Bussgang algorithms are a class of simple stochastic gradient type solutions for blind channel equalization. We investigate the degradation of performance in the source estimation resulting from the stochastic jitter around stationary points of Bussgang algorithms (which correspond to the equalizers of the channel). More precisely, we derive a closed form approximation of the excess mean square error (EMSE) defined as the variance of the jitter which depends on the effects of the channel characteristics, the source distribution and the non-linearity used in the update equation. The analysis is performed in a context of spatiotemporal channel diversity involving a single-input/multiple outputs data model.

This paper discusses methods for calculating and implementing the update error term for the popular blind equalization algorithm known as Godard's (1980) algorithm, or the constant modulus algorithm (CMA), without the use of multipliers so that chip area and signal latency are both substantially reduced. One approach uses a decision-directed CMA update term, and another uses region-based quantization. The quantized error term can be calculated using a look-up table in place of costly multipliers and adders. Baseband and passband implementations are discussed, and computer simulations verify our methods.

This paper discusses methods for calculating and implementing the update error term for the popular blind equalization algorithm known as Godard's (1980) algorithm, or the constant modulus algorithm (CMA), without the use of multipliers so that the chip area and signal latency are both substantially reduced. A decision-directed CMA update term is derived for higher-order (non-constant modulus) source alphabets. The modified update error term can be calculated using a look-up table in place of costly multipliers and adders. Baseband and passband implementations for one-dimensional and two-dimensional signaling are discussed.

One of the most popular blind equalization techniques is the constant modulus algorithm (CMA), and it has gained popularity in the literature and in practice because of its LMS-like complexity and its robustness to non-ideal, but practical, conditions. Although the CMA has been well-studied in the literature, these analyses have typically implemented the algorithm using "infinite" precision arithmetic. The motivation for this paper is a VLSI implementation of a high data rate, fractionally spaced, linear forward equalizer whose taps are adjusted using the CMA. We examine how implementing the CMA using finite bit precision affects the algorithm's performance.

A common technique in a blind equalization communication system is to use the constant modulus algorithm (CMA) to open the channel eye and then to switch to decision-directed LMS once the error rate has dropped to a sufficiently low level. The propose a new algorithm, blended CMA, which dynamically selects to use either the CMA or DD-LMS update term when adapting the equalizer taps. The decision rule governing this selection is also adaptive. Simulation results presented in this paper demonstrate how the algorithm performs when equalizing 64-QAM over real-world channels and highlights the performance gain over using traditional transfer methods.

The improved convergence speed and tracking properties of fractionally-spaced equalizers are analyzed. We consider in particular the effect of a frequency offset between the transmitter baud rate and the receiver sampling clock that induces important time-variations. We show that a fractionally-spaced equalizer can handle the intersymbol interference (ISI) induced when the propagation channel does not introduce too much ISI.

This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical decisions utilized in this tutorial can be used to help catalog the emerging literature on the CM criterion and on the behavior of (stochastic) gradient descent algorithms used to minimize it.

For pt. I see Proc. 1st IEEE Workshop on Signal Proc. Advances in Wireless Comm., 1997. This paper studies the constant modulus (CM) criterion specifically for the case where the time span of the fractionally-spaced equalizer (FSE) is less than that of the channel. Hence, there necessarily exists an error in the equalized signal. Results for the binary case (Part I) are extended to multi-level signalling. This analysts is connected with the previous work of Fijalkow et al. (see IEEE Trans. on Signal Proc., 1995) on misadjustment of a CM receiver to suggest a finite interval of acceptable FSE length which shows that a longer FSE may not be better than a shorter FSE-in some cases, matching the FSE length to that of the channel may not reduce the MSE to a prescribed threshold, while a shorter FSE may be successful in achieving this threshold.

A number of papers have studied blind channel identification/equalization algorithms relying purely on second-order statistics of the fractionally sampled received signal. A class of cyclic allpass channels is shown to be the only class of IIR channels whose cascade with a core channel results in no change in the second-order-statistics indicators used by several of these algorithms. FIR approximations to the poles of these allpass channels result in robustness concerns for the second-order-statistics algorithms, even when FIR identifiability conditions are well satisfied. This sensitivity suggests that excluding only those channels with common subchannel roots is insufficient when applying these second-order-statistics algorithms.