Blind equalization for correlated input symbols: A Bussgang approach

Abstract

This paper addresses the problem of blind equalization in the case of correlated input symbols, and it shows how the knowledge of the symbol sequence probability distribution can be directly incorporated in a Bussgang blind equalization scheme. Numerical results pertaining to both linear and nonlinear modulation schemes show that a significant improvement in equalization performance is obtained by exploiting the symbol sequence probability distribution using the approach herein described

Joint source and relay precoding for generally correlated MIMO with full and partial CSIT

“…The matrix n 1 has the vector of eigenvalues [1.5000, 1.2000 1 . Like previous references [28][29][30][31][45][46][47], the colored noise vector n 1 ∼ CN (0, σ 2 1 n 1 ) is generated as…”

“…where U 1 , U θ , V 1 , and V θ are unitary matrices, and 1 and θ are diagonal matrices of non-negative eigenvalues in descending order. In order to achieve a maximum oḟ I erg (B, F) in Problem (47), B and F should are in forms as:…”

Blind Fractionally Spaced Channel Equalization for Shallow Water PPM Digital Communications Links

“…Hence, as indicated in [23], to simplify the evaluation of (8) the following two assumptions are here retained: The expectation in (8) is conditionally taken with respect to the last M equalizer outputs: truec^[n]=deftruec^[n],⋯,truec^[n − M + 1]normalTThe output of the FSE is assumed to satisfy the following additive white gaussian noise (AWGN) signal model: truec^[n]≃c[n]+w[n] being w[n] a realization of stationary white Gaussian random series of power scriptPw and statistically independent of bMPPM[n].…”

“…Nonetheless, significant performance improvement is expected when the peculiar spectral redundancy of M PPM signals is properly taken into account in the equalizer design. One of the aims of this contribution is to show how the minimum mean square error (MMSE) form of the so-called Bussgang blind equalization technique, firstly presented in [20] and then extended in [21,22,23,24,25], can be also applied to the M PPM signal representations (1), (2), and (3). Specifically, in the sequel the following three major items will be addressed:The development of the MMSE nonlinearity that fully exploits the probabilistic description of the M PPM symbol formed as in (1);The proof of how the probabilistic description of the M PPM symbol (1) can be employed to recover the symbol timing;The introduction of a blind channel phase recovery technique that exploits the redundancy present in band-pass M PPM signals; it is worth highlighting that such a phase recovery stage is mandatory for band-pass transmission and coherent detection, and it is a critical step even in data aided (trained) equalization.…”

“…It is worth noting that assumption A1 extends to the M PPM case already developed in [23] for correlated QAM binary symbols used in Global Systems for Mobile Communications digital links, and it is here applied to PPM for the first time.…”