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Perfect binary array pairs have good autocorrelation properties and can meet two conditions required by the processing of perfect signal in communications. By analyzing the properties of perfect binary array pairs and differences set pairs, the differences set pairs method for constructing perfect binary array pairs is presented. Polynomial is a common method for designing the perfect discrete signal. This paper presents characteristic polynomial method for constructing perfect binary array pairs. A lot of perfect binary array pairs can be constructed by using these two methods, and more choices are provided for communication engineering.

Most subspace identification methods are developed for linear time-invariant system. However, in reality, most systems are time-varying. Hence the recursive version of subspace identification methods is urgently desired. In this paper, we propose a unifying framework of recursive subspace model identification algorithm, which is based on the orthogonal projection and principal component analysis (PCA). Based on our framework, the bona fide recursive algorithm is applied to update the QR factorization. Two recursive subspace model identification algorithms are developed for open loop and closed loop condition, respectively. The numerical simulations demonstrate the efficiency of the two algorithms comparing with other algorithms.