mohatta2015.pdf

PROBLEMS 67
b) What is the detected value of «i?
c) What is the value of z 2 with ZF DFE?
d) What is the detected value of s 2 ?
3.2 Suppose the received samples can be modeled as r\ = 2s\ + so + n\ and
r 2 = 2s 2 + «i + n 2 . Also, s ( , = +1, r\ — 3.1, and r 2 = —1.01. The noise power is
σ 2 = 0.1.
a) Using ZF DFE, what are the detected values for s\ and s 2 ?
b) Do you think the detected values are correct? Why?
c) Suppose the noise power is σ 2 = 100. Do you think the detected values
are correct?
3.3 Suppose the received samples can be modeled as T\ = 2s\ + s» + n\ and
r 2 — 2s 2 + si + n 2 . Also, σ 2 = 10, s () = +1, Γχ = 8, and r 2 = -20.
a) Using ZF DFE, what are the detected values for si and s 2 ?
b) Do you think the detected values are correct? Why?
More details
3.4 Consider the MIMO scenario in which c = 10, d = 7, e = 9 and / = 6.
a) What is the matrix A that triangularizes the channel while maintaining
the noise power?
b) What is the matrix C that is the new channel matrix?
c) If ri =9 and r 2 = 11, what is the detected value for s\ using triangularization?
d) Using ZF DFE, what is the detected value for s 2 ?
3.5 For the general dispersive scenario, determine the SINR lower bound when a
decision error is made.
3.6 For the general MIMO scenario, determine the SINR lower bound for s 2 when
a decision error is made on S\.
3.7 For the general MIMO scenario, suppose we want to detect s 2 first, instead
of s\.
a) If we first replace r\ with yi = n — pr 2 , what should g be set to make t/i
independent of s\l
b) What is the resulting noise u\ in terms of n\ and n 2 ?
c) If we then replace r 2 with j/ 2 = r 2 + hr\, what should h be set to so that
the resulting noise is uncorrelated with u\ ?
d) What is the resulting channel matrix C?
The math
3.8 For the general dispersive SC6n&riO [Vrn — £^m -r dSm — \ + n m ), determine the
input SNR such that MF and ZF DFE have the same performance (same output
SINR),
a) assuming the ZF DFE makes no decision errors.