  Communication at millimeter wave frequencies will be one of the essential new
technologies in 5G. Acquiring an accurate channel estimate is the key to
facilitate advanced millimeter wave hybrid multiple-input multiple-output
(MIMO) precoding techniques. Millimeter wave MIMO channel estimation, however,
suffers from a considerably increased channel use overhead. This happens due to
the limited number of radio frequency (RF) chains that prevent the digital
baseband from directly accessing the signal at each antenna. To address this
issue, recent research has focused on adaptive closed-loop and two-way channel
estimation techniques. In this paper, unlike the prior approaches, we study a
non-adaptive, hence rather simple, open-loop millimeter wave MIMO channel
estimation technique. We present a simple random design of channel subspace
sampling signals and show that they obey the restricted isometry property (RIP)
with high probability. We then formulate the channel estimation as a low-rank
subspace decomposition problem and, based on the RIP, show that the proposed
framework reveals resilience to a low signal-to-noise ratio. It is revealed
that the required number of channel uses ensuring a bounded estimation error is
linearly proportional to the degrees of freedom of the channel, whereas it
converges to a constant value if the number of RF chains can grow
proportionally to the channel dimension while keeping the channel rank fixed.
In particular, we show that the tighter the RIP characterization the lower the
channel estimation error is. We also devise an iterative technique that
effectively finds a suboptimal but stationary solution to the formulated
problem. The proposed technique is shown to have improved channel estimation
accuracy with a low channel use overhead as compared to that of previous
closed-loop and two-way adaptation techniques.
