Uplink-Downlink Duality for Integer-Forcing

摘要

Consider a Gaussian multiple-input multiple-output (MIMO) multiple-accesschannel (MAC) with channel matrix $\mathbf{H}$ and a Gaussian MIMO broadcastchannel (BC) with channel matrix $\mathbf{H}^{\mathsf{T}}$. For the MIMO MAC,the integer-forcing architecture consists of first decoding integer-linearcombinations of the transmitted codewords, which are then solved for theoriginal messages. For the MIMO BC, the integer-forcing architecture consistsof pre-inverting the integer-linear combinations at the transmitter so thateach receiver can obtain its desired codeword by decoding an integer-linearcombination. In both cases, integer-forcing offers higher achievable rates thanzero-forcing while maintaining a similar implementation complexity. This paperestablishes an uplink-downlink duality relationship for integer-forcing, i.e.,any sum rate that is achievable via integer-forcing on the MIMO MAC can beachieved via integer-forcing on the MIMO BC with the same sum power and viceversa. Using this duality relationship, it is shown that integer-forcing canoperate within a constant gap of the MIMO BC sum capacity. Finally, the paperproposes a duality-based iterative algorithm for the non-convex problem ofselecting optimal beamforming and equalization vectors, and establishes that itconverges to a local optimum.