Advantages And Disadvantages Of Smart Antenna

Advantages And Disadvantages Of Smart Antenna The Direction of Arrival (DOA) estimation algorithm which may take various forms generally follows from the homogeneous solution of the wave equation. The models of interest in this dissertation may equally apply to an EM wave as well as to an acoustic wave. Assuming that the propagation model is fundamentally the same, we will, for analytical expediency, show that it can follow from the solution of Maxwells equations, which clearly are only valid for EM waves. In empty space the equation can be written as: =0 (3.1) =0 (3.2) (3.3) (3.4) where . and ÃÆ'-, respectively, denote the divergence and curl. Furthermore, B is the magnetic induction. E denotes the electric field, whereas and are the magnetic and dielectric constants respectively. Invoking 3.1 the following curl property results as: (3.5) (3.6) (3.7) The constant c is generally referred to as the speed of propagation. For EM waves in free space, it follows from the derivation c = 1 / = 3 x m / s. The homogeneous wave equation (3.7) constitutes the physical motivation for our assumed data model, regardless of the type of wave or medium. In some applications, the underlying physics are irrelevant, and it is merely the mathematical structure of the data model that counts. 3.2 Plane wave In the physics of wave propagation, a plane wave is a constant-frequency wave whose wave fronts are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector[]. Actually, it is impossible to have a rare plane wave in practice, and only a plane wave of infinite extent can propagate as a plane wave. Actually, many waves are approximately regarded as plane waves in a localized region of space, e.g., a localized source such as an antenna produces a field which is approximately a plane wave far enough from the antenna in its far-field region. Likely, we can treat the waves as light rays which correspond locally to plane waves, when the length scales are much longer than the waves wavelength, as is often appearing of light in the field of optics. 3.2.1 Mathematical definition Two functions which meet the criteria of having a constant frequency and constant amplitude are defined as the sine or cosine functions. One of the simplest ways to use such a sinusoid involves defining it along the direction of the x axis. As the equation shown below, it uses the cosine function to express a plane wave travelling in the positive x direction. (3.8) Where A(x,t) is the magnitude of the shown wave at a given point in space and time. is the amplitude of the wave which is the peak magnitude of the oscillation. k is the waves wave number or more specifically the angular wave number and equals 2à Ã¢â€š ¬/ÃŽÂ », where ÃŽÂ » is the wavelength of the wave. k has the units of radians per unit distance and is a standard of how rapidly the disturbance changes over a given distance at a particular point in time. x is a point along the x axis. y and z are not considered in the equation because the waves magnitude and phase are the same at every point on any given y-z plane. This equation defines what that magnitude and phase are. is the waves angular frequency which equals 2à Ã¢â€š ¬/T, and T is the period of the wave. In detail, omega, has the units of radians per unit time and is also a standard of how rapid the disturbance changing in a given length of time at a particular point in space. is a given particular point in time, and varphi , is the wave phase shift with the units of radians. It must make clear that a positive phase shift will shifts the wave along the negative x axis direction at a given point of time. A phase shift of 2à Ã¢â€š ¬ radians means shifting it one wavelength exactly. Other formulations which directly use the waves wavelength, period T, frequency f and velocity c, are shown as follows: A=A_o cos[2pi(x/lambda- t/T) + varphi], (3.9) A=A_o cos[2pi(x/lambda- ft) + varphi], (3.10) A=A_o cos[(2pi/lambda)(x- ct) + varphi], (3.11) To appreciate the equivalence of the above set of equations denote that f=1/T,! and c=lambda/T=omega/k,! 3.2.2 Application Plane waves are solutions for a scalar wave equation in the homogeneous medium. As for vector wave equations, e.g., waves in an elastic solid or the ones describing electromagnetic radiation, the solution for the homogeneous medium is similar. In vector wave equations, the scalar amplitude is replaced by a constant vector. e.g., in electromagnetism is the vector of the electric field, magnetic field, or vector potential. The transverse wave is a kind of wave in which the amplitude vector is perpendicular to k, which is the case for electromagnetic waves in an isotropic space. On the contrast, the longitudinal wave is a kind of wave in which the amplitude vector is parallel to k, typically, such as for acoustic waves in a gas or fluid. The plane wave equation is true for arbitrary combinations of à Ã¢â‚¬ ° and k. However, all real physical mediums will only allow such waves to propagate for these combinations of à Ã¢â‚¬ ° and k that satisfy the dispersion relation of the mediums. The dispersion relation is often demonstrated as a function, à Ã¢â‚¬ °(k), where ratio à Ã¢â‚¬ °/|k| gives the magnitude of the phase velocity and dà Ã¢â‚¬ °/dk denotes the group velocity. As for electromagnetism in an isotropic case with index of refraction coefficient n, the phase velocity is c/n, which equals the group velocity on condition that the index is frequency independent. In linear uniform case, a wave equation solution can be demonstrated as a superposition of plane waves. This method is known as the Angular Spectrum method. Actually, the solution form of the plane wave is the general consequence of translational symmetry. And in the more general case, for periodic structures with discrete translational symmetry, the solution takes the form of Bloch waves, which is most famous in crystalline atomic materials, in the photonic crystals and other periodic wave equations. 3.3 Propagation Many physical phenomena are either a result of waves propagating through a medium or exhibit a wave like physical manifestation. Though 3.7 is a vector equation, we only consider one of its components, say E(r,t) where r is the radius vector. It will later be assumed that the measured sensor outputs are proportional to E(r,t). Interestingly enough, any field of the form E(r,t) = , which satisfies 3.7, provided with T denoting transposition. Through its dependence on only, the solution can be interpreted as a wave traveling in the direction, with the speed of propagation. For the latter reason, ÃŽÂ ± is referred to as the slowness vector. The chief interest herein is in narrowband forcing functions. The details of generating such a forcing function can be found in the classic book by Jordan [59]. In complex notation [63] and taking the origin as a reference, a narrowband transmitted waveform can be expressed as: (3.12) where s(t) is slowly time varying compared to the carrier . For, where B is the bandwidth of s(t), we can write: (3.13) In the last equation 3.13, the so-called wave vector was introduced, and its magnitude is the wavenumber. One