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.