Statistics of blind spatial signature estimators

A spatial signature is used to model a communication signal that is received by an array of antennas in a multipath environment. If the transmitted waveform is not known, a blind estimate of the unknown spatial signature may be obtained by cross-correlating an estimate of the transmitted waveform with the received data. This paper presents the mean and variance of a blind spatial signature estimator that is obtained by either a constant modulus mapping or by mapping onto a known finite alphabet. These results are compared to those for an estimator that exploits a known waveform.