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# 5 ofdm

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### 5 ofdm

1. 1. 5 OFDM In the last chapter we introduced the multipath propagation and its inﬂuence on the transmission. In sec. 4.4 OFDM is mentioned as one possible solution for mitigating the inﬂuence of delay spread and to increase the robustness of the transmission. Transmitting digital signals with high data rates using single carrier results in a lot of diﬃculties because of the multipath propagation. Due to the short symbol time and the long channel response time for it, this results in very high requirements for the equaliser. Dividing the data rate in N subcarriers results in an N times longer symbol duration. In spite of this improvement there are still some inter-symbol-interferences due to the dif- ferent runtimes of the signals in the multipath environment. To reduce the inter-symbol- interference a guard interval is introduced. This guard interval provides some time for the symbols to raise and decay. The following paragraph explains some special features of OFDM compared to other multi carrier systems. One of the most advantages is the abdication of complex ﬁlter banks due to the use of digital signal processing. A characteristic of an OFDM system is the equidis- tant subchannel order. The distance between diﬀerent subchannels is chosen in a way that they do not disturb each other. To obtain this, the carriers of two adjacent subchannels are orthogonal. This results in the distance of two subchannels ∆f = 1 Ts . (5.1) Rectangular pulses are used for calculating the magnitude spectrum. In ﬁg. 5.1 the known form of the function si(x) = sin(x) x is shown. Fig. 5.2 shows the spectrum of an OFDM signal as a composition of frequency shifted subcarriers. If the frequency shift is exactly an integer multiple of 1/T (refering to 5.1), the interference of adjacent cariers is equal to zero. There are no inter-carrier-interferences in spite of an overlapping spectrum. 5.1 Overview about an OFDM system In this section we are going to shortly discuss the elements which can be found in an OFDM system. Some elements have been already discussed in previous chapters. In the following sections each of the new elements will be descriped in detail. Looking at our simulation chain so far, we notice that we have already discussed the OFDM system up to the encoder element. First new element we want to introduce is the interleaver. The interleaver is used to increase the performance gain by changing the bit order within the bitstream to avoid errors in adjacent bits caused by interferences on adja- cent subchannels. How an interleaver is working is explained in sec. 5.2. The next element 57
2. 2. 5 OFDM −5pi −4pi −3pi −2pi −1pi 0 pi 2pi 3pi 4pi 5pi −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 Figure 5.1: Sinc function −5pi −4pi −3pi −2pi −1pi 0 pi 2pi 3pi 4pi 5pi −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 1.2 Figure 5.2: OFDM spectrum as a composition of frequency shifted subcarriers. 58