PROPOSING A MATHEMATICAL SOFTWARE TOOL IN PHYSICS SECONDARY EDUCATION

Abstract: MathCad ® is a very popular software tool for mathematical and statistical analysis in science and engineering. Its low cost, ease of use, extensive function library, and worksheet-like user interface distinguish it among other commercial packages. Its features are also well suited to educational process. The use of natural mathematical notation and built-in measurement units are its two major advantages in teaching and learning. In this paper, its complementary use in the upper secondary physics education in Greece is explored. In order to demonstrate its application in the teaching process, a set of representative examples are presented. The main features and advantages of the software are also pointed out. The paper aims to present the benefits of the application of mathematical information technology tools in secondary physics education. In this effort, MathCad ® is probably the most promising solution

A Semi-Stochastic Propagation Model for the Study of Beam Tilting in Cellular Systems

Base station antenna downtilt mitigates interference and improves the downlink performance of wireless systems. A semi-stochastic propagation model is presented and applied to the study of the impact of the base station beam tilting in cellular communications. The two-ray approximation of the proposed model is described analytically. Beam tilting is evaluated in relation to the base station antenna radiation pattern, the antennas height, the propagation environment, the bit error rate, and the signal-to-noise ratio at the receiver front end. Analytically derived expressions for the fading envelopes, the error probability, the optimum tilting angle, and the downlink capacity of a WCDMA system are derived. Theoretical analysis and simulation results are provided to show the characteristics of the model. Comparisons with data in the literature confirm its validity. Furthermore, the effect of beam tilting on system downlink performance in terms of bit error rate and capacity is investigated

A Geometrical-Based Model for Cochannel Interference Analysis and Capacity Estimation of CDMA Cellular Systems

A common assumption in cellular communications is the circular-cell approximation. In this paper, an alternative analysis based on the hexagonal shape of the cells is presented. A geometrical-based stochastic model is proposed to describe the angle of arrival of the interfering signals in the reverse link of a cellular system. Explicit closed form expressions are derived, and simulations performed exhibit the characteristics and validate the accuracy of the proposed model. Applications in the capacity estimation of WCDMA cellular networks are presented. Dependence of system capacity of the sectorization of the cells and the base station antenna radiation pattern is explored. Comparisons with data in literature validate the accuracy of the proposed model. The degree of error of the hexagonal and the circular-cell approaches has been investigated indicating the validity of the proposed model. Results have also shown that, in many cases, the two approaches give similar results when the radius of the circle equals to the hexagon inradius. A brief discussion on how the proposed technique may be applied to broadband access networks is finally made

Characterization of Fading Statistics of mmWave (28 GHz and 38 GHz) Outdoor and Indoor Radio Propagation Channels

Extension of usable frequency spectrum from microwave to millimeter-wave (mmWave) is one of the key research directions in addressing the capacity demands of emerging 5th-generation communication networks. This paper presents a thorough analysis on the azimuthal multipath shape factors and second-order fading statistics (SOFS) of outdoor and indoor mmWave radio propagation channels. The well-established analytical relationship of plain angular statistics of a radio propagation channel with the channel’s fading statistics is used to study the channel’s fading characteristics. The plain angle-of-arrival measurement results available in the open literature for four different outdoor radio propagation scenarios at 38 GHz, as well as nine different indoor radio propagation scenarios at 28 GHz and 38 GHz bands, are extracted by using different graphical data interpretation techniques. The considered quantifiers for energy dispersion in angular domain and SOFS are true standard-deviation, angular spread, angular constriction, and direction of maximum fading; and spatial coherence distance, spatial auto-covariance, average fade duration, and level-crossing-rate; respectively. This study focuses on the angular spread analysis only in the azimuth plane. The conducted analysis on angular spread and SOFS is of high significance in designing modulation schemes, equalization schemes, antenna-beams, channel estimation, error-correction techniques, and interleaving algorithms; for mmWave outdoor and indoor radio propagation environments