  The one-dimensional (1-D) Golay complementary set (GCS) has many well-known
properties and has been widely employed in engineering. The concept of 1-D GCS
can be extended to the two-dimensional (2-D) Golay complementary array set
(GCAS) where the 2-D aperiodic autocorrelation of constituent arrays sum to
zero except for the 2-D zero shift. The 2-D GCAS includes the 2-D Golay
complementary array pair (GCAP) as a special case when the set size is 2. In
this paper, 2-D generalized Boolean functions are introduced and novel
constructions of 2-D GCAPs, 2-D GCASs, and 2-D Golay complementary array mates
based on generalized Boolean functions are proposed. Explicit expressions of
2-D Boolean functions for 2-D GCAPs and 2-D GCASs are given. Therefore, they
are all direct constructions without the aid of other existing 1-D or 2-D
sequences. Moreover, for the column sequences and row sequences of the
constructed 2-D GCAPs, their peak-to-average power ratio (PAPR) properties are
also investigated.
