A complex gradient operator and its applica-tion in adaptive array theory

The problem of minimising a real scalar quantity (for example array output power, or mean square error) as a function of a complex vector (the set of weights) frequently arises in adaptive array theory. A complex gradient operator is defined in the paper for this purpose and its use justified. Three examples of its application to array theory problems are given.

[1]  Randy L. Haupt,et al.  Introduction to Adaptive Arrays , 1980 .

[2]  B. Widrow,et al.  The complex LMS algorithm , 1975, Proceedings of the IEEE.

[3]  J. E. Hudson.  Adaptive Array Principles , 1981 .

[4]  B. Widrow,et al.  Adaptive antenna systems , 1967 .

[5]  I. Herstein,et al.  Topics in algebra , 1964 .