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Array Gain
In array antenna systems, array gain is the measure of the improvement in signal-to-noise ratio (SNR) achieved by the array. It is calculated as the SNR of the array output signal divided by the SNR of the array input signal. Intuitively, the array gain is realized by the fact that the signal is coherently added from ''N'' array elements, while the noise is incoherently added from those same elements. If the noise is presumed to be uncorrelated the array gain is ≤ ''N'', the number of array elements, and the array gain reduces to the inverse of the square of the 2-norm of the array weight vector, under the assumption that the weight vector is normalized such that its sum is unity, so that :A = For a uniformly weighted array (un-tapered such that all elements contribute equally), the array gain is equal to ''N''. Array gain is not the same thing as "gain," "power gain," "directive gain," or "directivity," but if the noise environment around the array is isotropic and the ...
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Array Antenna
An antenna array (or array antenna) is a set of multiple connected antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas (called ''elements'') are usually connected to a single receiver or transmitter by feedlines that feed the power to the elements in a specific phase relationship. The radio waves radiated by each individual antenna combine and superpose, adding together ( interfering constructively) to enhance the power radiated in desired directions, and cancelling ( interfering destructively) to reduce the power radiated in other directions. Similarly, when used for receiving, the separate radio frequency currents from the individual antennas combine in the receiver with the correct phase relationship to enhance signals received from the desired directions and cancel signals from undesired directions. More sophisticated array antennas may have multiple transmitter or receiver modules, each connected to a separate an ...
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Signal-to-noise Ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. SNR, bandwidth, and channel capacity of a communication channel are connected by the Shannon–Hartley theorem. Definition Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful input) to the power of background noise (meaningless or unwanted input): : \mathrm = \frac, where is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system bandwidth. Depending on whether the signal is a constant () or a random variable (), the signal-to-noise ratio for random noise becomes: : \mathrm = \frac where E refers to the expected value, i.e. in this ...
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Coherence (physics)
In physics, two wave sources are coherent if their frequency and waveform are identical. Coherence is an ideal property of waves that enables stationary (i.e., temporally or spatially constant) interference. It contains several distinct concepts, which are limiting cases that never quite occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics. More generally, coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets. Interference is the addition, in the mathematical sense, of wave functions. A single wave can interfere with itself, but this is still an addition of two waves (see Young's slits experiment). Constructive or destructive interference are limit cases, and two waves always interfere, even if the result of the addition is complicated or not remarkable. When interfering, two waves can add together to create a wave ...
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2-norm
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance of a vector from the origin is a norm, called the Euclidean norm, or 2-norm, which may also be defined as the square root of the inner product of a vector with itself. A seminorm satisfies the first two properties of a norm, but may be zero for vectors other than the origin. A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a ''seminormed vector space''. The term pseudonorm has been used for several related meanings. It may be a synonym of "seminorm". A pseudonorm may satisfy the same axioms as a norm, with the equality replaced by an inequality "\,\leq\," in the homogeneity axiom. It can also r ...
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Radio Astronomy
Radio astronomy is a subfield of astronomy that studies celestial objects at radio frequencies. The first detection of radio waves from an astronomical object was in 1933, when Karl Jansky at Bell Telephone Laboratories reported radiation coming from the Milky Way. Subsequent observations have identified a number of different sources of radio emission. These include stars and galaxies, as well as entirely new classes of objects, such as radio galaxies, quasars, pulsars, and masers. The discovery of the cosmic microwave background radiation, regarded as evidence for the Big Bang theory, was made through radio astronomy. Radio astronomy is conducted using large radio antennas referred to as radio telescopes, that are either used singularly, or with multiple linked telescopes utilizing the techniques of radio interferometry and aperture synthesis. The use of interferometry allows radio astronomy to achieve high angular resolution, as the resolving power of an interferometer ...
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Decibel
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 (approximately ) or root-power ratio of 10 (approximately ). The unit expresses a relative change or an absolute value. In the latter case, the numeric value expresses the ratio of a value to a fixed reference value; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1 volt, a common suffix is " V" (e.g., "20 dBV"). Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the logarithm in base 10. That is, a change in ''power'' by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in ''am ...
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Diversity Gain
Diversity gain is the increase in signal-to-interference ratio due to some diversity scheme, or how much the transmission power can be reduced when a diversity scheme is introduced, without a performance loss. Diversity gain is usually expressed in decibels, and sometimes as a power ratio. An example is soft handoff gain. For selection combining N signals are received, and the strongest signal is selected. When the N signals are independent and Rayleigh distributed, the expected diversity gain has been shown to be \sum_^\frac, expressed as a power ratio.D.G. Brennan, "Linear diversity combining techniques," Proc. IRE, vol.47, no.1, pp.1075–1102, June 1959 See also * Array gain * Diversity combining Diversity combining is the technique applied to combine the multiple received signals of a diversity reception device into a single improved signal. Various techniques Various diversity combining techniques can be distinguished: * Equal-gain com ... References Radio resourc ...
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