2015/04/28 by Jan Schreck, Peter Jung, Schreck, Jan +3
Computer Science · Engineering · #Advanced MIMO Systems Optimization #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1504.07365
openalex publication_date 2015/04/28 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We develop a framework that we call compressive rate estimation. We assume\nthat the composite channel gain matrix (i.e. the matrix of all channel gains\nbetween all network nodes) is compressible which means it can be approximated\nby a sparse or low rank representation. We develop and study a novel sensing\nand reconstruction protocol for the estimation of achievable rates. We develop\na sensing protocol that exploits the superposition principle of the wireless\nchannel and enables the receiving nodes to obtain non-adaptive random\nmeasurements of columns of the composite channel matrix. The random\nmeasurements are fed back to a central controller that decodes the composite\nchannel gain matrix (or parts of it) and estimates individual user rates. We\nanalyze the rate loss for a linear and a non-linear decoder and find the\nscaling laws according to the number of non-adaptive measurements. In\nparticular if we consider a system with N nodes and assume that each column\nof the composite channel matrix is k sparse, our findings can be summarized\nas follows. For a certain class of non-linear decoders we show that if the\nnumber of pilot signals M scales like M \∼ k \log(N/k), then the rate\nloss compared to perfect channel state information remains bounded. For a\ncertain class of linear decoders we show that the rate loss compared to perfect\nchannel state information scales like 1/\√(M).\n