# Mathematical calculation during transmission

We exploit physical layer properties of a communication channel in order to compute mathematical functions during transmission on the wireless channel.

In particular, this covers the design of a neural network overlay on a distributed set of sensor nodes utilising beamforming techniques to generate separated communication links; a scheme utilising random burst sequences for the simultaneous, non-synchronised data transmission at from RFID nodes; as well as the offloading of computational load for the calculation of mathematical functions to the wireless channel.

We have conducted simulations and case studies in order to demonstrate the pracitcal feasibility of the proposed transmission schemes.
By abstracting from classical packet-based synchronised transmission schemes, we can empower simplest classes of nodes to perform sophisticated computational and communication tasks.
These schemes are enabling real smart spaces consisting of parasitic or reader-powered nodes to compute complex functions.

## Contributions

- A neuron overlay on a wireless sensor network utilising distributed transmit beamforming in order to realise arbitrary computations among nodes in smart spaces
- A transmission scheme for collective, non-synchronised information transmission in networks of densely deployed nodes
- A scheme to compute mathematical functions by means of superimpositions of transmit burst sequences utilising convolutions of random variables
- Realisation of the computation of the four basic mathematical operations by poisson-distributed burst sequences
- A discussion of convolutions of further random variables suitable for the computation of distinct mathematical functions

## Results

### A neural-network overlay utilising distributed adaptive beamforming techniques

We establish a wireless sensor network that emulates biological neuronal structures for the purpose of creating smart spaces.
Two different types of wireless nodes working together are used to mimic the behaviour of a neuron consisting of dendrites, soma and synapses.
The transmission among nodes that establish such a neuron structure is established by distributed beamforming techniques to enable simultaneous information transmission among neurons.
Through superposition of transmission signals, data from neighbouring nodes is perceived as background noise and does not interfere.
In this way we show that beamforming and computation on the channel can be powerful tools to establish intelligent sensing systems even with minimal computational power.

In mathematical simulations, we demonstrated how a cost efficient wireless sensor network is able to perform the transmission from synapse to dendrite, the addition of weighted signals and the transmission of the result from the soma to synapse.
In particular, the impact of the count of synapses, the count of dendrites, the location of dendrites and the transmission data rate impacts the bit error rate of the simultaneous superimposed transmission from dendrites to several respective synapses.
With this construction we are able to establish smart spaces capable of executing complex computations on computationally limited wireless nodes.

### Non-synchronised spontaneous data transmission via random burst sequences

Intelligent Environments are currently implemented with standard WSN technologies using conventional connection-based communications.
However, connection-based communications may impede progress towards IE scenarios involving high mobility or massive amounts of sensor nodes.

We present a novel approach based on collective transmission for item level tagging using printed organic electronics, which implements robust, collective, approximate read-out of large numbers of simple tags.
Our approach uses mechanisms for calculation by simultaneous transmission.
We detail the collective transmission approach, discuss its implementation in the organic printed label scenario, and show first results of experiments conducted with our smart label test bed.

The experiments have for the first time shown, that collective information transmission is possible, which enables reading out of a wireless sensor network at once.
It has proved that superimposed signals can be used efficiently to transmit data simultaneously by concurrent usage of simple analog sensor nodes.
The different classes of sensory information sent in a collective information transmission are in more than 85% detected by using binary query. Further on, in the proportion query the number of the senders, which have sent the same sensory information are estimated with an averaged deviation error of 2.06%.

### Offloading computational load to the communication channel

We consider the calculation of mathematical functions at the time of wireless superimposition of data sequences.
Highly resource restricted IoT or sensor devices, possibly parasitic or reader powered nodes can, although restricted in their computational capabilities, draw on a virtually unlimited power source.
We exploit this property by trading computational load for communication load.
In particular, we present a communication scheme by which mathematical computations can be executed at the time of wireless transmission.
In order to achieve this, we exploit rules for convolutions of random functions and utilise burst sequences to represent repeated random experiments on the wireless channel.
This transmission scheme enables the execution of complex computations by a network of resource restricted, cooperating nodes at a computational load below the operationâ€™s computational complexity.
We derive the scheme analytically, explore its feasibility for dense networks in mathematical simulations and demonstrate its practicability in case studies.

In particular, we show how the four basic mathematical operations can be realised and how convolutions of distinct random variables are suited for the realisation of further, specific operations.

## Publications

- Stephan Sigg, Predrag Jakimovski, Yusheng Ji and Michael Beigl: Utilising convolutions of random functions to realise function calculation via a physical channel, accepted for presentation at the 2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC)
- Stephan Sigg, Predrag Jakimovski and Michael Beigl: Calculation of functions on the RF-channel for IoT, in Proceedings of the 3rd international conference on the Internet of Things (IoT2012), October 2012 (DOI)
- Predrag Jakimovski, Hedda R. Schmidtke, Stephan Sigg, Leonardo Weiss, Ferreira Chaves and Michael Beigl: Collective Communication for Dense Sensing Environments, in Journal of Ambient Intelligence and Smart Environments (JAISE), 2012 (DOI)
- Stephan Sigg, Predrag Jakimovski, Florian Becker, Hedda Schmidtke, Martin Alexander Neumann, Yusheng Ji and Michael Beigl: Neuron-inspired collaborative transmission in wireless sensor networks, in Proceedings of the 8th International ICST Conference on Mobile and Ubiquitous Systems (MobiQuitous 2011), 2011 (DOI,slides)
- Predrag Jakimovski, Florian Becker, Stephan Sigg, Hedda R. Schmidtke and Michael Beigl: Collective Communication for Dense Sensing Environments, in 7th IEEE International Conference on Intelligent Environments (IE), 2011 (**Best paper**) (DOI)