mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
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 ?