Estimation of Temporal and Spatial Parameters of Wideband Signals

ln this paper a common technique for estimating both spatial and temporal parameters of nonstationary !ransi.-:it likc sig~als and stationary noiselike signals is introduced. The procedure ielies on obtaining the rank redlicing numbers of three separate matrix pencils. Effectiveness of the method is demonstrated by several computer simulated examples. 1. ~ntr~~~~~i~~ Many high resolution zlgoritlms have successfully been devclopcd for tlic case of nar;o\vbar?d signals. However, narrowband modeling is not appropriate for wideband signals. In particular, the time delay which contains the infxmation about the targets cannot be approximated by a phase shift. Recently, several narrowband algorithms have been successfully extended to the wideband case [2-71. Su et. al. suggested using a modal decomposition of the signals along with MUSIC to solve for the angles of amval. A set of angles of amval is obtained for each pole in the received spectrum. More parameters such as poles and residues of the system have to be estimated first before obtaining the angles of amval. A different approach consists of decomposing the wideband signals into sums of narrowband signals [2-4]. Wax et. al. [3j used the MUSIC algorithm to obtain a spectral estimate by averaging either arithmetically or geometrically the contributions from all bands. This post-processing is referred to as incoherent processing. Wang et. al. used linear transformations to combine the diffcrcnt bands into a choscn band. This method is known as Coherent Signal Subspace processing (CSS). However, in this case only one eigendecoinposition is needed to obtain the needed spectral estimate. ESPRIT,MUSIC, Root-MUSIC [6] and the Moving Wmdow [7] have a11 successfully been applied in conjunction with CSS. A disadvantage of this mcthod is that preliminary estimates of the angles of arrival aie needed in order to apply the linear transformations. If these angles are clustered within a beamwidth, the method performs well. Otherwise, spatial prefiltering is needed. More recently, Ottersten et al. [7] proposed extending thc ESPMT algorithm to wideband signals. The same model as describcd in [2] was used and ESPRIT is applied at each of the signal poles. In this paper two different models arc considered. In the first case, thc wideband signals are modeled as transients (i.e; signal bursts of short duration). This representation is appropriate for non stationary wideband sources. In the second case, the sources are modeled as the outputs of a linear system driven by white noise.This modeling is used for the case of stationary signals. The matrix pencil appioach [l] is used in conjunction with the moving window operator to determine This work was supported in part by AERITALIA under a contract awarded through ITALIAN ADVANCED INDUSTRIES, P. 0 #88H907 and RADC under contract F30602-81-C-0169. the source locations for both models. Each source is characterized by both its angle of amval and poles (natural frequencies or poles in the L-plane), all of which are assumed to be unknown at the receiver. A matnx pencil generated by the outputs of a tapped delay line connected to the first sensor enables the estimation of all signal poles. The rank reducing numbers of a second matrix pencil that is generatcd from the array outputs are shown to be functions of both the angles of arrival and poles. However, it is not apparent which pules should be associatcd with which angles of amval. To resolve this ambiguity a third matrix pencil is generated from an appropriately placed second tap delay line. Consistency requirements on the rank reducing numbers of the matrix pencils enable resolution of the ambiguities. The method can easily be extended to handle the case of common poles between the sources at different angles. This paper is organized as follows: in section 2 the signal models are discussed and the problem is iormulated with respect to these models. In section 3 the poles and the angles of amval are estimated using the moving window operator. Computer simulations demonstrating the effectiveness of the proposed methods are included in section 4.