A Deterministic Least Squares Approach to Adaptive Antennas

Sarkar, T. K., Park, S., Koh, J., and Schneible, R. A., A Deterministic Least Squares Approach to Adaptive AntenConsider a linear array of uniformly spaced receivnas, Digital Signal Processing 6 (1996), 185–194. ing elements (isotropic) separated by a distance d as A direct data domain approach to adaptively receiving a shown in Fig. 1. We further assume that narrowband signal coming from a given direction in the presence of strong signals consisting of a desired signal plus multipaths jammers and clutter is presented. In conventional adaptive and jammers with center frequency f0 are impinging algorithms, the statistical approach is based on forming an on the array from various angles u, with the conestimate of the covariance matrix of the received antenna straint 0 £ u £ 1807. Let us consider that the signal voltages (measured voltages at the antenna terminals) withwe want to estimate is arriving from an a priori out the signal. In this article, first a review of the convenknown angle us and the various jamming signals are tional approaches is presented, where the number of adaparriving from various angles uJ including coherent/ tive weights is usually equal to the number of antenna elements. The equations for solutions of the weights are then noncoherent multipaths. The jamming signal may generated by performing an averaging in time. This makes be located in the main beam of the array, i.e., us 0 it possible to handle the unequally spaced antenna case (as uJ £ 50.87/( L/l) [1], where L is the length of the in MUSIC). Unfortunately this methodology cannot handle array. l is the wavelength corresponding to f0 (i.e., coherent jammers (which may be due to multipath effects) l Å 2pc/ f0, c being the velocity of eight) and typically or cases where the noise statistics change quite rapidly. To d the spacing between the elements is chosen as l/2. mitigate the above problems this article presents a direct In conventional adaptive beam forming one snapdata domain approach to the adaptive problem, where an shot is defined as the complex voltages Vn measured equation error is minimized. This is ideally suited to a highly at the antenna elements at a particular instance of nonstationary environment, particularly in the presence of time. So the measured voltages Vn contain signal, blinking jammers and for problems where the clutter characjammer, and clutter components. A set of weights teristics change quite rapidly. Hence the processing in the data domain is done on a snapshot-by-snapshot basis. Two Wj ( j Å 1, . . . , N ) is attached to each antenna and new direct data domain approaches are presented. One is the values of the weights are solved from generating based on the computation of a generalized eigenvalue for the the covariance matrix of the data sets Vn taken over signal strength, and the other is based on the solution of a multiple snapshots. In this case, the number of set of block Hankel matrix equations. Since the system maweights is equal to the number of antenna elements. trix has a block Hankel structure, the conjugate gradient The relevant equations are then generated by taking method and the Fast Fourier transform can be utilized for several snapshots over a time interval. Then all the efficient solution of the adaptive problem in hardware in real snapshots are processed together. The covariance time. Also a methodology which prevents signal cancellation matrix is then formed by taking the data in the snapwhen the direction of arrival is not known precisely is preshots where the signal is assumed to be absent. This sented. Limited examples are presented to illustrate the efcreates a hardship on the part of the user, as this ficacy of this technique. q 1996 Academic Press, Inc. information is not readily available. One way to get