A new blind equalization algorithm based on convex combination

The convex combination is a mathematic approach to keep the advantages of its component algorithms for better performance. In this paper, we employ convex combination in the blind equalization to achieve better blind equalization. By combining the blind constant modulus algorithm (CMA) and decision directed algorithm, the combinative blind equalization (CBE) algorithm can retain the advantages from both. Furthermore, the convergence speed of the CBE algorithm is faster than both of its component equalizers. Simulation results are also given to verify the proposed algorithm.

Preconditioning 2D integer data for fast convex hull computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.