One-Bit Null Space Learning for MIMO underlay cognitive radio

We present a new algorithm, called the One-Bit Null Space Learning Algorithm (OBNSLA), for MIMO cognitive radio Secondary Users (SU) to learn the null space of the interference channel to the Primary User (PU). The SU observes 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´s transmitted signal or control channel and extracting information from it about whether the PU´s Signal to Interference plus Noise power Ratio has increased or decreased. In addition to introducing the OBNSLA, the paper provides a thorough convergence analysis of this algorithm. The OBNSLA is shown to have a linear convergence rate and an asymptotic quadratic convergence rate.