Showing papers by "Piya Pal published in 2010"

Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom

Abstract: A new array geometry, which is capable of significantly increasing the degrees of freedom of linear arrays, is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide O(N2) degrees of freedom using only N physical sensors when the second-order statistics of the received data is used. The concept of nesting is shown to be easily extensible to multiple stages and the structure of the optimally nested array is found analytically. It is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. This cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than the number of physical sensors. In minimum-input-minimum-output (MIMO) radar, the degrees of freedom are increased by constructing a longer virtual array through active sensing. The method proposed here, however, does not require active sensing and is capable of providing increased degrees of freedom in a completely passive setting. To utilize the degrees of freedom of the nested co-array, a novel spatial smoothing based approach to DOA estimation is also proposed, which does not require the inherent assumptions of the traditional techniques based on fourth-order cumulants or quasi stationary signals. As another potential application of the nested array, a new approach to beamforming based on a nonlinear preprocessing is also introduced, which can effectively utilize the degrees of freedom offered by the nested arrays. The usefulness of all the proposed methods is verified through extensive computer simulations.

Sparse sensing with coprime arrays

Abstract: Coprime sampling has, in the past, been used for signal processing applications such as range and doppler improvement in radar, and for identifying sinusoids in noise. This paper considers a coprime pair of samplers in space or time from the point of view of the difference coarray, which is key to the increased freedom available for processing with such arrays. First, two uniform linear arrays with N and M elements in space are considered. With the interelement spacings in the two arrays given by Mλ/2 and Nλ/2 where M and N are coprime integers, it is shown that the difference coarray has O(MN) freedoms, so that the number of freedoms available for DOA estimation and beamforming is O(MN). This implies in particular that a passive array can identify O(MN) sources using only M + N sensor elements. It is then shown that by using an N-band DFT filter bank and an M-band DFT filter bank in conjunction with the two arrays, it is possible to create a virtual filter bank with MN bands (i.e., MN beams). The increased number of freedoms can be exploited either in a passive setting (using time-domain averaging) or in an active setting as in radar and sonar.1

A novel array structure for directions-of-arrival estimation with increased degrees of freedom

Abstract: A novel array structure for significantly increasing the degrees of freedom of linear arrays is proposed. This structure is obtained by systematically nesting two or more uniform linear arrays and can provide O(N2) degrees of freedom using only O(N) physical sensors. It is possible to provide closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors. This cannot be done for existing classes of arrays like minimum redundancy arrays which have been used earlier for detecting more sources than sensors. A novel spatial smoothing based technique is also proposed to exploit the increased degrees of freedom offered by the array to perform DOA estimation ofmore sources than sensors, using only second order statistics of the received data. This method does not suffer from inherent weaknesses of techniques employing higher order statistics or quasi stationarity of sources. The validity of all the proposed methods is verified through numerical examples.

System Identification With Sparse Coprime Sensing

Abstract: Given a continuous time LTI system with impulse response hc(t), it is shown that the uniformly spaced samples hc(nT) can be identified for any chosen spacing T by using an impulse train input with an arbitrarily small rate 1/NT and sampling the system output with an arbitrarily small rate 1/MT , provided M and N are coprime. This idea, referred to here as the sparse coprime sensing method for system identification, is closely related to well known results in multirate signal processing. It is shown that the problem can be related to the identification of a decimation filter from input-output measurements. It is also shown that the problem is equivalent to the identification of a discrete time N × M LTI system from a knowledge of the full rate input and output vector sequences.

Beamforming using passive nested arrays of sensors

Abstract: A novel approach to beamforming using a new class of sensor arrays is proposed, which can increase the achievable degrees of freedom significantly beyond the conventional limits obtained from uniform linear arrays (ULA). This class of arrays is named as "nested arrays" since they are obtained by nesting two or more ULAs with increasing inter-sensor spacing. Using the second order statistics of the signal received by such an array in a novel way, it is possible to perform beamforming with 0(N2) de grees of freedom using only O(N) physical elements. This kind of beamforming will be shown to be essentially non linear in nature and theoretically, it is capable of nulling the effect of noise provided enough snapshots are available.l

Efficient frequency invariant beamforming using virtual arrays

Abstract: In wideband array processing, frequency invariant beamforming provides a popular means to make the beampattern allpass with respect to frequency Traditionally, such beampatterns are realized as a two dimensional filter, using tapped delay-line (TDL) filters following each spatial sensor However it has been recently shown that with the help of a rectangular antenna array, it is possible to generate fixed frequency invariant beampatterns without using filters In this paper, this concept is generalized to the case of two dimensional arrays with elements on a (possibly nonseparable) lattice Since performance of the frequency invariant beamformer depends on the number of sensors which could be large for a 2D array of size M × N, a novel approach to beamforming based on the difference co-array of a physical array is also proposed, which avoids use of additional physical sensors The realization of the frequency invariant beams using second order statistics of the impinging signal with only M + N physical sensors, instead of the two dimensional array of size M×N, is demonstrated The usefulness of the proposed method is verified through computer simulation1

Erratum to nested arrays: a novel approach to array processing with enhanced degrees of freedom

Abstract: In the above titled paper (ibid., vol. 58, no. 8, pp. 4167-4181, Aug. 10), the second unnumbered equation in the left column was incorrect. The correct version is presented here.