paper develops the theory and constructions of polyphase zero-ambiguity-zone (ZAZ) sequences for ISAC waveforms, enabling the ZAZ shape to be designed over delay–Doppler regions of interest and supporting flexible (including multi-mode) sensing–communication operation. We first prove that a polyphase sequence with an optimal rectangular auto-ZAZ must be a member of some uncorrelated optimal ZCZ sequence family, and conversely, any member of an uncorrelated optimal ZCZ sequence family has an optimal rectangular auto-ZAZ (Theorems 1, 2 and 3). We generalize the optimality condition on the rectangular ZAZ to that on centrally symmetric convex ZAZs in general (Theorem 4). We propose some constructions of families of polyphase sequences with a strictly or asymptotically optimal rectangular ZAZ (Theorem 1), dual asymptotically optimal rectangular ZAZs (Theorems 5 and 6), and asymptotically optimal rhombic or hexagonal ZAZ (Remarks 5 and 6) from the flexible ZAZ configuration

In this paper, we propose some constructions for the uncorrelated zero-correlation-zone (ZCZ) sequence families over phase shift keying (PSK) / PSK + alphabet as the characteristic sequences of a relative difference set (RDS). The proposed sequence families feature some significant reduction in alphabet size at the price of relaxing the optimality condition, specifically reducing the number of sequences.

This paper proves that Popovi´c's construction describes all the uncorrelated optimal ZCZ sequence families.

In this paper, we define (m,n,r) zero-correlation-zone (ZCZ) sonar sequences and present some of their properties. We prove an upper bound on r for (m,n,r) ZCZ sonar sequences and propose a new and simple construction for (m,n,r) ZCZ sonar sequences with m = r2− 1 and any positive integer n. We also propose two constructions for (m,n,2) ZCZ-DD sonar sequences for some m and n which are some variations of well-known sonar sequence constructions. We report a lot of exhaustive search results and some interesting open problems.

In this paper, we derive a lower bound on the alphabet size of the optimal uncorrelated polyphase ZCZ sequence families, assuming that Mow’s Conjecture is true. We also propose some new optimal uncorrelated polyphase ZCZ sequence families for all the optimal ZCZ parameters. All our proposed families achieve our proposed alphabet size bound so that this bound is the minimum alphabet size (assuming Mow’s conjecture is true). We also derive some interesting facts regardless of the truth of Mow’s Conjecture: an optimal ZCZ family of normalized sequence (not necessarily uncorrelated) is always periodic complementary; therefore, a sequence generated by interleaving all the sequences in an optimal uncorrelated ZCZ family of normalized sequences is always a perfect sequence.

We define run sequences of period$2^{n}-1$as the binary sequences where the distribution of runs of 0’s and runs of 1’s is exactly same as that for the maximal length linear shift resister sequences of period$2^{n}-1$. We first count the number of all the cyclically distinct run sequences of period$2^{n}-1$. For each$n$-tuple, we consider the average number of occurrences over all the run sequences of period$2^{n}-1$. We identify the$n$-tuples with average number 1 and, in particular, those that occur exactly once in every run sequence of period$2^{n}-1$. We finally prove that, as$n$increases, the average number of every non-zero$n$-tuple approaches to 1.

In this paper, we calculate the number of sequences with run property and propose two methods for generating sequences with run property. One of them, generating sequences in order, is useful for exhaustive search, and another, ranking and unranking method, is useful for scatter search.

We analyze the symbol measures for iterative erasure insertion and decoding of a Reed-Solomon coded SFH/MFSK system over jamming channels. In contrast to conventional erasure insertion schemes, iterative schemes do not require any preoptimized threshold or channel state information at the receiver. We confirm the performance improvement using a generalized minimum distance (GMD) decoding method with three different symbol measures. To analyze performance, we propose a new analysis framework considering the “trapped-error” probability. From analysis and the simulation results, we show that ratio-based GMD decoding has the best performance among the one-dimensional iterative erasure insertion and decoding schemes.