An adaptive antenna array or a smart antenna is named a software anten
na because it can form a desired antenna pattern and adaptively contro
l it if an appropriate set of antenna weights is provided and updated
in software. It can be a typical tool for realizing a software radio.
An adaptive antenna array can be considered an adaptive filter in spac
e and time domains for radio communications, so the communication theo
ry can be generalized from a conventional time domain into both space
and time domains. This article introduces a spatial and temporal commu
nication theory based on an adaptive antenna array, such as spatial an
d temporal channel modeling, equalization, optimum detection for singl
e-user and multi-user CDMA, precoding in transmitter, and joint optimi
zation of both transmitter and receiver. Such spatial and temporal pro
cessing promises significant improvement of performance against multip
ath fading in mobile radio communications.