The paper aims to give considerable insights into how the use of the well-known second-order Newton method along with a whitening filter may help adaptive blind decision feedback equalizer (DFE) achieve excellent performances. Our analytical and simulation results confirmed that the proposed Newton-like adaptive blind DFE scheme significantly outperformed the ex-isting adaptive blind DFE scheme in terms of both the symbol error rate (SER) and the mean- squared error (MSE) perfor-mances.

Compressive sensing techniques can be employed to choose the locations of active tap-weights in the design of a sparse decision feedback equalizer (DFE), thus reducing the DFE’s computational complexity. This paper proposes sparse predictive DFEs (PDFEs) by using the orthogonal matching pursuit (OMP) and the subspace pursuit (SP), which are two popular greedy algorithms. In contrast to the optimal nonsparse PDFE, which may achieve the minimum mean-squared-error (MSE) performance, the sparse PDFEs yielded significant complexity reductions at an acceptable MSE performance loss. Simulation results demonstrated that the sparse PDFE employing the SP algorithm (SP-PDFE) offers superior symbol error rate (SER) performance as compared with the sparse PDFE employing the OMP algorithm (OMP-PDFE) by using two sparse digital television channels. Moreover, the SER performance of the SP-PDFE tends to be much closer to that of the optimal nonsparse PDFE than the OMP-PDFE does for the same sparsity of tap-weight vector.

This paper proposes the use of a novel recursive zero-pole whitening filter (ZPWF) instead of the all-pole whitening filter (APWF) and the all-zero whitening filter (AZWF) in the adaptive blind decision feedback equalizer (DFE) system. Both the APWF and the AZWF are special cases of the proposed ZPWF. The rationale for proposing the ZPWF may be explained as follows. Any arbitrary non-minimum phase channel may be approximated by the following three different types of channel: the moving-average (MA) channel, the autoregressive (AR) channel and the autoregressive-moving-average (ARMA) channel. The MA channel or the AR channel may be more effectively approximated by the ARMA channel with a much smaller total (numerator and denominator) number of coefficients. From the perspective of channel equalization, the APWF and the AZWF may merely suit a particular type of channel, while the proposed ZPWF may suit most channels in general.

This paper develops infinite impulse response (IIR) lattice structures based on two widely known blind equalization algorithms, which are the multi-modulus algorithm (MMA) and the constant modulus algorithm (CMA). The motivation for doing so is that generally for algorithms to achieve the same performance, an IIR filter requires fewer coefficients than its corresponding finite impulse response (FIR) counterpart. Moreover, the monitoring of the stability of an IIR lattice filter is simpler and less computationally complicated than that of the direct-form IIR filter. Computer simulations that compare the IIR lattice-based blind equalization algorithm with the corresponding FIR transversal algorithms and FIR-based lattice algorithms demonstrate that the former is especially suitable for equalizing channels, yielding inter-symbol interference (ISI) that mostly results from the post-cursor term.

This paper analyzes and compares the robustness of the constant modulus algorithm (CMA) and multimodulus algorithm (MMA) in the presence of additive channel noise when the channel satisfies the zero-forcing conditions. A generalized formulation of the relocation of stationary points toward the origin in terms of signal-to-noise ratio (SNR) was developed for both the CMA and the MMA to facilitate the comparison of the sensitivity to channel noise of CMA with that of MMA for various source constellations. Relationships between the relocation of the stationary points for the MMA and CMA were derived. Simulation results appear to confirm the main results of this work, regarding the sensitivity to channel noise when the fractionally spaced CMA (FS-CMA) and fractionally spaced MMA (FS- MMA) criteria were applied with various sources.

This work investigates the effect of channel noise on the performances of the constant modulus algorithm (CMA), the multimodulus algorithm (MMA), and a phase tracker (PT), following the CMA for carrier phase recovery, when various symmetrical two-dimensional complex-valued source constellations are used. The contributions of this work are two-fold. First, a generalized formulation of the relocation of stationary points toward the origin owing to channel noise is derived for both the CMA and the MMA, allowing their sensitivity to channel noise to be explicitly compared when various constellations are used. Second, the curvatures of the error surface at the stationary points in both the radial and the angular directions are reduced in a way that is linearly proportional to the square of the distances between the stationary points and the origin as the stationary points of the CMA and the MMA relocate toward the origin in the presence of additive channel noise. The reduction of the error surface curvature in the radial direction reduces the rate of blind equalization convergence, whereas the reduction in the angular direction degrades the capacity for carrier phase recovery.

