8/20/2019 Virtual Array Processing Using Wideband Cyclostationary Signals http://slidepdf.com/reader/full/virtual-array-processing-using-wideband-cyclostationary-signals 1/5 Virtual Array Processing Using Wideband Cyclostationary Signals Marilynn P. Wylie * WINLAB Rutgers University P.O. Box 909 Piscataway, NJ 08855 Abstract A new spatio-temporal array signal processing tech- nique for wideband array data is presented that im- proves spatial resolution and increases the number of resolvable sources. The method is predicated on digi- tal communication signals that are temporally cyclo- stationary. We show that the (frequency-dependent) array manifold has a separable representation in the directions of arrival (DOAs) and the array geometry and exploit the structure of the cyclic cross spectral density matrix in order to obtain virtual array ‘obser- vations’ wzthout a-priori knowledge of the DOAs. 1 Introduction Frequency focusing techniques for direction of ar- rival estimation (DOA) of temporally wideband sig- nals is a problem of considerable continuing interest motivated, for example, by developments in mobile communications. One approach to this problem for wide-band array data as will be shown) is to design frequency-dependent transformations which focus the DOA information to a reference frequency and, simul- taneously, generate virtual. array ‘observations’. With proper design, the new, virtual array geometry may be selected so as to increase the aperture and hence obtain improved DOA estimates. An important contribution to wide-band DOA es- timation can be traced to the subspace focusing tech- nique introduced by [l] termed as Coherent Signal Subspace Method (CSSM). In this method, stationary wide-band array data is decomposed into narrowband components followed by focusing of the narrowband components to a reference frequency. Subsequent to frequency focusing, the DOA estimates are obtained using conventional signal subspace methods (such as MUSIC) for narrowband signals. Some new interpre- tations and results related to CSSM were proposed [2]-[3]. Unfortunately, performance o the CSSM is critically dependent on some a-priori initial estimate of the DOAs close to the true value, in order to con- struct the focusing matrix. An important contribu- tion to resolution of the above dilemna was provided by [GI, who demonstrated the separability of the array manifold into two functions: one of the DOAs and an- ot,her of the array geometry and temporal frequencies, *Author for all correspondence; e-mail: mwyIieQ winl ab Tu gers edu Sumit Roy Divn. of Engineering University of Texas San Antonio, TX 78249 respectively. The resulting array manifold interpola- tion matrix (focusing matrix) is then computed wzth- out any a-priori knowledge of the DOAs of the sources. In this work, we develop a new technique for DOA estimation of wide-band signals for 2-D (planar) arrays by combining the separability of the array manifold with exploitation of the wide-sense cyclostationarity of the signals of interest (SOIs). It is shown that the array manifold has a separable representation which may be exploited in order to focus its information to a reference frequency bin without a-priori knowledge of th e DOAs. We also introduce a spatial extrapo- lation parameter which, if judiciously selected during the frequency focusing procedure, generates ‘virtual’ array observations at the reference frequency. i) A-priori DOA estimates are not required to gener- ate the ‘virtual’ array observations; ii) Rejection of wide-sense stationary or cyclostation- ary interference and noise; iii) Increased resolution by spatial extrapolation. The salient features of this new method are: 2 Problem Formulation The signal observed by an M-element planar array is assumed to be the superposition of La cyclostation- ary waveforms received in the presence of interference and noise. The signal measured at the output of the mth sensor can be described by I=1 over the observation interval 0 5 t 5 TO and for m = 1, ..., M. { ~ ~ ( t ) } ~ ~ re the radiated signals, and {n,(t)}Z=, is interference. The delay T~ BI) = , where 01 denotes the DOA of the cm sin h+ym cos ) lth radiated waveform as measured from the array broadside and ( xm, m) denotes the 2-D coordinates of the mth array element normalized relatzve to the wavelength, A0 = c/fo. The Fourier coefficient of (1) at frequency 6 s de- fined as Zm fk) = ? zm(t)e-l”fktdt In vector fo 1058-6393/96 5.00 1996 EEE Proceedings of ASILOMAR-29 506
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Virtual Array Processing Using Wideband Cyclostationary Signals
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8/20/2019 Virtual Array Processing Using Wideband Cyclostationary Signals