2,226 research outputs found
Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms
This paper considers three problems in sparse filter design, the first involving a weighted least-squares constraint on the frequency response, the second a constraint on mean squared error in estimation, and the third a constraint on signal-to-noise ratio in detection. The three problems are unified under a single framework based on sparsity maximization under a quadratic performance constraint. Efficient and exact solutions are developed for specific cases in which the matrix in the quadratic constraint is diagonal, block-diagonal, banded, or has low condition number. For the more difficult general case, a low-complexity algorithm based on backward greedy selection is described with emphasis on its efficient implementation. Examples in wireless channel equalization and minimum-variance distortionless-response beamforming show that the backward selection algorithm yields optimally sparse designs in many instances while also highlighting the benefits of sparse design.Texas Instruments Leadership University Consortium Progra
Sparse Array DFT Beamformers for Wideband Sources
Sparse arrays are popular for performance optimization while keeping the
hardware and computational costs down. In this paper, we consider sparse arrays
design method for wideband source operating in a wideband jamming environment.
Maximizing the signal-to-interference plus noise ratio (MaxSINR) is adopted as
an optimization objective for wideband beamforming. Sparse array design problem
is formulated in the DFT domain to process the source as parallel narrowband
sources. The problem is formulated as quadratically constraint quadratic
program (QCQP) alongside the weighted mixed -norm squared
penalization of the beamformer weight vector. The semidefinite relaxation (SDR)
of QCQP promotes sparse solutions by iteratively re-weighting beamformer based
on previous iteration. It is shown that the DFT approach reduces the
computational cost considerably as compared to the delay line approach, while
efficiently utilizing the degrees of freedom to harness the maximum output SINR
offered by the given array aperture
Unveiling The Tree: A Convex Framework for Sparse Problems
This paper presents a general framework for generating greedy algorithms for
solving convex constraint satisfaction problems for sparse solutions by mapping
the satisfaction problem into one of graph traversal on a rooted tree of
unknown topology. For every pre-walk of the tree an initial set of generally
dense feasible solutions is processed in such a way that the sparsity of each
solution increases with each generation unveiled. The specific computation
performed at any particular child node is shown to correspond to an embedding
of a polytope into the polytope received from that nodes parent. Several issues
related to pre-walk order selection, computational complexity and tractability,
and the use of heuristic and/or side information is discussed. An example of a
single-path, depth-first algorithm on a tree with randomized vertex reduction
and a run-time path selection algorithm is presented in the context of sparse
lowpass filter design
Multichannel Speech Separation and Enhancement Using the Convolutive Transfer Function
This paper addresses the problem of speech separation and enhancement from
multichannel convolutive and noisy mixtures, \emph{assuming known mixing
filters}. We propose to perform the speech separation and enhancement task in
the short-time Fourier transform domain, using the convolutive transfer
function (CTF) approximation. Compared to time-domain filters, CTF has much
less taps, consequently it has less near-common zeros among channels and less
computational complexity. The work proposes three speech-source recovery
methods, namely: i) the multichannel inverse filtering method, i.e. the
multiple input/output inverse theorem (MINT), is exploited in the CTF domain,
and for the multi-source case, ii) a beamforming-like multichannel inverse
filtering method applying single source MINT and using power minimization,
which is suitable whenever the source CTFs are not all known, and iii) a
constrained Lasso method, where the sources are recovered by minimizing the
-norm to impose their spectral sparsity, with the constraint that the
-norm fitting cost, between the microphone signals and the mixing model
involving the unknown source signals, is less than a tolerance. The noise can
be reduced by setting a tolerance onto the noise power. Experiments under
various acoustic conditions are carried out to evaluate the three proposed
methods. The comparison between them as well as with the baseline methods is
presented.Comment: Submitted to IEEE/ACM Transactions on Audio, Speech and Language
Processin
Optimal Sensor Collaboration for Parameter Tracking Using Energy Harvesting Sensors
In this paper, we design an optimal sensor collaboration strategy among
neighboring nodes while tracking a time-varying parameter using wireless sensor
networks in the presence of imperfect communication channels. The sensor
network is assumed to be self-powered, where sensors are equipped with energy
harvesters that replenish energy from the environment. In order to minimize the
mean square estimation error of parameter tracking, we propose an online sensor
collaboration policy subject to real-time energy harvesting constraints. The
proposed energy allocation strategy is computationally light and only relies on
the second-order statistics of the system parameters. For this, we first
consider an offline non-convex optimization problem, which is solved exactly
using semidefinite programming. Based on the offline solution, we design an
online power allocation policy that requires minimal online computation and
satisfies the dynamics of energy flow at each sensor. We prove that the
proposed online policy is asymptotically equivalent to the optimal offline
solution and show its convergence rate and robustness. We empirically show that
the estimation performance of the proposed online scheme is better than that of
the online scheme when channel state information about the dynamical system is
available in the low SNR regime. Numerical results are conducted to demonstrate
the effectiveness of our approach
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