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In this dissertation, efficient receiver algorithms and architectures for digital communications are studied. As the demand for higher data communication rate increases, the dimension of communication systems is rapidly growing, thereby requiring computationally efficient detection and decoding algorithms in the receiver. Hence, it is crucial to develop receiver algorithms that can offer good performance-complexity trade-offs in high dimensional communication systems such as multi-input multi-output (MIMO) systems and systems with a large delay spread. In this dissertation, computationally efficient receiver algorithms and low-power implementation of receiver architectures are investigated. First, a low-complexity near maximum-likelihood (ML) detector, called the reduced-dimension ML search (RD-MLS), is proposed. The main idea of the RD-MLS is based on reduction of search space dimension. That is, a solution is searched over a subset of symbols to reduce the search complexity. In order to minimize the inevitable performance loss due to the search space reduction, a list tree search (LTS) algorithm is employed, which finds the best K candidates over the reduced search space. A final solution is chosen among the K candidates after extension to the full dimension via an MMSE decision-feedback (MMSE-DF) detector. To determine the candidate size, K adaptively, a stopping criterion is incorporated into the LTS. Through computer simulations, we demonstrate that the RD-MLS algorithm achieves significant complexity reduction over the existing near ML detectors while limiting performance loss to within one dB from ML detection. Second, a low complexity MIMO tree detector, called the improved soft-input soft-output M-algorithm (ISS-MA), is presented. The proposed detector is developed for iterative detection and decoding (IDD) systems, which are known to achieve near-optimal detection performance for MIMO channels. In order to improve the performance of tree detection, a look-ahead path metric is employed that accounts for the impact of unvisited paths of the tree via an unconstrained linear MMSE estimator. Based on an analysis of the probability of correct path loss, we show that the improved path metric offers better detection performance than the conventional path metric. We also demonstrate through simulations that the ISS-MA provides a better performance-complexity trade-off than existing soft-input soft-output detection algorithms. Third, a computationally efficient turbo equalization algorithm for underwater acoustic communications is studied. The performances of two popular linear turbo equalizers, a channel estimate-based minimum mean square error TEQ (CE-based MMSE-TEQ) and a direct-adaptive TEQ (DA-TEQ) technique, are compared in the presence of channel estimation errors and adjustment errors of a least mean square (LMS) adaptive algorithm. Next, an underwater receiver architecture built upon the LMS DA-TEQ technique is introduced. To maintain a performance gains over time-varying channels, the convergence speed of the LMS algorithm is improved via two methods: (1) data reusing and gear-shifting LMS and (2) reducing the length of the equalizer by capturing the sparse structure of underwater acoustic channels. In addition, the sparse structure resulting from the underwater channel can be exploited to reduce the complexity of the equalizer and mitigate error propagation. Receiver performance for different modulation orders, channel codes, and hydrophone configurations was examined at a variety of distances, up to 1 km, from the transmitters. Experimental results show great promise for this approach, as data rates in excess of 15 kbit/s could readily be achieved without error. Lastly, an energy efficient estimation and detection problem is formulated for low-power digital filtering. Building on the soft digital signal processing technique that combines algorithmic noise tolerance and voltage scaling to reduce power, a minimum power soft error cancellation (MP-SEC) technique detects, estimates and corrects transient errors that arise from voltage over-scaling. These timing violation-induced errors, called soft errors, can be detected and corrected by exploiting the correlation structure induced by the filtering operation being protected, together with a reduced-precision replica of the protected operation. By exploiting a spacing property of soft errors in certain architectures, MP-SEC can achieve up to 30 % power savings with no SNR loss and up to 55 % power savings with less than 1 dB SNR loss, according to logic-level simulations performed for an example 25-tap frequency-selective filter.
