High-Order-QAM Source Equalization for Cognitive Communication Systems

Source equalization can not only counteract channel multi-path fading but also guarantee the transmission efficiency of a communication system. However, determining an optimal source equalizer is typically NP hard. The cost function of such source equalizer involves an exponentially increasing number of local minima. To reduce the complexity, this study develops an efficient two-stage source equalization algorithm for quadrature-amplitude-modulation (QAM) systems. To reduce the number of local minima, the multimodulus algorithm (MMA) is implemented in the first stage, and to reduce the steady state error, an improved soft decision-directed algorithm (ISDDA) is implemented in the second stage. A novel modified least squares method (MLSM) is proposed to quickly search for the desired equalizer. The MLSM can converge to the invariance set of the MMA and ISDDA cost functions and has a quadratic termination property. In particular, theoretical analysis shows that the MLSM has a considerably lower computational load than the Newton methods by computing the constant Hessian matrix and its inverse only once. Furthermore, to ensure that the proposed algorithm switches to the second stage as early and suitably as possible, an attainable switching threshold between the two stages is provided on the basis of a hypothesis that the equalizer output error obeys a normal distribution, and the rationale of this hypothesis is also provided. Simulation results illustrate that the proposed algorithm has better convergence stability, superior equalization quality, and considerably faster convergence speed than the traditional stochastic-gradient-type dual-mode source equalization algorithms.