Maximum-likelihood approaches to blind adaptive signal extraction using narrowband antenna arrays

A unifying approach to the design of blind adaptive signal extraction algorithms is presented, based on maximum-likelihood (ML) estimation of unknown signals with known modulation properties. The ML estimator of a signal-of-interest (SOI) waveform is derived, under the assumption that the SOI is received by a narrowband antenna array in the presence of temporally white interference with unknown spatial covariance and complex Gaussian probabilistic fraction-of-time-distribution. It is shown that the ML waveform estimate can be computed from the dominant mode of a generalized eigenequation if the SOI is a burst, narrowband, or spread spectrum waveform, or if the SOI is a perfectly conjugate self-coherent waveform, such as a DSB-AM or BPSK signal. It is also shown that the ML waveform estimate can be computed using an alternating projections formula if the SOI is a constant modulus waveform, such as an FM or CPFSK (continuous-phase frequency shift keying) signal. It is demonstrated that many of the blind array adaptation algorithms developed to date can be interpreted as ML waveform estimators