Spectrometers are widely used for characterizing materials. Recently, filter-based spectrometers have been pro- posed to lower the manufacturing cost by replacing optical components with low-cost wavelength-selective filters, but at the expense of possibly lowered signal quality. We present compressive spectrometers which, based on the compressive sensing principle, are able to recover signal with improved quality from measurements acquired by a relatively small number of low-cost filters. We achieve high quality recovery by leveraging the fact that spectrometer measurements typically follow the shape of a smooth curve with a few spikes. We validate our method with real-world measurements, and release our dataset to facilitate future research.
It is of interest to find compare optimum beamforming communications between a random antenna array of sensors and a uniform antenna array base station to MIMO communications between the two arrays. For these purposes we examine a specific example. Channel capacity is compared for various versions of MIMO communications. Channel state information is assumed to be known a.) at the receiving array only, and b) at both the transmitting and receiving arrays. When the signal to noise ratio is high, the blind transmitter and the knowledgeable transmitter MIMO provides higher channel capacity than the beamformer, but for very low signal to noise ratio only the knowledgeable transmitter MIMO equals the beamformer channel capacity.
We consider communications and network systems whose properties are characterized by the gaps of the leading eigenvalues of (A Hermitian) times A for some matrix A . We show that a sufficient and necessary condition for a large eigen-gap is that A is a "hub" matrix in the sense that it has dominant columns. We describe an application of this hub theory in multiple-input and multiple-output (MIMO) wireless systems.