Browsing by Author "Holub, James R."

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    Cellular diagnostic systems using hidden Markov models
    Mohammad, Maruf H. (Virginia Tech, 2006-10-19)
    Radio frequency system optimization and troubleshooting remains one of the most challenging aspects of working in a cellular network. To stay competitive, cellular providers continually monitor the performance of their networks and use this information to determine where to improve or expand services. As a result, operators are saddled with the task of wading through overwhelmingly large amounts of data in order to trouble-shoot system problems. Part of the difficulty of this task is that for many complicated problems such as hand-off failure, clues about the cause of the failure are hidden deep within the statistics of underlying dynamic physical phenomena like fading, shadowing, and interference. In this research we propose that Hidden Markov Models (HMMs) be used as a method to infer signature statistics about the nature and sources of faults in a cellular system by fitting models to various time-series data measured throughout the network. By including HMMs in the network management tool, a provider can explore the statistical relationships between channel dynamics endemic to a cell and its resulting performance. This research effort also includes a new distance measure between a pair of HMMs that approximates the Kullback-Leibler divergence (KLD). Since there is no closed-form solution to calculate the KLD between the HMMs, the proposed analytical expression is very useful in classification and identification problems. A novel HMM based position location technique has been introduced that may be very useful for applications involving cognitive radios.
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    Lie derivations on rings of differential operators
    Chung, Myungsuk (Virginia Tech, 1995-04-04)
    Derivations on rings of differential operators are studied. In particular, we ask whether Lie derivations are forced to be associative derivations. This is established for the Weyl algebras, which provides the details of a theorem of A. Joseph. The ideas are extended to localizations of Weyl algebras. As a corollary, the implication is verified for the universal enveloping algebras of nilpotent Lie algebras.
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    Multi-layered Space Frequency Time Codes
    Al-Ghadhban, Samir Naser (Virginia Tech, 2005-11-04)
    This dissertation focuses on three major advances on multiple-input multiple-output (MIMO) systems. The first studies and compares decoding algorithms for multi-layered space time coded (MLSTC) systems. These are single user systems that combine spatial multiplexing and transmit diversity. Each layer consists of a space time code. The detection algorithms are based on multi-user detection theory. We consider joint, interference nulling and cancellation, and spatial sequence estimation algorithms. As part of joint detection algorithms, the sphere decoder is studied and its complexity is evaluated over MIMO channels. The second part contributes to the field of space frequency time (SFT) coding for MIMO-OFDM systems. It proposes a full spatial and frequency diversity codes at much lower number of trellis states. The third part proposes and compares uplink scheduling algorithms for multiuser systems with spatial multiplexing. Several scheduling criteria are examined and compared. The capacity and error rate study of MLSTBC reveals the performance of the detection algorithms and their advantage over other open loop MIMO schemes. The results show that the nulling and cancellation operations limit the diversity of the system to the first detected layer in serial algorithms. For parallel algorithms, the diversity of the system is dominated by the performance after parallel nulling. Theoretically, parallel cancellation should provide full receive diversity per layer but error propagations as a result of cancellation prevent the system from reaching this goal. However, parallel cancellation provides some gains but it doesn't increase the diversity. On the other hand, joint detection provides full receive diversity per layer. It could be practically implemented with sphere decoding which has a cubic complexity at high SNR. The results of the SFT coding show the superiority of the IQ-SFT codes over other codes at the same number of sates. The IQ-SFT codes achieve full spatial and frequency diversity at much lower number of trellis states compared to conventional codes. For V-BLAST scheduling, we propose V-BLAST capacity maximizing scheduler and we show that scheduling based on optimal MIMO capacity doesn't work well for V-BLAST. The results also show that maximum minimum singularvalue (MaxMinSV) scheduling performs very close to the V-BLAST capacity maximizing scheduler since it takes into account both the channel power and the orthogonality of the channel.
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    A note on best approximation and invertibility of operators on uniformly convex Banach spaces
    Holub, James R. (Hindawi Publishing Corp, 1991-01-01)
    It is shown that if X is a uniformly convex Banach space and S a bounded linear operator onX for which ?I-S?=1, then S is invertible if and only if ?I-12S? <1. From this it follows thatif S is invertible on X then either (i) dist(I,[S])<1, or (ii) 0 is the unique best approximation toI from [S], a natural (partial) converse to the well-known sufficient condition for invertibility thatdist(I,[S])<1.
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    Riesz bases and positive operators on Hilbert space
    Holub, James R. (Hindawi, 2003-01-01)
    It is shown that a normalized Riesz basis for a Hilbert space H (i.e., the isomorphic image of an orthonormal basis in H) induces in a natural way a new, but equivalent, inner product onH in which it is an orthonormal basis, thereby extending thesense in which Riesz bases and orthonormal bases are thought ofas being the same. A consequence of themethod of proof of this result yields a series representation forall positive isomorphisms on a Hilbert space.