  Interference alignment is a transmission technique for exploiting all
available degrees of freedom in the interference channel with an arbitrary
number of users. Most prior work on interference alignment, however, neglects
interference from other nodes in the network not participating in the alignment
operation. This paper proposes three generalizations of interference alignment
for the multiple-antenna interference channel with multiple users that account
for colored noise, which models uncoordinated interference. First, a minimum
interference-plus-noise leakage algorithm is presented, and shown to be
equivalent to previous subspace methods when noise is spatially white or
negligible. A joint minimum mean squared error design is then proposed that
jointly optimizes the transmit precoders and receive spatial filters, whereas
previous designs neglect the receive spatial filter. This algorithm is shown to
be a generalization of previous joint MMSE designs for other system
configurations such as the broadcast channel. Finally, a maximum
signal-to-interference-plus-noise ratio algorithm is developed that is proven
to converge, unlike previous maximum SINR algorithms. The latter two designs
are shown to have increased complexity due to non-orthogonal precoders, more
required iterations, or more channel state knowledge than the min INL or
subspace methods. The sum throughput performance of these algorithms is
simulated in the context of a network with uncoordinated co-channel interferers
not participating in the alignment protocol. It is found that a network with
cochannel interference can benefit from employing precoders designed to
consider that interference, but in some cases, ignoring the co-channel
interference is advantageous.
