  In this paper, we investigate the optimization of non-uniform linear antenna
arrays (NULAs) for millimeter wave (mmWave) line-of-sight (LoS) multiple-input
multiple-output (MIMO) channels. Our focus is on the maximization of the system
effective multiplexing gain (EMG), by optimizing the individual antenna
positions in the transmit/receive NULAs. Here the EMG is defined as the number
of signal streams that are practically supported by the channel at a finite
SNR. We first derive analytical expressions for the asymptotic channel
eigenvalues with arbitrarily deployed NULAs when, asymptotically, the
end-to-end distance is sufficiently large compared to the aperture sizes of the
transmit/receive NULAs. Based on the derived expressions, we prove that, the
asymptotically optimal NULA deployment that maximizes the achievable EMG should
follow the groupwise Fekete-point distribution. Specifically, the antennas
should be physically grouped into K separate uniform linear antenna arrays
(ULAs) with the minimum feasible antenna spacing within each ULA, where K is
the target EMG to be achieved; in addition, the centers of these K ULAs follow
the Fekete-point distribution. We numerically verify the asymptotic optimality
of such an NULA deployment and extend it to a groupwise projected arch type
(PAT) NULA deployment, which provides a more practical option for mmWave LoS
MIMO systems with realistic non-asymptotic configurations. Numerical examples
are provided to demonstrate a significant capacity gain of the optimized NULAs
over traditional ULAs.
