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More information about this seller Contact this seller 5. About this Item: Syngress. Light rubbing wear to cover, spine and page edges. Very minimal writing or notations in margins not affecting the text. Possible clean ex-library copy, with their stickers and or stamp s. Because the symbol duration increases for the lower rate parallel subcarriers, the relative amount of dispersion in time caused by multipath delay spread is decreased, as introduced in Chapter 2. This whole process of generating an OFDM signal and the reasoning behind it are described in Chapter 3. In OFDM system development, it is necessary to understand its performance characteristics, which are given qualitatively in .
This chapter presents the performance analysis of the OFDM system in great detail.
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After Section 4. Then, after introducing the robustness against frequency selective fading in Section 4. Sections 4.
The sensitivity to analog to Section 4. In a radio channel, generally, a transmitted signal is not only distorted by multipath fading but also corrupted. Equation 4. Defining n ni as the noise component in the DFT output, substituting 4. For the current form of an OFDM system, the signal is transmitted even in the guard interval, so its power is not used for detection. Figure 4. We will discuss subcarrier recovery methods and their attainable BER performance in detail in Chapters 5 and 6, so here we will show a BER lower bound when assuming a perfect subcarrier recovery. Therefore, by averaging 4.
This equation is valid as the lower bound regardless of the frequency selectivity and time selectivity of the channel. Substituting 4. Here, focusing our attention on a case where the receiver. This means that the power of intersubcarrier interference depends on the position of subcarrier that we pay attention to. Therefore, to calculate the BER in a strict sense, we need to average 4. Equations 4. Therefore, when setting f D to be zero, we can obtain the BER in a frequency selective slow time nonselective Rayleigh fading channel, whereas when setting L 2 to be one, we can obtain the BER in a frequency nonselective flat time selective fast Rayleigh fading channel.
This equation is equivalent to 4. On the other hand, the transmission performance becomes poor as the length of guard interval increases because the signal transmission in the guard interval introduces a power loss, whereas it becomes more sensitive to the frequency selectivity as the length of guard interval decreases because the shorter guard interval is less robust to the delay spread.
Here, we assume an exponentially decaying multipath delay profile with 20 paths and normalize the Doppler frequency with the total symbol transmission rate R whereas the RMS delay spread with the total symbol transmission period T. This means that the BER degradation is less than Table 4. The theoretical analysis and computer simulation results are in complete agreement, and there is little difference in the BER between the optimized OFDM system and the lower bound. Here, we will discuss the robustness of an OFDM system against frequency selective fading.
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Assume a time-invariant impulse response of a channel that has a support shorter than the guard interval in other words, the largest time delay is smaller than the length of the guard interval. It is also interesting to compare 4. These communications systems have already adopted OFDM as their physical layer standards, so it must be important to discuss the performance of OFDM systems in impulsive manmade noises.
An OFDM system replaces the use of a bank of bandpass filters by that of the DFT, so it could give us an impression that it is robust to impulsive noises, because it can split the spectrally widespread noise energy into many subbands. Indeed, the robustness of an OFDM system against impulsive noises has been long believed [15—18].
However, the effect of impulsive noise in SCM systems has been intensively investigated so far [19, 20], whereas its effect on OFDM systems has not yet been well studied . Heavy-tailed distribution functions decay slowly and their impulsive characteristics are more interesting than those of Gaussian with large variance and Rayleigh distributions, which have been commonly used in most analysis papers.
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The received signal is then applied to the matched filter root-Nyquist filter to recover the desired data symbols. From the figure, it can be seen that the effect of GSN depends on where the impulses are present, namely, t m. We heuristically assume that the impulses that occur outside the interval Wo do not introduce bit errors, so we can only be concerned with the impulses that occur within the interval Wo.
For example, around In addition, we assume that t m is uniformly distributed over Wo . Note that the normalization can avoid dependency on the symbol duration in the obtained results. Now, we define p j and P b j as the probability that exactly j impulses occur in the observation interval Wo and the conditional bit error probability given that j impulses occur in the observation interval Wo. The BER is then written as. Without loss of generality, we can drop the subscript i, then the inphase component of the n th subcarrier is written as ts.
The analysis from now is similar to that of an SCM system, so we will be brief. We normalize y n in 4. The BER can be written as 4.
The numerical computation of P b j with the above direct integration is time consuming and its result converges slowly; furthermore, it would be. However, fortunately, when j becomes larger, the p. With the Gaussian approximation, 4.
As shown, the direct evaluation of 4. The discussion here is brief; one can find more details on this method in . Taking into consideration all the components in 4.
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We can evaluate this integration by the numerical quadrature passing straightly through the positive real-valued saddle-point s0 also see how to find s 0 in . Even though this path is not an optimum one, namely, not an exactly steepest descent path, it still gives a very fast convergence. There appears only one integration in 4. On the other hand, this method has one drawback, that is, g s must be known in a closed form. However, to understand the robustness of an OFDM system against impulsive noises, it is enough to show two examples for impulsive noises; a lognormal distribution.
We can apply the saddle-point method for the Laplacian example. In Figures 4. The main difference in the effect of impulsive noise on the detection process is that impulsive noise interferes with only a few symbols nearby in the SCM system, whereas the energy of Table 4. So, as a result, the BER can be improved as the number of subcarriers increases. The performance in Figure 4.
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This is because the lognormal distribution has a little longer tail than the Laplace distribution. Our results obtained in this section gives system designers some considerations to choose the appropriate number of subcarriers in an OFDM system so as to obtain the highest robustness against the man-made noise encountered. This sensitivity to frequency offset is often pointed out as a major OFDM disadvantage. The theoretical analysis agrees well with the computer simulation result.