130
6 Detection of Radio Signals and Its Parameters Measuring
where β m and β f a —corresponding coefficients of incorrect decisions “cost” (weight)
at targets miss or false alarm; P t —priori absolute (unconditional) probability at
specified point and at a given moment of time.
However, it is almost impossible to define or set a probability P t beforehand.
Besides, it is difficult or even impossible to evaluate a cost of wrong decisions and,
consequently, to set coefficients β m and β f a . It is impossible to set a conditional
probability of target miss P tm (1 − P cd ) for all possible values of RCS of radar targets,
which are included as a parameter (in a form of amplitude of reflected signal) into
conditional probabilities distribution densities p(y out |S t = 0).
Neyman–Pearson criterion is the most commonly used in radar location. This
criterion sets a probability of false alarm P f a by a specified value, that permits
ambivalently to determine a required threshold. There is no necessity to set any other
parameters and coefficients. The most important, that a threshold value does not
depend on signal presence, reflected from a target and its energy.
In should be noted that in the mentioned form the Neyman–Pearson criterion is
used at condition of already found algorithm of optimum signals processing and
optimum processing unit.
However, the Neyman–Pearson criterion can be used at selection of optimum
signals processing unit or at comparison of different real non-optimal target detection
units (at comparison, e.g., of optimum and none-optimum systems). In this case, the
Neyman–Pearson criterion is formulated in a slightly different way. It is considered
that signal energy, reflected from a target, is specified (e.g., signal amplitude is
specified). Probability of false alarm P f a is specified and probabilities of target miss
P tm or P cd are evaluated. The more P cd in these conditions, the closer this unit to an
optimal. In this case, average losses C ls = P tm + P f a are also minimized.
Detection characteristics. Properties of radar systems at targets detection problems solution can fully be estimated through plotting of so-called detection characteristics, which represent a dependence of probability of correct detection P cd
from a value of signal energy relation, reflected from a target and spectral noise
density (R = 2E/N o ) at specified as a parameter value of false alarm probability
P f a (Fig. 6.3).
It is possible another variation of detection characteristic, when probabilities P cd
and P f a are specified in a form of parametric dependence, where parameter is a
relation of signal energy and noise R (Fig. 6.4).
Detection characteristics are used, for example, at calculation of maximum range
of targets detection. At specified probabilities P cd and P f a , the required value of
relation R is found, i.e., relation of signal energy E at input of radar system to spectral
noise density, at which obtaining of specified probabilities P cd is provided at detection
of a target. Often such a required value R is called a detection parameter and for an
ideal (perfect) radar system without any deviations (without additional losses) and
is designated as R d (Fig. 6.3). If energy losses and deviations from ideal (perfect)
operation conditions are observed in the system, then detection characteristics at
specified value P f a are lower than imperfect. Detection parameter in this case has
a larger, than R d value. Let us designate this parameter for imperfect (real) system
6 Detection of Radio Signals and Its Parameters Measuring
where β m and β f a —corresponding coefficients of incorrect decisions “cost” (weight)
at targets miss or false alarm; P t —priori absolute (unconditional) probability at
specified point and at a given moment of time.
However, it is almost impossible to define or set a probability P t beforehand.
Besides, it is difficult or even impossible to evaluate a cost of wrong decisions and,
consequently, to set coefficients β m and β f a . It is impossible to set a conditional
probability of target miss P tm (1 − P cd ) for all possible values of RCS of radar targets,
which are included as a parameter (in a form of amplitude of reflected signal) into
conditional probabilities distribution densities p(y out |S t = 0).
Neyman–Pearson criterion is the most commonly used in radar location. This
criterion sets a probability of false alarm P f a by a specified value, that permits
ambivalently to determine a required threshold. There is no necessity to set any other
parameters and coefficients. The most important, that a threshold value does not
depend on signal presence, reflected from a target and its energy.
In should be noted that in the mentioned form the Neyman–Pearson criterion is
used at condition of already found algorithm of optimum signals processing and
optimum processing unit.
However, the Neyman–Pearson criterion can be used at selection of optimum
signals processing unit or at comparison of different real non-optimal target detection
units (at comparison, e.g., of optimum and none-optimum systems). In this case, the
Neyman–Pearson criterion is formulated in a slightly different way. It is considered
that signal energy, reflected from a target, is specified (e.g., signal amplitude is
specified). Probability of false alarm P f a is specified and probabilities of target miss
P tm or P cd are evaluated. The more P cd in these conditions, the closer this unit to an
optimal. In this case, average losses C ls = P tm + P f a are also minimized.
Detection characteristics. Properties of radar systems at targets detection problems solution can fully be estimated through plotting of so-called detection characteristics, which represent a dependence of probability of correct detection P cd
from a value of signal energy relation, reflected from a target and spectral noise
density (R = 2E/N o ) at specified as a parameter value of false alarm probability
P f a (Fig. 6.3).
It is possible another variation of detection characteristic, when probabilities P cd
and P f a are specified in a form of parametric dependence, where parameter is a
relation of signal energy and noise R (Fig. 6.4).
Detection characteristics are used, for example, at calculation of maximum range
of targets detection. At specified probabilities P cd and P f a , the required value of
relation R is found, i.e., relation of signal energy E at input of radar system to spectral
noise density, at which obtaining of specified probabilities P cd is provided at detection
of a target. Often such a required value R is called a detection parameter and for an
ideal (perfect) radar system without any deviations (without additional losses) and
is designated as R d (Fig. 6.3). If energy losses and deviations from ideal (perfect)
operation conditions are observed in the system, then detection characteristics at
specified value P f a are lower than imperfect. Detection parameter in this case has
a larger, than R d value. Let us designate this parameter for imperfect (real) system