20092ee132A_1_ca4_09 - EE 132A Spring 2009 Prof John...

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EE 132A, Spring 2009 Communication Systems Prof. John Villasenor Handout # 18 TA: Pooya Monajemi, Yuxing Han Computer Assignment 4 Assigned: Wednesday, May 20, 2009 Due: Monday, June 1, 2009 This computer assignment addresses Orthogonal Frequency Division Multiplexing (OFDM). OFDM is a popular technique used in several current and emerging technologies such as IEEE 802.11a/g (WiFi), UWB, and LTE. We will explore OFDM generation and detection, its ability to reduce ISI, and its performance in noise. We will start by generating a binary PAM signal and sending it through a channel that introduces ISI. Then we will send the same information using OFDM with 4 subcarriers and an appropriate cyclic prefix, and observe how ISI is eliminated. Finally we will send information using OFDM through a noisy channel and compute bit error probabilities. What to turn in: Answers to questions and required plots. Source file for programs (.m files). Suggestions: Start working on this assignment early. Do not wait until the last moment. Make your code parametric. You will be required to design an OFDM modulator and demodulator, and then change the different parameters to observe different situations. It is easier to do this if you define your modules in terms of these parameters. Introduction to OFDM The basic principle of OFDM is to split a high-rate data stream into a number of lower rate streams that are transmitted simultaneously over a number of sub-carriers. Because the symbol duration increases for lower rate parallel sub-carriers, the relative amount of dispersion in time caused by multi-path delay spread is decreased. Inter Symbol Interference (ISI) is addressed by introducing a guard time at the beginning of every OFDM symbol. The frequency spacing between these sub-carriers is chosen to be equal to the inverse of the OFDM symbol interval. When no cyclic prefix is added, this causes the sub-carriers to be orthogonal over the symbol interval, and the spectrum of each of the sub-carrier signals to be zero at the peak frequency of all signals in the other sub-carrier frequencies, thus eliminating Inter Carrier Interference (ICI). The basic diagram of the OFDM system is shown in Figure 1.
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Figure 1: OFDM system In an OFDM system with N subcarriers, input (information) symbols are grouped in blocks of N information symbols each. Each one of these blocks of N symbols are transmitted using what we will call an OFDM symbol . If there are a total of M blocks transmitted, this corresponds to MN input symbols. For the m th block, the transmitted symbols are { x 0, m , x 1, m , , x N-1, m }, as shown in Figure 1. We wish to transmit a total (across all N subcarriers) of 1/ T s information symbols per second. Since every OFDM symbol can transmit the outcome of N information symbols, the duration of each OFDM symbol is T=NT s . This corresponds to the OFDM symbol interval. In principle we could make the subcarriers orthogonal by choosing a spacing of 1/ T Hz between them. However, since the first portion of the OFDM
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20092ee132A_1_ca4_09 - EE 132A Spring 2009 Prof John...

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