An algebraic identification method for the demodulation of QPSK signal through a convolutive channel

We present a straightforward algebraic setting for the demodulation of a QPSK (Quadrature Phase Shift Keying) signal over a convolutive and additive noise channel. Our method exploits the form of the continuous-time received signal without questioning the digital nature of the communication system. The developments rely on classical deterministic numerical analysis. No assumption is required for the statistical properties of the signals and noises. The proposed method estimates the channel using a very short training sequence (typically 5 symbols) and, afterwards, directly reconstructs the transmitted symbols using a very fast (online) estimation procedure. The simulation results show a good robustness to additive noise disturbance and to channel´s order mismatch.