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Array Elements
Fixed beam broadside arrays may employ low- or moderate-gain elements, but most arrays employ low-gain elements owing to the effects of grating and quantization lobes (see Chapter 3).
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Fixed beam arrays are usually either linear arrays or assemblies of linear arrays to make a planar array. Thus the linear array is a basic building block. When the array elements are in series along a transmission line, the array is termed “series.” Similarly, when the elements are in parallel with a feed line or network, the array is termed “shunt.” A further division of series feeds is into resonant or standing wave feeds, and travelling wave feeds. Shunt feeds are generally of corporate type, or distributed. Each of these types is discussed below.
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It will be shown below that mutual coupling is responsible for all the unique characteristics of phased arrays. The task, then, is to understand it, and to make advantageous use of it. This chapter is concerned with infinite arrays for two reasons. First, the essential characteristics of all scanning arrays exist in infinite arrays, and are most easily calculated there. Second, most array design starts with an infinite array, with finite array (edge) effects included near the end of the design process.These edge effects are the subject of Chapter 8. Mutual coupling fundamentals are discussedfirst. ...
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Although the infinite array techniques of Chapter 7 are excellent for system trades and preliminary design, final design requires a finite array simulation. Direct impedance (admittance) matrix methods were described in Section 7.3.2. These were developed by Oliner and Malech, 1966a; Galindo, 1972; Bailey, 1974; Bailey and Bostian, 1974; Cha and Hsiao, 1974; Steyskal, 1974; Bird, 1979; Luzwick and Harrington, 1982; Clarricoats et al., 1984; Pozar, 1985, 1986; Fukao et al., 1986; Deshpande and Bailey, 1989; Silvestro, 1989; Usoff and Munk, 1994; and others. When moment methods are not necessary (thin half~wave dipoles, for example), sizeable planar arrays may be...
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A useful operational definition of antenna array superdirectivity (formerly called supergain) is directivity (see Chapter 2) higher than that obtained with the same array length and elements uniformly excited (constant amplitude and linear phase). Excessive array superdirectivity inflicts major problems in low radiation resistance (hence low efficiency), sensitive excitation and position tolerances, and narrow bandwidth.
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Multiple simultaneous beams exist when an array of N elements is connected to a beamformer with 1M beam ports, where N and 1M may be different. Multiplebeam systems have many uses: in electronic countermeasures, in satellite communications, in multiple-target radars, and in adaptive nulling, for example. The last application uses adaption in beam space as it avoids several serious difficulties that arise with adaption in array space. (Mayhan, 1972). Not included in this chapter are array feeds for parabolic reflectors, where amplitude and phase control of the elements allows coma correction, beam switching, adaptive nulling, and to a limited degree...
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The essential constituent of a conformal array is curvature. Authorities disagree on whether the array must be part of a curved metallic structure; in this chapter curvature alone is sufficient. Arrays of one or more concentric rings of elements, here called “ring arrays,” are treated first. The term “circular array” is not used, as it often means a planar array of circular perimeter. The following sections deal with arrays on curved metallic bodies. Most simple is the cylinder; Section 11.3 treats cylindrical arrays with elements around the full circumference....
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Measurements and Tolerances
There are excellent books on measurements, listed below, Thus only special topics pertinent to arrays will be discussed herein. These are: measurement of low sidelobe antennas; array diagnostics; and scan impedance simulators. Because array performance is affected by random errors, tolerances are also discussed in this chapter. A. E. Bailey, Microwave Measurement, IEE/Peregrinus, 1985. 1988. G. H. Bryant, PrincipZe~ of Microwave Measurement, IEE/Peregrinus, G. E. Evans, Antenna Measurement techniques, Artech House, 1990. layton, Microwave Antenna Measurements, Scientific Atlanta, 1970. IEEE Standard Test Procedures for Antennas, Std 149, 1979.
12.1
MEASUREMENT
OF...
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Random phenomena have their basis in the nature of the physical order (e.g., the nature of electron movement) and limit the performance of many systems including electronic and communication systems. For example, the minimum sensitivity of an amplifier and the distance a signal can be transmitted and recovered, are both limited by random signal variations. On the other hand, there are applications where introduced randomness will enhance aspects of system performance.
