Abstract
Consider a Gaussian multiple-input multiple-output (MIMO) multiple-access channel (MAC) with channel matrix $\mathbf{H}$ and a Gaussian MIMO broadcast channel (BC) with channel matrix $\mathbf{H}^{\mathsf{T}}$. For the MIMO MAC, the integer-forcing architecture consists of first decoding integer-linear combinations of the transmitted codewords, which are then solved for the original messages. For the MIMO BC, the integer-forcing architecture consists of pre-inverting the integer-linear combinations at the transmitter so that each receiver can obtain its desired codeword by decoding an integer-linear combination. In both cases, integer-forcing offers higher achievable rates than zero-forcing while maintaining a similar implementation complexity. This paper establishes an uplink-downlink duality relationship for integer-forcing, i.e., any sum rate that is achievable via integer-forcing on the MIMO MAC can be achieved via integer-forcing on the MIMO BC with the same sum power and vice versa. Using this duality relationship, it is shown that integer-forcing can operate within a constant gap of the MIMO BC sum capacity. Finally, the paper proposes a duality-based iterative algorithm for the non-convex problem of selecting optimal beamforming and equalization vectors, and establishes that it converges to a local optimum.
Highlights
The capacity region of the Gaussian multiple-input multiple-output (MIMO) multiple-access channel (MAC) is wellknown [1, Sec. 10.1] and can be attained via joint maximum likelihood (ML) decoding
We demonstrate that integer-forcing can operate within a constant gap of the MIMO broadcast channel (BC) capacity using only “digital” dirty-paper coding, again assuming channel state information (CSI) is available at the transmitter
The “Capacity” curves correspond to the MIMO MAC sum capacity from (1) or to the MIMO BC sum capacity (2)
Summary
The capacity region of the Gaussian MIMO MAC is wellknown [1, Sec. 10.1] and can be attained via joint maximum likelihood (ML) decoding. Even with optimal minimum mean-squared error (MMSE) estimation, linear receivers fall short of the MIMO MAC sum capacity. This gap can be closed via successive interference cancellation (SIC), provided that the transmitters operate at one of the corner points of the capacity region. To motivate the first application, prior work [19], [20] established that integer-forcing can operate within a constant gap of the MIMO MAC sum capacity. We demonstrate that integer-forcing can operate within a constant gap of the MIMO BC capacity using only “digital” dirty-paper coding, again assuming CSI is available at the transmitter. Recent follow-up work has used a variation of our algorithm to identify good integer-forcing interference alignment solutions [22]
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