can also write, where is the wavelength. Make sure that k also points in the direction of propagation, e.g., in the x-y plane we can get: (3.14) where is the direction of propagation, defined counter clockwise relative the x axis. It should be noted that 3.12 implicitly assumed far-field conditions, since an isotropic, which refers to uniform propagation/transmission in all directions, point source gives rise to a spherical traveling wave whose amplitude is inversely proportional to the distance to the source. All points lying on the surface of a sphere of radius R will then share a common phase and are referred to as a wave front. This indicates that the distance between the emitters and the receiving antenna array determines whether the spherical degree of the wave should be taken into account. The reader is referred to e.g., [10, 24] for treatments of near field reception. Far field receiving conditions imply that the radius of propagation is so large that a flat plane of constant phase can be considered, thus resulting in a plane wave as indicated in Eq. 8. Though not necessary, the latter will be our assumed working mode l for convenience of exposition. Note that a linear medium implies the validity of the superposition principle, and thus allows for more than one traveling wave. Equation 8 carries both spatial and temporal information and represents an adequate model for distinguishing signals with distinct spatial-temporal parameters. These may come in various forms, such as DOA, in general azimuth and elevation, signal polarization, transmitted waveforms, temporal frequency etc. Each emitter is generally associated with a set of such characteristics. The interest in unfolding the signal parameters forms the essence of sensor array signal processing as presented herein, and continues to be an important and active topic of research. 3.4 Smart antenna Smart antennas are devices which adapt their radiation pattern to achieve improved performance either range or capacity or some combination of these [1]. The rapid growth in demand for mobile communications services has encouraged research into the design of wireless systems to improve spectrum efficiency, and increase link quality [7]. Using existing methods more effective, the smart antenna technology has the potential to significantly increase the wireless. With intelligent control of signal transmission and reception, capacity and coverage of the mobile wireless network, communications applications can be significantly improved [2]. In the communication system, the ability to distinguish different users is essential. The smart antenna can be used to add increased spatial diversity, which is referred to as Space Division Multiple Access (SDMA). Conventionally, employment of the most common multiple access scheme is a frequency division multiple access (FDMA), Time Division Multiple Access (TDMA), and Code Division Multiple Access (CDMA). These independent users of the program, frequency, time and code domain were given three different levels of diversity. Potential benefits of the smart antenna show in many ways, such as anti-multipath fading, reducing the delay extended to support smart antenna holding high data rate, interference suppression, reducing the distance effect, reducing the outage probability, to improve the BER (Bit Error Rate)performance, increasing system capacity, to improve spectral efficiency, supporting flexible and efficient handoff to expand cell coverage, flexible management of the district, to extend the battery life of mobile station, as well as lower maintenance and operating costs. 3.4.1 Types of Smart Antennas The environment and the systems requirements decide the type of Smart Antennas. There are two main types of Smart Antennas. They are as follows: Phased Array Antenna In this type of smart antenna, there will be a number of fixed beams between which the beam will be turned on or steered to the target signal. This can be done, only in the first stage of adjustment to help. In other words, as wanted by the moving target, the beam will be the Steering [2]. Adaptive Array Antenna Integrated with adaptive digital signal processing technology, the smart antenna uses digital signal processing algorithm to measure the signal strength of the beam, so that the antenna can dynamically change the beam which transmit power concentrated, as figure 3.2 shows. The application of spatial processing can enhance the signal capacity, so that multiple users share a channel. Adaptive antenna array is a closed-loop feedback control system consisting of an antenna array and real-time adaptive signal receiver processor, which uses the feedback control method for automatic alignment of the antenna array pattern. It formed nulling interference signal offset in the direction of the interference, and can strengthen a useful signal, so as to achieve the purpose of anti-jamming [3]. Figure 2 click for text version Figure 3.2 3.4.2 Advantages and disadvantages of smart antenna Advantages First of all, a high level of efficiency and power are provided by the smart antenna for the target signal. Smart antennas generate narrow pencil beams, when a big number of antenna elements are used in a high frequency condition. Thus, in the direction of the target signal, the efficiency is significantly high. With the help of adaptive array antennas, the same amount times the power gain will be produce, on condition that a fixed number of antenna elements are used. Another improvement is in the amount of interference which is suppressed. Phased array antennas suppress the interference with the narrow beam and adaptive array antennas suppress by adjusting the beam pattern [2]. Disadvantages The main disadvantage is the cost. Actually, the cost of such devices will be more than before, not only in the electronics section, but in the energy. That is to say the device is too expensive, and will also decrease the life of other devices. The receiver chains which are used must be decreased in order to reduce the cost. Also, because of the use of the RF electronics and A/D converter for each antenna, the costs are increasing. Moreover, the size of the antenna is another problem. Large base stations are needed to make this method to be efficient and it will increase the size, apart from this multiple external antennas needed on each terminal. Then, when the diversity is concerned, disadvantages are occurred. When mitigation is needed, diversity becomes a serious problem. The terminals and base stations must equip with multiple antennas. 