Several papers have been shown equalization in the reception side. However, equalization in transmission side that is partial response signaling (PRS) or precoding is also possible in a two-way interactive communication such as time or frequency division duplex (TDD of FDD). This paper proposes and investigates a system which includes a transmission equalization and reception equalization based on an array antenna. This system is the extension in spatial and temporal domains. The channel capacity can be improved in the super channel which includes the transmitter and receiver array antenna.

This paper describes a spatial and temporal multipath channel model which is useful in array antenna environments for mobile radio communications. From this model, a no distortion criterion, that is an extension of the Nyquist criterion, is derived for equalization in both spatial and temporal domains. An adaptive tapped-delay-line (TDL) array antenna is used as a tool for equalization in both spatial and temporal domains. Several criterion for such spatial and temporal equalization such as ZF (Zero Forcing) and MSE (Mean Square Error), are available to update the weights and tap coefficients. In this paper, we discuss the optimum weights based on the ZF criterion in both spatial and temporal domains. Since the ZF criterion satisfies the Nyquist criterion in case of noise free, this paper applies the ZF criterion for the spatial and temporal equalization as a simple case. The Z transform is applied to represent the spatial and temporal model of the multipath channel and to derive the optimal weights of the TDL array antenna. However, in some cases the optimal antenna weights cannot be decided uniquely. Therefore, the effect on the equalization errors due to a finite number of antenna elements and tap coefficients can be shown numerically by computer simulations.