ISI.
The Nyquist study the receiving end does not produce the ISI received pulse shape. He proved: make the code rateRs code / s signal is not present the ISI, the theoretically required minimum system bandwidth Rs/2Hz. Minimum conditions set up by the system bandwidth, the system transfer function H?f? is the rectangular function as shown in Figure a. Baseband system, H?f? The unilateral bandwidth 1/2T rectangular function (ideal Nyquist filter), the system's impulse response H?f? the inverse Fourier transform
h?t? ( called the ideal Nyquist pulse) = sinc(t / T), sinc(t / T), multiple lobe, including a main lobe and side lobe, side lobe, also known as the main valve before and after the trailing pulse to both sides of the infinite extension. Nyquist proved that if the received sequence of each pulse is sinc(t / T) shape, the pulse sequence free from the effects of intersymbol interference is detected. Figure b illustrates the reasons to avoid intersymbol interference. There are two adjacent pulses h?t?and h?t-T?, h?t? has a long trailing pulse, but the sampling points inh?t-T? t = T-time h?t? = 0, Similarly, in the pulse
h?t-T? (k=?1，?2，…. ), the sampling of h (t) sidelobe values are zero. Therefore, the sampling time accurate and not exist inter-symbol interference. Baseband system ISI detect the symbol rate 1 / T pulse (symbol) the required bandwidth of 1/2T; In other words, the bandwidth 2W?1T?Rs/2Hz. The system in ensuring no inter crosstalk conditions can support the maximum transmission rate of 2W?1T?Rscode / s (Nyquist limit). Thus, the ideal Nyquist filter system (to ensure no inter crosstalk) every Hertz the maximum possible transmission rate (called the code rate compression) for 2 symbol / s / Hz. Ideal Nyquist filter transfer function of a rectangular shape, the corresponding impulse response for an infinitely long, it is clear that the filter can not be achieved, can only approximate to achieve.
2.1 Pulse Shaping to Reduce ISI
More narrow spectrum of the signal allows the data rate higher, while the number of users receiving services and more. Communications service provider, which has great significance, because the higher the income the more you can use the bandwidth utilization. Most of the communication system (Chapter 12, except for Spread Spectrum
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Systems) goal is to minimize the required bandwidth. Nyquist reduce system bandwidth limit. If the system bandwidth is what will happen? Pulses in time domain will be extended, the resulting code will reduce the crosstalk between the error performance of the system. Therefore a reasonable target, the compressed data pulse so that it has Nyquist minimum bandwidth slightly larger bandwidth. This can be a Nyquist filter pulse formation. If the band edge of the filter is relatively steep, close to the rectangle in Figure 3.16b, the signal spectrum of the narrowest. However, the duration of the impulse response of this filter is close to infinity (see Figure b), the entire sequence of pulse overlap. Time domain width of the impulse response corresponding to the characteristics in the frequency domain is the amplitude of each near the main lobe, side lobe. These sidelobe is undesirable, because from Figure b sampling only in the correct sampling time does not exist in ISI; large sidelobe level, a small sampling of the timing deviation will lead to inter-symbol crosstalk. So, while the narrow-band spectrum signals can provide the best bandwidth utilization, but its timing errors caused by inter-symbol interference is very sensitive.
2.2 Two Types of Error-Performance Degradation
Reduce the error performance of digital communication systems, there are two cases. The first, due to increase in the energy of the received signal energy to reduce or noise (interference signal) the signal to noise ratioEbN0 reduction, making the performance degradation; the second is attributed to the signal distortion, such as by the inter-symbol crosstalk caused by distortion. The following discuss the difference of these two cases.
Assume that the need to design the comme that the constmunication system, Wu-bit rate (BER) of SN curve in Figure a practice. Assuructed system, test system performance can be found in Wu bit rate of EbN0 curve is not a theoretical curve, but the dotted line in Figure Because the signal is less bad and noise (interference) to improve the level, causing the signal to noise ratio of EbN0 is less bad. Assume that expectations of the bit error rate of 10, then in theory, the EbN0 10dB. The bit error rate of the same case, due to a decline in system performance required for EbN0 rose to 12dB (known by the dashed lines). If you can not solve less bad, need to achieve the
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same bit error rate of the number of EbN0? The answer is 2dB. This is a very serious problem, especially in the system is a power limit, multi-2dB signal to noise ratio is very difficult. However, the signal distortion caused by performance degradation compared to the reduction of signal to noise ratio is not too terrible.
