Outage Constrained Design in NOMA-Based D2D Offloading Systems

Non-orthogonal multiple access (NOMA) is a new multiple access method that has been considered in 5G cellular communications in recent years, and can provide better throughput than traditional orthogonal multiple access (OMA) to save communication bandwidth. Device-to-device (D2D) communication, as a key technology of 5G, can reuse network resources to improve the spectrum utilization of the entire communication network. Combining NOMA technology with D2D is an effective solution to improve mobile edge computing (MEC) communication throughput and user access density. Considering the estimation error of channel, we investigate the power of the transmit nodes optimization problem of NOMA-based D2D networks under the rates outage probability (OP) constraints of all single users. Specifically, under the channel statistical error model, the total system transmit power is minimized with the rate OP constraint of a single device. Unfortunately, the problem presented is thorny and non-convex. After equivalent transformation of the rate OP constraints by the Bernstein inequality, an algorithm based on semi-definite relaxation (SDR) can efficiently solve this challenging non-convex problem. Numerical results show that the channel estimation error increases the power consumption of the system. We also compare NOMA with the OMA mode, and the numerical results show that the D2D offloading systems based on NOMA are superior to OMA.

Point-wise estimates for the derivative of algebraic polynomials

We give a sufficient condition on coefficients $a_k$ of an algebraic polynomial $P(z)=\sum\limits_{k=0}^{n}a_kz^k$, $a_n\not=0,$ such that the pointwise Bernstein inequality $|P'(z)|\le n|P(z)|$ is true for all $z,\ |z|\le 1$.

Holonomic modules for rings of invariant differential operators

We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings. Our main tool is the filter dimension introduced by Bavula. We extend the results for the invariants of the Weyl algebra with respect to the symplectic action of a finite group, for the rings of invariant differential operators on quotient varieties, and invariants of certain generalized Weyl algebras under the linear actions. We show that the filter dimension of all above mentioned algebras equals [Formula: see text].

Derived Equivalences for Symplectic Reflection Algebras

In this paper we study derived equivalences for symplectic reflection algebras. We establish a version of the derived localization theorem between categories of modules over these algebras and categories of coherent sheaves over quantizations of $\mathbb{Q}$-factorial terminalizations of the symplectic quotient singularities. To do this we construct a Procesi sheaf on the terminalization and show that the quantizations of the terminalization are simple sheaves of algebras. We will also sketch some applications to the generalized Bernstein inequality and to perversity of wall crossing functors.