<title>Adaptive equalization techniques for indoor dynamic wireless communication channels</title>

Abstract

A modified constant modulus algorithm (MCMA) algorithm for adaptive channel equalization for QAM signals is proposed. The proposed algorithm minimizes a cost function that consists of amplitude-and phase-dependent terms. The phase term complements the amplitude-dependent term that is provided by the conventional constant modulus algorithm (CMA). This term should satisfy several properties that guarantee extremum values at the QAM signal levels and at maximum deviations from these levels. Further, the properties should allow symmetry and uniformity across all alphabets. It is shown that the even power co-sinusoidal functions are appropriate for phase term representations. The MCMA is compared with the CMA and the Stop-and-Go Algorithm (SGA) for blind equalization. The performance is evaluated for indoor wireless channels using both transient and steady-state behaviors of the mean square error (MSE). A channel model is developed based on spectral observations of the unlicensed U-NII frequency band, and shown to be time-varying and to exhibit frequency selective fading. While the CMA is successful in achieving good performance, it is shown that both MCMA and SGA are superior and more robust in low SNR environments. The paper also presents a performance comparison of symbol-spaced and sample-spaced equalizations for a single and two-antenna receiver. Simulation results demonstrate that using multi-antenna receiver can effectively improve adaptive channel equalizations by increasing convergence rate and decreasing steady-state mean square error.

New hybrid adaptive blind equalization algorithms for QAM signals

“…Corresponding ψ k for g c can be found in [6]. We shall refer to MCMA with g c (x) and g G (x) penalty terms, as the Cos-MCMA and the Gauss-MCMA respectively.…”

“…MCMA criteria [6] are designed for QAM modulations. They consist in adding a positive penalty term to the CMA.…”

“…CME functions are generally, positive function, constrained to meet certain properties : symmetry around constellation coordinates, uniformity (that is, even level of local maxima) and zero value at constellation points. As CME examples, we can cite powers of sine and cosine functions and polynomials [6]. In this work, we propose two CME terms leading to new criteria.…”

“…To overcome these drawbacks, other algorithms like the multimodulus algorithm (MMA) [11], the square contour algorithm (SCA) [12,13] and the extended CMA (ECMA) [14] have been proposed. The most interesting extensions of the CMA are those based on hybrid approaches [6][7][8], where it is proposed to augment the standard CMA cost function by a penalty term that takes into account the location of constellation symbols. This penalty term is often referred to as the constellation matching error (CME).…”

“…Blind equalizers endeavor to filter transmitted signals without need to initializing sequences but only suppose a priori knowledge about some statistical properties of these signals. To deal with this problem, the constant modulus algorithm (CMA), pioneered by Godard [1] and extended later on [2][3][4][5][6][7][8], has been extensively used over the last two decades, since it is easy to implement and has good convergence properties [9,10]. CMA minimizes a cost function related to signal amplitude, generally via the stochastic gradient descent algorithm.…”