Still assume that the system does not meet expectations of performance shown in practice, as shown in Figure 3.18b. At this point is not a simple SNR impairment, but there is system performance degradation caused by ISI (shown in dotted line). If you can not resolve this problem, in order to achieve the desired bit error rate, but also provide more signal to noise ratio it? The answer is infinity, meaning that there is no way to achieve. When the curve to reach can not reduce the point PB (assuming that the lowest point above the system requirements,PB), to increase the signal to noise ratio does not improve the error performance. There is no doubt that the lowest point of each of PB and
EbN0 curve can fall anywhere, if the point does not cause any effect in the region under consider.
Increased crosstalk between signal to noise ratio can not solve the code problem (PB curve reaches the lowest point, increasing the signal to noise ratio can not solve the problem). Observe in Figure b overlapping pulses can infer this conclusion: if we increase the EbN0, the ratio does not reduce the overlapping pulses, the waveform is really the same. So how to solve the problem of inter-symbol interference? In balanced (see 3.4). Since the inter-symbol interference caused by the filtering effect of the transmitter and channel, then the equilibrium can be seen as the inverse process of the non-optimal filtering.
3 CHANNEL CHARACTERIZATION
Transmission characteristics of the communication channel (such as telephone, wireless channel) is equivalent to the impulse response as h?t? band-limited linear filter, the frequency response
Hc?f??Hc?f?ej?c?f? (3.1)
hc?t? and Hc?f? is the Fourier transform, the amplitude of the channel frequency
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response, Hc?f? is the phase-frequency response. 1.6.3 The section has proved to achieve the ideal of the channel (lossless) transmission, must meet the W within the signal bandwidth is constant, ?c(f) is a linear function of frequency (ie, all frequencies of the signal component, the time delay constant). W within the scope is not constant, it will cause amplitude distortion; Hc?f? in the range of the linear function of the frequency will cause phase distortion, the number of channels (such as fading channel), the amplitude and phase distortion is usually at the same time exist. In the transmission of the pulse sequence, this distortion performance for signal dispersion or smearing, waveform demodulation sequence of deformation. Waveform overlapping or tailing known as inter-symbol interference, and it exists in most of the modulation system is one of the main obstacles to reliable high-speed transmission in bandwidth-limited channel. Broadly speaking, the \refers to all signal processing or filtering techniques to eliminate or reduce the ISI.
The balance can be divided into two categories, shown in Figure 2.1. The first category is the maximum likelihood estimation (maximum-likelihood estimation. The sequence MLSE), need to obtain estimates of hc?t?, adjust the receiver to adapt the transmission environment. The purpose of this adjustment is to make a better estimate of the detector had really demodulation pulse sequence. MLSE receiver, re-shaping or other direct compensation is not a distortion of sampling, but to adjust itself to better deal with the true waveform. An example of this approach is to section 15.7.1 to introduce Bite balanced. The second category is the equalization filter, filter compensation signal distortion. Kind of equalizer, demodulator sampled sequence by the equalizer to eliminate inter-symbol interference (ISI) and enter the detector. This section describes the common equalization filter, such equalizer can be further divided. A classification is based on the structure of the filter can be divided into the linear system (transversal filter) with feed forward unit and both before the collapse unit and feedback unit of the nonlinear system (Decision Feedback Equalizer); can also be divided into preset style based on their adaptability and adaptive; can also be classified according to the resolution and update rate of the filter. Detection signal can be sampled value of the symbol boundary (that is,
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each symbol is only sampled once), this sampling known as the symbol interval sampling; can also be sampled many times each symbol, this sampling called sampling of part of the code interval.
Receiver / equalizer filter in the separation of the receiver filter Hr?f? and the equalizer He?f? instead of equation (3.77), the transfer function He?f? of the whole system is raised cosine function, denoted as HRC?f? , so
HRC?f??Ht?f?Hc?f?Hr?f?He?f? (3.2)
In the real system, can not be fully known channel frequency transfer function
Hc?f?and its impact response hc?t?, and thus designed not to crosstalk at any moment have no inter conveyor. Usually selected to match the transmit filter and receive filter, the following expression:
HRC?f??Ht?f?Hr?f? (3.3)
In this way,Ht?f? and the frequency transfer function Hr?f?are both the square root of the cosine function (square root raised cosine function). Used to compensate for channel distortion equalizer transfer function is the inverse of the channel transfer function:
He?f??11?e-j?c?f? (3.4) Hc(f)Hc?f?Sometimes deliberately chosen to inter-symbol interference in the frequency transfer function (such as Gaussian filter transfer function), the sampling point and its purpose is to improve the bandwidth utilization (using the raised cosine filter). The task of equalization filter is not only compensate for the channel, but also to compensate for the transmit filter and receive filter due to inter-symbol interference.
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