3.5 White noise White noise is a random signal with a flat power spectral density []. In another word, the signal contains the equal power within a particular bandwidth at the centre frequency. White noise draws its name from white light where the power spectral density of the light is distributed in the visible band. In this way, the eyes three colour receptors are approximately equally stimulated []. In statistical case, a time series can be characterized as having weak white noise on condition that {} is a sequence of serially uncorrelated random vibrations with zero mean and finite variance. Especially, strong white noise has the quality to be independent and identically distributed, which means no autocorrelation. In particular, the series is called the Gaussian white noise [1], if is normally distributed and it has zero mean and standard deviation. Actually, an infinite bandwidth white noise signal is just a theoretical construction which cannot be reached. In practice, the bandwidth of white noise is restricted by the transmission medium, the mechanism of noise generation, and finite observation capabilities. If a random signal is observed with a flat spectrum in a mediums widest possible bandwidth, we will refer it as white noise. 3.5.1 Mathematical definition White random vector A random vector W is a white random vector only if its mean vector and autocorrelation matrix are corresponding to the follows: mu_w = mathbb{E}{ mathbf{w} } = 0 (3.15) R_{ww} = mathbb{E}{ mathbf{w} mathbf{w}^T} = sigma^2 mathbf{I} . (3.16) That is to say, it is a zero mean random vector, and its autocorrelation matrix is a multiple of the identity matrix. When the autocorrelation matrix is a multiple of the identity, we can regard it as spherical correlation. White random process A time continuous random process where is a white noise signal only if its mean function and autocorrelation function satisfy the following equation: mu_w(t) = mathbb{E}{ w(t)} = 0 (3.17) R_{ww}(t_1, t_2) = mathbb{E}{ w(t_1) w(t_2)} = (N_{0}/2)delta(t_1 t_2). (3.18) That is to say, it is zero mean for all time and has infinite power at zero time shift since its autocorrelation function is the Dirac delta function. The above autocorrelation function implies the following power spectral density. Since the Fourier transform of the delta function is equal to 1, we can imply: S_{ww}(omega) = N_{0}/2 ,! (3.19) Since this power spectral density is the same at all frequencies, we define it white as an analogy to the frequency spectrum of white light. A generalization to random elements on infinite dimensional spaces, e.g. random fields, is the white noise measure. 3.5.2 Statistical properties The white noise is uncorrelated in time and does not restrict the values a signal can take. Any distribution of values about the white noise is possible. Even a so-called binary signal that can only take the values of 1 or -1 will be white on condition that the sequence is statistically uncorrelated. Any noise with a continuous distribution, like a normal distribution, can be white noise certainly. It is often incorrectly assumed that Gaussian noise is necessarily white noise, yet neither property implies the other. Gaussianity refers to the probability distribution with respect to the value, in this context the probability of the signal reaching amplitude, while the term white refers to the way the signal power is distributed over time or among frequencies. Spectrogram of pink noise (left) and white noise (right), showed with linear frequency axis (vertical). We can therefore find Gaussian white noise, but also Poisson, Cauchy, etc. white noises. Thus, the two words Gaussian and white are often both specified in mathematical models of systems. Gaussian white noise is a good approximation of many real-world situations and generates mathematically tractable models. These models are used so frequently that the term additive white Gaussian noise has a standard abbreviation: AWGN. White noise is the generalized mean-square derivative of the Wiener process or Brownian motion. 3.6 Normal Distribution In probability theory, the normal (or Gaussian) distribution is a continuous probability distribution that has a bell-shaped probability density function, known as the Gaussian function or informally as the bell curve[1]. f(x;mu,sigma^2) = frac{1}{sigmasqrt{2pi}} e^{ -frac{1}{2}left(frac{x-mu}{sigma}right)^2 } The parameter ÃŽÂ ¼ is the mean or expectation (location of the peak) and à Ã†â€™Ãƒ ¢Ã¢â€š ¬Ã¢â‚¬ °2 is the variance. à Ã†â€™ is known as the standard deviation. The distribution with ÃŽÂ ¼ = 0 and à Ã†â€™Ãƒ ¢Ã¢â€š ¬Ã¢â‚¬ °2 = 1 is called the standard normal distribution or the unit normal distribution. A normal distribution is often used as a first approximation to describe real-valued random variables that cluster around a single mean value. http://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Standard_deviation_diagram.svg/325px-Standard_deviation_diagram.svg.png The normal distribution is considered the most prominent probability distribution in statistics. There are several reasons for this:[1] First, the normal distribution arises from the central limit theorem, which states that under mild conditions, the mean of a large number of random variables drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution. This gives it exceptionally wide application in, for example, sampling. Secondly, the normal distribution is very tractable analytically, that is, a large number of results involving this distribution can be derived in explicit form. For these reasons, the normal distribution is commonly encountered in practice, and is used throughout statistics, natural sciences, and social sciences [2] as a simple model for complex phenomena. For example, the observational error in an experiment is usually assumed to follow a normal distribution, and the propagation of uncertainty is computed using this assumption. Note that a normally distributed variable has a symmetric distribution about its mean. Quantities that grow exponentially, such as prices, incomes or populations, are often skewed to the right, and hence may be better described by other distributions, such as the log-normal distribution or Pareto distribution. In addition, the probability of seeing a normally distributed value that is far (i.e. more than a few standard deviations) from the mean drops off extremely rapidly. As a result, statistical inference using a normal distribution is not robust to the presence of outliers (data that are unexpectedly far from the mean, due to exceptional circumstances, observational error, etc.). When outliers are expected, data may be better described using a heavy-tailed distribution such as the Students t-distribution. 3.6.1 Mathematical Definition The simplest case of a normal distribution is known as the standard normal distribution, described by the probability density function phi(x) = frac{1}{sqrt{2pi}}, e^{- frac{scriptscriptstyle 1}{scriptscriptstyle 2} x^2}. The factor scriptstyle 1/sqrt{2pi} in this expression ensures that the total area under the curve à Ã¢â‚¬ ¢(x) is equal to one[proof], and 12 in the exponent makes the width of the curve (measured as half the distance between the inflection points) also equal to one. It is traditional in statistics to denote this function with the Greek letter à Ã¢â‚¬ ¢ (phi), whereas density functions for all other distributions are usually denoted with letters f or p.