Network sum-rate maximization via joint power allocation and antenna selection for clustered downlink/uplink NOMA networks

This paper considers the problem of joint power allocation and antenna selection (J-PA-AS) for downlink (DL) and uplink (UL) clustered non-orthogonal multiple-access (NOMA) networks. In particular, the goal is to perform antenna selection for each user cluster and allocate transmit power to its users so as to maximize the network sum-rate in the DL and UL directions, while satisfying quality-of-service (QoS) requirements. The formulated problem happens to be non-convex and NP-hard, and thus, there is no systematic or computationally-efficient approach to solve it directly. In turn, a low-complexity two-stage algorithm is proposed. Specifically, the first stage optimally solves the sum-rate maximizing power allocation for each (antenna, user cluster) pair. After that, antenna selection is optimally solved in polynomial-time complexity via the Kuhn–Munkres with backtracking (KMB) algorithm. Extensive simulation results are provided to validate the proposed algorithm, which is shown to efficiently yield the optimal network sum-rate in each link direction, in comparison to the optimal J-PA-AS scheme (solved via a global optimization package), and superior to other benchmark schemes. Light is also shed on the impact of spatial-diversity on the network sum-rate, where it is shown that the greater the number of base-station antennas is, the higher the network sum-rate, and the lower the outage events. Additionally, the significance of decoupling antenna selection in each link direction on the network sum-rate is highlighted. Lastly, the cases of imperfect channel state information (CSI) and imperfect successive interference cancellation (SIC) have been investigated, where it is demonstrated that spatial-diversity gains reduce the adverse effects of imperfect CSI and SIC on the network sum-rate.     

AN-aided beamforming for IRS-assisted SWIPT systems

This paper studies artificial noise (AN)-aided beamforming design in an intelligent reflecting surface (IRS)-assisted system empowered by simultaneous wireless information and power transfer (SWIPT) technique. Multiple power splitting (PS) single-antenna receivers simultaneously receive information and energy from a multi-antenna base station (BS). Although all users are legitimate, in each transmission interval only one receiver is authorized to receive information and the others are only allowed to harvest power which are considered as unauthorized receivers (URs). To prevent information decoding by URs, AN signal is transmitted from the BS. We adopt a non-linear model for energy harvesting. In the optimization problem, we minimize the total transmit power, and for this purpose, we utilize an alternating optimization (AO) algorithm. For the non-convex rank-one constraint for IRS phase shifts, we utilize a sequential rank-one constraint relaxation (SROCR) algorithm. In addition to single antenna URs scenario, we investigate multi-antenna URs scenario and evaluate their performance. Simulation results validate the effectiveness of using IRS.     

Power Series Rings Satisfying a Zero Divisor Property

In this note we continue to study zero divisors in power series rings and polynomial rings over general noncommutative rings. We first construct Armendariz rings which are not power-serieswise Armendariz, and find various properties of (power-serieswise) Armendariz rings. We show that for a semiprime power-serieswise Armendariz (so reduced) ring R with a.c.c. on annihilator ideals, R[[x]] (the power series ring with an indeterminate x over R) has finitely many minimal prime ideals, say B ₁,…,B _m , such that B ₁… B _m  = 0 and B _i  = A _i [[x]] for some minimal prime ideal A _i of R for all i, where A ₁,…,A _m are all minimal prime ideals of R. We also prove that the power-serieswise Armendarizness is preserved by the polynomial ring extension as the Armendarizness, and construct various types of (power-serieswise) Armendariz rings.     

A New Criterion for Finite Noncyclic Groups

Let H be a subgroup of a group G. We say that H satisfies the power condition with respect to G, or H is a power subgroup of G, if there exists a non-negative integer m such that H = G ^m  = 〈 g ^m |g ? G 〉. In this note, the following theorem is proved: Let G be a group and k the number of nonpower subgroups of G. Then (1) k = 0 if and only if G is a cyclic group (theorem of F. Szász); (2) 0 < k < ∞ if and only if G is a finite noncyclic group; (3) k = ∞ if and only if G is a infinte noncyclic group. Thus we get a new criterion for the finite noncyclic groups.     

On the exact distribution and mean value function of a geometric process with exponential interarrival times

The geometric process is considered when the distribution of the first interarrival time is assumed to be exponential. An analytical expression for the one dimensional probability distribution of this process is obtained as a solution to a system of recursive differential equations. A power series expansion is derived for the geometric renewal function by using an integral equation and evaluated in a computational perspective. Further, an extension is provided for the power series expansion of the geometric renewal function in the case of the Weibull distribution.     

Computer simulations of the interaction between a heavy charge and a classical harmonic oscillator

The interaction of a heavy, point-like charge with a classical electron harmonically bound to a positive, heavy nucleus was simulated. Attention was focused on the stopping of the moving charge. Although most results in this paper can be explained within the framework of Bohr's and more recent theoretical studies, discrepancies do appear. The stopping number ( L ) does not seem to be a universal function of \xi = mv_{0}^{3}/(Z_{1}e^{2}\omega) as was previously proposed. Actually, L seems to be also a function of the amplitude A , the oscillator frequency \omega and the sign of the ion charge. For \xi \ll 1 , and provided the ion is positively charged, simulations yield L 's which are greater than theoretical predictions. This seems to be caused by the fact that, during the collision, the electron is first virtually captured by the ion and released later in a higher energy state. In the high velocity regime, a partition rule similar to that which holds for a quantum harmonic oscillator seems to also hold for the classical counterpart. However, instead of the quantum equipartition a two-third partition rule appears to hold in the classical case.     

Exact laser line-width requirements evaluation for optical PSK homodyne communication systems with Dither loop

The laser line-width required in PSK homodyne communication systems with Dither phase-locked loop receivers are exactly evaluated. It is shown that second-order phase-locked loops require at least 0.2 pW of signal power per every Hz of laser line-width (this number refers to the system with the detector responsivity 0.94 A/W, damping ratio 0.707, and the phase error standard deviation 10°). This signal power is used for phase locking, and is, therefore lost from the data receiver. This study for the first time shows the imperfect-phase-recovery-induced power penalty as a function of laser line-width. It can be estimated from the theoretical result that an optimal dither phase locked-loop receiver requires the laser line-width as Δυ ≤ 3.14 × 10⁻⁵ × R_b, where R_b is the system bit rate. This number refers to the system with power penalty of 1 dB at BER = 10⁻¹⁰.