  Naturally complex-valued information or those presented in complex domain are
effectively processed by an augmented complex least-mean-square (ACLMS)
algorithm. In some applications, the ACLMS algorithm may be too
computationally- and memory-intensive to implement. In this paper, a new
algorithm, termed partial-update ACLMS (PU-ACLMS) algorithm is proposed, where
only a fraction of the coefficient set is selected to update at each iteration.
Doing so, two types of partial-update schemes are presented referred to as the
sequential and stochastic partial-updates, to reduce computational load and
power consumption in the corresponding adaptive filter. The computational cost
for full-update PU-ACLMS and its partial-update implementations are discussed.
Next, the steady-state mean and mean-square performance of PU-ACLMS for
non-circular complex signals are analyzed and closed-form expressions of the
steady-state excess mean-square error (EMSE) and mean-square deviation (MSD)
are given. Then, employing the weighted energy-conservation relation, the EMSE
and MSD learning curves are derived. The simulation results are verified and
compared with those of theoretical predictions through numerical examples.