[5] The alternative glyph à Ã¢â‚¬   is also used quite often, however within this article à Ã¢â‚¬   is reserved to denote characteristic functions. Every normal distribution is the result of exponentiating a quadratic function (just as an exponential distribution results from exponentiating a linear function): f(x) = e^{a x^2 + b x + c}. , This yields the classic bell curve shape, provided that a 0 everywhere. One can adjust a to control the width of the bell, then adjust b to move the central peak of the bell along the x-axis, and finally one must choose c such that scriptstyleint_{-infty}^infty f(x),dx = 1 (which is only possible when a Rather than using a, b, and c, it is far more common to describe a normal distribution by its mean ÃŽÂ ¼ = à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã¢â€š ¬Ã¢â‚¬ °b2a and variance à Ã†â€™2 = à ¢Ã‹â€ Ã¢â‚¬â„¢Ãƒ ¢Ã¢â€š ¬Ã¢â‚¬ °12a. Changing to these new parameters allows one to rewrite the probability density function in a convenient standard form, f(x) = frac{1}{sqrt{2pisigma^2}}, e^{frac{-(x-mu)^2}{2sigma^2}} = frac{1}{sigma}, phi!left(frac{x-mu}{sigma}right). For a standard normal distribution, ÃŽÂ ¼ = 0 and à Ã†â€™2 = 1. The last part of the equation above shows that any other normal distribution can be regarded as a version of the standard normal distribution that has been stretched horizontally by a factor à Ã†â€™ and then translated rightward by a distance ÃŽÂ ¼. Thus, ÃŽÂ ¼ specifies the position of the bell curves central peak, and à Ã†â€™ specifies the width of the bell curve. The parameter ÃŽÂ ¼ is at the same time the mean, the median and the mode of the normal distribution. The parameter à Ã†â€™2 is called the variance; as for any random variable, it describes how concentrated the distribution is around its mean. The square root of à Ã†â€™2 is called the standard deviation and is the width of the density function. The normal distribution is usually denoted by N(ÃŽÂ ¼,à ¢Ã¢â€š ¬Ã¢â‚¬ °Ãƒ Ã†â€™2).[6] Thus when a random variable X is distributed normally with mean ÃŽÂ ¼ and variance à Ã†â€™2, we write X sim mathcal{N}(mu,,sigma^2). , 3.6.2 Alternative formulations Some authors advocate using the precision instead of the variance. The precision is normally defined as the reciprocal of the variance (à Ã¢â‚¬Å¾ = à Ã†â€™Ãƒ ¢Ã‹â€ Ã¢â‚¬â„¢2), although it is occasionally defined as the reciprocal of the standard deviation (à Ã¢â‚¬Å¾ = à Ã†â€™Ãƒ ¢Ã‹â€ Ã¢â‚¬â„¢1).[7] This parameterization has an advantage in numerical applications where à Ã†â€™2 is very close to zero and is more convenient to work with in analysis as à Ã¢â‚¬Å¾ is a natural parameter of the normal distribution. This parameterization is common in Bayesian statistics, as it simplifies the Bayesian analysis of the normal distribution. Another advantage of using this parameterization is in the study of conditional distributions in the multivariate normal case. The form of the normal distribution with the more common definition à Ã¢â‚¬Å¾ = à Ã†â€™Ãƒ ¢Ã‹â€ Ã¢â‚¬â„¢2 is as follows: f(x;,mu,tau) = sqrt{frac{tau}{2pi}}, e^{frac{-tau(x-mu)^2}{2}}. The question of which normal distribution should be called the standard one is also answered differently by various authors. Starting from the works of Gauss the standard normal was considered to be the one with variance à Ã†â€™2 = 12 : f(x) = frac{1}{sqrtpi},e^{-x^2} Stigler (1982) goes even further and insists the standard normal to be with the variance à Ã†â€™2 = 12à Ã¢â€š ¬ : f(x) = e^{-pi x^2} According to the author, this formulation is advantageous because of a much simpler and easier-to-remember formula, the fact that the pdf has unit height at zero, and simple approximate formulas for the quintiles of the distribution. 3.7 Cramer-Rao Bound In estimation theory and statistics, the Cramà ©r-Rao bound (CRB) or Cramà ©r-Rao lower bound (CRLB), named in honor of Harald Cramer and Calyampudi Radhakrishna Rao who were among the first to derive it,[1][2][3] expresses a lower bound on the variance of estimators of a deterministic parameter. The bound is also known as the Cramà ©r-Rao inequality or the information inequality. In its simplest form, the bound states that the variance of any unbiased estimator is at least as high as the inverse of the Fisher information. An unbiased estimator which achieves this lower bound is said to be (fully) efficient. Such a solution achieves the lowest possible mean squared error among all unbiased methods, and is therefore the minimum variance unbiased (MVU) estimator. However, in some cases, no unbiased technique exists which achieves the bound. This may occur even when an MVU estimator exists. The Cramà ©r-Rao bound can also be used to bound the variance of biased estimators of given bias. In some cases, a biased approach can result in both a variance and a mean squared error that are below the unbiased Cramà ©r-Rao lower bound; see estimator bias. statement The Cramà ©r-Rao bound is stated in this section for several increasingly general cases, beginning with the case in which the parameter is a scalar and its estimator is unbiased. All versions of the bound require certain regularity conditions, which hold for most well-behaved distributions. These conditions are listed later in this section. Scalar unbiased case Suppose theta is an unknown deterministic parameter which is to be estimated from measurements x, distributed according to some probability density function f(x;theta). The variance of any unbiased estimator hat{theta} of theta is then bounded by the reciprocal of the Fisher information I(theta): mathrm{var}(hat{theta}) geq frac{1}{I(theta)} where the Fisher information I(theta) is defined by I(theta) = mathrm{E} left[ left( frac{partial ell(x;theta)}{partialtheta} right)^2 right] = -mathrm{E}left[ frac{partial^2 ell(x;theta)}{partialtheta^2} right] and ell(x;theta)=log f(x;theta) is the natural logarithm of the likelihood function and mathrm{E} denotes the expected value. The efficiency of an unbiased estimator hat{theta} measures how close this estimators variance comes to this lower bound; estimator efficiency is defined as e(hat{theta}) = frac{I(theta)^{-1}}{{rm var}(hat{theta})} or the minimum possible variance for an unbiased estimator divided by its actual variance. The Cramà ©r-Rao lower bound thus gives e(hat{theta}) le 1. General scalar case A more general form of the bound can be obtained by considering an unbiased estimator T(X) of a function psi(theta) of the parameter theta. Here, unbiasedness is understood as stating that E{T(X)} = psi(theta). In this case, the bound is given by mathrm{var}(T) geq frac{[psi'(theta)]^2}{I(theta)} where psi'(theta) is the derivative of psi(theta) (by theta), and I(theta) is the Fisher information defined above. Bound on the variance of biased estimators Apart from being a bound on estimators of functions of the parameter, this approach can be used to derive a bound on the variance of biased estimators with a given bias, as follows. Consider an estimator hat{theta} with biasb(theta) = E{hat{theta}} theta, and let psi(theta) = b(theta) + theta. By the result above, any unbiased estimator whose expectation is psi(theta) has variance greater than or equal to (psi'(theta))^2/I(theta). Thus, any estimator hat{theta} whose bias is given by a function b(theta) satisfies mathrm{var} left(hat{theta}right) geq frac{[1+b'(theta)]^2}{I(theta)}. The unbiased version of the bound is a special case of this result, with b(theta)=0. Its trivial to have a small