Abstract
A multichannel characterization for autoregressive moving average (ARMA) spectrum estimation in subbands is considered in this article. The fullband ARMA spectrum estimation can be realized in two-channels as a special form of this characterization. A complete orthogonalization of input multichannel data is accomplished using a modified form of sequential processing multichannel lattice stages. Matrix operations are avoided, only scalar operations are used, and a multichannel ARMA prediction filter with a highly modular and suitable structure for VLSI implementations is achieved. Lattice reflection coefficients for autoregressive (AR) and moving average (MA) parts are simultaneously computed. These coefficients are then converted to process parameters using a newly developed Levinson–Durbin type multichannel conversion algorithm. Hence, a novel method for spectrum estimation in subbands as well as in fullband is developed. The computational complexity is given in terms of model order parameters, and comparisons with the complexities of nonparametric methods are provided. In addition, the performance is visually and statistically compared against those of the nonparametric methods under both stationary and nonstationary conditions.
Highlights
While parametric or model-based methods are used extensively for high-resolution spectrum estimation, these methods perform poorly when SNR and spacing between frequencies is small
Such statistics may not be known in many cases, and instead, noise may incorrectly be assumed white. Such shortcomings can be overcome by applying subband decomposition methods in spectrum estimation. It was shown by Rao and Pearlman [1] that the wellknown AR modeling was a promising method for spectrum estimation in subbands, and it was proved that pth-order prediction from subbands is superior to pthorder prediction in the fullband when p is finite, and subband decomposition of a source resulted in a whitening of the composite subband spectrum
Since the mathematical link between process parameters and reflection coefficients of a lattice prediction filter is provided by the Levinson–Durbin algorithm [48,49], we develop a new Levinson–Durbin type conversion algorithm for sequential processing multichannel lattice stages (SPMLSs) in order to convert lattice reflection coefficients to subband autoregressive moving average (ARMA) process parameters
Summary
While parametric or model-based methods are used extensively for high-resolution spectrum estimation, these methods perform poorly when SNR and spacing between frequencies is small. We introduced the complete orthogonalization concept previously in linear and nonlinear adaptive decision feedback equalization frameworks in [37,38], its application to adaptive spectrum estimation problem in subbands as well as in fullband results in novel implementations, to the development of a new Levinson–Durbin type conversion algorithm for the modified SPMLSs in order to compute ARMA process parameters from lattice reflection coefficients. The method is applicable for both off-line and on-line implementations; it is especially possible to monitor the forward prediction error signal, start the parameter estimation for a fullband AR(p) or ARMA(p,q) or ARMA(p,p) process; if performance requirements are not met, end up for subband ARMA(pk, qk) or ARMA(pk, pk) realizations It dynamically extends the lattice parametrization of fullband spectrum into subbands, and thereby arises as an useful and practical method for radar signal analysis/classification, speech analysis/synthesis, adaptive multiple frequency tracking, and cognitive radio spectrum sensing tasks. The variable m represents the stage number while n and i are the time indexes related to data and coefficients, respectively, till we equate them in Section 3 to have a single time index
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