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Background: Signal and System Theory
2.1 INTRODUCTION The power spectral density arises from signal analysis of deterministic signals, and random processes, and is required to be evaluated over both the finite and infinite time intervals. While signal analysis for the finite case, for example, the integral on a finite interval of a finite summation of bounded signals, causes few problems, signal analysis for the infinite case is more problematic. For example, it can be the case that the order of the integration and limit operators cannot be interchanged. With the infinite case, careful attention to detail and a reasonable knowledge of...
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The Power Spectral Density
The power spectral density is widely used to characterize random processes in electronic and communication systems. One common application of the power spectral density is to characterize the noise in a system. From such a characterization the noise power, and hence, the system signal to noise ratio, can be evaluated. This chapter gives a detailed justification of the two distinct, but equivalent ways of defining the power spectral density.
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Power Spectral Density Analysis
In this chapter, general results for the power spectral density that facilitate evaluation of the power spectral density of specific random processes are given. First, the nature of the Fourier transform on the infinite interval is discussed and a criterion is given for the power spectral density to be bounded on this interval. Second, the use of an alternative power spectral density function that can be defined for the case where a signal consists of a sum of orthogonal or disjoint waveforms is discussed. ...
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Power Spectral Density of Standard Random Processes — Part 1
In Chapters 5 and 6 the power spectral density of commonly encountered random processes are given in detail. Specifically, the power spectral density of random processes associated with signaling, quantization, jitter, and shot noise are discussed in this chapter, while the power spectral density associated with sampling, quadrature amplitude modulation, random walks, and 1/ f noise, are discussed in Chapter 6.
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Power Spectral Density of Standard Random Processes — Part 2
This chapter continues the discussion of standard random processes commenced in Chapter 5. Specifically, the power spectral density associated with sampling, quadrature amplitude modulation, and a random walk, are discussed. It is shown that a 1/ f power spectral density is consistent with a summation of bounded random walks. 6.2 SAMPLED SIGNALS Sampling of signals is widespread with the increasing trend towards processing signals digitally. One goal is to establish, from samples of the signal, the Fourier transform of the signal....
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Memoryless Transformations of Random Processes
This chapter uses the fact that a memoryless nonlinearity does not affect the disjointness of a disjoint random process to illustrate a procedure for ascertaining the power spectral density of a signaling random process after a memoryless transformation. Several examples are given, including two illustrating the application of this approach to frequency modulation (FM) spectral analysis. Alternative approaches are given in Davenport (1958 ch. 12) and Thomas (1969 ch. 6).
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Linear System Theory
In this chapter, the fundamental relationships between the input and output of a linear time invariant system, as illustrated in Figure 8.1, are detailed. Specifically, the relationships between the input and output time signals, Fourier transforms and power spectral densities, are established. Such relationships are fundamental to many aspects of system theory, including analysis of noise in linear systems, and low noise amplifier design.
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Principles of Low Noise Electronic Design
This chapter details noise models and signal theory, such that the effect of noise in linear electronic systems can be ascertained. The results are directly applicable to nonlinear systems that can be approximated around an operating point by an affine function. An introductory section is included at the start of the chapter to provide an insight into the nature of Gaussian white noise — the most common form of noise encountered in electronics. This is followed by a description of the standard types of noise encountered in electronics and noise models for standard electronic components....
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MOTIVATION
Information processing system designers need methods for the quantification of system design factors such as performance and reliability. Modern computerr communicationI’ and production line systems process complex workloads with random service demands. Probabilistic and statistical methods are commonly employed for the purpose of performance and reliability evaluation. The purpose of this book is to explore major probabilistic modeling techniques for the performance analysis of information processing systems....
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Markov Chains
MARKOV PROCESSES
Markov processes provide very flexible, powerful, and efficient means for the description and analysis of dynamic (computer) system properties. Performance and dependability measures can be easily derived. Moreover, Markov processes constitute the fundamental theory underlying the concept of queueing systems. In fact, the notation of queueing systems has been viewed sometimes as a high-level specification technique for (a sub-class of) Markov processes.
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Steady-State Solutions of Markov Chains
In this chapter, we restrict ourselves to the computation of the steady-state probability vector’ of ergo&c Markov chains. Most of the literature on solution techniques of Markov chains assumes ergodicity of the underlying model. A comprehensive source on algorithms for steady-state solution techniques is the book by Stewart [Stew94]. From Eq. (2.15) and Eq. (2.58), we have v = VP and 0 = nQ, respectively, as points of departure for the study of steady-state solution techniques. Eq. (2.15) can be transformed so that: 0 = Y(P -1). Therefore, both for CTMC and DTMC, a linear system...
