Equalizing Without Altering or Detecting Data

Abstract

For terrestrial digital radio systems that use Quadrature Amplitude Modulation, the idea of adapting equalizers to multipath distortion, without relying on accurate data estimates, is attractive. Prompt adaptation following a severe fade, when accurate data estimates are unavailable, is useful for reducing outage time. To avoid processing and administrative overhead, the adaptation method should not involve violating the transmitted signal with the insertion of equalizer training signals. We approach this kind of equalization by building on an algorithm of D. Godard (IEEE Transactions on Communications, November 1980)1 that was devised for voiceband polling networks. The method involves a very simple tap update procedure. However, the technique lacks the foundation of the years of analysis and experimentation that underlie least‐mean‐square adaptation algorithms. The main purpose of this paper is to present new findings, including (1) a proof that the algorithm, thought to require special equalizer initialization, converges regardless of initialization (this offers useful flexibility in digital radio systems, since, after a severe fade, the algorithm could start with any tap misalignment); (2) a preliminary look at convergence speed suggesting the possibility of significant outage reduction; (3) an algorithm that provides phase coherence (the original algorithm requires a follow‐on phase‐locked loop); and (4) an algorithm for cross‐polarization cancellation as well as equalization.

An analysis of constant modulus algorithm for array signal processing

“…Foschini [2] was the first to show that all CM local minima inverse the channel matrix for the equalization problem. We consider here the general source condition including signals with arbitrary (sub-Gaussian, Gaussian and super-Gaussian) sources.…”

“…Without loss of generality, we assume that the first M \ users are sub-Gaussian followed by M Gaussian sources, and the last M > signals are super-Gaussian. The complete characterization of CM local minima is given by the following theorem which generalizes that of Foschini [2].…”

Length- and cost-dependent local minima of unconstrained blind channel equalizers

“…If a doubly infinite length SGA equalizer with [ j = 2 is used in the system, we Based on similar derivations, it can be shown that local minima of DDE for all n1 # n z # n3 since both the SGA and the decision feedback equalizers may have local minima even when the equalizers are double infinite. Hence, the center-tap initialization strategy [7], [ 121 cannot avoid the local convergence. This behavior will be demonstrated by computer simulations in the next section.…”

“…Both the CA and SWA are well-known and effective algorithms. The analysis of GA is given in [ 3 ] , [4], and [7]. It is shown in [3] that Godard cost function also has length-dependent local minima (LDLM), but it has no cost-dependent local minima (CDLM) [7].…”

“…The analysis of GA is given in [ 3 ] , [4], and [7]. It is shown in [3] that Godard cost function also has length-dependent local minima (LDLM), but it has no cost-dependent local minima (CDLM) [7]. Based on results in [ 121 that a one-to-one correspondence exists between the minima of the GA and SWA, the SWA has the same convergence performance as the GA.…”