Neighbor discovery is a significant research topic in wireless sensor networks. After wireless sensor devices are deployed in specific areas, they attempt to determine neighbors within their communication range. This paper proposes a new Block design-based Asynchronous Neighbor Discovery protocol for sensor networks calledBAND. We borrow the concept of combinatorial block designs for neighbor discovery. First, we summarize a practical challenge and difficulty of using the original block designs. To address this challenge, we create a new block generation technique for neighbor discovery schedules and provide a mathematical proof of the proposed concept. A key aspect of the proposed protocol is that it combines two block designs in order to construct a new block for neighbor discovery. We analyze the worst-case neighbor discovery latency numerically between our protocol and some well-known protocols in the literature. Our protocol reveals that the worst-case latency is much lower than others. Finally, we evaluate the performance ofBANDand existing representative protocols through the simulation study. The results of our simulation study show that the average and maximum latency ofBANDis about 40% lower than that of existing protocols. Furthermore,BANDspends approximately 30% less energy than others during the neighbor discovery process.

Due do the various requirements of sensor applications, it is desired to design a neighbor discovery protocol that supports both the symmetric and asymmetric duty cycles. This letter proposes a new block-based neighbor discovery protocol for asymmetric sensor networks by adapting the theory of balanced incomplete block designs and the Chinese remainder theorem. Through the simulation study, it is demonstrated that the proposed block-based neighbor discovery protocol outperforms other neighbor discovery methods, such as Disco, U-Connect, SearchLight, Hedis, and Todis.

During the initial deployment time, wireless sensors continually search their neighbors. The neighbor discovery is not an one-time event because the network topology can be changed anytime due to node mobility and failure. The neighbor discovery protocol helps sensor nodes to find neighboring sensors within their communication range. This study proposes a novel neighbor discovery protocol called the prime-number-assisted block-based neighbor discovery protocol, which intelligently changes the sensor schedules based on the greater common divisor of two sensors’ discovery cycle lengths. For example, for two sensors whose duty cycles are different, if the lengths of their discovery schedules are relatively prime, the prime-number-assisted block-based neighbor discovery protocol simply uses the balanced incomplete block design–based neighbor discovery protocol without adding any additional active slots; otherwise, it changes the original balanced incomplete block design–based schedule using a prime number. In this study, we compare the performances of prime-number-assisted block-based neighbor discovery protocol and other recently proposed neighbor discovery protocols (U-Connect, Disco, SearchLight, and Hedis) using a TOSSIM simulator. The experimental results confirm the superiority of prime-number-assisted block-based neighbor discovery protocol over other neighbor discovery protocols in terms of discovery latency and energy consumptions.

Cameron and Storvick introduced the concept of a sequential Fourier-Feynman transform and established the existence of this transform for functionals in a Banach algebra $\hat {\mathcal S}$ of bounded functionals on classical Wiener space. In this paper we investigate various relationships between the sequential Fourier-Feynman transform and the convolution product for functionals which need not be bounded or continuous. Also we study the relationships involving this transform and the first variation.