Article
Broadband beamforming using TDLform IIR filters
Inf. Syst. Res. Lab., Nanyang Technol. Univ., Singapore
IEEE Transactions on Signal Processing (Impact Factor: 2.79). 04/2007; 55(3):990  1002. DOI: 10.1109/TSP.2006.887134 Source: IEEE Xplore
ABSTRACT
Conventional broadband beamforming structures make use of finiteimpulseresponse (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signaltointerferenceplusnoiseratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequencydependent array weighting of broadband beamformers could be better approximated by infiniteimpulseresponse (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frostbased and generalized sidelobe canceller (GSC)based broadband beamformers utilizing a kind of tappeddelaylineform (TDLform) IIR filters are proposed; 2) the combined recursive GaussNewton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frostbased implementation; and 3) in the GSCbased structure, the unconstrained RGN algorithm is customized for the TDLform IIR filters in the adaptive beamforming part. Compared with the beamformer using directform IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved

 "Moreover, contrary to the previous studies, this approach allows us to consider arrays of arbitrary geometry with a limited but arbitrary number of sensors and arbitrary interference and signal of interest spectra. Thus, we can compute a theoretical upper bound associated with an infinite number of taps, useful for comparisons with the SINR obtained after different space–time processing algorithms based for instance on FIR (e.g., see [4]), subband decomposition (e.g., see [12] [13]), or IIR filters (e.g., see [14]). "
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ABSTRACT: In many detection applications, the main performance criterion is the signal to interference plus noise ratio (SINR). After linear filtering, the optimal SINR corresponds to the maximum value of a Rayleigh quotient, which can be interpreted as the largest generalized eigenvalue of two covariance matrices. Using an extension of Szegö's theorem for the generalized eigenvalues of Hermitian block Toeplitz matrices, an expression of the theoretical asymptotic optimal SINR w.r.t. the number of taps is derived for arbitrary arrays with a limited but arbitrary number of sensors and arbitrary spectra. This bound is interpreted as an optimal zerobandwidth spatial SINR in some sense. Finally, the speed of convergence of the optimal wideband SINR for a limited number of taps is analyzed for several interference scenarios. 
 "On the contrary, under non narrowband conditions, spacetime or subband processing allows one to compensate for performance losses due to bandwidth, see, e.g., [2,, ch. 6], [7]–[10]. Under nonzero bandwidth conditions, the SINR expression is given by (2) where and are defined in the previous Section and is a spatial filter. "
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ABSTRACT: This paper addresses the robustness of adaptive narrowband beamforming with respect to bandwidth based on the loss of performance in terms of signaltointerferenceplusnoise ratio (SINR). The criterion used by Zatman to define a narrowband environment, i.e., the ratio between the jammer plus noise covariance matrix and the noise eigenvalue, is studied from the point of view of a loss of SINR after narrowband beamforming under non narrowband conditions. Using theoretical results about the eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency by Lee, it is shown that Zatman's criterion can be interpreted as an upper bound on the SINR loss which is nearly reached under certain conditions that are specified.  [Show abstract] [Hide abstract]
ABSTRACT: A spatialtemporal scheme based on nonuniform subband general parameter filter banks for broadband beamforming of scaled aperture array is proposed in this paper. The scaled aperture array is composed of several uniformlyspaced linear subarrays, each of which processes an octave subband signal respectively. The nonuniform subband signal is implemented by treestructure general parameter filter banks. Each subarray broadband beamforming is carried out by a kind of tappeddelayline (TDL) infiniteimpulseresponse (IIR) filters beamformer, and four subarrays share the same weights. This processing architecture based beamformer splits the broadband signal into several narrower subband ones which are processed in parallel, and subarray is operating with lower sampling rate, which contributes to decreasing the computational load significantly and improving the speed and performances as well. Simulations show that computation complexity and load of this beamformer are much lower relative to the conventional TDL broadband beamfomer.
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