mohatta2015.pdf

186 PRACTICAL CONSIDERATIONS
a) Suppose channel estimates and a noise power estimate are used to determine
weights. Is this direct or indirect adaptation?
b) Suppose the LMS algorithm is used to adapt the weights. Is this direct or
indirect adaptation?
More details
8.6 Consider estimating three channel coefficients: c, d, and e such that r m =
cs m + ds m -i + es m -2- Suppose We have four known symbols, «n through s ; ¡, and
we plan on using Γ2 and r,¡ to estimate the channel coefficients.
a) Give the equations for c, d, and ê in terms of ri and r%.
b) What properties of the known symbols must be satisfied so that paths
don't interfere with one another in channel estimation.
c) Given So = +1 and s\ = —1, can these properties be met? If so, what
values for S2 and s.-¡ work?
8.7 Consider MMSE DFE and determining the weights for the forward filter.
a) Suppose channel estimates and a noise power estimate are used to form a
data correlation matrix, which is then used to determine weights. Is this
parametric or nonparametric?
b) Suppose data correlations are estimated directly from the received samples.
These data correlation estimates are used to determine weights. Is this
parametric or nonparametric?
8.8 Suppose QPSK symbols are being sent through a single-path channel with
coefficient c = 1.
a) Copy the constellation diagram from Fig. 1.7. In practice, one would
receive one of these four points plus noise.
b) Add the lines y = x and y = —x to the diagram. If we think of the
diagram as possible received values, these lines divide up the diagram into
four regions, determining which symbol we would detect if the received
value fell into that region. Notice that the constellation points are midway
between two lines.
c) Now, suppose there is an unknown phase error that rotates the signal 22.5
degrees counterclockwise. If there were no noise, would the receiver make
an error?
d) Now, suppose there is an unknown phase error that rotates the signal 50
degrees counter clockwise. If there were no noise, would the receiver make
an error?
e) Now, suppose there is an unknown phase error that rotates the signal 10
degrees counter clockwise. If 1 + j is transmitted and there is noise, the
receiver will sometimes make mistakes. Which mistaken value will the
receiver decide more often, 1 — j or — 1 + p.
8.9 Suppose QPSK symbols are being sent through a single-path channel with
coefficient c = 1. Also, suppose there is I/Q imbalance, so that the real part is
scaled by 0.8.