Incohernet Adaptive Reception of Signal with Unknown Envelope

This paper deals with the design of adaptive algorithms for reception of a narrowband signal with an unknown envelope in a noisy channel (Gaussian noise). We here consider a system (with a "real teacher") which learns from the samples classified by this self-learning system (decision directed adaptive receiver). By using those samples which are accepted as learning samples, the parameters of the unknown envelope are estimated. The envelope's parameters appear in the form of coefficients of the generalized Fourier series expansion of the signal (with respect to eigenfunctions of appropriate integral equation). It is possible to utilize any orthonormal set with respect to the interval
(0, T)
under the usual assumption, that the complex autocovariance function is
R(\tau) = N\delta (\tau)
(i.e., that the noise bandwidth is much greater than both
1/T
and the signal bandwidth and
N
is the unilateral spectral density of the noise in the neighborhood of the signal spectrum). We present expressions that enable the upper bound estimates of the error probability to be found for the derived algorithms. The results obtained for the binary detection are readily generalized to the case of an
M
-ary signal.