COMPLEX-VALUED ADAPTIVE SIGNAL PROCESSING - Adaptive Signal Processing: Next Generation Solutions - page 74

Figure 1.21 ISI as a function of the shape parameter c six GGD sources.
For all cases, we note the best performance by the CML algorithm, and the almost
identical performance of the CML-unitary and CMN updates that have equivalent
cost functions as discussed in Section 1.6.3. Other complex ICA approaches provide
considerably satisfactory performance at a lower cost, in particular, JADE for the
sub-Gaussian 4-QAM and BPSK sources, complex nonlinear decorrelations with
2 asinh( u ) þ u nonlinearity for BPSK sources, and C-FastICA and complex
Infomax that assume circularity for the circular GGD sources. The performance
advantage of density matching comes at a computational cost as expected. The ML
class of algorithms are computationally most costly when employed with density
matching followed by the CMN algorithm. For example, the computational cost
measured in terms of time for a single run of CML (and similarly for CML-unitary),
without any optimization for implementation speed, is approximately 15 times that of
KM, C-FastICA, and JADE, and three times that of CMN for six 4-QAM sources
for 5000 samples. For the GGD sources, it is approximately 12 times that of
KM, C-FastICA, JADE, CMN, and six times that of the ML / Infomax or nonlinear
decorrelation approaches with a fixed nonlinearity.
1.7 SUMMARY
In this chapter, we provide the necessary tools for the development and analysis of
algorithms in the complex domain and introduce their application to two important
signal processing problems—filtering and independent component analysis. Complex-
valued signal processing, we note, is not a simple extension of the real-valued case.