307 research outputs found
Optimal Multiuser Transmit Beamforming: A Difficult Problem with a Simple Solution Structure
Transmit beamforming is a versatile technique for signal transmission from an
array of antennas to one or multiple users [1]. In wireless communications,
the goal is to increase the signal power at the intended user and reduce
interference to non-intended users. A high signal power is achieved by
transmitting the same data signal from all antennas, but with different
amplitudes and phases, such that the signal components add coherently at the
user. Low interference is accomplished by making the signal components add
destructively at non-intended users. This corresponds mathematically to
designing beamforming vectors (that describe the amplitudes and phases) to have
large inner products with the vectors describing the intended channels and
small inner products with non-intended user channels.
While it is fairly easy to design a beamforming vector that maximizes the
signal power at the intended user, it is difficult to strike a perfect balance
between maximizing the signal power and minimizing the interference leakage. In
fact, the optimization of multiuser transmit beamforming is generally a
nondeterministic polynomial-time (NP) hard problem [2]. Nevertheless, this
lecture shows that the optimal transmit beamforming has a simple structure with
very intuitive properties and interpretations. This structure provides a
theoretical foundation for practical low-complexity beamforming schemes.
(See this lecture note for the complete abstract/introduction)Comment: Accepted for publication as lecture note in IEEE Signal Processing
Magazine, 11 pages, 3 figures. The results can be reproduced using the
following Matlab code: https://github.com/emilbjornson/optimal-beamformin
Spectral and Energy Efficiency of Superimposed Pilots in Uplink Massive MIMO
Next generation wireless networks aim at providing substantial improvements
in spectral efficiency (SE) and energy efficiency (EE). Massive MIMO has been
proved to be a viable technology to achieve these goals by spatially
multiplexing several users using many base station (BS) antennas. A potential
limitation of Massive MIMO in multicell systems is pilot contamination, which
arises in the channel estimation process from the interference caused by
reusing pilots in neighboring cells. A standard method to reduce pilot
contamination, known as regular pilot (RP), is to adjust the length of pilot
sequences while transmitting data and pilot symbols disjointly. An alternative
method, called superimposed pilot (SP), sends a superposition of pilot and data
symbols. This allows to use longer pilots which, in turn, reduces pilot
contamination. We consider the uplink of a multicell Massive MIMO network using
maximum ratio combining detection and compare RP and SP in terms of SE and EE.
To this end, we derive rigorous closed-form achievable rates with SP under a
practical random BS deployment. We prove that the reduction of pilot
contamination with SP is outweighed by the additional coherent and non-coherent
interference. Numerical results show that when both methods are optimized, RP
achieves comparable SE and EE to SP in practical scenarios.Comment: 32 pages, 12 figures, 3 tables. Submitted in March 2017 to IEEE
Transactions on Wireless Communication
Energy-Efficient Future Wireless Networks: A Marriage between Massive MIMO and Small Cells
How would a cellular network designed for high energy efficiency look like?
To answer this fundamental question, we model cellular networks using
stochastic geometry and optimize the energy efficiency with respect to the
density of base stations, the number of antennas and users per cell, the
transmit power levels, and the pilot reuse. The highest efficiency is neither
achieved by a pure small-cell approach, nor by a pure massive MIMO solution.
Interestingly, it is the combination of these approaches that provides the
highest energy efficiency; small cells contributes by reducing the propagation
losses while massive MIMO enables multiplexing of users with controlled
interference.Comment: Published at IEEE Workshop on Signal Processing Advances in Wireless
Communications (SPAWC 2015), 5 pages, 5 figure
Pilot Clustering in Asymmetric Massive MIMO Networks
We consider the uplink of a cellular massive MIMO network. Since the spectral
efficiency of these networks is limited by pilot contamination, the pilot
allocation across cells is of paramount importance. However, finding efficient
pilot reuse patterns is non-trivial especially in practical asymmetric base
station deployments. In this paper, we approach this problem using coalitional
game theory. Each cell has its own unique pilots and can form coalitions with
other cells to gain access to more pilots. We develop a low-complexity
distributed algorithm and prove convergence to an individually stable coalition
structure. Simulations reveal fast algorithmic convergence and substantial
performance gains over one-cell coalitions and full pilot reuse.Comment: Published in Proc. of IEEE International Workshop on Signal
Processing Advances in Wireless Communications (SPAWC '15), 5 pages, 1
tables, 5 figure
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,
7 figure
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