variance à ¢Ã‹â€ Ã¢â‚¬â„¢ an estimator that is constant has a variance of zero. But from the above equation we find that the mean squared errorof a biased estimator is bounded by mathrm{E}left((hat{theta}-theta)^2right)geqfrac{[1+b'(theta)]^2}{I(theta)}+b(theta)^2, using the standard decomposition of the MSE. Note, however, that this bound can be less than the unbiased Cramà ©r-Rao bound 1/I(ÃŽÂ ¸). See the example of estimating variance below. Multivariate case Extending the Cramà ©r-Rao bound to multiple parameters, define a parameter column vector boldsymbol{theta} = left[ theta_1, theta_2, dots, theta_d right]^T in mathbb{R}^d with probability density function f(x; boldsymbol{theta}) which satisfies the two regularity conditions below. The Fisher information matrix is a d times d matrix with element I_{m, k} defined as I_{m, k} = mathrm{E} left[ frac{d}{dtheta_m} log fleft(x; boldsymbol{theta}right) frac{d}{dtheta_k} log fleft(x; boldsymbol{theta}right) right]. Let boldsymbol{T}(X) be an estimator of any vector function of parameters, boldsymbol{T}(X) = (T_1(X), ldots, T_n(X))^T, and denote its expectation vector mathrm{E}[boldsymbol{T}(X)] by boldsymbol{psi}(boldsymbol{theta}). The Cramà ©r-Rao bound then states that the covariance matrix of boldsymbol{T}(X) satisfies mathrm{cov}_{boldsymbol{theta}}left(boldsymbol{T}(X)right) geq frac {partial boldsymbol{psi} left(boldsymbol{theta}right)} {partial boldsymbol{theta}} [Ileft(boldsymbol{theta}right)]^{-1} left( frac {partial boldsymbol{psi}left(boldsymbol{theta}right)} {partial boldsymbol{theta}} right)^T where The matrix inequality A ge B is understood to mean that the matrix A-B is positive semi definite, and partial boldsymbol{psi}(boldsymbol{theta})/partial boldsymbol{theta} is the Jacobian matrix whose ijth element is given by partial psi_i(boldsymbol{theta})/partial theta_j. If boldsymbol{T}(X) is an unbiased estimator of boldsymbol{theta} (i.e., boldsymbol{psi}left(boldsymbol{theta}rig

The Ghost Story of the Banshee Essay -- Urban Legends Ghost Stories

The Tale of the Banshee On a dark and stormy night it happened. Not too far in the recent past, two teenaged girls were out camping in the woods. There, they sat in their tent while exchanging frightening ghost stories by the flickering candle-light. What began as a normal, cool, summer’s night, took an eerie turn for the worse when, in the middle of one particularly terrifying tale, an ominous howl rang out too close for comfort and a thunderous crash was heard. As they scrambled to be near each other for warmth and security against the tingling feeling arising on the backs of their necks, and the fear of their impending doom, what jumped out at them was a horrifyingly great big... just kidding. This all started with two teenaged girls telling stories one night, but it was spring, not summer, in a dorm room, not at a camp site, and completely calm, not alarming in the least. For this assignment, I chose to ask a friend to tell me a story regarding ghosts, magic, or the supernatural, and what she came up with I considered to be very helpful for this project. I collected a version of the Tale of the Banshee from my roommate here at the University of Maryland, who is also a college freshman. This young woman is a 19-year-old from Montgomery, New Jersey, with a very diverse and complex background. Her father is from Pakistan, her mother is a European-American Christian, and she herself is Muslim. What she told me was told to her by older relatives when she was just a child, and accused of â€Å"screaming like a Banshee.† The curious little girl that she was, she asked what it meant; based on the explanation she received she never wanted to scream like that again. In her retelling she presented the story with a straigh... ...fter an attack, the yowl could have been considered a warning cry. All peoples across cultures and time need things to believe in and to trust. The people of ancient Ireland chose to believe in a deceased, friendly relative to warn them of tragedy. That is a much happier belief than the evil, menacing idea of Banshees that I had prior to this assignment, so I am happy for having learned more. Works Cited Ireland Now  ©1997-2005 http://www.ireland-now.com/banshee.html Irelandseye.com and contributors  © 1999-2004 http://www.irelandseye.com/animation/explorer/banshee.html Jelsoft Enterprises Ltd Copyright  ©2000 - 2005 http://www.boards.ie/vbulletin/showthread.php?t=229025 Morey, Eibhlin: Submitted on Thursday 17th of March 2005 http://www.constant-content.com/article/1788/The-Banshee/ Susan Sheppard http://magick.wirefire.com/newpage5.htm The Ghost Story of the Banshee Essay -- Urban Legends Ghost Stories The Tale of the Banshee On a dark and stormy night it happened. Not too far in the recent past, two teenaged girls were out camping in the woods. There, they sat in their tent while exchanging frightening ghost stories by the flickering candle-light. What began as a normal, cool, summer’s night, took an eerie turn for the worse when, in the middle of one particularly terrifying tale, an ominous howl rang out too close for comfort and a thunderous crash was heard. As they scrambled to be near each other for warmth and security against the tingling feeling arising on the backs of their necks, and the fear of their impending doom, what jumped out at them was a horrifyingly great big... just kidding. This all started with two teenaged girls telling stories one night, but it was spring, not summer, in a dorm room, not at a camp site, and completely calm, not alarming in the least. For this assignment, I chose to ask a friend to tell me a story regarding ghosts, magic, or the supernatural, and what she came up with I considered to be very helpful for this project. I collected a version of the Tale of the Banshee from my roommate here at the University of Maryland, who is also a college freshman. This young woman is a 19-year-old from Montgomery, New Jersey, with a very diverse and complex background. Her father is from Pakistan, her mother is a European-American Christian, and she herself is Muslim. What she told me was told to her by older relatives when she was just a child, and accused of â€Å"screaming like a Banshee.† The curious little girl that she was, she asked what it meant; based on the explanation she received she never wanted to scream like that again. In her retelling she presented the story with a straigh... ...fter an attack, the yowl could have been considered a warning cry. All peoples across cultures and time need things to believe in and to trust. The people of ancient Ireland chose to believe in a deceased, friendly relative to warn them of tragedy. That is a much happier belief than the evil, menacing idea of Banshees that I had prior to this assignment, so I am happy for having learned more. Works Cited Ireland Now  ©1997-2005 http://www.ireland-now.com/banshee.html Irelandseye.com and contributors  © 1999-2004 http://www.irelandseye.com/animation/explorer/banshee.html Jelsoft Enterprises Ltd Copyright  ©2000 - 2005 http://www.boards.ie/vbulletin/showthread.php?t=229025 Morey, Eibhlin: Submitted on Thursday 17th of March 2005 http://www.constant-content.com/article/1788/The-Banshee/ Susan Sheppard http://magick.wirefire.com/newpage5.htm

