122 research outputs found
Deterministic Cramer-Rao bound for strictly non-circular sources and analytical analysis of the achievable gains
Recently, several high-resolution parameter estimation algorithms have been
developed to exploit the structure of strictly second-order (SO) non-circular
(NC) signals. They achieve a higher estimation accuracy and can resolve up to
twice as many signal sources compared to the traditional methods for arbitrary
signals. In this paper, as a benchmark for these NC methods, we derive the
closed-form deterministic R-D NC Cramer-Rao bound (NC CRB) for the
multi-dimensional parameter estimation of strictly non-circular (rectilinear)
signal sources. Assuming a separable centro-symmetric R-D array, we show that
in some special cases, the deterministic R-D NC CRB reduces to the existing
deterministic R-D CRB for arbitrary signals. This suggests that no gain from
strictly non-circular sources (NC gain) can be achieved in these cases. For
more general scenarios, finding an analytical expression of the NC gain for an
arbitrary number of sources is very challenging. Thus, in this paper, we
simplify the derived NC CRB and the existing CRB for the special case of two
closely-spaced strictly non-circular sources captured by a uniform linear array
(ULA). Subsequently, we use these simplified CRB expressions to analytically
compute the maximum achievable asymptotic NC gain for the considered two source
case. The resulting expression only depends on the various physical parameters
and we find the conditions that provide the largest NC gain for two sources.
Our analysis is supported by extensive simulation results.Comment: submitted to IEEE Transactions on Signal Processing, 13 pages, 4
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R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis
High-resolution parameter estimation algorithms designed to exploit the prior
knowledge about incident signals from strictly second-order (SO) non-circular
(NC) sources allow for a lower estimation error and can resolve twice as many
sources. In this paper, we derive the R-D NC Standard ESPRIT and the R-D NC
Unitary ESPRIT algorithms that provide a significantly better performance
compared to their original versions for arbitrary source signals. They are
applicable to shift-invariant R-D antenna arrays and do not require a
centrosymmetric array structure. Moreover, we present a first-order asymptotic
performance analysis of the proposed algorithms, which is based on the error in
the signal subspace estimate arising from the noise perturbation. The derived
expressions for the resulting parameter estimation error are explicit in the
noise realizations and asymptotic in the effective signal-to-noise ratio (SNR),
i.e., the results become exact for either high SNRs or a large sample size. We
also provide mean squared error (MSE) expressions, where only the assumptions
of a zero mean and finite SO moments of the noise are required, but no
assumptions about its statistics are necessary. As a main result, we
analytically prove that the asymptotic performance of both R-D NC ESPRIT-type
algorithms is identical in the high effective SNR regime. Finally, a case study
shows that no improvement from strictly non-circular sources can be achieved in
the special case of a single source.Comment: accepted at IEEE Transactions on Signal Processing, 15 pages, 6
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On ideal and subalgebra coefficients in a class k-algebras
Let k be a commutative field with prime field and A a k- algebra. Moreover, assume that there is a k-vector space basis
of A that satisfies the following condition: for all ,the product is contained in the -vector space spanned by . It is proven that the concept of minimal field of definition from polynomial rings and semigroup algebras can be generalized to the above class of (not necessarily associative) k-algebras. Namely, let U be a one-sided ideal in A or a k-subalgebra of A. Then there exists a smallest with U-as one-sided ideal resp. as k-algebra—being generated by elements in the -vector space spanned by
Pitfalls in public key cryptosystems based on free partially commutative monoids and groups
At INDOCRYPT 2003 Abisha, Thomas, and Subramanian proposed two public key schemes based on word problems in free partially commutative monoids and groups. We show that both proposals are vulnerable to chosen ciphertext attacks, and thus in the present form must be considered as insecure.This work has been partially supported by the German Academic Exchange Service DAAD and the Spanish M.E.C. as part of the BaSe CoAT project within the Acciones Integradas Hispano-Alemanas
08491 Executive Summary -- Theoretical Foundations of Practical Information Security
Designing, building, and operating secure information processing
systems is a complex task, and the only scientific way to address the
diverse challenges arising throughout the life-cycle of security
criticial systems is to consolidate and increase the knowledge of the
theoretical foundations of practical security problems. To this aim,
the mutual exchange of ideas across individual security research
communities can be extraordinary beneficial. Accordingly, the
motivation of this Dagstuhl seminar was the integration of different
research areas with the common goal of providing an integral
theoretical basis that is needed for the design of secure information
processing systems
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