Array processing involves manipulation of signals induced on various antenna elements. Its capabilities of steering nulls to reduce cochannel interferences and pointing independent beams toward various mobiles, as well as its ability to provide estimates of directions of radiating sources, make it attractive to a mobile communications system designer. Array processing is expected to play an important role in fulfilling the increased demands of various mobile communications services. Part I of this paper showed how an array could be utilized in different configurations to improve the performance of mobile communications systems, with references to various studies where feasibility of apt array system for mobile communications is considered. This paper provides a comprehensive and detailed treatment of different beam-forming schemes, adaptive algorithms to adjust the required weighting on antennas, direction-of-arrival estimation methods-including their performance comparison-and effects of errors on the performance of an array system, as well as schemes to alleviate them. This paper brings together almost all aspects of array signal processing.

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Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

The use of multi-amplitude signaling schemes in wireless OFDM systems requires the tracking of the fading radio channel. The paper addresses channel estimation based on time-domain channel statistics. Using a general model for a slowly fading channel, the authors present the MMSE and LS estimators and a method for modifications compromising between complexity and performance. The symbol error rate for a 18-QAM system is presented by means of simulation results. Depending upon estimator complexity, up to 4 dB in SNR can be gained over the LS estimator.

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On channel estimation in OFDM systems

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.

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

This paper considers the sampling of temporal or spatial wide sense stationary (WSS) signals using a co-prime pair of sparse samplers. Several properties and applications of co-prime samplers are developed. First, for uniform spatial sampling with M and N sensors where M and N are co-prime with appropriate interelement spacings, the difference co-array has O(MN) freedoms which can be exploited in beamforming and in direction of arrival estimation. An M -point DFT filter bank and an N-point DFT filter bank can be used at the outputs of the two sensor arrays and their outputs combined in such a way that there are effectively MN bands (i.e., MN narrow beams with beamwidths proportional to 1/MN), a result following from co-primality. The ideas are applicable to both active and passive sensing, though the details and tradeoffs are different. Time domain sparse co-prime samplers also generate a time domain co-array with O(MN) freedoms, which can be used to estimate the autocorrelation at much finer lags than the sample spacings. This allows estimation of power spectrum of an arbitrary signal with a frequency resolution proportional to 2π/(MNT) even though the pairs of sampled sequences xc(NTn) and xc(MTn) in the time domain can be arbitrarily sparse - in fact from the sparse set of samples xc(NTn) and xc(MTn) one can estimate O(MN) frequencies in the range |ω| <; π/T. It will be shown that the co-array based method for estimating sinusoids in noise offers many advantages over methods based on the use of Chinese remainder theorem and its extensions. Examples are presented throughout to illustrate the various concepts.

Sparse Sensing With Co-Prime Samplers and Arrays

A spatial smoothing scheme is further investigated in the context of coherent signal classification. It is shown that by making use of a set of forward and complex conjugated backward subarrays simultaneously, it is always possible to estimate any K directions of arrival using at most 3K/2 sensor elements. This is achieved by creating a smoothed array output covariance matrix that is structurally identical to a covariance matrix in some noncoherent situation. By incorporating eigenstructure-based techniques on this smoothed covariance matrix, it then becomes possible to correctly identify all directions of arrival irrespective of their correlation. >

Forward/backward spatial smoothing techniques for coherent signal identification

Optimal detection of a target return contaminated by signal-dependent interference, as well as additive channel noise, requires the design of a transmit pulse f(t) and a receiver impulse response h(t) jointly maximizing the output signal to interference plus noise ratio (SINR). Despite the highly nonlinear nature of this problem, it has been possible to show that f(t) may always be chosen minimum-phase. A full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs (f,h) that appears to converge satisfactorily for most values of input SINR. Extensive simulation reveals that the shape of f(t) can be a critical factor. In particular, the performance of a chirp-like pulse is often unacceptable, especially when clutter and channel noise are low-pass dominant and comparable.

Optimal transmit-receiver design in the presence of signal-dependent interference and channel noise

In this letter, we address the problem of element placement in a linear aperiodic array for use in spatial spectrum estimation. By making use of a theorem by Caratheodory, it is shown that, for a given number of elements, there exists a distribution of element positions which, for uncorrelated sources, results in superior spatial spectrum estimators than are otherwise achievable. The improvement is obtained by constructing an augmented covariance matrix, made possible by the choice of element positions, with dimension greater than the number of array elements. The augmented matrix is then used in any of the known spectrum estimation methods in conjunction with a correspondingly augmented search pointing vector. Examples are given to show the superior detection capability, the larger dynamic range for spectral peak to background level, the lower sidelobes, and the relatively low bias values, when one of the known spectrum estimation techniques based on eigenstructure is used.

A new approach to array geometry for improved spatial spectrum estimation

Optimal detection of a target return contaminated by signal-dependent interference, as well as additive channel noise, requires the design of a transmit pulse f(t) and a receiver impulse response h(t) jointly maximizing the output signal to interference plus noise ratio, SINR. Despite the highly nonlinear nature of this problem, it has been possible to show that f(t) may always be chosen minimum-phase. A full analysis concludes with the construction of an effective numerical procedure for the determination of optimal pairs (f,h) that appears to converge satisfactorily for most values of input SINR. Extensive simulation reveals that the shape of f(t) can be a critical factor. In particular the performance of a chirp-like pulse is often unacceptable, especially when the clutter and channel noise are low-pass dominant and comparable.

Optimum transmit-receiver design in the presence of signal-dependent interference and channel noise

The optimisation of the transmission radar pulse shape to maximise either target detection or identity discrimination between the T-72 and M1 main battle tanks is investigated. Significant performance improvements in target detection and identification are obtained using such matched illumination transmission waveforms over that of standard chirped pulses.

S.U. Pillai

Papers

Forward/backward spatial smoothing techniques for coherent signal identification

Optimal transmit-receiver design in the presence of signal-dependent interference and channel noise

A new approach to array geometry for improved spatial spectrum estimation

Optimum transmit-receiver design in the presence of signal-dependent interference and channel noise

Enhanced target detection and identification via optimised radar transmission pulse shape