This paper investigates construction methods of perfect 16-QAM sequences and arrays, since such sequences and arrays play quite an important role in synchronization of communication systems making use of 16-QAM signals. The method used for obtaining the results is to establish a relationship between the known perfect quaternary sequences/arrays and the required ones so that the former is transformed into the latter. Consequently, the sufficient conditions for implementing the required transformations are derived, and several examples are given. Our methods can provide perfect 16-QAM sequences with lengths 2, 4, 8, and 16, which are given in Table A·1 and infinite families of perfect 16-QAM arrays, whose existing sizes up to dimension 5 and volume 2304 are listed in Tables A·2 and A·3.

A perfect array is an array for which the autocorrelation function is impulsive. A parameterization of perfect arrays of real numbers is presented. Perfect arrays are represented by trigonometric functions. Three formulae are obtained according to the parities of the size of the array. Examples corresponding to each formula are shown. In the case of 66 arrays, the existence of a set of perfect arrays having integer components is shown.

Sequences with good correlation properties are of substantial interest in many applications. By interleaving a perfect array with shift sequences, a new method of constructing binary array set with zero correlation zone (ZCZ) is presented. The interleaving operation can be performed not only row-by-row but also column-by-column on the perfect array. The resultant ZCZ binary array set is optimal or almost optimal with respect to the theoretical bound. The new method provides a flexible choice for the rectangular ZCZ and the set size.

Multi-dimensional (MD) periodic complementary array sets (CASs) with impulse-like MD periodic autocorrelation function are naturally generalized to (one dimensional) periodic complementary sequence sets, and such array sets are widely applied to communication, radar, sonar, coded aperture imaging, and so forth. In this letter, based on multi-dimensional perfect arrays (MD PAs), a method for constructing MD periodic CASs is presented, which is carried out by sampling MD PAs. It is particularly worth mentioning that the numbers and sizes of sub-arrays in the proposed MD periodic CASs can be freely changed within the range of possibilities. In particular, for arbitrarily given positive integers M and L, two-dimensional periodic polyphase CASs with the number M2 and size L L of sub-arrays can be produced by the proposed method. And analogously, pseudo-random MD periodic CASs can be given when pseudo-random MD arrays are sampled. Finally, the proposed method's validity is made sure by a given example.

This paper presents a new generative approach for generating two-dimensional signals having both a low peak factor (crest factor) and a flat power spectrum. The flat power spectrum provides zero auto-correlation, except at the zero shift. The proposed method is a generative scheme, not a search method, and produces a two-dimensional signal of size 2(2n1+1)2(2n2+1)2 for an arbitrary pair of positive integers n1 and n2 without any computer search. The peak factor of the proposed signal is equal to the peak factor of a single trigonometric function.