No abstract

This paper deals with fading and/or near-far effects with or without power control on the evaluation of the sum capacity of finite dimensional Code Division Multiple Access (CDMA) systems for binary and finite nonbinary inputs and signature matrices. Important results of this paper are that the knowledge of the received power variations due to input power differences, fading and/or near-far effects can significantly improve the sum capacity. Also traditional power controls can not improve the sum capacity; for the asymptotic case, any type of power control on the near-far effects is equivalent to the case without any power control. Moreover, for the asymptotic case, we have developed a method that determines bounds for the fading/near-far sum capacity with imperfect power estimation from the actual sum capacity of a CDMA system with perfect power estimation. To show the power and utility of the results, a number of sum capacity bounds for special cases are numerically evaluated.

Recovery of sparse signals from linear, dimensionality reducing measurements broadly fall under two well-known formulations, named the synthesis and the analysisá la Elad et al. Recently, Chandrasekaran et al. introduced a new algorithmic sparse recovery framework based on the convex geometry of linear inverse problems, called the atomic norm formulation. In this paper, we prove that atomic norm formulation and synthesis formulation are equivalent for closed atomic sets. Hence, it is possible to use the synthesis formulation in order to obtain the so-called atomic decompositions of signals. In order to numerically observe this equivalence we derive exact linear matrix inequality representations, also known as the theta bodies, of the centrosymmertic polytopes formed from the columns of the simplex and their antipodes. We then illustrate that the atomic and synthesis recovery results agree on machine precision on randomly generated sparse recovery problems.