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Unformatted text preview: ECE 5670 : Digital Communications Lecture 12: Intersymbol Interference Management: High SNR Regime 1 3/3/2011 Instructor: Salman Avestimehr Introduction We have seen that the key aspect of the wireline channel is the intersymbol interference (ISI), and our focus is to develop receiver techniques that will mitigate and potentially harness the effects of interference. In Lecture 10, we focused on the low SNR regime. Here the noise power dominates the total signal power and hence the interference power. Essentially, we saw that in this regime, interference is not the issue and treating interference as noise is indeed a good strategy. The matched filter, which focusses on collecting the signal energy and ignores the interference, performs well in this regime. The focus of this lecture is on high SNR regime. Now the total signal power, and hence the interference power, dominates the noise power. Hence, the main aspect of the receiver design is on how to handle interference. It makes no sense in this regime to naively ignore interference and treat it as noise. Matched filter will not perform well in this regime and we need to develop new techniques to deal with interference. In this lecture, we will again adopt the receiver centric approach and will focus on simple linear processing schemes that will handle interference and convert the ISI channel into an effective AWGN channel. We can then use our analysis and codes developed for AWGN channel. In particular, we will study two schemes, viz., zero forcing equalizer (ZFE) and successive interference cancellation (SIC), that perform well in high SNR regime. Both of these schemes pay attention to the fact that interference has a structure and given the knowledge of present symbol, interference can be predicted. We will begin with a simple calculation to understand why matched filter fails in High SNR regime. Performance of Matched Filter at High SNR The received voltage of the wireline channel is y [ m ] = L − 1 summationdisplay ℓ =0 h ℓ x [ m − ℓ ] + n [ m ] , m > . (1) 1 Based on lecture notes of Professor Pramod Viswanath at UIUC. Recall that the SINR at the output of the matched filter is SINR MF = parenleftBig ∑ L − 1 l =0 h 2 l parenrightBig SNR P L − 1 ℓ =0 P L − 1 k =0; k negationslash = ℓ h 2 ℓ h 2 k P L − 1 ℓ =0 h 2 ℓ SNR + 1 , (2) where SNR = E [( x [ m ]) 2 ] σ 2 . (3) Note that the SINR at the output of the matched filter depends on the operating SNR. Two different regimes are of keen interest: • Low SNR: For small values of SNR , the SINR is close to linear in SNR . In other words, a doubling of the operating SNR also doubles the SINR MF . Mathematically, this regime happens when the interference ∑ L − 1 l =0 ∑ L − 1 k =0; k negationslash = l h 2 l h 2 k ∑ L − 1 l =0 h 2 l SNR ≪ 1 . (4) In this regime, the interference is much smaller than the background noise and it makes fine sense to just ignore the interference. The channel is almost like an AWGNmakes fine sense to just ignore the interference....
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- Spring '11
- Additive white Gaussian noise, SNR, SIC