We study spectral representation and its applications for non-decaying continuous-time signals that are not necessarily bounded at ±∞ . We introduce the notions of transfer functions, spectrum degeneracy, spectrum gaps, and band-limitedness, for these unbounded signals. As an example of applications, we give explicit formulas for transfer functions of low-pass and high-pass filters suitable for these signals. As another example of applications, we show that non-decaying unbounded signals with a single point spectrum degeneracy and polynomial rate of growth are predictable. The corresponding transfer functions for the predictors are obtained explicitly. In addition, we obtain an interpolation sampling formula for unbounded bandlimited signals.
The key elements of Industrial Internet of Things networks are RTA (Real-Time Application) stations, which detect events and deliver alerts about them within a limited time with high probability. Since such stations are often located in hard-to-reach places and cannot always be connected to the power supply, they must consume little energy. A promising solution for ensuring low latency and energy consumption is the use of Target Wake Time (TWT) and Restricted Target Wake Time (R-TWT) mechanisms, introduced in the latest Wi-Fi standards: Wi-Fi 6 and Wi-Fi 7. However, the effectiveness of using these mechanisms in a heterogeneous network consisting of both RTA stations and regular stations operating in saturation mode has not been studied extensively. In this paper, we conduct a comparative study of the effectiveness of using TWT and R-TWT mechanisms in scenarios of low-intensity traffic service for RTA stations. To do this, we develop an analytical model that, for the first time, makes it possible to evaluate the probability of RTA station frame delivery within a given time and the throughput for regular stations.
We discuss modern applied problems of discrete optimization at a mathematical level, and for one of them, clustering points in multidimensional real space, we examine in detail the algorithm for solving it. A characteristic feature of these problems is the large size of the initial data, often represented by matrices with tens of thousands of rows and tens of thousands of columns. This leads to problems of processing large amounts of data in the context of a complex computational algorithm; moreover, it is often essential to obtain a reasonably accurate solution to the problem quickly, so the question of the algorithm complexity is of fundamental importance. Solving such a clustering problem leads to difficult mathematical problems: removing hidden parameters; identifying significant features; switching to optimal and informationally significant point coordinates; specific representation (manifold maps) of the vertices of a weighted graph; selection of a function depending on the current clustering of vertices, the maximization of which leads to the desired clustering; for each cluster, selection of features that individually characterize it; and, finally, reduction of the dimensionality of the source data.
Wi-Fi standardization continues: IEEE 802.11bn (Wi-Fi 8) reached Draft 1.0 in August 2025 and is progressing through comment resolution. The wireless industry now stands at a pivotal crossroads as it begins to define Wi-Fi 9. This paper analyzes technical directions and candidate features for the post-802.11bn amendment, tentatively referred to as Wi-Fi 9. We synthesize contributions from device manufacturers, network operators, and research institutions presented to the IEEE 802.11 Wireless Next Generation Standing Committee in early 2026. The emerging consensus indicates that, rather than increasing the nominal data rates, the next generation will likely prioritize deterministic performance, reliability, and expanded application domains. The paper examines the market forces driving this transition, including AI workloads that invert traditional traffic asymmetry, industrial robotics that demand sub-millisecond latency, and immersive entertainment that requires the simultaneous satisfaction of throughput, latency, and reliability constraints. Then the paper analyzes candidate technologies spanning PHY and MAC layer transformations, coordination between multiple networks, and AI integration throughout the protocol stack. Implementation challenges, including backward compatibility tradeoffs and spectrum availability, are discussed. Finally, the paper outlines the anticipated standardization timeline targeting commercial deployment of Wi-Fi 9 in the 2030s.
Among known random multiple access (RMA) algorithms, the part-and-try (splitting) algorithm demonstrates the highest throughput. However, its implementation in cellular random access channels is challenging, since the correct operation of the algorithm requires absolute time synchronization among all users to uniquely identify events in a Poisson arrival process. In this paper, we propose a modified RMA algorithm based on the principles of the part-and-try algorithm, in which the introduction of randomization eliminates the need for temporal event identification. This modification enables the algorithm to be implemented in practical random access systems. The achieved throughput of the algorithm is 0.485 .
