A multiple-input multiple-output (MIMO) version of the dirty paper channel isstudied, where the channel input and the dirt experience the same fadingprocess and the fading channel state is known at the receiver (CSIR). Thisrepresents settings where signal and interference sources are co-located, suchas in the broadcast channel. First, a variant of Costa's dirty paper coding(DPC) is presented, whose achievable rates are within a constant gap tocapacity for all signal and dirt powers. Additionally, a lattice coding anddecoding scheme is proposed, whose decision regions are independent of thechannel realizations. Under Rayleigh fading, the gap to capacity of the latticecoding scheme vanishes with the number of receive antennas, even at finiteSignal-to-Noise Ratio (SNR). Thus, although the capacity of the fading dirtypaper channel remains unknown, this work shows it is not far from its dirt-freecounterpart. The insights from the dirty paper channel directly lead totransmission strategies for the two-user MIMO broadcast channel (BC), where thetransmitter emits a superposition of desired and undesired (dirt) signals withrespect to each receiver. The performance of the lattice coding scheme isanalyzed under different fading dynamics for the two users, showing thathigh-dimensional lattices achieve rates close to capacity.
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