A blind carrier phase derotator can be employed to correct and track carrier phase offset either before or after equalization in a blind adaptive receiver. This work proposes a computationally efficient blind carrier offset recovery algorithm for 8-vestigial side-band (8-VSB) signals by designing its cost function such that its cost surface has only two global minima without any undesirable local minima. Consequently, the proposed algorithm is not complicated by the possibility of a stochastic gradient descent (SGD) algorithm converging to a false local minimum, and global convergence can always be ensured. Moreover, the proposed algorithm can adopt a large step size in the transient period to accelerate the convergence speed along with a small step size in the convergence period to reduce the stochastic gradient noise.

This paper develops a fast order-recursive square-root-free (SRF) QR-decomposition-based least-squares lattice (QRD-LSL) interpolation algorithm that significantly improves the numerical stability of its square-root (SR) version. The proposed interpolation algorithm can be used to implement the widely known recursive least-squares (RLS) algorithm with a computational complexity of O(N log2N) per iteration, where N is the order of the RLS filter.

This work derives general formulas for the widely known constant modulus algorithm (CMA) and multimodulus algorithm (MMA) error surface curvatures at all of the stationary points with arbitrary symmetric two-dimensional signal constellations, regardless of the in-phase and quadrature dependency of the source symbols. Once these curvatures are computed, the effect of the source distributions on the capabilities of equalizer convergence and phase tracking may be accurately predicted and evaluated.

Multimodulus blind equalization algorithm (MMA) using square and cross quadrature amplitude modulation (QAM) signal constellations is known to be capable of simultaneously accomplishing joint blind equalization and carrier phase recovery. This work mathematically analyzes the MMA using QAM oblong (non-square rectangular) constellations and indicates that it performs significantly better than its cross counterpart in the recovery of the phase rotation introduced by channels, without requiring additional average transmitted power. This is because the average gradient of the cost surface of oblong constellation toward global minima is much sharper than that of cross constellation.

The constant modulus algorithm (CMA) for blind equalization requires a separate carrier-recovery system for phase recovery. This letter mathematically analyzes a modified CMA, called the multimodulus algorithm (MMA), which may perform joint blind equalization and carrier recovery without the need for a separate carrier-recovery system for quadrature amplitude modulation signal constellations. The analyses focus on five aspects of the MMA: 1) derivation of the general formulation of the MMA cost function; 2) stationary points of the MMA; 3) desired global minima of the MMA; 4) unstable equilibria (saddle points) of the MMA; and 5) analytic verification of a discrete-time first-order phase-locked loop hidden inside the MMA, which is absent from the conventional CMA. Analysis results indicate that the MMA alone may be able to remove intersymbol interference and simultaneously correct the phase error, because it implicitly incorporates a phase-tracking loop, which automatically recovers carrier phase.

This paper introduces order-recursive QRD-based least-squares lattice (QRD-LSL) smoothers for adaptive equalization. The QRD-LSL smoothers use past, present and future received data sequences to estimate the present value of the transmitted data sequence. Except for an overall delay needed for physical realization, QRD-LSL smoothers can substantially outperform conventional QRD-LSL filters in adaptive equalization while retaining all the advantages of an order-recursive structure.

In this paper, we derive a quadratic residue decomposition-least squares lattice (QRD-LSL) interpolation algorithm that can be used to construct order-recursive QRD-LSL interpolators based on the exact decoupling property developed in Yuan (1998). QRD-LSL predictors are well known and use past data samples to predict the present data sample while the QRD-LSL interpolators use both past and future data samples to estimate the present data sample. Except for an overall delay needed for physical realization, QRD-LSL interpolators may achieve much better performance than that of the QRD-LSL predictors.

This paper develops a time as well as order update recursion for linear least-squares lattice (LSL) interpolation filters. The LSL interpolation filter has the nice stage-to-stage modularity which allows its length to be increased or decreased "two-sidedly" (i.e., both past and future) without affecting the already computed parameters. The LSL interpolation filter is also efficient in computation, flexible in implementation and fast in convergence. The computer simulation results shown in this paper reveal that although interpolation needs more computing power than prediction does, interpolation can generate much smaller error power and thus reduces much more temporal redundancy than prediction does.>