The redundancy factor is determined on such formula

Source redundancy.

. (3.11)

When H(A/A’) = logm, r_s = 0.

1. Optimal estimation of several unknown parameters of the signal.

Such task arises at measurement of signal amplitude or channel gain Average frequency or time of signal arrival, timing slot in synchronous discrete communication systems and other parameters are estimated similarly. Let’s accept for definiteness, that transmitted signal had single amplitude, and after passage through the channel it has accepted value k, then z(t) = ks (t) + x(t). Our purpose is to apply the method of maximal likelihood for optimal dot estimating of k.

It is impossible to define k precisely. It is caused by a number of the reasons: by presence of noise x(t), limitation of observation time, presence of measuring devices errors and etc. Therefore it is necessary to receive such optimal dot estimation k*, which is functional of received realization z(t) and in the best way reflects true value of k. Certainly, it is desirable, that according to basic principle of statistical estimation theory the received estimation would be valid, unbiased and effective [9, 13, 15].

At white gaussian noise x(t) with spectral density Ω₀ the likelihood function is

The logarithm of this function is

Differentiation L on k and result equating to zero gives the following equation of maximal likelihood:

(1.1)

Let's transform it to a kind convenient for the decision

(1.2)

The decision of equation (10.6) is

(1.3)

Hence, it is necessary for receiving of optimum estimation k* to apply one kind of optimal linear processing (see § 6.1). For example, it can be applied the correlation receiver, in which for circuit simplification the integrator gain should be chosen equal to 1/Е.

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