Existence and performance of Shalvi-Weinstein estimators

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

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...

Domains of attraction of Shalvi-Weinstein receivers

Domains of attraction (DoA) of Shalvi–Weinstein (SW) receivers are analyzed. It is shown that there is a one-to-one correspondence between DoA in the receiver parameter space and those in the global (or combined channel-receiver) parameter space. For general noiseless channels, DoA of SW receivers in the global response space are the minimum distance decision regions on a unit sphere. In the pr...

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...