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Unformatted text preview: ECE 5670 : Digital Communications Lecture 14: Transmitter-Centric ISI Management: Precoding 1 3/8/2011 Instructor: Salman Avestimehr Introduction The ISI channel with L taps, y [ m ] = L- 1 X ‘ =0 h ‘ x [ m- ‘ ] + w [ m ] (1) can alternatively be represented as y [ m ] = h x [ m ] + I [ m ] + w [ m ] , (2) where I [ m ] = L- 1 X ‘ =1 h ‘ x [ m- ‘ ] (3) is the ISI. So far, we have looked at how the receiver can work to overcome the impact of ISI; all this while, the transmitter was continuing with sequential communication. In this lecture, we will take a different line of attack towards mitigating ISI: we do this by enlisting the transmitter as well in our efforts. The key point is that the ISI caused at time m , denoted by I [ m ], is known noncausally at the transmitter: • the channel tap coefficients h 1 ,...,h L- 1 are constant and known to the transmitter ahead of time; • the previously transmitted symbols x [ m- 1] ,...,x [ m- L +1] are surely known to the transmitter. Thus, the transmitter is in a position to adapt its present transmitted symbol x [ m ] as a function of what ISI is being caused. Such an adaption is known in the literature as precoding and in this lecture we will investigate the most basic form of precoding. A Simple Precoding Strategy Since the transmitter knows what the ISI is going to be, the simplest idea is to just cancel it off: if we wanted to send a voltage d [ m ] on an AWGN channel (with no ISI) we could transmit x [ m ] = d [ m ]- I [ m ] h . (4) 1 Based on lecture notes of Professor Pramod Viswanath at UIUC. This way the received voltage is simply y [ m ] = h d [ m ] + w [ m ] , (5) a regular AWGN channel with no-ISI! This is an easy way to get rid of ISI, particularly when compared to the travails of the receiver-centric schemes we have seen in the last couple of lectures. But there is a catch, and that is we need more energy at the transmitter to cancel ISI than that present in d [ m ]....
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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.
- Spring '11