UCSB
Spring 2011
ECE146B:
CommunicationsII
Lab 3: Introduction to Channel Equalization
Assigned:
April 22
Due:
May 13 (at the beginning of the lab session)
Reading:
Chapter 4 (linear modulation) and Chapter 6 (Section 6.1 on Gaussian random variables
and
Q
function). We also state and use probability of error expressions from Chapter 6, but reading
about how these are derived is not required at this point.
LabObjectives:
To understand the need for equalization in communication systems, and to implement
linear MMSE equalizers adaptively.
Laboratory Assignment
0) Use your own code from Lab 1 or Lab 2 as a starting point. If you had difficulty in completing these
labs, ask the instructor or TA for a template. As before, the transmit, channel, and receive filters are
implemented at rate 4
/T
. For simplicity, we consider BPSK signaling throughout this lab, and consider
only realvalued signals. Generate
nsymbols
=
ntraining
+
npayload
(numbers to be specified later)
±
1 BPSK symbols as in Lab 2, and pass them through the transmit, channel, and receive filters to get
noiseless received samples at rate 4
/T
.
1) Let us start with a trivial channel filter as before. Set
nsymbols
= 200. The number of rate 4
/T
samples at the output of the receive filter is therefore 800, plus tails at either end because the length
of the effective pulse modulating each symbol extends over multiple symbol intervals. Take, say, 400
samples from somewhere in the middle of these samples, avoiding the tails. Divide these into segments
of length equal to 2 symbol intervals, or 8 samples (you can do this by reshaping the column vector of
400 samples into an 8
×
50 matrix). Plot these overlapped intervals against time, expressed in units of
the symbol interval (i.e., the x axis goes from 0 to 2, since you are plotting segments of the received
waveform spanning two symbol intervals). You should get something like Figure
??
, which is called an
eye diagram
because of its shape.
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 Spring '11
 UpamanyuMadhow
 Probability, Minimum mean square error, Equalization

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