ECE 442 Communication System Design Lecture 3. OFDM

1. ECE 442 Communication System DesignLecture 3. OFDM Husheng Li Dept. of EECS The University of Tennessee

2. Peak-to-Average Power Ratio • Peak-to-average power ratio (PAR) is an important attribute of a communication system: • A low PAR allows the transmit power amplifier to operate efficiently. • A high PAR forces the transmit power amplifier to have a large backoff in order to ensure linear amplification of the signal. • PAR is defined as

3. Typical Power Amplifier Response

4. Distribution and Max of PAR • When N (the number of subcarriers) is large, the PAR satisfies • The maximum PAR for N subcarriers is N. • There are many approaches to reduce PAR, such as signal clipping, peak cancellation and special coding techniques.

5. Frequency and Timing Offset • The signal of OFDM is orthogonal when the subcarrier frequency separation is 1/T (T is the duration of a symbol). But what if it is not exactly 1/T?

6. Inter Carrier Inference (ICI) • The total ICI power on subcarrier i is given by where δ/T is the frequency deviation. • Properties: • The ICI increases with T • ICI increases (quadratically) with δ • The ICI is not explicitly affected by N.

7. Case Study in IEEE 802.11a • IEEE 802.11a is a wireless LAN standard, which occupies 300MHz n the 5GHz unlicensed band. • In 802.11a, N=64. The prefix occupies 16 samples. • There are three coding rates (1/2, 2/3, 3/4) and four modulations (BPSK, QPSK, 16-QAM and 64-QAM). • The 300MHz is divided into 15 channels, each occupying 20MHz.

8. Why Want Hopping in OFDM? • Hopping means the same user transmitting over different subcarriers in different times. • In the uplink multi-cell systems, the transmission of a user may experience the inference from other users in neighbors cells. • If hopping is used, the interference will be averaged, thus achieving interference diversity. • In the downlink, the interference diversity comes from the different powers for different users.

9. Hopping Pattern • Virtual channel: each virtual channel contains N subcarriers and N OFDM symbols. It can be assigned to one user time frequency

10. Latin Square • Each base station has its own hopping pattern which can be represented by a Latin square. • The virtual channels in the previous slide corresponds to the following Latin square: A virtual channel subcarrier OFDM symbols

11. Orthogonal Latin Squares • For neighboring base stations, the virtual channels should have minimal overlaps. • If two Latin squares have exactly one collisions for every pair of virtual channels, we call them orthogonal. • When N is prime, for a =1,…,N-1, we can define an N by N matrix R(a) with

12. Flash-OFDM

13. Homework • Problem1. Write down the justification of the cyclic prefix in OFDM systems. • Problem 2. Find the data rate of an 802.11a system assuming QPSK modulation and rate ¾ coding. • Problem 3. Find the PAR of a raised cosine pulse with β=0., 0.5, and 1. Which pulse shape has the lowest PAR?