1,344 research outputs found
Hybrid Beamforming via the Kronecker Decomposition for the Millimeter-Wave Massive MIMO Systems
Despite its promising performance gain, the realization of mmWave massive
MIMO still faces several practical challenges. In particular, implementing
massive MIMO in the digital domain requires hundreds of RF chains matching the
number of antennas. Furthermore, designing these components to operate at the
mmWave frequencies is challenging and costly. These motivated the recent
development of hybrid-beamforming where MIMO processing is divided for separate
implementation in the analog and digital domains, called the analog and digital
beamforming, respectively. Analog beamforming using a phase array introduces
uni-modulus constraints on the beamforming coefficients, rendering the
conventional MIMO techniques unsuitable and call for new designs. In this
paper, we present a systematic design framework for hybrid beamforming for
multi-cell multiuser massive MIMO systems over mmWave channels characterized by
sparse propagation paths. The framework relies on the decomposition of analog
beamforming vectors and path observation vectors into Kronecker products of
factors being uni-modulus vectors. Exploiting properties of Kronecker mixed
products, different factors of the analog beamformer are designed for either
nulling interference paths or coherently combining data paths. Furthermore, a
channel estimation scheme is designed for enabling the proposed hybrid
beamforming. The scheme estimates the AoA of data and interference paths by
analog beam scanning and data-path gains by analog beam steering. The
performance of the channel estimation scheme is analyzed. In particular, the
AoA spectrum resulting from beam scanning, which displays the magnitude
distribution of paths over the AoA range, is derived in closed-form. It is
shown that the inter-cell interference level diminishes inversely with the
array size, the square root of pilot sequence length and the spatial separation
between paths.Comment: Submitted to IEEE JSAC Special Issue on Millimeter Wave
Communications for Future Mobile Networks, minor revisio
Secure Transmission in Multi-Cell Massive MIMO Systems
In this paper, we consider physical layer security provisioning in multi-cell
massive multiple-input multiple-output (MIMO) systems. Specifically, we
consider secure downlink transmission in a multi-cell massive MIMO system with
matched-filter precoding and artificial noise (AN) generation at the base
station (BS) in the presence of a passive multi-antenna eavesdropper. We
investigate the resulting achievable ergodic secrecy rate and the secrecy
outage probability for the cases of perfect training and pilot contamination.
Thereby, we consider two different AN shaping matrices, namely, the
conventional AN shaping matrix, where the AN is transmitted in the null space
of the matrix formed by all user channels, and a random AN shaping matrix,
which avoids the complexity associated with finding the null space of a large
matrix. Our analytical and numerical results reveal that in multi-cell massive
MIMO systems employing matched-filter precoding (1) AN generation is required
to achieve a positive ergodic secrecy rate if the user and the eavesdropper
experience the same path-loss, (2) even with AN generation secure transmission
may not be possible if the number of eavesdropper antennas is too large and not
enough power is allocated to channel estimation, (3) for a given fraction of
power allocated to AN and a given number of users, in case of pilot
contamination, the ergodic secrecy rate is not a monotonically increasing
function of the number of BS antennas, and (4) random AN shaping matrices
provide a favourable performance/complexity tradeoff and are an attractive
alternative to conventional AN shaping matrices
Massive MIMO has Unlimited Capacity
The capacity of cellular networks can be improved by the unprecedented array
gain and spatial multiplexing offered by Massive MIMO. Since its inception, the
coherent interference caused by pilot contamination has been believed to create
a finite capacity limit, as the number of antennas goes to infinity. In this
paper, we prove that this is incorrect and an artifact from using simplistic
channel models and suboptimal precoding/combining schemes. We show that with
multicell MMSE precoding/combining and a tiny amount of spatial channel
correlation or large-scale fading variations over the array, the capacity
increases without bound as the number of antennas increases, even under pilot
contamination. More precisely, the result holds when the channel covariance
matrices of the contaminating users are asymptotically linearly independent,
which is generally the case. If also the diagonals of the covariance matrices
are linearly independent, it is sufficient to know these diagonals (and not the
full covariance matrices) to achieve an unlimited asymptotic capacity.Comment: To appear in IEEE Transactions on Wireless Communications, 17 pages,
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