Comments, with reply, on 'convergence properties of Gram-Schmidt and SMI adaptive algorithms' by K. Gerlach and F.F. Kretschmer, Jr

The commenter summarizes Q-R decomposition techniques for solving the least squares (LS) problem and comments on associated aspects of the work presented by K. Gerlach and F.F. Kretschmer, Jr. (ibid., vol.267, no.1, Jan.90). In response to the commenter's statement that the statistical properties of the LS that determine the convergence performance are well known. Gerlach and Kretschmer assert that this is true only under the assumptions that have been used in the past to analyze the convergence performance of the canceler and for only a limited number of convergence performance measures. Gerlach and Kretschmer also address the commenter's points on overmatching degrees of freedom.<>     

Algorithmic, architectural, and beam pattern issues of sidelobecancellation

Various important issues concerning the sidelobe cancellation (SLC) approach for suppressing sidelobe interference signals in radar are investigated. The concepts are presented in a tutorial manner and include: formulating the calculation of the complex weights for the auxiliary channels as an exact least-squares (LS) problem; computing the LS weights using orthogonal transformation for improved numerical accuracy; and mapping orthogonalization-based algorithms onto systolic arrays. The problem of excessive degrees of freedom (EDOF) associated with utilizing too many auxiliary elements when a relatively small number of jammers are present, is also considered. A divisionless orthogonalization-based algorithm is presented for the computation of the auxiliary weights. Many of these issues have previously been either implicitly stated or only individually addressed in various sources by a number of researchers. Besides showing simulation results and the divisionless procedure for obtaining the final auxiliary weights, a major consideration was to present all of the aforementioned concepts in a coherent and unified framework     

On First Cycle Slip Time of Phase-Locked Loops in Cascade

Precise measurement and spacecraft tracking are obtained by using phase-locked loops in cascade in two-way communications links. Statistics on cycle slip time are of vital importance in system planning and design. This paper presents: 1) results of a computer simulation study of the mean time to first cycle slip of cascade phase-locked loops preceded by bandpass limiters, and 2) the determination of probability distributions of cycle slip. Numerical results are obtained for a typical coherent communication system.     

Exact least squares adaptive beamforming using an orthogonalizationnetwork

The pros and cons of various classical and state-of-the-art methods in adaptive array processing are discussed, and the relevant concepts and historical developments are pointed out. A set of easy-to-understand equations for facilitating derivation of any least-squares-based algorithm is derived. Using this set of equations and incorporating all of the useful properties associated with various techniques, an efficient solution to the real-time adaptive beamforming problem is developed