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Register a new userMulti-Slot Over-The-Air Computation in Fading Channels
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Added by
Suhua Tang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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IoT systems typically involve separate data collection and processing, and the former faces the scalability issue when the number of nodes increases. For some tasks, only the result of data fusion is needed. Then, the whole process can be realized in an efficient way, integrating the data collection and fusion in one step by over-the-air computation (AirComp). Its shortcoming, however, is signal distortion when channel gains of nodes are different, which cannot be well solved by transmission power control alone in times of deep fading. To address this issue, in this paper, we propose a multi-slot over-the-air computation (MS-AirComp) framework for the sum estimation in fading channels. Compared with conventional data collection (one slot for each node) and AirComp (one slot for all nodes), MS-AirComp is an alternative policy that lies between them, exploiting multiple slots to improve channel gains so as to facilitate power control. Specifically, the transmissions are distributed over multiple slots and a threshold of channel gain is set for distributed transmission scheduling. Each node transmits its signal only once, in the slot when its channel gain first gets above the threshold, or in the last slot when its channel gain remains below the threshold. Theoretical analysis gives the closed-form of the computation error in fading channels, based on which the optimal parameters are found. Noticing that computation error tends to be reduced at the cost of more transmission power, a method is suggested to control the increase of transmission power. Simulations confirm that the proposed method can effectively reduce computation error, compared with state-of-the-art methods.
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Over-the-air computation (AirComp) has been recognized as a low-latency solution for wireless sensor data fusion, where multiple sensors send their measurement signals to a receiver simultaneously for computation. Most existing work only considered performing AirComp over a single frequency channel. However, for a sensor network with a massive number of nodes, a single frequency channel may not be sufficient to accommodate the large number of sensors, and the AirComp performance will be very limited. So it is highly desirable to have more frequency channels for large-scale AirComp systems to benefit from multi-channel diversity. In this letter, we propose an $M$-frequency AirComp system, where each sensor selects a subset of the $M$ frequencies and broadcasts its signal over these channels under a certain power constraint. We derive the optimal sensors transmission and receivers signal processing methods separately, and develop an algorithm for joint design to achieve the best AirComp performance. Numerical results show that increasing one frequency channel can improve the AirComp performance by threefold compared to the single-frequency case.
In typical sensor networks, data collection and processing are separated. A sink collects data from all nodes sequentially, which is very time consuming. Over-the-air computation, as a new diagram of sensor networks, integrates data collection and processing in one slot: all nodes transmit their signals simultaneously in the analog wave and the processing is done in the air. This method, although efficient, requires that signals from all nodes arrive at the sink, aligned in signal magnitude so as to enable an unbiased estimation. For nodes far away from the sink with a low channel gain, misalignment in signal magnitude is unavoidable. To solve this problem, in this paper, we investigate the amplify-and-forward based relay, in which a relay node amplifies signals from many nodes at the same time. We first discuss the general relay model and a simple relay policy. Then, a coherent relay policy is proposed to reduce relay transmission power. Directly minimizing the computation error tends to over-increase node transmission power. Therefore, the two relay policies are further refined with a new metric, and the transmission power is reduced while the computation error is kept low. In addition, the coherent relay policy helps to reduce the relay transmission power by half, to below the limit, which makes it one step ahead towards practical applications.
The fading wire-tap channel is investigated, where the source-to-destination channel and the source-to-wire-tapper channel are corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information is assumed to be known at both the transmitter and the receiver. The parallel wire-tap channel with independent subchannels is first studied, which serves as an information-theoretic model for the fading wire-tap channel. The secrecy capacity of the parallel wire-tap channel is established. This result is then specialized to give the secrecy capacity of the fading wire-tap channel, which is achieved with the source node dynamically changing the power allocation according to the channel state realization. An optimal source power allocation is obtained to achieve the secrecy capacity.
Analog over-the-air computation (OAC) is an efficient solution to a class of uplink data aggregation tasks over a multiple-access channel (MAC), wherein the receiver, dubbed the fusion center, aims to reconstruct a function of the data distributed at edge devices rather than the individual data themselves. Existing OAC relies exclusively on the maximum likelihood (ML) estimation at the fusion center to recover the arithmetic sum of the transmitted signals from different devices. ML estimation, however, is much susceptible to noise. In particular, in the misaligned OAC where there are channel misalignments among transmitted signals, ML estimation suffers from severe error propagation and noise enhancement. To address these challenges, this paper puts forth a Bayesian approach for OAC by letting each edge device transmit two pieces of prior information to the fusion center. Three OAC systems are studied: the aligned OAC with perfectly-aligned signals; the synchronous OAC with misaligned channel gains among the received signals; and the asynchronous OAC with both channel-gain and time misalignments. Using the prior information, we devise linear minimum mean squared error (LMMSE) estimators and a sum-product maximum a posteriori (SP-MAP) estimator for the three OAC systems. Numerical results verify that, 1) For the aligned and synchronous OAC, our LMMSE estimator significantly outperforms the ML estimator. In the low signal-to-noise ratio (SNR) regime, the LMMSE estimator reduces the mean squared error (MSE) by at least 6 dB; in the high SNR regime, the LMMSE estimator lowers the error floor on the MSE by 86.4%; 2) For the asynchronous OAC, our LMMSE and SP-MAP estimators are on an equal footing in terms of the MSE performance, and are significantly better than the ML estimator.
In this paper, we design a new polar slotted ALOHA (PSA) protocol over the slot erasure channels, which uses polar coding to construct the identical slot pattern (SP) assembles within each active user and base station. A theoretical analysis framework for the PSA is provided. First, by using the packet-oriented operation for the overlap packets when they conflict in a slot interval, we introduce the packet-based polarization transform and prove that this transform is independent of the packets length. Second, guided by the packet-based polarization, an SP assignment (SPA) method with the variable slot erasure probability (SEP) and a SPA method with a fixed SEP value are designed for the PSA scheme. Then, a packet-oriented successive cancellation (pSC) and a pSC list (pSCL) decoding algorithm are developed. Simultaneously, the finite-slots throughput bounds and the asymptotic throughput for the pSC algorithm are analyzed. The simulation results show that the proposed PSA scheme can achieve an improved throughput with the pSC/SCL decoding algorithm over the traditional repetition slotted ALOHA scheme.
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