Baseband Demodulation/Detection
In the case of baseband signaling, the received waveforms are already in a pulse-like form. One might ask , why then ,is a demodulator needed to recover the pulse waveforms? The answer is that the arriving baseband pulses are not in the form of ideal pulse shapes, each one occupying its own symbol interval. The filtering to suffer from inter-symbol interference (ISI) and thus appear as an amorphous “smeared” signal, not quite ready for sampling and detection .The goal of the demodulator (receiving filter) is to receiver a baseband pulse with the best possible signal-to-noise ration (SNR),free of any ISI. Equalization, covered in this chapter, is a technique used to help accomplish this goal. The equalization process is not required for every type of communication channel. However, since equalization embodies a sophisticated set of signal-processing techniques, making it possible to compensate for channel-induced interference, it is an important area for many systems.
The band-pass model of the fourth chapter deals with the detection process, and described in this chapter essentially the same as the baseband model. Before testing, you must first bandpass conversion to the baseband signal. For signal detection in linear systems mathematical expressions do not accept the frequency move, and have the following equivalence theorem (equivalence theorem states): the current processing is first bandpass signal is converted to the base, and then using the heterodyne method band signal; the results with the first heterodyne signal is converted to the baseband signal, the corresponding linear processing on the baseband signal. \(heterodying) refers to a technique called \the frequency a shame that software mixing is signal processing, he realized the spectrum of the signal move. A corollary of the equivalence theorem, and linear simulation process the Cheng Duiji band signal (generally) the result is the same as the result of bandpass role, This indicates that most of digital communication systems as a baseband system to describe and analyze.
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1 SIGNALS AND NOISE
1.1 Error-performance Degradation in Communication Systems
The purpose of the detector is based on as few errors as possible to restore the original signal stream from the received waveform distortion. There are two main reasons for the error performance degradation. The first reason is that 3.3 will introduce a sender channel and receiver filter, non-ideal system transfer function will cause the symbol \arising from inter-symbol interference (ISI).
Another reason is that the electronic noise and other noise sources, such as atmospheric noise of the universe, the switching transient noise, inter-modulation noise and interference signals from other noise sources (these will be discussed in Chapter 5). Appropriate preventive measures can effectively reduce or even eliminate the number of receiver noise and interference. However, there is a noise can not be eliminated, is the electronic thermal motion of the conductor thermal noise, the noise is an additive noise, exist in the amplifier circuit. The use of quantum mechanics has been informed of the statistical properties of the thermal noise.
1.2 The Basic SNR Parameter for Digital Communication Systems
Learned analog communication readers are familiar with an indicator that the signal average power and noise average power ratio, referred to as the signal to noise ratio (SNor SNR) of In digital communication systems, usually using the normalized form of signal to noise ratio EbN0 as the performance index. Eb is the energy per bit is equal to the product of the signal energy S with each bit durationTb, N0is the noise power spectral density equal to the ratio of the noise power N and bandwidth W; reciprocal and because each bit duration T and the bit rate R can be used 1Tbinstead of Rb, therefore the following expression set up:
STbS/RbEb== (1.1) N0N/WN/WN0b/s data rate is one of the most commonly used indicator of the digital communications to simplify the description, the book will remember the bit rate R is R.
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To underline the EbN0, SN normalized bandwidth and bit rate form of equation (1.1) into
EbS?W???? (1.2) N0N?R?Digital communication systems, the most important performance measure is one of the bit error rate PB and EbN0 curve (see Figure 1.1), the EbN0?x0, of PB?P0. Dimensionless ratio EbN0 is a standard digital communications system performance indicators that can be EbN0 as a measure of comparative performance advantages and disadvantages of the two communication systems: the conditions for a given error probability, the required EbN0 is smaller, the higher accuracy of detection.
x0 Eb/N P0 PBFor EbN0?x0,PB?P0 EbS?W???? N0N?R?Figure 1.1 General shape of the PBversus Eb/Nocurve
1.3 Why Eb/Nois a Natural Figure of Merit
Beginner digital communication, the reader may doubt the usefulness of the parameter EbN0. In analog communication, SN is a very useful indicator of the molecular expect to maintain the transmission of power, the denominator represents the size of the noise. But why you want to use in digital communication with the different indicators (per bit energy to noise power spectral density ratio)? The explanation is given below .
