# lecture13 - ECE 5670 : Digital Communications Lecture 13:...

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Unformatted text preview: ECE 5670 : Digital Communications Lecture 13: Intersymbol Interference Management at all SNRs: Minimum Mean Square Error (MMSE) Filter 1 3/3/2011 and 3/8/2011 Instructor: Salman Avestimehr Introduction In the previous lectures, we have seen two linear processing techniques that deal with ISI: the matched filter (which worked well at low SNRs) and the zero forcing equalizer (which worked well at high SNRs). The matched filter harnessed the multiple delayed copies of each transmit symbol. The zero forcing equalizer worked to entirely null all the multiple delayed copies (and hence zero out the interference). In this lecture we study the optimal linear filter that balances both these effects: the need to harness the multiple delayed copies while still mitigating the effect of interference. As usual, our performance metric will be the SINR of the transmit symbol at the output of the filter. This filter, known as the minimum mean square error (MMSE) equalizer, in conjunction with the successive interference cancelation (SIC) technique, is routinely used in practical communication schemes over wireline channels (an example: the voiceband telephone line modem). We have seen that the matched filter ignores the interference and combines the received voltage points to collect the signal energy. This strategy works well at low SNRs. In particular, the SINR at the output of matched filter is of the form SINR MF = a SNR 1 + b SNR (1) where a and b are the appropriate constants (that are independent of SNR). The zero forcing equalizer works well in high SNR regime. It essentially ignores noise and removes ISI by solving an overspecified set of linear equations. The SINR at the output of ZFE is of the form SINR ZFE = c SNR (2) where c is the appropriate constant. Both these equalizers are simple linear processing that perform well in different SNR regimes. In this lecture, we study a linear processing strategy that combines the best of both the equalizers and strictly outperform them in both regimes. We will motivate it by studying an example. 1 Based on lecture notes of Professor Pramod Viswanath at UIUC. Getting Started To motivate the design of this filter, consider the simple 2-tap ISI channel: y [ m ] = h x [ m ] + h 1 x [ m 1] + n [ m ] , m 1 . (3) Suppose we communicate information sequentially, say one bit at a time: so x [ m ] is E for each m and independent over different time samples. We want to filter only the first two received voltages y [1] , y [2] to estimate the first transmit voltage x [1]: y [1] = h x [1] + n [1] (4) y [2] = h 1 x [1] + ( h x [2] + n [2]) . (5) The matched filter receiver would be y MF [1] = h y [1] + h 1 y [2] , (6) while the ZFE would be y ZFE [1] = y [1] . (7) We are interested in choosing...
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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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lecture13 - ECE 5670 : Digital Communications Lecture 13:...

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