An efficient and flexible multiple mainbeam architecture for performing adaptive sidelobe cancellation using a single set of n auxiliary antennas is described. The design can easily incorporate constrained and/or excess degrees-of-freedom processing if this proves necessary in a given application. The approach is to compute the QR decomposition of the auxiliary data matrix and then send this information to mainbeam processors, where the residual for each mainbeam is computed without explicitly calculating and applying auxiliary weights. A new fast algorithm and architecture for implementing constraints are presented. The proposed approach reduces the number of operations in the constrained mainbeam processor from order n/sup 3/ to order n/sup 2/.>

The construction of a class of balanced binary sequences with optimal autocorrelation properties is described. Given any odd primepand any positive integerm, a balanced( \pm 1)binary sequence of lengthp^{m} - 1whose cyclic autocorrelation functionc (\tau)satisfiesc (0) = p^{m} - 1, and, for\tau \neq 0, c (\tau) = +2or-2when(p^{m} - 1)/2is odd, andc(\tau) = 0or-4when(p^{m} - 1)/2is even is constructed. Optimality is proved by showing that every balanced binary sequence has at least two distinct out-of-phase correlation values which are at least as large as those obtained here.

The construction described in this note makes possible the generation of any given linear shift register sequence of maximal period p= 2n-1, at a rate k times faster than the shift pulse rate. The construction is valid for any positive integer k which is not a multiple of p and it employs at most k linear shift registers of degree n or less.

A construction is given which produces maximal (in number of words) comma-free codes for any odd word lengthnand any alphabet size\sigma.

A (finite) code is called synchronizable ofMth order if, and only if, there exists a least positive integerMsuch that the knowledge of the lastMletters of any message suffices to determine a separation of code words. This condition is less constraining than the comma-free restriction. Sections I-IV is a description of a way of selecting a synchronizable block codeC_{\sigma , n}for a given alphabet with\deltaletters and a given code-word length n. It is proved thatC_{\sigma , n}is maximal in the sense that it contains as many words as possible; and an expression is given for the number of words inC_{\sigma , n}.^{1}Sections V-VIII is a description of a construction of phase-shift-keying synchronizable codes. In the PSK case the letters themselves cannot be identified by the receiver. Only the differences between successive letters can be detected. Thus, if the sequenceX_{1},X_{2}, \cdots , X_{l}is transmitted, then the observed sequence in the receiver isX_{2} - X_{1}, X_{3}- X_{2}, \cdots , X_{i+1}- X_{i}, \cdots , X_{l} - X_{l-1}. The letters are assumed to be the integers mod\delta; andX_{i+1} - X_{i}is taken mod\delta. This situation occurs in the reading of phase-modulated signals. The construction of these codes (calledK_{\sigma , n}) is based onC_{\sigma , n}.