The Impact of Stereotypes on Teens at Point Loma High School Essay

The Impact of Stereotypes on Teens at PLHS 1.)Stereotypes and racism have always been an issue in this and many other societies.Teenagers are commonly the most impacted by stereotypes, not unlike most teens at Point Loma High School. To further analyze this, my class read â€Å"How a Self-Fulfilling Stereotype Can Drag Down Performance† by Shankar Vedantam, a science correspondent for NPR. In his informative article, Vedantam discusses how research proves that self-fulfilling stereotypes can drag down many individuals’ performance. He supports his claim by presenting statistics such as â€Å"When black people and white people answered 10 vocabulary questions posed by a white interviewer, blacks on average answered 5.49 questions correctly and whites answered 6.33 correctly†, and talking about how black students tend to score better on tests that are administered by other blacks, and finally explaining how all students’ performance increases when they are not reminded of their race/gender before beginning a test. Vedantam’s purpose is to inform the audience about the negatives of reminding students of their race before a test in an effort to prevent poor performance and boost test scores. Upon reading this, my class has decided to carry out a research project about the stereotypes at our school, and how they affect a variety of students. 2.) We began our study by interviewing a classmate, then interviewing another PLHS student for homework and recording our data. We then proceeded to fill out a Google form, which aided us in planting the anonymous data in a data table and combining it. Following that, we sorted and graphed the data by gender and ethnicity to see how different groups responded to each inquiry. Upon doing th... ...In my opinion, it’s as simple as attempting to avoid judging another individual at first glance or categorizing them into a certain stereotype or group. Removing the part of the test where the students have to bubble in their race would also serve as a beneficial gesture. I am certain that this society has done almost everything that is reasonable to prevent the growing stereotypes and racism, and the rest depends on the individuals. If one person stopped judging others based on stereotypes, then others would gradually begin to do so as well. It doesn’t sound like much, but overall, this can truly make a difference. Also, I believe that we should accept the fact that there is no such thing as immaculate perception, and work on improving ourselves, our perception of this world and how we view and analyze other human beings. Works Cited Shanka vedentam, Jerry Kong

Recent Addition Essay

Childhood should be a time when children are carefree and without any responsibilities or worries. This however, is not the case in all children, particularly children who are shy, anxious or socially withdrawn from their new surroundings, people and new social situations. This therefore does not allow them to feel comfortable enough to interact and or make new friends easily. With the recent addition to my class of one such learner I felt compelled to try and assist with this new learners feeling of being isolated and alone in a new environment. To ensure this new learner did not feel singled out or further disadvantaged, I used the African philosophy concept of â€Å"Caring Communities† as a form of welcoming and embracing this shy and anxious learner into our group. Through the love and caring shown to all members of our group or class community, no one member need ever feel alone, left out of an activity or interacting without at least one friend at a time. This means we are all embracing our other community members, treating them equally and treating them as we want to be treated. This creates social security or a safe sense of community for all and ensures our new learner is feeling less socially awkward, isolated and alone. This sense of community is one of the fundamental corner stone’s of African philosophy and one of the greatest differences with the western philosophy. It is a spoken tradition where great emphasises is placed â€Å"for the good of the community† rather than one individual person and is marked by communalism and communal interdependence in many spheres of community life. African philosophy is a natural response to the strife, dilemmas and obstacles faced by Africa, together with the elimination and repudiation of colonisation and domination by the Western world. African philosophy has captivated the Western world, who incorporated the various facets into their own New Age Movement. Included in African philosophy is the extensive and all-embracing principle of Ubuntu. Ubuntu is the part of African philosophy that contributes and provides us with insight into understanding our own lives in relation to the world around us. Ubuntu is the capacity to express compassion, dignity,  harmony and humanity in the best interest of our community above self-interest. The community is therefore the core or essence of Ubuntu. There exists a common bond or interconnectedness between all humans and through shared synergy and intercommunication we are able to recognise, identify and discover our own human qualities of humanness, trustworthiness, goodness, respect and kindness and then attest to them in others around us. It gives human beings their humanity, and we are affirming our humanity when acknowledging that of others. Ubuntu embodies the concept of mutual understanding and the appreciation of differences in humans; respect others if you are to respect yourself. Ubuntu is therefore an important new concept introduced to my group or community of learners who need to ensure that they actively adopt these African philosophy principles within their everyday lives. By adopting these principles all members of our group or community, including the new learner, will enjoy a spirit of mutual support, understanding and caring for each other’s well-being. The learners will come to understand that we must treat each other with dignity, respect, compassion, humaneness, humbleness and share a brotherly/sisterly love within our community or group. That all members of our group or community need to be included and no person ever isolated, therefore we must ensure that our new community member, learner, is invited and accepted within our community or group thereby encapsulating and embracing the principle of Ubuntu and promoting the African identity and a participatory group or community. Through African philosophy we have come to teach our young grou p or young community about our African identity and promoting cultural unity through our diversity. By putting into practice the fundamentals of African philosophy we are ensuring all our learners come to know compassion, kindness, selflessness and respect at school, making it a place of effective learning and teaching within a safe environment with happy school community members. References 1.Higgs, P & Smith, J. 2000. Rethinking our world. Cape Town: Juta.

