Fractional order constant modulus blind algorithms with application to channel equalisation

A novel methodology is developed for blind equalisation where the output of the linear filter is passed through a nonlinear fractional update term derived from the cost function using fractional calculus. The final weights update is a combination of the conventional constant modulus algorithm (CMA) weights and a fractional update part. As an improvement over the traditional approach, the new fractional strategy helps capture the parameters of the model at a faster rate while keeping the error small. The algorithm is applied for the blind equalisation of flat and frequency-selective channels. To assess the suitability of the proposed technique, different fractional orders and step sizes are used; the performance metric considered is the mean squared error for a quadrature phase shift keying transmission scheme. The simulation results show that the proposed technique outperforms the conventional CMA, exhibits faster convergence and yields an improved steady-state response.