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The cubic metric (CM) is being regarded as a more accurate metric for envelope fluctuations of orthogonal frequency division multiplexing (OFDM) signals than peak-to-average power ratio (PAPR). Iterative clipping and filtering (ICF) is a simple and efficient technique for PAPR reduction. However, analysis shows that it cannot achieve sufficient CM reduction due to the difference between the two metrics. Proposed is a new technique called descendent clipping and filtering (DCF) for CM reduction. Unlike ICF, DCF introduces a new parameter termed descent factor to improve its performance. Simulation results show that DCF can achieve better performance with only one iteration than ICF with multiple iterations

We consider the space of geodesic laminations on a surface, endowed with the Hausdorff metric d_H and with a variation of this metric called the d_log metric. We compute and/or estimate the Hausdorff dimensions of these two metrics. We also relate these two metrics to another metric which is combinatorially defined in terms of train tracks.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper13.abs.htm

We continue our investigation of the space of geodesic laminations on a surface, endowed with the Hausdorff topology. We determine the topology of this space for the once-punctured torus and the 4-timespunctured sphere. For these two surfaces, we also compute the Hausdorff dimension of the space of geodesic laminations, when it is endowed with the natural metric which, for small distances, is −1 over the logarithm of the Hausdorff metric. The key ingredient is an estimate of the Hausdorff metric between two simple closed geodesics in terms of their respective slopes. AMS Classification 57M99, 37E35Keywords Geodesic lamination, simple closed curve This article is a continuation of the study of the Hausdorff metric d H on the space L(S) of all geodesic laminations on a surface S , which we began in the article [10]. The impetus for these two papers originated in the monograph [3] by Andrew Casson and Steve Bleiler, which was the first to systematically exploit the Hausdorff topology on the space of geodesic laminations.In this paper, we restrict attention to the case where the surface S is the once-punctured torus or the 4-times-punctured sphere. To some extent, these are the first non-trivial examples, since L(S) is defined only when the Euler characteristic of S is negative, is finite when S is the 3-times-punctured sphere or the twice-punctured projective plane, and is countable infinite when S is the once-punctured Klein bottle (see for instance Section 9).We will also restrict attention to the open and closed subset L 0 (S) of L(S) consisting of those geodesic laminations which are disjoint from the boundary. This second restriction is only an expository choice. The results and techniques of the paper can be relatively easily extended to the full space L(S), but at the expense of many more cases to consider; the corresponding strengthening of the results did not seem to be worth the increase in size of the article.The first two results deal with the topology of L 0 (S) for these two surfaces. Theorem 1 When S is the once-punctured torus, the space L 0 (S) naturally splits as the disjoint union of two compact subsets, the closure L cr 0 (S) of the set of simple closed curves and its complement L 0 (S) − L cr 0 (S). The first subspace L cr 0 (S) is homeomorphic to a subspace K ∪ L 1 of the circle S 1 , where K is the standard Cantor set and where L 1 is a countable set consisting of one isolated point in each component of, union of the Cantor set K ⊂ S 1 and of a countable set L 3 consisting of exactly 3 isolated points in each component of S 1 − K .Theorem 2 When S is the 4-times-punctured sphere, the space L 0 (S) is homeomorphic to a subspace K ∪ L 7 of S 1 , union of the Cantor set K and of a countable set L 7 consisting of exactly 7 isolated points in each component of S 1 − K . In this case, the closure L cr 0 (S) of the set of simple closed curves is the union K ∪ L 1 of K and of a discrete set L 1 ⊂ L 7 consisting of exactly one point in each component ofHowever, it is convenient to keep a dist...