In section 1.2.4, we define the power signal average power is limited, while the infinite energy of the large signal, and the energy signal is defined as the average power is
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equal to zero while the energy-limited signal. This classification is very useful to compare the analog and digital signals. The analog signal is classified as a power signal. What is the significance? Usually the duration of the simulation waveform of infinite length, do not need to partition or increase the time window. Infinite time domain signal waveform, its energy is infinite and therefore can not use the energy to describe the signal. For analog signals, the power (or energy transfer rate) is a more useful parameter.
However, in the digital communication system using the length of time for the waveform of the symbol interval Ts to send and receive code. The average power for each symbol (average) is equal to zero throughout the timeline, so the power can not be used to describe a digital signal. Therefore, the digital signal should be used within the time window to measure the signal measure. In other words, the symbol energy (power points) in Ts is a more suitable description of the digital signal waveform parameters.
Received energy can be well described by the digital signal, but it did not say why the SN is a good indicator of the digital system. The digital waveform is a medium for representing digital information, the information may contain a bit (binary) bit (quaternary), ..., 10-bit (1024 hex). This discrete information structure is completely different source of information of the analog communication system of unlimited quantified continuous wave. The digital system metrics must be more than the premium on the performance of both systems. Because the digital signal waveform may contain only 1 bit, 2 bits ... 10 bits, etc., so the SN of the digital signal can not be described. For example, if a given error probability, a binary digital signal required for the SN is 20. Note that the meaning of the figures contained in its equivalent of the digital signal waveform. Binary waveform contains a bit of information per bit required for the SN is 20. If the signal is 1024 hex, the required SN is still 20. The waveform contains 10 bits of information per bit required for the SN 2. Thus raises the question of why is it not more suitable parameters - the bit level on the energy parameters EbN0 to describe this indicator? With the same SN, EbN0 is a dimensionless ratio, the following expression to prove this point:
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Watt-sEbJoule==
per HzWatt-sN0Watt 2 INTERSYMBOL INTERGERENCE
Figure a describes the filtering problem of a typical digital communication system. The entire system (transmitter, receiver and channel) is different types of filters (as well as inert circuit components such as inductors and capacitors). In the transmitter, the message symbols of the form of pulses or level debugging filtered into pulses that meet the bandwidth requirements. The baseband has system, the channel (cable) distribution reactance pulse signal distortion. Band-pass system (such as wireless systems) is usually fading channel (see Chapter 15), this type of channel is equivalent to do not expect the filter resulting in signal distortion. To compensate for the transmitter and channel is distortion caused by the acceptance filter equalization filter or accept / equalization filter (receiving / equalizing filter). Figure b shows a simple model of such systems, it will be all the filtering effect is equivalent to a system transfer function:
H?f??Ht?f?Hc?f?Hr?f? (2.1)
Ht?f? transmit filter Hc?f? channel filter Hr?f? acceptance / equalization filter. H?f? on behalf of the entire system transfer function, a combination of all of the filtering effect of the transmitter, channel and receiver link. In a binary PCM communication system (such as NRZ-L), the detector according to the received signal sampling and threshold decision. For example, in Figure a of the detector, if accepted signal is greater than zero, then the judgment sent bit is 1; if less than zero, then the judgment bit is 0. Due to the filtering effect of the system to receive the pulse overlap, shown in Figure b. Trailing pulse appears to occupy the adjacent symbol interval, thus interfering with the signal detection process, thereby resulting in the reduction of the error performance; this type of interference called ISI (inter-symbol interference, ISI). Even without the distortion caused by the noise, filtering, and channel will also result in intersymbol interference. In some cases,Hc?f? is fixed, the problem becomes how to determineHt?f?andHr?f?, so that the output signal ofHr?f? to obtain the minimum
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