The One-Bit Null Space Learning Algorithm and its Convergence

TL;DR

This paper introduces the One-Bit Null Space Learning Algorithm (OBNSLA) for MIMO cognitive radios, enabling secondary users to learn the interference null space with minimal feedback and providing convergence guarantees and interference control.

Contribution

The paper presents a novel one-bit feedback algorithm for null space learning with proven convergence rates and interference bounds, advancing blind interference management in cognitive radios.

Findings

OBNSLA achieves linear and quadratic convergence rates.

The algorithm effectively controls interference to primary users.

Bounds on interference levels are derived as a function of SU parameters.

Abstract

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 (OBNSLA), 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 Interference plus Noise power Ratio (SINR) has increased or decreased. In addition to introducing the OBNSLA, this 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. 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.