Abstract-Two point sets { pi } and { p' }; i = 1, 2,9 , N are related by p' = Rpi + T + Ni, where R is a rotation matrix, T a translation vector, and Ni a noise vector. Given { pi } and { p' }, we present an algorithm for finding the least-squares solution of R and T, which is based on the singular value decomposition (SVD) of a 3 x 3 matrix. This new algorithm is compared to two earlier algorithms with respect to computer time requirements.

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We analyze the performance of multiple input/multiple output (MIMO) communications systems employing spatial multiplexing and zero-forcing detection (ZF). The distribution of the ZF signal-to-noise ratio (SNR) is characterized when either the intended stream or interfering streams experience Rician fading, and when the fading may be correlated on the transmit side. Previously, exact ZF analysis based on a wellknown SNR expression has been hindered by the noncentrality of the Wishart distribution involved. In addition, approximation with a central-Wishart distribution has not proved consistently accurate. In contrast, the following exact ZF study proceeds from a lesser-known SNR expression that separates the intended and interfering channel-gain vectors. By first conditioning on, and then averaging over the interference, the ZF SNR distribution for Rician-Rayleigh fading is shown to be an infinite linear combination of gamma distributions. On the other hand, for Rayleigh-Rician fading, the ZF SNR is shown to be gammadistributed. Based on the SNR distribution, we derive new series expressions for the ZF average error probability, outage probability, and ergodic capacity. Numerical results confirm the accuracy of our new expressions, and reveal effects of interference and channel statistics on performance.

Abstract-The distributed nature of cooperative networks may result in multiple carrier frequency offsets (CFOs), which make the channels time varying and overshadow the diversity gains promised by collaborative communications. This paper seeks to address multiple CFO estimation using training sequences in space-division multiple access (SDMA) cooperative networks. The system model and CFO estimation problem for cases of both decode-and-forward (DF) and amplify-and-forward (AF) relaying are formulated and new closed-form expressions for the Cramer-Rao lower bound (CRLB) for both protocols are derived. The CRLBs are then applied in a novel way to formulate training sequence design guidelines and determine the effect of network protocol and topology on CFO estimation. Next, two computationally efficient iterative estimators are proposed that determine the CFOs from multiple simultaneously relaying nodes. The proposed algorithms reduce multiple CFO estimation complexity without sacrificing bandwidth and training performance. Unlike existing multiple CFO estimators, the proposed estimators are also accurate for both large and small CFO values. Numerical results show that the new methods outperform existing algorithms and reach or approach the CRLB at mid-to-high signal-to-noise ratio (SNR). When applied to system compensation, simulation results show that the proposed estimators significantly reduce average-bit-error-rate (ABER).Index Terms-Cooperative communications, synchronization, carrier frequency offset estimation, Cramer-Rao lower bound (CRLB), MUltiple SIgnal Characterization (MUSIC).

A new algorithm is proposed for the solution of an important class of multidimensional detection problems: the detection of small, barely discernible, moving objects of unknown position and velocity in a sequence of digital images. A large number of candidate trajectories, orgavized into a tree structure, are hypothesized at each pixel io the sequence and tested sequentially for a shift in mean intensity. The practicality of the algorithm is facilitated by the use of multistage bypothesis testing (MHT) for simultaneous inference, as well as the existence of exact expressions for MHT test performance in Gaussian white noise (GWN). These expressions predict the algorithm's computation and memory requirements, where it is shown theoretically that several orders of magnitude of processing are saved over a brute-force approach based on fixed sample-size tests. The algorithm is applied to real data by using a robust preprocessing procedure to eliminate background structure and transform the image sequence into a residual representation, modeled as GWN. Results are verified experimentally on a variety of video image sequences.

Abstract-Multiple distributed nodes in cooperative networks generally are subject to multiple carrier frequency offsets (MCFOs) and multiple timing offsets (MTOs), which result in time varying channels and erroneous decoding. This paper seeks to develop estimation and detection algorithms that enable cooperative communications for both decode-and-forward (DF) and amplify-and-forward (AF) relaying networks in the presence of MCFOs, MTOs, and unknown channel gains. A novel transceiver structure at the relays for achieving synchronization in AF-relaying networks is proposed. New exact closed-form expressions for the Cramér-Rao lower bounds (CRLBs) for the multi-parameter estimation problem are derived. Next, two iterative algorithms based on the expectation conditional maximization (ECM) and space-alternating generalized expectation-maximization (SAGE) algorithms are proposed for jointly estimating MCFOs, MTOs, and channel gains at the destination. Though the global convergence of the proposed ECM and SAGE estimators cannot be shown analytically, numerical simulations indicate that through appropriate initialization the proposed algorithms can estimate channel and synchronization impairments in a few iterations. Finally, a maximum likelihood (ML) decoder is devised for decoding the received signal at the destination in the presence of MCFOs and MTOs. Simulation results show that through the application of the proposed estimation and decoding methods, cooperative systems result in significant performance gains even in presence of impairments.Index Terms-Cooperative communications, Cramér-Rao lower bounds (CRLB), expectation conditional maximization (ECM), space-alternating generalized expectation-maximization (SAGE), timing and carrier synchronization.

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