On duality in the MISO interference channel

SINR duality is shown in a multi-input single-output (MISO) interference channel (IFC) and its dual SIMO with linear transmit (Tx) beamformers (BF). While uplink (UL) downlink (DL) duality for the SINR balancing (max min SINR) beamforming problem under the sum power constraint is well-established between the Broadcast channel (BC) 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 a different UL noise. The beamformers, Tx powers and noise variances are found through an iterative algorithm.