Computing functions via simo multiple-access channels: How much channel knowledge is needed?

We view a wireless sensor network as a collection of sensor nodes that observe sources of information, process the picked up data and send it to a sink node, with the goal of computing a desired function of the measurements. To this end, we consider a previously proposed coding scheme that exploits the underlying fading multiple-access channel (MAC) to efficiently estimate the function values. The main problem addressed in this paper is how much channel state information (CSI) is needed at the sensor nodes to obtain sufficiently good estimates? First we show that there is no performance loss, independent of fading distributions, if, instead of perfect CSI, each sensor node has only access to the modulus of its channel coefficient. In the case of multiple antenna elements at the sink node and specific independent distributed fading environments, it is shown that CSI at sensor nodes is not necessary and a very simple correction of fading effects can be performed at the sink based on some statistical channel knowledge. In many cases, fading improves the estimation accuracy due to the multiple-access nature of the channel.