Analog computation over the wireless channel: A proof of concept

Kortke, Andreas; Goldenbaum, Mario; Stańczak, Sławomir

doi:10.1109/icsens.2014.6985230

Cited by 44 publications

(38 citation statements)

References 7 publications

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“…On the other hand, coding can be still useful for other settings such as sensing correlated Gaussian sources [7]. The satisfactory performance (with optimality in certain cases) of simple analog AirComp have led to an active area focusing on designing and implementing techniques for receiving a desired function of concurrent signals, namely a targeted coherent combination of the signal waveforms [3], [8]- [16]. In particular, considering analog AirComp, power control at sensors was optimized in [8], [9], the computation rate (defined as the number of functional values computed per time slot) analyzed in [10], and the effect of channel estimation error characterized in [11].…”

Section: A Over-the-air Computation For Sensor Networkmentioning

confidence: 99%

MIMO Over-the-Air Computation for High-Mobility Multimodal Sensing

Zhu

Huang

2019

IEEE Internet Things J.

232

211

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In future Internet-of-Things (IoT) networks, sensors or even access points can be mounted on ground/aerial vehicles for smart-city surveillance or environment monitoring. For such high-mobility sensing, it is impractical to collect data from a large population of sensors using any traditional orthogonal multi-access scheme as it would lead to excessive latency. To tackle the challenge, a technique called over-the-air computation (AirComp) was recently developed to enable a data-fusion to receive a desired function (e.g., averaging or geometric mean) of sensing data from concurrent sensor transmissions. This is made possible by exploiting the superposition property of a multiaccess channel. Targeting a multi-antenna sensor network, this work aims at developing multiple-input-multiple output (MIMO) AirComp for enabling high-mobility multi-modal sensing where a multi-modal sensor monitors multiple environmental parameters such as temperature, pollution and humidity. To be specific, we design MIMO-AirComp equalization and channel feedback techniques for spatially multiplexing multi-function computation, each corresponding to a particular sensing-data type. Given the objective of minimizing sum mean-squared error via spatial diversity, a close-to-optimal equalizer is derived in closed-form using differential geometry. The solution can be computed as the weighted centroid of points (subspaces) on a Grassmann manifold, where each point represents the subspace spanned by the channel coefficient matrix of a sensor. As a by-product, the problem of MIMO-AirComp equalization is proved to have the same form as the classic problem of multicast beamforming, establishing the AirComp-multicasting duality. Its significance lies in making the said Grassmannian-centroid solution method transferable to the latter problem which otherwise is solved using the more computation-intensive semidefinite relaxation method in the literature. Last, building on the AirComp equalization solution, an efficient channel-feedback technique is designed for an access point to receive the equalizer from simultaneous sensor transmissions of designed signals that are functions of local channel-state information. This overcomes the difficulty of provisioning orthogonal feedback channels for many sensors.

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Section: A Over-the-air Computation For Sensor Networkmentioning

confidence: 99%

MIMO Over-the-Air Computation for High-Mobility Multimodal Sensing

Zhu

Huang

2019

IEEE Internet Things J.

232

211

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“…A closer look at (8) reveals that the optimal classifier is nomographic with ϕ k (s k ) = w ⋆ k s k and ψ(y) = sgn(y + b ⋆ ), where w ⋆ k and s k denote the k-th elements of w ⋆ and s, respectively. In the following two subsections, we describe how this special structure permits to let the wireless channel (1) help in the computation.…”

Section: The Wireless Channel As a Helpermentioning

confidence: 99%

“…Proposition 1. Let f be the classifier given in (8) andf its estimate as defined in (15). Then, with the transmission scheme proposed in Sections IV-A and IV-B, any system state s ∈ S can be reliably classified, in the sense of (3), over the channel (1).…”

Section: Proving Reliabilitymentioning

confidence: 99%

Energy-efficient classification for anomaly detection: The wireless channel as a helper

Ralinovski

Goldenbaum

Stańczak

2016

2016 IEEE International Conference on Communications (ICC)

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Anomaly detection has various applications including condition monitoring and fault diagnosis.The objective is to sense the environment, learn the normal system state, and then periodically classify whether the instantaneous state deviates from the normal one or not. A flexible and cost-effective way of monitoring a system state is to use a wireless sensor network. In the traditional approach, the sensors encode their observations and transmit them to a fusion center by means of some interference avoiding channel access method. The fusion center then decodes all the data and classifies the corresponding system state. As this approach can be highly inefficient in terms of energy consumption, in this paper we propose a transmission scheme that exploits interference for carrying out the anomaly detection directly in the air. In other words, the wireless channel helps the fusion center to retrieve the sought classification outcome immediately from the channel output. To achieve this, the chosen learning model is linear support vector machines. After discussing the proposed scheme and proving its reliability, we present numerical examples demonstrating that the scheme reduces the energy consumption for anomaly detection by up to 53 % compared to a strategy that uses time division multiple-access.

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“…Considering that each node only has imperfect CSI, the worst-case MSE for analog CP-MAC was formulated and solved in [15]. Some experimental platforms were built to verify the idea of analog CP-MAC in [16], [17]. In order to obtain reliable functions, channel coding has been adopted to combat additive white gaussian noise (AWGN) for CP-MAC.…”

Section: Introductionmentioning

confidence: 99%