Twin tree hierarchy: a regularized approach to construction of signature matrices for overloaded CDMA

Abstract

Overloaded code division multiple access being the only means of the capacity extension for conventional code division multiple access accommodates more number of signatures than the spreading gain. Recently, ternary Signature Matrices with Orthogonal Subsets (SMOS) has been proposed, where the capacity maximization is 200%. The proposed multi-user detector using matched filter exploits the twin tree hierarchy of correlation among the subsets to guarantee the errorless recovery. In this paper, we feature the non-ternary version of SMOS (i.e., 2k-ary SMOS) of same capacity, where the binary alphabets in all the k constituent (orthogonal) subsets are unique. Unlike ternary, the tree hierarchy for 2k-ary SMOS is non-uniform. However, the errorless detection of the multi-user detector remains undeviated. For noisy transmission, simulation results show the error performance of the right child for each subset of 2k-ary to be significantly improved over the left. The optimality of the right child of the largest (Hadamard) subset is also discovered. At higher loading, for larger and smaller subsets the superiority is reported for the 2k-ary and ternary, respectively, and the counter-intuitive deviations observed for the lower loading scenarios are logically explained. For the overall capacity maximization being 150%, superiority is featured by the 2k-ary, but beyond, it becomes a conditional entity.where y and r D CAx are the noisy and noiseless received vector for C D OEc 1 , c 2 , c 3 , , c M being a N M matrix representing M signatures of length N, x D OEx 1 , x 2 , x 3 , , x M T represents the input data vector corresponding to all M users or signatures, A D I M M = Identity matrix with diagonal elements representing the amplitudes assuming the system to be perfectly power controlled, and n denotes zero mean Additive white Gaussian noise vector. While for conventional (underloaded) CDMA the maximum achievable value of M is N (i.e., M Ä N), this capacity limit can be maximized beyond N (i.e., M > N) using the feature of overloaded CDMA, which subsequently leads to the significant rise in the loading (overloading) factorˇD . M =N/.Over a decade, the popularity of CDMA besides the military applications can be well-speculated from its growing commercialization of the wireless communication systems like Third Generation cellular architecture using wideband CDMA (WCDMA). Although for the Fourth Generation architecture, the scope of participation of CDMA has been fully obliterated, its further advancement in terms of sparse coded multiple access [1] using low density signature [2] has regained its priority and been prospectively provisioned for the Fifth Generation [3] cellular architecture.

A Mobile Computing Method Using CNN and SR for Signature Authentication with Contour Damage and Light Distortion

“…This supports daily social life and economic activities and contributes greatly to the sustainable growth of the economy and solves various social problems [1]. A signature is a commonly used human feature for identity authentication [2][3][4]. Artificial intelligence approaches to signature authentication have been evolving from offline methods to online methods to meet modern demands.…”