Linear matrix inequality formulation of spectral mask constraints with applications to FIR filter design

Davidson, T.N.; Luo, Zhi-Quan; Sturm, J.F.

doi:10.1109/tsp.2002.804079

Cited by 125 publications

(113 citation statements)

References 26 publications

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“…The search interval is set to [M l , M u ] = [1,32] where both designs are tested feasible at 32 sensors. The beampatterns for both designs using M u = 32 sensors by the method of [5] are shown.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Given the same prior information that the optimum solution M opt lies in [M l , M u ] = [1,32] as in the examples, the direct application of the method of [5] to find the minimum number of sensors for beampattern designs would involve either increasing the number of sensors one by one from M l = 1 or reducing the number of sensors one by one from M u = 32. However, this results in a large number of iterations (20 and 14 iterations for the first and second designs, respectively for the latter case).…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Note that in the case of applying the method of [5] using more array sensors than required, the extra degrees of freedom are wellutilized as the generated beampatterns in Figs. 1-2 have exceeded the beampattern specifications.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Second, the cost per sensor can be significant in many applications due to the sensor itself and the associated electronics [1]. Hence, we modify the method of Davidson et al in [5] and propose a new formulation that can find the minimum number of array sensors required to achieve prescribed beampattern specifications and the corresponding beamforming weights, systematically. A related problem arises in minimum order filter design [6].…”

Section: Introductionmentioning

confidence: 99%

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Beampattern Synthesis With Linear Matrix Inequalities Using Minimal Array Sensors

Nai¹,

Ser²,

Yu³

et al. 2009

PIER M

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Abstract-A new beampattern synthesis formulation is proposed to compute the minimum number of array sensors required. In order to satisfy all the prescribed specifications of the beampattern, the proposed method imposes linear matrix inequality (LMI) constraints on the beampattern as developed by Davidson et al., which remove the need to discretize the beampattern region. As the proposed formulation is quasi-convex, an iterative procedure is used to decompose it into a systematic sequence of convex feasibility problems, in order to find the minimum number of sensors. The proposed method guarantees convergence if the globally optimum solution lies in the search interval, which is easy to ensure at the start of the search.Corresponding author: S. E. Nai (NAIS0001@ntu.edu.sg). 166Nai et al.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Simulation Resultsmentioning

confidence: 99%

Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Beampattern Synthesis With Linear Matrix Inequalities Using Minimal Array Sensors

Nai¹,

Ser²,

Yu³

et al. 2009

PIER M

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“…Therefore, it can be readily solved using interior-point methods; see, e.g., [2], [5], [6]. Semidefinite programming (SDP) techniques have also been used in the FIR filter design; see, e.g., [7].…”

Section: A Chebyshev Fir Equalizationmentioning

confidence: 99%

Robust Chebyshev FIR Equalization

Mutapcic

Kim

Boyd

2007

IEEE GLOBECOM 2007-2007 IEEE Global Telecommunications Conference

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Abstract-In Chebyshev finite-impulse response (FIR) equalization, we design an FIR filter that minimizes the Chebyshev equalization error, i.e., the maximum absolute deviation between the equalized and the desired frequency response functions, assuming the unequalized response function is known exactly. In robust Chebyshev FIR equalization, we take into account uncertainty in the unequalized response function, described as a set of possible values for the unequalized response at each frequency, by designing an FIR filter that minimizes worst-case Chebyshev equalization error over all possible unequalized response functions. When the uncertainty in unequalized response function is described by a complex uncertainty ellipsoid, at each frequency, we show that the robust Chebyshev FIR equalization design problem can be formulated as a semidefinite program (SDP), and therefore efficiently (and globally) solved. When the uncertainty is given by a complex disk, the design problem can be formulated as a second-order cone program (SOCP), which can be solved almost as fast as the nominal Chebyshev equalization problem (ignoring uncertainty). The robust equalizer design method is demonstrated with a numerical example.

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Convex Optimization Theory Applied to Joint Transmitter‐Receiver Design in MIMO Channels

Palomar

Pascual‐Iserte

Cioffi

et al. 2005

Space‐Time Processing for MIMO Communications

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Linear matrix inequality formulation of spectral mask constraints with applications to FIR filter design

Cited by 125 publications

References 26 publications

Beampattern Synthesis With Linear Matrix Inequalities Using Minimal Array Sensors

Beampattern Synthesis With Linear Matrix Inequalities Using Minimal Array Sensors

Robust Chebyshev FIR Equalization

Convex Optimization Theory Applied to Joint Transmitter‐Receiver Design in MIMO Channels

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