974 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
Constrained Bayesian Active Learning of Interference Channels in Cognitive Radio Networks
In this paper, a sequential probing method for interference constraint
learning is proposed to allow a centralized Cognitive Radio Network (CRN)
accessing the frequency band of a Primary User (PU) in an underlay cognitive
scenario with a designed PU protection specification. The main idea is that the
CRN probes the PU and subsequently eavesdrops the reverse PU link to acquire
the binary ACK/NACK packet. This feedback indicates whether the probing-induced
interference is harmful or not and can be used to learn the PU interference
constraint. The cognitive part of this sequential probing process is the
selection of the power levels of the Secondary Users (SUs) which aims to learn
the PU interference constraint with a minimum number of probing attempts while
setting a limit on the number of harmful probing-induced interference events or
equivalently of NACK packet observations over a time window. This constrained
design problem is studied within the Active Learning (AL) framework and an
optimal solution is derived and implemented with a sophisticated, accurate and
fast Bayesian Learning method, the Expectation Propagation (EP). The
performance of this solution is also demonstrated through numerical simulations
and compared with modified versions of AL techniques we developed in earlier
work.Comment: 14 pages, 6 figures, submitted to IEEE JSTSP Special Issue on Machine
Learning for Cognition in Radio Communications and Rada
Robust Monotonic Optimization Framework for Multicell MISO Systems
The performance of multiuser systems is both difficult to measure fairly and
to optimize. Most resource allocation problems are non-convex and NP-hard, even
under simplifying assumptions such as perfect channel knowledge, homogeneous
channel properties among users, and simple power constraints. We establish a
general optimization framework that systematically solves these problems to
global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles
general multicell downlink systems with single-antenna users, multiantenna
transmitters, arbitrary quadratic power constraints, and robustness to channel
uncertainty. A robust fairness-profile optimization (RFO) problem is solved at
each iteration, which is a quasi-convex problem and a novel generalization of
max-min fairness. The BRB algorithm is computationally costly, but it shows
better convergence than the previously proposed outer polyblock approximation
algorithm. Our framework is suitable for computing benchmarks in general
multicell systems with or without channel uncertainty. We illustrate this by
deriving and evaluating a zero-forcing solution to the general problem.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 9
figures, 2 table
Successive Convex Approximation Algorithms for Sparse Signal Estimation with Nonconvex Regularizations
In this paper, we propose a successive convex approximation framework for
sparse optimization where the nonsmooth regularization function in the
objective function is nonconvex and it can be written as the difference of two
convex functions. The proposed framework is based on a nontrivial combination
of the majorization-minimization framework and the successive convex
approximation framework proposed in literature for a convex regularization
function. The proposed framework has several attractive features, namely, i)
flexibility, as different choices of the approximate function lead to different
type of algorithms; ii) fast convergence, as the problem structure can be
better exploited by a proper choice of the approximate function and the
stepsize is calculated by the line search; iii) low complexity, as the
approximate function is convex and the line search scheme is carried out over a
differentiable function; iv) guaranteed convergence to a stationary point. We
demonstrate these features by two example applications in subspace learning,
namely, the network anomaly detection problem and the sparse subspace
clustering problem. Customizing the proposed framework by adopting the
best-response type approximation, we obtain soft-thresholding with exact line
search algorithms for which all elements of the unknown parameter are updated
in parallel according to closed-form expressions. The attractive features of
the proposed algorithms are illustrated numerically.Comment: submitted to IEEE Journal of Selected Topics in Signal Processing,
special issue in Robust Subspace Learnin
Optimality Properties, Distributed Strategies, and Measurement-Based Evaluation of Coordinated Multicell OFDMA Transmission
The throughput of multicell systems is inherently limited by interference and
the available communication resources. Coordinated resource allocation is the
key to efficient performance, but the demand on backhaul signaling and
computational resources grows rapidly with number of cells, terminals, and
subcarriers. To handle this, we propose a novel multicell framework with
dynamic cooperation clusters where each terminal is jointly served by a small
set of base stations. Each base station coordinates interference to neighboring
terminals only, thus limiting backhaul signalling and making the framework
scalable. This framework can describe anything from interference channels to
ideal joint multicell transmission.
