The Breadth-one DD-invariant Polynomial Subspace

We demonstrate the equivalence of two classes of $D$-invariant polynomial subspaces introduced in [8] and [9], i.e., these two classes of subspaces are different representations of the breadth-one $D$-invariant subspace. Moreover, we solve the discrete approximation problem in ideal interpolation for the breadth-one $D$-invariant subspace. Namely, we find the points, such that the limiting space of the evaluation functionals at these points is the functional space induced by the given $D$-invariant subspace, as the evaluation points all coalesce at one point

Fundamental Green Tradeoffs: Progresses, Challenges, and Impacts on 5G Networks

With years of tremendous traffic and energy consumption growth, green radio has been valued not only for theoretical research interests but also for the operational expenditure reduction and the sustainable development of wireless communications. Fundamental green tradeoffs, served as an important framework for analysis, include four basic relationships: spectrum efficiency (SE) versus energy efficiency (EE), deployment efficiency (DE) versus energy efficiency (EE), delay (DL) versus power (PW), and bandwidth (BW) versus power (PW). In this paper, we first provide a comprehensive overview on the extensive on-going research efforts and categorize them based on the fundamental green tradeoffs. We will then focus on research progresses of 4G and 5G communications, such as orthogonal frequency division multiplexing (OFDM) and non-orthogonal aggregation (NOA), multiple input multiple output (MIMO), and heterogeneous networks (HetNets). We will also discuss potential challenges and impacts of fundamental green tradeoffs, to shed some light on the energy efficient research and design for future wireless networks.Comment: revised from IEEE Communications Surveys & Tutorial