~ This paper derives a generalized matched Alter in spatial a n d temporal domains using a n adaptive array antenna. T h e matched filter provides t h e optimal transfer function so as t o maximize SINR(Signa1 t o Interference-plus-Noise Ratio) in t h e array output. Moreover, if t h e generalized matched Alter is followed b y maximum likelihood sequence estimator in order t o utiliie memory in t h e channel, a generalized optimal receiver based on array antenna can be realized.
I. SPATIAL AND TEMPORAL CHANNEL MODELLet us consider a tapped delay line (TDL) array antenna of which each element antenna has TDL with several weight coefficients[l]. A TDL array antenna can spatially and temporally sample signals. Let the desired received signal and its spatial and temporal spectrum be z d ( t , a ) and Xd(wr,w,), respectively. wI = 2nf1 and wa = 2nfs are temporal frequency and spatial one, respectively. Let the I-th delayed or interfering signal with the le-th arrival angle be s , ,~. t ( t , s)(l = 1,2,. . . ,L-1 for different arrival angle, k = 1,2,. . . , K -1 for the same arrival angle) and its spatial and temporal spectrum be X,,I,L(WI,W.). The received signal is represented by t -1 I(-1 I=1 k = 1 where x,(t, s) is white Gaussian noise at antenna input. When the element antenna receives a plain signal wave propagated at location a and at instant t, the output of array antenna is denoted by y(t, s) y(t,.) = Jp, Jp, X ( w l , w a ) W ( W I r w . ) e J~~~e J~.~ df1 df. (2) W(WI,W,) is the transfer function of the array antenna.
SPATIAL AND TEMPORAL MATCHED FILTERWhen the interfering signal's power is relatively very much smaller than the noise power, SINR is rewritten byThe optimal transfer function can be derived so that spatial and temporal filter can maximize SINR, as WOpr(wt,w.) = Xd(wr,w.).e-lw"oe-JL.. O (4) and the impulse response of the optimal filter isThis denotes a generalized matched filter in spatial and temporal domains and includes a conventional matched filter without consideration of their spatial characteristics.When the interfering signal's power is not negligible, the optimal filter is derived as follows. Let the sum of interfering signal z , ( t , s ) and noise zn(t,s) be the undired signal zy(t,a), which has the power spectrum Sc(wi,w.) = E[lX.(wrw.)lz].
