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This paper proposes a blind technique that enables a MIMO cognitive radio Secondary User (SU) to transmit in the same band simultaneously with a Primary User (PU) by utilizing separate spatial dimensions than the PU. Specifically, the SU transmits in the null space of the interference channel to the PU. The SU learns this null space without burdening the PU with any knowledge or explicit cooperation with the SU. The only condition required is that during the learning period, the SU is allowed to inflict "non-harmful" interference to the PU. The SU measures a monotonic function of this interference in order to learn the null space. Specifically, during the learning interval, the SU learns the null space by iteratively modifying the spatial orientation of its transmitted signal and measures the effect of this modification on the monotonic function that it observes. We provide simulation results demonstrating that the algorithm converges rapidly and is robust to quantization noise and other sources of interference.Index Terms-Underlay cognitive radio, cognitive radio (CR), MIMO, null space, learning, blind, interference constraint, interference suppression, opportunistic spectrum sharing, spatial multiplexing.

This paper proposes a new algorithm for MIMO cognitive radio secondary users (SU) to learn the null space of the interference channel to the primary user (PU) without burdening the PU with any knowledge or explicit cooperation with the SU. The knowledge of this null space enables the SU to transmit in the same band simultaneously with the PU by utilizing separate spatial dimensions than the PU. Specifically, the SU transmits in the null space of the interference channel to the PU. We present a new algorithm, called the one-bit null space learning algorithm (OB-NSLA), in which the SU learns the PU's null space by observing a binary function that indicates whether the interference it inflicts on the PU has increased or decreased in comparison to the SU's previous transmitted signal. This function is obtained by listening to the PU transmitted signal or control channel and extracting information from it about whether the PU's signal-to-interferenceplus-noise power ratio (SINR) has increased or decreased. The OB-NSLA is shown to have a linear convergence rate and an asymptotic quadratic convergence rate. Finally, we derive bounds on the interference that the SU inflicts on the PU as a function of a parameter determined by the SU. This lets the SU control the maximum level of interference, which enables it to protect the PU completely blindly with minimum complexity. The asymptotic analysis and the derived bounds also apply to the recently proposed blind null space learning algorithm.

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Gene expression analysis is generally performed on heterogeneous tissue samples consisting of multiple cell types. Current methods developed to separate heterogeneous gene expression rely on prior knowledge of the cell-type composition and/or signatures - these are not available in most public datasets. We present a novel method to identify the cell-type composition, signatures and proportions per sample without need for a-priori information. The method was successfully tested on controlled and semi-controlled datasets and performed as accurately as current methods that do require additional information. As such, this method enables the analysis of cell-type specific gene expression using existing large pools of publically available microarray datasets.