Sub-Function Allocation for Computation over Wide-Band MAC

Future networks are expected to connect an enormous number of nodes wirelessly using wide-band transmission. This brings great challenges. To avoid collecting a large amount of data from the massive number of nodes, computation over multi-access channel (CoMAC) is proposed to compute a desired function over the air utilizing the signal-superposition property of multi-access channel (MAC). Due to frequency selective fading, wide-band CoMAC is more challenging and has never been studied before. In this work, we propose the use of orthogonal frequency division multiplexing (OFDM) in wide-band CoMAC to transmit functions in a similar way to bit sequences through division, allocation and reconstruction of functions. To prevent a vanishing computation rate from the increase of the number of nodes, a novel sub-function allocation (SFA) of sub-carriers is derived. The improved computation rate of the proposed framework and the corresponding allocation has been verified through both theoretical analysis and simulation.

[1]  Omid Salehi-Abari,et al.  Over-the-air Function Computation in Sensor Networks , 2016, ArXiv.

[2]  Guo Wei,et al.  Over-the-air Computation for Cooperative Wideband Spectrum Sensing and Performance Analysis , 2018 .

[3]  Michael Gastpar,et al.  Compute-and-Forward: Harnessing Interference Through Structured Codes , 2009, IEEE Transactions on Information Theory.

[4]  Panganamala Ramana Kumar,et al.  Computing and communicating functions over sensor networks , 2005, IEEE Journal on Selected Areas in Communications.

[5]  Michael Gastpar,et al.  Computation Over Multiple-Access Channels , 2007, IEEE Transactions on Information Theory.

[6]  Yung-Fang Chen,et al.  A Fast Subcarrier, Bit, and Power Allocation Algorithm for Multiuser OFDM-Based Systems , 2008, IEEE Transactions on Vehicular Technology.

[7]  Mario Goldenbaum,et al.  Computation of Real-Valued Functions Over the Channel in Wireless Sensor Networks , 2014 .

[8]  Li Chen,et al.  Over-the-Air Computation for IoT Networks: Computing Multiple Functions With Antenna Arrays , 2018, IEEE Internet of Things Journal.

[9]  Simon Litsyn,et al.  Lattices which are good for (almost) everything , 2005, IEEE Transactions on Information Theory.

[10]  Slawomir Stanczak,et al.  Robust Analog Function Computation via Wireless Multiple-Access Channels , 2012, IEEE Transactions on Communications.

[11]  Michael Gastpar,et al.  Computation over Gaussian networks with orthogonal components , 2013, 2013 IEEE International Symposium on Information Theory.

[12]  Bang Chul Jung,et al.  Opportunistic Function Computation for Wireless Sensor Networks , 2016, IEEE Transactions on Wireless Communications.

[13]  Li Chen,et al.  A Uniform-Forcing Transceiver Design for Over-the-Air Function Computation , 2018, IEEE Wireless Communications Letters.

[14]  Gerhard Fettweis,et al.  5G: Personal mobile internet beyond what cellular did to telephony , 2014, IEEE Communications Magazine.

[15]  Guo Wei,et al.  Over-the-air Computation for IoT Networks: Computing Multiple Functions with Antenna Arrays , 2018 .