A Guide to Writing Research Papers for Every University Students

Research papers are detailed documents containing results of an experiment or investigations. Research papers contain the details of the investigation from the gathering of data, the background of the study, materials or procedures in arriving with such conclusions and most importantly the recording and analysis of the results.According to Thomas R. Brown1, research papers make statements then attempt to prove it by doing current research, it enables the student to pursue his own specific interests within a given area of study. Thus, research papers helps the student stimulate thinking in discovering and sharing his findings with the aid of a paper.There are a lot to consider in writing a research paper, the thesis statement, the citing of the references, grammar, making the necessary footnotes and of course the selection of the topic.What every student should know is that a research paper can only be realized once a topic is selected. Usually the selection of the topic depends upon the researcher and the course of subject regarding the topic he wishes to undertake.It is best to read several articles regarding the topic to understand fully the topic with no difficulty. But a researcher must bear in mind that whatever topic he chooses, he must be certain that the researcher takes interest in the topic, he must select a topic that is not too broad so that references will be easy to find and most importantly the researcher will go to extreme measures in order to complete the research sacrificing time, the use of money and the need for energy.Once a preferred topic is selected, an outline or project plan is made where random thoughts and ideas of the researcher are arranged so that the creation of the paper will easily follow.Then the researcher will make the draft. It is advisable to make the draft with the aid of the computer so that revisions and modifications will not be hard. The draft contains the research itself but it is still subjected to revisions, it als o contains your thesis statement.   A   thesis statement   tells what the research paper   is about   and its significance and.1 â€Å"the rearch paper.† Thomas R. Brown. June 12, 2004, on mywebpages. 06 Jun. 2007 .what the researcher intends to verify. The thesis statement must not be too broad so that specific issues can be discussed thoroughly. In the words of Zachary M. Schurg2, a thesis is an argument that can be supported by evidence, and it must have three qualities: interpretation, precision, and surprise.In interpretation, the statement must explain what the paper intends to prove thus answering the question â€Å"why†. The second element in a thesis statement, precision, deals with the discussion of facts with accuracy which further explains the research paper. And the last element, surprise, a thesis statement must present revelations regarding the subject that the reader does not know in order to catch the researcher’s attention and give th e research value.Example of a thesis statement is: Children nowadays do not stay children, effects of the society and the media may have caused such behavior in children. Since the thesis statement is indeed a statement, it must not be in a form of a question. This statement only requires two to three sentences. The thesis statement is usually found in the introductory paragraph.The only problem now is how to write the paper in such a fashion that everyone can understand it. Research papers, like all important documents containing information, follows rules in order to be understood by those who take interest in the topic. Generally the research paper, have margins of 1† on top, bottom and right side, and 1.5 â€Å"on the right side. The researcher must write with double line spacing with the exemption of quotations and the list of reference.And the paper must observe font size should be 10 points or larger, Times New Roman. Page numbers should also be observed upon making th e paper and must be reflected on the upper right of the paper. The paper should be justified. And of course in writing important documents of research and information grammar should be observed to avoid ridicule and mockery of the paper.

Schema

Schema as Hirsch has defined it is an â€Å"unified system of background relationships† that allows people to understand the â€Å"surface meaning† of a statement (Hirsch 54). If people can find ways to influence students about things that are important in the world, they would grow up connecting series of things important nowadays, and end up having the knowledge to choose what they can do next. If a person contains schema about environmental problems, and how to solve them, they would automatically put things side by side and build a solution for it. With the help of schema, people most especially students can be able to focus on what is important in the society today. If the student graduates with the mental ability to know automatically what is right for their health and be aware of the environment problems, they can lessen the cause of it and the world would be a better place. If the student graduates with the general knowledge of choosing healthy foods, obesity would be lessened and if they graduate with the general knowledge to be aware of what they do to the environment, global warming would slow down. In the end, since schema cannot be taught, institutions should change the curriculum to teach information that will inform the schemata, so that the generation to come would automatically do what is right for them and for the environment.

Leading your work team Essay

Difference between leadership and management Both managers and leaders have positive and some flawed qualities with any organisation. Leaders establish direction and have vision for the future. They tend to plan ahead by developing new ideas to achieve goals set out. Other qualities they have are that they drive people to exceed their own limitations, give others some responsibility by delegating some duties. Leading using these methods and communicating inspires trust from people, colleagues and employees. When trust is achieved respects is grown from each individual and vice versa, the leaders respect each individual and each person’s merits as everyone can make different contribution but on their own level. Through empowering people with involvement they create motivation and energise people to overcome some obstacles and can defiantly have a positive outcome and see a marked improvement or change with a team and or individual. But on the other hand, leadership can be flawed and sometimes can have a negative impact on a team, especially when leaders become too friendly, they try to please everyone and sometimes within an organisation this cannot be possible. It is then that a break in mutual respect, motivation and trust appears. There should always be a line between staff, leaders and managers. Management do tend to manage the processes such as timetable, budgets and actions on a day to day basis by controlling and allocating resources to maintain the status quo or ensure things happen according to already established plans. Another difference is that they rely on control and they work on solving problems but are focused people who focus on systems, policy and procedures. Decision-making is also amongst a managers strengths. Managers tend to monitor every result against each plan and if necessary will take corrective action which makes them predictable but on the other consistent and have clear defined order. However sometimes there can be an overemphasis on outcome at the expense of neglecting the people. Why leadership is important within own team? Team leader plays an important role in guiding team members and motivating them to stay focused as every member contributes to their own level to best achieve their assigned targets or goals. Every team should have a team leader who can hold his team together and extract the best out its team members. Leaders should be a role model and be such that individuals can draw inspiration from and seek advice and guidance whenever required. An effective leadership must be impartial, support one and all equally and discuss any goals that needs to set or issues on an open forum where applicable and make tram members aware of their roles and responsibilities and not impose things on their members. Within my working organisation, we have teams that consist of ten team members of which are of mixed skill levels and each team are assigned a clinical team leader. Team leaders are approachable and they should lead by example by providing what we as organisation set out to achieve which is the best p ossible care for each person we attend to regardless of our skill level within the trust. Guidance within our work base could be from anything from personal circumstances to any clinical issues that employees require assistance, guidance, reassurance or clarification of practices. This is why it is important to have a good leadership style and person within our teams, someone who is approachable and on top of their game to be able to provide support and drive the staff to work to the best of their ability. Team leaders need to recognise each team members needs and be able to help and guide each member of its team to achieve their best potential this could be organising further training, provide emotional support after some difficult clinical cases and also show some appreciation of the diisfulct