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Precoding and Bandlimited Signals

Module by: Behnaam Aazhang

Summary: A description of various ways to deal with the problem of intersymbol interference which occurs in bandlimited channels.

Precoding

The data symbols are manipulated such that
y k kT= a k u0+ISI+νkT y k k T a k u 0 ISI ν k T (1)

Design of Bandlimited Modulation Signals

Recall that modulation signals are
X t =∑n=-∞∞ a n st-nT X t n a n s t n T (2)
We can design st s t such that
unT=largeifn=0zero or smallifn≠0 u n T large n 0 zero or small n 0 (3)
where ykT= a k u0+∑n=-∞∞ a n ukT-nT+νkT y k T a k u 0 n a n u k T n T ν k T (ISI is the sum term, and once again, n≠k n k .) Also, ynT=s¯g¯ h opt nT y n T s g h opt n T The signal st s t can be designed to have reduced ISI.

Design Equalizers at the Receiver

Linear equalizers or decision feedback equalizers reduce ISI in the statistic y t y t

Maximum Likelihood Sequence Detection

ykT=∑n=-∞∞ a n kT-nT+νkT y k T n a n k T n T ν k T (4)
By observing yT , y2T , … y T , y 2 T ,… the date symbols are observed frequently. Therefore, ISI can be viewed as diversity to increase performance.

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