The resource allocation (i.e., precoding and scheduling) is formulated as an
optimization problem (P1) with performance described by arbitrary monotonic
functions of the signal-to-interference-and-noise ratios (SINRs) and arbitrary
linear power constraints. Although (P1) is non-convex and difficult to solve
optimally, we are able to prove: 1) Optimality of single-stream beamforming; 2)
Conditions for full power usage; and 3) A precoding parametrization based on a
few parameters between zero and one. These optimality properties are used to
propose low-complexity strategies: both a centralized scheme and a distributed
version that only requires local channel knowledge and processing. We evaluate
the performance on measured multicell channels and observe that the proposed
strategies achieve close-to-optimal performance among centralized and
distributed solutions, respectively. In addition, we show that multicell
interference coordination can give substantial improvements in sum performance,
but that joint transmission is very sensitive to synchronization errors and
that some terminals can experience performance degradations.Comment: Published in IEEE Transactions on Signal Processing, 15 pages, 7
figures. This version corrects typos related to Eq. (4) and Eq. (28
Energy efficiency optimization in MIMO interference channels: A successive pseudoconvex approximation approach
In this paper, we consider the (global and sum) energy efficiency
optimization problem in downlink multi-input multi-output multi-cell systems,
where all users suffer from multi-user interference. This is a challenging
problem due to several reasons: 1) it is a nonconvex fractional programming
problem, 2) the transmission rate functions are characterized by
(complex-valued) transmit covariance matrices, and 3) the processing-related
power consumption may depend on the transmission rate. We tackle this problem
by the successive pseudoconvex approximation approach, and we argue that
pseudoconvex optimization plays a fundamental role in designing novel iterative
algorithms, not only because every locally optimal point of a pseudoconvex
optimization problem is also globally optimal, but also because a descent
direction is easily obtained from every optimal point of a pseudoconvex
optimization problem. The proposed algorithms have the following advantages: 1)
fast convergence as the structure of the original optimization problem is
preserved as much as possible in the approximate problem solved in each
iteration, 2) easy implementation as each approximate problem is suitable for
parallel computation and its solution has a closed-form expression, and 3)
guaranteed convergence to a stationary point or a Karush-Kuhn-Tucker point. The
advantages of the proposed algorithm are also illustrated numerically.Comment: submitted to IEEE Transactions on Signal Processin
Receive Combining vs. Multi-Stream Multiplexing in Downlink Systems with Multi-Antenna Users
In downlink multi-antenna systems with many users, the multiplexing gain is
strictly limited by the number of transmit antennas and the use of these
antennas. Assuming that the total number of receive antennas at the
multi-antenna users is much larger than , the maximal multiplexing gain can
be achieved with many different transmission/reception strategies. For example,
the excess number of receive antennas can be utilized to schedule users with
effective channels that are near-orthogonal, for multi-stream multiplexing to
users with well-conditioned channels, and/or to enable interference-aware
receive combining. In this paper, we try to answer the question if the data
streams should be divided among few users (many streams per user) or many users
(few streams per user, enabling receive combining). Analytic results are
derived to show how user selection, spatial correlation, heterogeneous user
conditions, and imperfect channel acquisition (quantization or estimation
errors) affect the performance when sending the maximal number of streams or
one stream per scheduled user---the two extremes in data stream allocation.
While contradicting observations on this topic have been reported in prior
works, we show that selecting many users and allocating one stream per user
(i.e., exploiting receive combining) is the best candidate under realistic
conditions. This is explained by the provably stronger resilience towards
spatial correlation and the larger benefit from multi-user diversity. This
fundamental result has positive implications for the design of downlink systems
as it reduces the hardware requirements at the user devices and simplifies the
throughput optimization.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 11
figures. The results can be reproduced using the following Matlab code:
https://github.com/emilbjornson/one-or-multiple-stream
Task-Based Information Compression for Multi-Agent Communication Problems with Channel Rate Constraints
A collaborative task is assigned to a multiagent system (MAS) in which agents
are allowed to communicate. The MAS runs over an underlying Markov decision
process and its task is to maximize the averaged sum of discounted one-stage
rewards. Although knowing the global state of the environment is necessary for
the optimal action selection of the MAS, agents are limited to individual
observations. The inter-agent communication can tackle the issue of local
observability, however, the limited rate of the inter-agent communication
prevents the agent from acquiring the precise global state information. To
overcome this challenge, agents need to communicate their observations in a
compact way such that the MAS compromises the minimum possible sum of rewards.
We show that this problem is equivalent to a form of rate-distortion problem
which we call the task-based information compression. We introduce a scheme for
task-based information compression titled State aggregation for information
compression (SAIC), for which a state aggregation algorithm is analytically
designed. The SAIC is shown to be capable of achieving near-optimal performance
in terms of the achieved sum of discounted rewards. The proposed algorithm is
applied to a rendezvous problem and its performance is compared with several
benchmarks. Numerical experiments confirm the superiority of the proposed
algorithm.Comment: 13 pages, 9 figure
Inexact Block Coordinate Descent Algorithms for Nonsmooth Nonconvex Optimization
In this paper, we propose an inexact block coordinate descent algorithm for
large-scale nonsmooth nonconvex optimization problems. At each iteration, a
particular block variable is selected and updated by inexactly solving the
original optimization problem with respect to that block variable. More
precisely, a local approximation of the original optimization problem is
solved. The proposed algorithm has several attractive features, namely, i) high
flexibility, as the approximation function only needs to be strictly convex and
it does not have to be a global upper bound of the original function; ii) fast
convergence, as the approximation function can be designed to exploit the
problem structure at hand and the stepsize is calculated by the line search;
iii) low complexity, as the approximation subproblems are much easier to solve
and the line search scheme is carried out over a properly constructed
differentiable function; iv) guaranteed convergence of a subsequence to a
stationary point, even when the objective function does not have a Lipschitz
continuous gradient. Interestingly, when the approximation subproblem is solved
by a descent algorithm, convergence of a subsequence to a stationary point is
still guaranteed even if the approximation subproblem is solved inexactly by
terminating the descent algorithm after a finite number of iterations. These
features make the proposed algorithm suitable for large-scale problems where
the dimension exceeds the memory and/or the processing capability of the
existing hardware. These features are also illustrated by several applications
in signal processing and machine learning, for instance, network anomaly
detection and phase retrieval
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