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signal processing from power amplifier operation control point of view

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68 ZERO-FORCING DECISION FEEDBACK EQUALIZATION<br />

b) assuming the ZF DFE makes a decision error half of the time, at random.<br />

3.9 Consider the received sample model in (3.31). Also, suppose transmission<br />

starts with symbol s(0) (there are no symbols s(m) for negative m) and assume we<br />

do not know s(0).<br />

a) Suppose the receiver has access to r 0 , rj, and so on. Is a zero-forcing<br />

strategy possible? If not, how many initial symbols would need be known<br />

to make ZF possible?<br />

b) Suppose the receiver has access to r\, Γ2, and so on. Is a zero-forcing<br />

strategy possible? If not, how many initial symbols would need be known<br />

to make ZF possible?<br />

c) Suppose the receiver has access to r¿, r^+1 , and so on. Is a zero-forcing<br />

strategy possible? If not, how many initial symbols would need be known<br />

to make ZF possible?<br />

3.10 Consider the received sample model in (3.31). Also, suppose transmission<br />

starts with symbol s(0) (there are no symbols s(m) for negative m) and ends with<br />

symbol s(N s ). The receiver has access to r n through rjv · Assume we do not know<br />

e(0).<br />

a) Suppose the medium response consists of two paths. Which would give<br />

better ZF DFE performance (running the DFE forward in time), having<br />

the first path larger or the second path larger?<br />

b) Suppose you could run the ZF DFE either forwards in time or backwards<br />

in time. If the second path is larger, which direction would you use and<br />

why?

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