EE578/EE978 Assignment 3
Blind and Fractionally Spaced Equalisation
February 13, 2020
Please submit electronic copies of your answers (scanned handwriting is acceptable) via MyPlace by Monday
9/3/2020, 12 noon. Your answers should contain appropriate plots of your results with any annotations
and brief discussions or justifications of your answers.
1. Blind Equalisation.
(a) For a QPSK transmission over a channel with transfer function C(z) = 1 + j 3
4z−1, implement a
CMA equaliser and demonstrate its correct working based on suitable criteria.
(b) A carrier frequency mismatch results in a residual modulation by Ωc = 2π · 10−3
, as shown below.
Demonstrate that the CMA algorithm still converges, and manages to extract a constant modulus
waveform.
r[n]s[n] c[n] ×ejΩcw y[n] n
(c) Assuming correct equalisation in Q1b), show that a carrier frequency offset can be detected from
E(y[n]y∗[n − 1])4, where y[n] is the output of the CMA equaliser.
(d) Over which range of values for Ωc will the approach designed in Q1c) work?
2. Fractionally Spaced Equalisation.
(a) Why can the channel C2(z) = 1 − 3z−1 +94z−2 −34z−3 +12z−4− not be directly inverted?
(b) Using the channel to transmit at twice the symbol rate (i.e. z
−1
represents a delay by half a
symbol period), derive a fractionally spaced equaliser for Q2a) that equalises C2(z) perfectly and
with a minimum equaliser length.
(c) Implement a fractionally spaced CMA algorithm, and discuss how the adapted response compares
to Q2b).
S. Weiss, February 13, 2020