mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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96 LINEAR EQUALIZATION<br />
4.2 If we had r» to work with as well, what would be the partial zero-forcing<br />
linear equalization weight for r» so that ISI from So is canceled when detecting s 2 l<br />
4.3 Consider the Alice and Bob example (n = 1, r 2 = —7). Suppose the noise<br />
power is σ 2 = 1 instead.<br />
a) What would the MMSE LE weights be?<br />
b) What is the value of z 2 and s 2 with MMSE LE?<br />
4.4 Consider the Alice and Bob example (r\ — 1, r 2 = —7). Suppose the noise<br />
power is σ 2 = 1000 instead.<br />
a) What would the MMSE LE weights be?<br />
b) What is the value of z 2 and s 2 with MMSE LE?<br />
More details<br />
4.5 In the dispersive scenario with c = —10 and d — 9, suppose the max-SINR<br />
weights for detecting s 2 are scaled by -10.<br />
a) Calculate the new output SINR.<br />
b) Did the SINR get better, worse, or stay the same?<br />
c) Can we still detect s 2 by taking the sign of ζ 2 Ί<br />
4.6 A better approach to the partial ZF approach is to minimize ISI.<br />
a) If w 2 = —0.1, determine Wi to minimize ISI when detecting s 2 .<br />
b) What is the resulting SINR?<br />
c) Is the SINR bigger or smaller than the partial ZF SINR?<br />
d) Is the SINR bigger or smaller than the MMSE SINR?<br />
4.7 In the dispersive scenario, consider detecting si using r\ and r 2 , setting<br />
w 2 = 1/c, and choosing w\ to minimize ISI in z 2 .<br />
a) Find the general expression for w\.<br />
b) As the noise power goes to 0, what happens to w\l<br />
c) Show that if the noise power is zero, the SINR is the same as the MMSE<br />
solution SINR.<br />
4.8 In the dispersive scenario with c = —10 and d = 9, consider MMSE detection<br />
of s i using r\ and r 2 .<br />
a) Find the MMSE solution for wi and w 2 .<br />
b) For r\ = 1, r 2 — — 7, what is the value of the decision variable for βχ?<br />
c) What is the detected value for si?<br />
4.9 Using the model for the received values for the general dispersive scenario,<br />
show that the average of r\ is c 2 + d 2 + σ 2 .<br />
4.10 Consider the MIMO scenario in which c = 10, d = 7, e = 9, and / = 6.<br />
a) What are the MMSE weights for detecting s 2 l<br />
b) What is the output SINR?<br />
c) If ri = 9 and r 2 = 11, what is the detected value for s 2 ?
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