to have a filter that can provide continuous estimates for any distribution. This is the motivation for the use of B-Splines in this thesis. One of the main focus of the thesis is the B-Spline based PHD (SPHD) filters. The Spline is a well developed theory and been used in academia and industry for more than five decades. The B-Spline can represent any numerical, geometrical and statistical functions and models including the PDF and PHD. The SPHD filter can be applied to linear, nonlinear, Gaussian and non-Gaussian multitarget tracking applications. The SPHD continuity can be maintained by selecting splines with order of three or more, which avoids the degeneracy-related problem. Another important characteristic of the SPHD filter is that the SPHD can be locally controlled, which allow the manipulations of the SPHD and its natural tendency for handling the nonlinear problems. The SPHD filter can be further extended to support maneuvering multitarget tracking, where it can be an alternative to any available PHD filter implementations. The PHD filter does not work well for very low observable (VLO) target tracking problems, where the targets SNR is normally very low. For very low SNR scenarios the PDF must be approximated by higher order moments. Therefore the PHD implementations may not be suitable for the problem considered in this thesis. One of the best estimator to use in VLO target tracking problem is the Maximum-Likelihood Probability Data Association (ML-PDA) algorithm. The standard ML-PDA algorithm is widely used in single target initialization or geolocation problems with high false alarm. The B-Spline is also used in the ML-PDA (SML-PDA) implementations. The SML-PDA algorithm has the capability to determine the global maximum of ML-PDA log-likelihood ratio with high efficiency in terms of state estimates and low computational complexity. For fast passive track initialization, search and rescue operations the SML-PDA algorithm can be used more efficiently compared to the standard ML-PDA algorithm. Also the SML-PDA algorithm with the extension supports the multitarget tracking. / Thesis / Doctor of Philosophy (PhD)