Recursive identification of FIR systems with binary-valued outputs and communication channels

This paper investigates the recursive identification of the finite impulse response systems whose outputs are subject to both the binary-valued quantization and the communication unreliability. The discrete memoryless channel with packet losses and the additive white Gaussian noise channel with time-delay are considered, a stochastic gradient type algorithm and a stochastic approximation type algorithm are respectively proposed to estimate the unknown system parameters. Under some mild conditions, the algorithms can be proved to be convergent in the almost sure and mean square senses. Also, the convergence rates are given. Numerical examples are included to illustrate the performance of the algorithms.