Domains of attraction of Shalvi-Weinstein receivers

Geometrical characterizations of constant modulus receivers

Convergence properties of the constant modulus (CM) and the Shalvi–Weinstein (SW) algorithms in the presence of noise remain largely unknown. A new geometrical approach to the analysis of constant modulus and Shalvi–Weinstein receivers is proposed by considering a special constrained optimization involving norms of the combined channel-receiver response. This approach provides a unified framewo...

Proof Details for “ Existence and Performance of Shalvi - Weinstein Estimators ” †

Existence and performance of Shalvi-Weinstein estimators

The Shalvi–Weinstein (SW) criterion has become popular in the design of blind linear estimators of i.i.d. processes transmitted through unknown linear channels in the presence of unknown additive interference. Here, we analyze SW estimators in a general multiple-input multiple-output (MIMO) setting that allows near-arbitrary source/interference distributions and noisy noninvertible channels. Th...

On the equivalence between the Godard and Shalvi-Weinstein schemes of blind equalization

Certain equivalences between the Godard and Shalvi—Weinstein schemes have been previously noted under special circumstances. We present here a simple proof for real signals that an equivalence can be established assuming little more than stationarity to fourth order of the equalizer input; the exact nature of the input sequence proves otherwise irrelevant to the validity of the equivalence. The...

A gradient search interpretation of the super-exponential algorithm

This correspondence reviews the super-exponential algorithm proposed by Shalvi and Weinstein for blind channel equalization. The principle of this algorithm—Hadamard exponentiation, projection over the set of attainable combined channel-equalizer impulse responses followed by a normalization—is shown to coincide with a gradient search of an extremum of a cost function. The cost function belongs...