接收机天线和信号(麻省理工大学).pdf
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1、1 CHAPTER 1: INTRODUCTION 1.1 SCOPE AND CONTENT Communications and sensing systems are ubiquitous. They are found in military, industrial, medical, consumer, and scientific applications employing radio frequency, infrared, visible, and shorter wavelengths. Even acoustic systems operate under similar
2、 principles. Communications examples range from optical fiber or satellite systems to wireless radio. Radio astronomy, radar, lidar, and sonar systems probe the environment and have counterparts in analytical instruments and memory systems used for a wide variety of purposes. HUMANPROCESSORTRANSDUCE
3、R AB HUMANPROCESSORTRANSDUCER G Electromagnetic Environment C FE Radio Optical, Infrared Acoustic, other D Figure 1.1: Architecture of communications and sensing systems. Figure 1.1 characterizes the major electromagnetic and signal processing elements of such systems, not all which of are necessari
4、ly involved in any particular case. For example, in communication systems a human (A) (or computer counter-part) typically generates signals which are first processed (B) and then coupled to an electromagnetic environment (D) by a transducer or antenna (C). After propagating through the environment
5、(D) the signals are intercepted by another transducer (E) which usually consists of an antenna followed by a detector which converts these electromagnetic signals into voltages and currents. The signals from the transducer (E) are then generally manipulated in processor (F) before transmission to th
6、e human or computer recipient (G). Communications and active systems that probe the environment generally involve all seven elements (A)-(G). Passive systems generally involve only the last four, from the environment (D) to the user (G). Examples of the latter include environmental or astronomical o
7、bservations, medical systems seeking spectral or thermal signatures of disease, and the readout of information from memory systems such as compact disks. To completely analyze such a broad range of systems would require several textbooks. Here the fundamentals for each of the elements in Figure 1.1
8、are presented in a generally complete 2 way but, for efficiency, only few of their possible combinations are presented in any detail. For example, the probability of symbol detection error is analyzed for communications systems, but this analysis is not repeated for other systems. It is hoped that r
9、eaders of this book will acquire sufficient understanding of the elements of Figure 1.1 to be able to conceive, design, and analyze a wide variety of electromagnetic signal-based systems by combining these elements appropriately. The chapters of this book can be divided into three groups. First Chap
10、ter 1 defines the basic notation and surveys briefly some of the basic notation fundamental to signal processing and electromagnetic waves. The second group of chapters focuses on the fundamental elements of communications and sensing systems. Chapter 2 discusses basic noise processes and the device
11、s used for detection of radio, infrared, and visible signals, including those first-stage signal processing operations that yield the desired signal, energy, or power spectral density estimates. Chapter 3 then discusses the transducers and antennas that link these detectors to the electromagnetic en
12、vironment, including wire antennas, apertures, simple optics, common propagation phenomena, and how the transmitting and receiving properties of systems are related in a simple way. The third group of chapters deals with complete systems applied to communications (Chapter 4) and both active and pass
13、ive sensing (Chapter 5). Estimation techniques for both sensing and communication systems are then discussed separately in Chapter 6. 1.2 MATHEMATICAL NOTATION Because physical signals are generally analog, we rely in this text more heavily on continuous functions and operators than on discrete sign
14、als and the z transform. Physical signals in time or space are generally represented by lower case letters followed by their arguments in parentheses, whereas their transforms are generally represented by capital letters, again followed by their arguments in parentheses. Complex quantities are gener
15、ally indicated by underbars. For example, the Fourier transform relating a voltage pulse v(t) to its spectrum V(f) is: ? ? ? j2 ft V f v t edt volts Hz voltsec ? ? ? ? (1.2.1) ? ? ? j2 ft v t V f edf volts ? ? ? ? (1.2.2) )f (V) t (v? (1.2.3) where frequency is generally represented by f(Hz) or ? ?
16、2?f(radians/second). We abbreviate this Fourier relationship as: v(t) ? V(f). These relations apply for pulses of finite energy, i.e.: 3 ? ? ? ?dt) t (v 2 (1.2.4) The energy spectrum ? ? ? 2 S fV f? and has units 2 voltsHz? ? for the case where v(t) has units volts. This energy density spectrum is t
17、he Fourier transform of the voltage autocorrelation function R(?), where: ? ? ? ? ? ? 2 2 V fS fR v t vtdt v sec or J , etc. ? ? ? ? ? ? ? ? (1.2.5) Parsevals theorem, which says that the integral of power over time equals the integral of energy spectral density S(f) over frequency, follows easily f
18、rom Equation (1.2.5) and the definition of a Fourier transform (1.2.2) for t = 0: ? ? ?dffS=dttv)0(R 2 ? ? ? ? ?. (1.2.6) These relationships for analytic pulse signals can be represented compactly by the following notation: ? ? ? ? ? ? ?fSfVR fVtv 2? ? ? ? (1.2.7) The single-headed arrows pointing
19、downward indicate that the transformations from v(t) to R(?), and from ? ?fV to ? ?2fV are irreversible. The units of these quantities depends on the units associated with v(t). For example, if v(t) represents volts as a function of time, then the units in clockwise order in (1.2.7) for these four q
20、uantities are: volts, volts/Hz, (volts/Hz)2, and volts2 seconds. If this voltage v(t) is across a 1-ohm resistor, then we can associate the autocorrelation function R(?) with the units Joules, and the energy density spectrum S(f) with the units Joules/Hz. Another important operator is convolution, r
21、epresented by an asterisk, where: 4 ? ? ?a(t) b(t) a b t- d = c t ? ? ? ?. (1.2.8) Note that a unit impulse convolved with any function yields the original function, where we define the unit impulse ?(t) as a function which is zero for |t| 0, and has an integral of value unity. Periodic signals with
22、 finite energy in each period T can be reversibly characterized by their Fourier series and irreversibly characterized by their autocorrelation function R(?) and its Fourier transform, the energy density spectrum ?m. These are related as suggested in Equation 1.2.9 ? ? ? ? ? m -1 m v tV (volts) Rwat
23、ts Hz or S(f) (Joules) ? ? ? ? (1.2.9) The Fourier series Vm can be simply computed from the original waveform v(t) as: o T 2 jm2 f t1 m T 2 VTv(t)edt ? ? ? ? ? (1.2.10) where T equals fo-1 and: o jm2 f t m m v(t)Ve ? ? ? ? ? ? (1.2.11) o T 2 2jm2 f m m T 2 R( )v(t)v (t)dtVe ? ? ? ? ? ? ? ? ? (1.2.1
24、2) o T 2 2jm2 f 1 mm T 2 VTR( )ed ? ? ? ? ? ? (1.2.13) Random signals x(t) can often be characterized by their autocorrelation function: ? ? ? ? x E x t x t.? ? (1.2.14) Such signals are called “wide-sense stationary” stochastic signals. For the special case where the signal x(t) is the voltage acro
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