An orthogonal learning rule for null-space tracking with implementation to blind two-channel identification

This paper is motivated by the blind channel identification problem under wireless communication environment. A temporal neural network is presented whose synapses vector globally converges to the null space of an input data matrix for almost all initial conditions. When it is implemented to the blind two-channel identification problem, it is shown that, under certain mild conditions, it converges exactly to the channel coefficients up to a scalar factor. Simulation shows that its convergent speed is fast enough to be able to track time-varying channels under mobile communication environment. This temporal neural network is based on a new learning rule, called the orthogonal learning rule.