Zero-forcing precoding for frequency selective MIMO channels with H INFINITY criterion and causality constraint

X iv :0 80 3. 04 28 v2 [ cs .I T ] 2 7 O ct 2 00 8 Zero-For ing Pre oding for Frequen y Sele tive MIMO Channels with H Criterion and Causality Constraint ⋆ Sander Wahls ∗ Holger Bo he Te hnis he Universität Berlin, Heinri h-Hertz-Lehrstuhl für Mobilkommunikation, Werner-von-Siemens-Bau (HFT6), Einsteinufer 25, 10587 Berlin, Germany Volker Pohl Te hnion Israel Institute of Te hnology, Department of Ele tri al Engineering, Haifa 32000, Israel Abstra t We onsider zero-for ing equalization of frequen y sele tive MIMO hannels by ausal and linear time-invariant pre oders in the presen e of intersymbol interferen e. Our motivation is twofold. First, we are on erned with the optimal performan e of ausal pre oders from a worst ase point of view. Therefore we onstru t an optimal ausal pre oder, whereas ontrary to other works our onstru tion is not limited to nite or rational impulse responses. Moreover we derive a novel numeri al approa h to omputation of the optimal perfoman e index a hievable by ausal preoders for given hannels. This quantity is important in the numeri al determination of optimal pre oders.