Frequency permutation arrays

Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n=m lambda and distance d is a set T of multipermutations on a multiset of m symbols, each repeated with frequency lambda, such that the Hamming distance between any distinct x,y in T is at least d. Such arrays have potential applications in powerline communication. In this paper, we establish basic properties of FPAs, and provide direct constructions for FPAs using a range of combinatorial objects, including polynomials over finite fields, combinatorial designs, and codes. We also provide recursive constructions, and give bounds for the maximum size of such arrays.Comment: To appear in Journal of Combinatorial Design

Resolvable designs with large blocks

Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information matrix and consequently given in terms of block concurrences. Equalizing block concurrences for given block sizes is often, but not always, the best strategy. Sufficient conditions are established for various strong optimalities and a detailed study of E-optimality is offered, including a characterization of the E-optimal class. Optimal designs are found to correspond to balanced arrays and an affine-like generalization.Comment: Published at http://dx.doi.org/10.1214/009053606000001253 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Low-complexity LSMR equalisation of FrFT-based multicarrier systems in doubly dispersive channels

The discrete fractional Fourier transform (FrFT) has been suggested to enhance performance over DFT-based multicarrier systems when transmitting over doubly-dispersive channels. In this paper, we propose a novel low-complexity equaliser for inter-symbol and inter-carrier interference arising in such multicarrier transmission system. Due to a lower spreading in the FrFT-domain compared to the DFTchannel matrix as compared to the DFT domain, the equaliser cam approximate the fractional-domain channel matrix by a band matrix. Further, we utilise the least squares minres (LSMR) algorithm in the calculation of the equalisation, which exhibits attractive numerical properties and low complexity. Simulation results demonstrate the superior performance of the proposed LSMR equaliser over benchmark schemes

Accurate Telescope Mount Positioning with MEMS Accelerometers

This paper describes the advantages and challenges of applying microelectromechanical accelerometer systems (MEMS accelerometers) in order to attain precise, accurate and stateless positioning of telescope mounts. This provides a completely independent method from other forms of electronic, optical, mechanical or magnetic feedback or real-time astrometry. Our goal is to reach the sub-arcminute range which is well smaller than the field-of-view of conventional imaging telescope systems. Here we present how this sub-arcminute accuracy can be achieved with very cheap MEMS sensors and we also detail how our procedures can be extended in order to attain even finer measurements. In addition, our paper discusses how can a complete system design be implemented in order to be a part of a telescope control system.Comment: Accepted for publication in PASP, 12 page