  The N+1 user, 1 x N single input multiple output (SIMO) Gaussian interference
channel where each transmitter has a single antenna and each receiver has N
antennas is studied. The symmetric capacity within O(1) is characterized for
the symmetric case where all direct links have the same signal-to-noise ratio
(SNR) and all undesired links have the same interference-to-noise ratio (INR).
The gap to the exact capacity is a constant which is independent of SNR and
INR. To get this result, we first generalize the deterministic interference
channel introduced by El Gamal and Costa to model interference channels with
multiple antennas. We derive the capacity region of this deterministic
interference channel. Based on the insights provided by the deterministic
channel, we characterize the generalized degrees of freedom (GDOF) of Gaussian
case, which directly leads to the O(1) capacity approximation. On the
achievability side, an interesting conclusion is that the generalized degrees
of freedom (GDOF) regime where treating interference as noise is found to be
optimal in the 2 user interference channel, does not appear in the N+1 user, 1
x N SIMO case. On the converse side, new multi-user outer bounds emerge out of
this work that do not follow directly from the 2 user case. In addition to the
GDOF region, the outer bounds identify a strong interference regime where the
capacity region is established.