and successful cases staff attend on a daily basis. Communication is vital in our work base as many new information, policy procedures is normally cascaded to each team member via team leaders and it is important that team leaders make sure that each individual knows exactly their new or enhanced responsibilities. Despite the best intention of organisations and team leaders, some leadership styles can be ineffective and for various reasons implications and impact of an ineffective leadership can affect teams morale, goals and standard set out will without a doubt be below the expected standard. Many reasons could be  too responsible such as environmental issues i.e. teams are not given adequate resources of equipment in my work place to do their job to the highest standard. Lack of recognition of good work can have a negative impact. Appreciation can be a big morale booster. Goals that are not set out clearly and lack of communication can lead to ineffective team and mistakes can happen. This could lead to everyone doing their own thing and poor relationship between team members including team leaders can lead to conflict and personality conflicts. These issues can be resolved with planning, processes and performance appraisals etc. Different leadership styles Democratic:- One of the leadership styles, which is effective and can lead to higher productivity, better contribution from team members and it is a style that can increase on teams’ morale. Reasons for this are because team members take more of a participative role in the decision-making process. This style has a positive effect when used in work place, sometimes I have to work with a new inexperienced trainee or even lower grade colleague. We discuss together where possible any issues i.e. diagnosis, treatment of patients etc. I ask them â€Å"What are their thoughts?† and get their valuable input and opinions. I find that trainees become more confident, will ask more questions and become more eager to learn new techniques, and take more responsibility. Benefits of democratic leadership are appropriate in my field of work; staff become more involved and cares more about end result. It does have its flaws, the process of consultation can turn into procrastination and if a business has urgent issues or in my work place if we have time critical patient then democratic leadership style is not a trait that is required. Democrats can’t normally work to these tight timescales. Talking to lots of people and gathering opinions take time but true democrats are unwilling to cut corners. They can also appear indecisive and unwilling to make a decision. Coercive:- This leadership style demands immediate compliance. It is more that the leader rules by fear â€Å"my way or the highway†. Coercive leaders take charge drives to achieve and have self-control but can have an overall detrimental effect on team members. This style would not be suitable in my role, as our working ethics on a day to basis is reliant on team work and a leader of this style could cause animosity between staff and leader and could possibly lead to mistakes being made on the frontline which could be catastrophic for patients. Bu these leader ships qualities could be useful when a company is in crisis or an organisation in trouble. Pacesetter style:- This leadership style sets high performance standards to all members including him. The style sounds very admirable but has more of a negative impact on members as they tend to have a problem with trusting their team. They rest on being smarter, more thorough than everyone else and can unintentionally undermine the effects of their team members. A pacesetter would have negative impact in my work place as trust in each other is required when working as a team to achieve our goals. Undermining even if unintentionally can have a negative effect on working relationships. But on the other hand can also be effective in other field of work especially if the team are highly motivated and the members’ style and competence already fit the expectations of the pacesetter. Paternalistic:- This style is by acting as a father/mother figure by taking care of their team members as a parent would their child. They receive complete trust and loyalty from their team when they lead with complete concern of their members. Teams are expected to become totally committed to what the leader believes. Relationships are solid, but can have a negative impact if the leader starts showing favouritism in decisions and could lead to breakdown of relationships. Most commonly used leadership and its effects on own team Within the organisation I work, there are a couple of main leadership styles used. As an organisation of uniformed and non uniformed public sector, and depending on the level of leadership or where in the chain of command the style vary somewhat. The higher the chain the more bureaucratic method of leading is used. They have fixed official duties under a hierarchy of authority, applying a system of rules of management and decision-making. Bureaucratic leadership can be broken down into different components which also outline the basic structure of the NHS. Fixed official duties – Accountability Authority Responsibility Hierarchy of authority – lower grades are answerable to and under supervision of level above CEO, Directors etc Technical expertise- – Medical director has a medical background as well as management. System of rules- behavioural and technical rules i.e. scope of practice – conduct and performance management, policies and procedure Written documentation – policies, procedures to help with accountability, decision-making guidance etc. However, if this style of leadership is used inappropriately then it can have negative impact, consequences causing lack of flexibility and work throughout the team from hierarchy through to the structures below. Democratic leadership style is also used within my immediate work place, especially when working with lower grade or new trainee staff during a shift. This approach encourages staff to become part of decision-making process. For example, whilst working with a new member of staff we can attend to numerous different patients with each requiring thorough can careful examination to help us be able to treat each patient to the best of our a bility. I try to encourage new staff and lower grades to become more confident and help in making decision, deciding on treatments by asking their opinions and what their thoughts are. I find this has a positive  effect on team members, improve communication, gain respect and can produce good working ethics. The leader still has full control of its members and still has final decision but it is a decision with input from team that is encouraged. But this is very time consuming and as public service we may not have time to do this, on a more personal note some patients are time critical and this leadership style would not be appropriate at that specific time as decision need to be made very quickly and make sure that team members, colleagues, patients are safe and not harmed. Laissez-faire leadership style is also commonly used in my field of work. This is a style that can be used between team leaders and its members as the leader doesn’t get involved with our day to day work and tends to leave staff to it. Team leaders need smart, dedicated and motivated team members that they can rely on to complete a task and work to the highest standard. For example, within the ambulance service during a major incident a team leader/ officer will leave paramedics to treat patients whilst he or she is outside securing and organising resources etc. They must have trusted in its team members for this to work effectively. Like many other style it can have a downfall and can be somewhat ineffective as some times teams can feel that they have no guidance or support when they are left to get on with it! Own leadership style I believe that I have a couple of leadership style and it totally depends on the situation. As long as patients are not time critical and time is on our side I think I use a coaching style leadership because it is a style that develops people by offering hands-on advice to problem solving. It can be summed up in a phrase â€Å"try this.† It works best when helping staff to build a lasting personal and professional strengths and confidence and make them more successful overall but I suppose it can be hampered if my colleagues are defiant and unwilling to learn or change. Along with coaching style I think that I adopt a bit of a democratic leading method. As we have teams of 10 members to each team leader it is a good quality in my opinion to lead in an open style, we discuss issues openly as a team and as individuals when necessary. Ideas move freely amongst the group and discussion is relatively free flowing. I believe this style is needed in our work place as it dynamic  and rapidly changing environment. The style means facilitating the conversation, encouraging staff to share their ideas, issues and opinions and using these to make the best possible decision. I can communicate very well and communicating is one of the key elements of democratic leadership where you must be able to communicate decision, information etc back to your group, this then keeps unity, good solid relationship m trust and mutual respect between leader and its members. I would like to think that leading in this way brings out an experienced, confident and professional team.