A New Design Framework for Sparse FIR MIMO Equalizers

Gomaa, Ahmad; Al-Dhahir, Naofal

doi:10.1109/tcomm.2011.053111.100231

Cited by 30 publications

(26 citation statements)

References 22 publications

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“…Problem (12) (10). Using a standard linear programming technique based on the representation in (11) to replace the absolute value functions in (8) with linear functions (see [19]), it can be seen that (8) is a special case of (12) (12) with B ± n = B ± * n is at least as large as that of (8) with B n = B * n , and therefore (12) is at least as strong a relaxation as (8).…”

Section: B Linear Relaxationmentioning

confidence: 99%

“…[3], [4], [8]- [10]), is that they do not indicate how close the resulting designs are to the true optimum. In the present paper, we take a different approach to address this shortcoming, specifically by combining branch-and-bound [14], an exact procedure for combinatorial optimization, with several methods for obtaining lower bounds on the optimal cost, i.e., bounds on the smallest feasible number of non-zero coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…Accordingly, sparse filters, i.e., filters with relatively few non-zero coefficients, offer a means to reduce cost, especially in hardware implementations. Sparse filter design has been investigated by numerous researchers in the context of frequency response approximation [1]- [4], communication channel equalization [5]- [10], speech coding [11], and signal detection [12].…”

Section: Introductionmentioning

confidence: 99%

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A Branch-and-Bound Algorithm for Quadratically-Constrained Sparse Filter Design

Wei

Oppenheim

2013

IEEE Trans. Signal Process.

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Abstract-This paper presents an exact algorithm for sparse filter design under a quadratic constraint on filter performance. The algorithm is based on branch-and-bound, a combinatorial optimization procedure that can either guarantee an optimal solution or produce a sparse solution with a bound on its deviation from optimality. To reduce the complexity of branchand-bound, several methods are developed for bounding the optimal filter cost. Bounds based on infeasibility yield incrementally accumulating improvements with minimal computation, while two convex relaxations, referred to as linear and diagonal relaxations, are derived to provide stronger bounds. The approximation properties of the two relaxations are characterized analytically as well as numerically. Design examples involving wireless channel equalization and minimum-variance distortionless-response beamforming show that the complexity of obtaining certifiably optimal solutions can often be significantly reduced by incorporating diagonal relaxations, especially in more difficult instances. In the case of early termination due to computational constraints, diagonal relaxations strengthen the bound on the proximity of the final solution to the optimum.

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Section: B Linear Relaxationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Branch-and-Bound Algorithm for Quadratically-Constrained Sparse Filter Design

Wei

Oppenheim

2013

IEEE Trans. Signal Process.

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“…This algorithm is shown to provide efficient allocations at a relatively low computational cost. There has been various greedy algorithms as well as convex relaxation based approach to sparse filter design in the literature [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Sparse approximation based resource allocation in DSL/DMT transceivers with per-tone equalization

2014

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a b s t r a c tPer-tone equalization has been proposed as an alternative to time domain equalization for DMT receivers in DSL modems. It optimizes the bit rate performance of the receiver as each tone can be equalized independently. It has also been shown that using variable length equalizers can significantly reduce the total number of equalizer taps and hence the run-time complexity, without compromising performance. For a given transmit power loading, it has been shown that the equalizer taps can be allocated optimally using a dual decomposition based approach with per-tone exhaustive searches over all possible equalizer lengths. However, a more general approach is needed when optimal transmit power allocation is also considered to maximize the overall bit rate, where in addition the per-tone exhaustive searches are replaced by a more efficient procedure. In this paper, a sparse approximation based resource allocation algorithm is presented to allocate equalizer taps and transmit power over tones and maximize the overall bit rate. This algorithm is shown to provide efficient allocations at a relatively low computational cost.

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“…Again, however, these works impose a constraint that the taps in the combined channel/filter response must be contiguous. One very recent work [9] has considered use of matching pursuit to find a sparse, non-contiguous target impulse response (TIR), and it is shown to yield a lower mean squared error (MSE) compared to the conventional contiguous approach.…”

Section: Introductionmentioning

confidence: 99%

Sparsening filter design for iterative soft-input soft-output detectors

Machado

Klein

Martin

2012

J Wireless Com Network

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A large body of research exists around the idea of channel shortening, where a prefilter is designed to reduce the effective channel impulse response to some smaller number of contiguous taps. This idea was originally conceived to reduce the complexity of Viterbi-based maximum-likelihood equalizers. Here, we consider a generalization of channel shortening which we term "channel sparsening". In this case, a prefilter is designed to reduce the effective channel to a small number of nonzero taps which do not need to be contiguous. When used in combination with belief-propagation-based maximum a posteriori (MAP) detectors, an analogous complexity reduction can be realized. We address the design aspects of sparsening filters, including several approaches to minimize the bit error rate of MAP detectors. We devote attention to the interaction of the sparsening filter and detector, and demonstrate the performance gains through simulation.

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A New Design Framework for Sparse FIR MIMO Equalizers

Cited by 30 publications

References 22 publications

A Branch-and-Bound Algorithm for Quadratically-Constrained Sparse Filter Design

A Branch-and-Bound Algorithm for Quadratically-Constrained Sparse Filter Design

Sparse approximation based resource allocation in DSL/DMT transceivers with per-tone equalization

Sparsening filter design for iterative soft-input soft-output detectors

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