Beamforming for the underlay cognitive MISO interference channel via UL-DL duality

SINR duality is shown in a multi-input single-output (MISO) downlink (DL) interference channel (IFC) and its uplink (UL) single-input multi-output (SIMO) dual with linear transmit (Tx) beamformers (BF). While UL-DL duality under the sum power constraint is well-established between the broadcast channel (BC) for the SINR balancing (max min SINR) beamforming problem and its (easier to solve) UL multiple-access (MAC) dual channel, such duality does not at first seem relevant for the IFC. We show that SINR duality under the sum power constraint nevertheless holds in the MISO IFC leading to BF design through similar considerations as the BC-MAC case. We next impose further per-Tx power constraints meaningful for the IFC structure and show continued existence of SINR duality in the MISO IFC and the corresponding UL SIMO dual channel, but this time with an uncertain UL noise scaling. The beamformers, Tx powers and noise variances are found through an iterative algorithm. We extend the solution to a cognitive radio network where this MISO IFC is co-deployed in a underlay fashion with a primary network with interference power constraints on primary single antenna receivers.