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In this section we introduce an efficient method for the steady-state analysis of Markov chains. Whereas direct and iterative techniques can be used for the exact analysis of Markov chains as previously discussed, the method computations of Courtois [Cour75, Cour77] is mainly applied to approximate u NN the desired state probability vector u. Courtois’s approach is based of on decomposability properties of the models under consideration.
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Transient Solution of Markov Chains
Transient solution is more meaningful than steady-state solution when the system under investigation needs to be evaluated with respect to its shortterm behavior, Using steady-state measures instead of transient measures could lead to substantial errors in this case. Furthermore, applying transient analysis is the onl y choice if non-ergodic models are investigated, Transient analysis of Markov chains has been attracting increasing attention and is of particular importance in dependability modeling. ...
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Queueing Networks
Queueing networks consisting of several service stations are more suitable for representing the structure of many systems with a large number of resources than models consisting of a single service station. In a queueing network at least two service stations are connected to each other. A station, i.e., a node, in the network represents a resource in the real system. Jobs in principle can be transferred between any two nodes of the network; in particular, a job can be directly returned to the node it has just left. A queueing network is called open when jobs can enter the...
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Algorithms for Product-Form Networks
Although product-form solutions can be expressed very easily as formulae, the computation of state probabilities in a closed queueing network is very time consuming if a straightforward computation of the normalization constant using Eq. (7.3.5) is carried out. As seen in Example 7.7, considerable computation is needed to analyze even a single class network with a small number of jobs, primarily because the formula makes a pass through all the states of the underlying CTMC. Therefore we need to develop efficient algorithms to reduce the computation time [Buze71]....
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Approximation Algorithms for Product-Form Networks
In Chapter 8, several efficient algorithms for the exact solution of queueing networks are introduced. However, the memory requirements and computation time of these algorithms grows exponentially with the number of job classes in the system. For computationally difficult problems of networks with a large number of job classes, we resort to approximation methods. In Sections 9.1, 9.2, and 9.3 we introduce methods for obtaining such approximate results. The first group of methods is based on the MVA. The approximate methods that we present need much less memory and computation time than the exact MVA and...
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Algorithms for Non-Product-Form Networks
Although many algorithms are available for solving product-form queueing networks (see Chapters 8 and 9), most practical queueing problems lead to non-product-form networks. If the network is Markovian (or can be Markovized), automated generation and solution of the underlying CTMC via stochastic Petri nets (SPNs) is an option provided the number of states is fewer than a million. Instead of the costly alternative of a discrete-event simulation, approximate solution may be considered. Many approximation methods for non-product-form networks are discussed in this chapter. ...
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Optimization
Analytic performance models are very well suited as kernels in optimization problems. Two major categories of optimization problems are static and dynamic optimization. In the former, performance measures are computed separately from an analytic queueing or CTMC model and treated simply as functions (generally complex and non-linear) of the control (decision) variables. In the latter class of problems, decision variables are integrated with the analytic performance model and hence optimization is intimately connected with performance evaluation. We limit our discussion to static optimization. ...
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Performance Analysis Tools
Performance analysis tools have acquired increased importance due to increased complexity of modern systems. It is often the case that system measurements are not available or are very difficult to get. In such cases the development and the solution of a system model is an effective method of performance assessment. Software tools that support performance modeling studies provide one or more of the following solution methods:
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This chapter considers several large applications. The set of applications organized into three sections. In Section 13.1, we present case studies queueing network applications. In Section 13.2 we present case studies Markov chains and stochastic Petri nets. In Section 13.3, case studies hierarchical models are presented.
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The correctness of many systems and devices in our modern society depends not only on the effects or results they produce but also on the time at which these results are produced. These real-time systems range from the anti-lock braking controller in automobiles to the vital-sign monitor in hospital intensive-care units. For example, when the driver of a car applies the brake, the anti-lock braking controller analyzes the environment in which the controller is embedded (car speed, road surface, direction of travel) and activates the brake with the appropriate frequency within fractions of a second. ...
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