# lecture15 - ECE 5670 : Digital Communications Lecture 15:...

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Unformatted text preview: ECE 5670 : Digital Communications Lecture 15: Transmitter-Centric ISI Harnessing: Orthogonal Frequency Division Modulation (OFDM)Part I 1 3/10/2011 Instructor: Salman Avestimehr Introduction In the previous lecture, we took a first order transmitter-centric approach to dealing with ISI: the focus was on eliminating the effects of ISI. In this lecture we take a more balanced view: harnessing the benefits of ISI instead of just treating it as interference, continuing our transmitter-centric approach. Our goal is to get the full benefit of the fact that multiple delayed copies of the transmit symbols appear at the receiver while still employing a receiver no more complicated than the one used over an AWGN channel. While this seems to be a tall order, we will see a remarkable scheme that achieves exactly this. In a sense, it is a natural culmination of the various ISI mitigation techniques we have seen in the course of the past several lectures. The scheme that converts the frequency selective ISI channel into a plain AWGN channel is known as orthogonal frequency division modulation (OFDM) and is the main focus of this lecture. An Ideal Situation Consider the frequency selective model that we have been working with as a good approxi- mation of the wireline channel: y [ m ] = L- 1 X =0 h x [ m- ] + w [ m ] , m 1 . (1) Since we know how to communicate reliably over an AWGN channel (cf. Lecture 7), it would be ideal (not to mention, easy) if the channel with ISI can somehow (by appropriate transmitter and reciever operations) be converted into an AWGN one: say, y [ m ] = hx [ m ] + w [ m ] , m 1 . (2) In such a case, we could simply and readily use the transmitter and receiver techniques developed already for the AWGN channel (available off-the-shelf, so to say). 1 Based on lecture notes of Professor Pramod Viswanath at UIUC. 1 While this is asking for a bit too much, we will see that we can get somewhat close: indeed, we will convert the ISI channel in Equation (1) into a collection of AWGN channels, each of different noise energy level: y [ N c k + n ] = h n x [ N c k + n ] + w [ N c k + n ] , k , n = 0 ...N c- 1 . (3) The idea is that the time index m is replaced by N c k + n . The inputs are voltages x . The additive noise w [ ] is white Gaussian (zero mean and variance 2 ). We observe that there are N c different AWGN channels, one for each n = 0 ,...,N c- 1. We can make two further observations: each of the N c AWGN channels has a different operating SNR: the n th channel has an SNR equal to h 2 n SNR where SNR is, as usual, the ratio of the transmit energy to the noise energy; each of the N c AWGN channels is available for use only a fraction 1 N c of the time....
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## This note was uploaded on 10/02/2011 for the course ECE 5670 taught by Professor Scaglione during the Spring '11 term at Cornell University (Engineering School).

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lecture15 - ECE 5670 : Digital Communications Lecture 15:...

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