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Six-rays Model
The six-rays model is applied in an urban or indoor environment where a radio signal transmitted will encounter some objects that produce reflected, refracted or scattered copies of the transmitted signal. These are called multipath signal components, they are attenuated, delayed and shifted from the original signal (LOS) due to a finite number of reflectors with known location and dielectric properties, LOS and multipath signal are summed at the receiver. This model approach the propagation of electromagnetic waves by representing wavefront as simple particles. Thus reflection, refraction and scattering effects are approximated using simple geometric equation instead Maxwell's wave equations. The simplest model is two-rays which predicts signal variation resulting from a ground reflection interfering with the loss path. This model is applicable in isolated areas with some reflectors, such as rural roads or hallway. The above two-rays approach can easily be extended to add as m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypotenuse
In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. For example, if one of the other sides has a length of 3 (when squared, 9) and the other has a length of 4 (when squared, 16), then their squares add up to 25. The length of the hypotenuse is the square root of 25, that is, 5. Etymology The word ''hypotenuse'' is derived from Greek (sc. or ), meaning " idesubtending the right angle" (Apollodorus), ''hupoteinousa'' being the feminine present active participle of the verb ''hupo-teinō'' "to stretch below, to subtend", from ''teinō'' "to stretch, extend". The nominalised participle, , was used for the hypotenuse of a triangle in the 4th century BCE (attested in Plato, ''Timaeus'' 54d). The Greek term was loaned into La ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ray Tracing (physics)
In physics, ray tracing is a method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces. Under these circumstances, wavefronts may bend, change direction, or reflect off surfaces, complicating analysis. Ray tracing solves the problem by repeatedly advancing idealized narrow beams called ''rays'' through the medium by discrete amounts. Simple problems can be analyzed by propagating a few rays using simple mathematics. More detailed analysis can be performed by using a computer to propagate many rays. When applied to problems of electromagnetic radiation, ray tracing often relies on approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray theory does not describe phenomena such as interference and diffraction, which require wave theory (invo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ten-rays Model
The ten-rays model is a mathematical model applied to the transmissions of radio signal in an urban area, to generate a model of ten rays typically four rays more are added to the six rays model, these are (R3 and R4 bouncing on both sides of the wall); This incorporate paths from one to three reflections: specifically, there is the LOS (Line-of-sight propagation, Line of sight), GR (ground reflected), SW (single-wall reflected), DW (double-wall reflected), TW (triple-wall reflected), WG (wall-ground reflected) and GW (ground-wall reflected paths). Where each one of the paths bounces on both sides of the wall. Experimentally, it has been demonstrated that the ten ray model simulates or can represent the Radio propagation, propagation of signals through a dielectric canyon, in it which the rays that travel from a transmitter point to a receiver point bounce many times. As example for this model it is assume: a rectilinear free space with two walls, one upper and the other lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression (including variables such as , and ). When the coefficients are themselves variables, they may also be called parameters. For example, the polynomial 2x^2-x+3 has coefficients 2, −1, and 3, and the powers of the variable x in the polynomial ax^2+bx+c have coefficient parameters a, b, and c. The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the number 3 and the parameter ''c'', respectively. The coefficient attached to the highest degree of the variable in a polynomial is referred to as the leading coefficient. For example, in the expressions above, the leading coefficients are 2 and ''a'', respectively. Terminology and definition In mathematics, a coefficient is a multiplicative factor in some term of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perpendicular
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can be defined between two lines (or two line segments), between a line and a plane, and between two planes. Perpendicularity is one particular instance of the more general mathematical concept of '' orthogonality''; perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced mathematics, the word "perpendicular" is sometimes used to describe much more complicated geometric orthogonality conditions, such as that between a surface and its '' normal vector''. Definitions A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Analysis
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largely to the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In the 1980s fundamental contributions by Karen Uhlenbeck,Jackson, Allyn. (2019)Founder of geometric anal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-ray Ground-reflection Model
The two-rays ground-reflection model is a multipath radio propagation model which predicts the path losses between a transmitting antenna and a receiving antenna when they are in line of sight (LOS). Generally, the two antenna each have different height. The received signal having two components, the LOS component and the reflection component formed predominantly by a single ground reflected wave. Mathematical derivation From the figure the received line of sight component may be written as :r_(t)=Re \left\ and the ground reflected component may be written as :r_(t)=Re\left\ where s(t) is the transmitted signal, l is the length of the direct line-of-sight (LOS) ray, x + x' is the length of the ground-reflected ray, G_ is the combined antenna gain along the LOS path, G_ is the combined antenna gain along the ground-reflected path, \lambda is the wavelength of the transmission (\lambda = \frac, where c is the speed of light and f is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transmitter
In electronics and telecommunications, a radio transmitter or just transmitter is an electronic device which produces radio waves with an antenna (radio), antenna. The transmitter itself generates a radio frequency alternating current, which is applied to the Antenna (radio), antenna. When excited by this alternating current, the antenna radiates radio waves. Transmitters are necessary component parts of all electronic devices that communicate by radio communication, radio, such as radio broadcasting, radio and television broadcasting stations, cell phones, walkie-talkies, Wireless LAN, wireless computer networks, Bluetooth enabled devices, garage door openers, two-way radios in aircraft, ships, spacecraft, radar sets and navigational beacons. The term ''transmitter'' is usually limited to equipment that generates radio waves for Communication engineering, communication purposes; or radiolocation, such as radar and navigational transmitters. Generators of radio waves for heatin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Triangle
A right triangle (American English) or right-angled triangle (British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry. The side opposite to the right angle is called the ''hypotenuse'' (side ''c'' in the figure). The sides adjacent to the right angle are called ''legs'' (or ''catheti'', singular: ''cathetus''). Side ''a'' may be identified as the side ''adjacent to angle B'' and ''opposed to'' (or ''opposite'') ''angle A'', while side ''b'' is the side ''adjacent to angle A'' and ''opposed to angle B''. If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a ''Pythagor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radio Wave
Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (shorter than a grain of rice); at 30 Hz the corresponding wavelength is (longer than the radius of the Earth). Like all electromagnetic waves, radio waves in a vacuum travel at the speed of light, and in the Earth's atmosphere at a close, but slightly lower speed. Radio waves are generated by charged particles undergoing acceleration, such as time-varying electric currents. Naturally occurring radio waves are emitted by lightning and astronomical objects, and are part of the blackbody radiation emitted by all warm objects. Radio waves are generated artificially by an electronic device called a transmitter, which is connected to an antenna which radiates the waves. They are received by another antenna connected to a radio receiver, which p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
