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1 Principles of Systems
Approach to Design
Complex Radar Systems
1.1 METHODOLOGY OF SYSTEMS APPROACH
The design and construction of any complex information and control systems, including complex radar systems (CRSs), involve a long-term multistage process. The most important stage of CRS development is the design. Therefore, an essential development carried out simultaneously with a reduction in lead time is an important issue of the day. The solution of this problem is based on designing and widespread occurrence of science-based methods of system development taking into consideration structural features of systems and conditions of functioning that are founded on widely used computer subsystems.
The essential methodological principle of this approach is systems engineering. In systems engineering, we understand the term designing as a stage of system cycle from a compilation of requirements specification for development of complex information and control systems, to prototype production and carrying out a comprehensive test operation. The designing process is divided into two sufficiently pronounced stages:
•System designing: to select and organize functional operations and complex information and control systems
•Engineering designing: to select and develop elements of complex information and control systems
Under system designing, an object is considered as a system intended to achieve definite goals at the expense of controlled interaction subsystems, mainly. A conception of complex information and control system integrity, makes specific owing to an idea of backbone communications, for example, structural and control communications. At the stage of system designing, the most important issue is a structure or architecture of the future complex information and control system, that is, a fixed totality of elements and communications between them.
Characteristics of such complex system structures are as follows:
•Autonomy of individual controlled subsystems: Each subsystem controls a limited number of sub subsystems.
•Subsystems are controlled under incomplete information: The high-level subsystem cannot know problems and restrictions for the low-level subsystems.
•Information packing (generalization) under hierarchy motion up.
•Presence of particular problems to control each subsystem and a general problem for the system as a whole.
•Interaction between subsystems due to the presence of total restrictions.
Investigation of possible variants of a complex radar system structure allows us to solve some problems concerning the architecture of the developed CRS while putting aside for the time being the concrete element base that is used in designing the system. In doing so, we take into account the fact
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that structural regularities are stable. Selection and comparison of structural variants is not a prime problem. However, this problem is important because an unsuccessful choice of the CRS structure may bring to one’s grave the results of the next stages of development.
Any CRS cannot be imagined without the so-called environment. Separation between the system and the environment is not well defined and can be realized in a large number of ways. The main problem is to define an optimal boundary between the system and the environment. At the same time, there is a need to take into consideration all factors affecting the system or the effects of system operation. In the case of information systems, including CRSs that operate in conflict situations, the most essential external factors are as follows:
•Environment: the weather, atmospheric precipitation, underlying terrain, etc.
•Facilities of counteracting forces (enemy)
•Level of development of the element base and modern technologies
•Economic factors: the facilities, timing of orders, time for completion of system designing, and so on
•Human element: the team with a good understanding and knowledge of how to perform a high-quality job
Based on a methodology viewpoint, we can emphasize the following aspects of the systems approach to design any complex information and control system:
1.The complex hierarchical system (the CRS) can be divided into a set of subsystems, and it is possible to design each individual subsystem. For this case, an optimization of subsystems does not solve the problem of optimization of the complex hierarchical system as a whole. Designing of the radar system as an integrated object with a predefined mission is related to the trade-off decisions ensuring a maximal efficiency thanks to the decrease in efficiency of some individual subsystems.
2.All alternative variants of CRS structure must be considered and analyzed at the initial designing, and a structure that satisfies all quality standards must be chosen. Now, a choice of the system structure variants, which must be optimized, is carried out by heuristic methods based on experience, intuition, creativeness, and ingenuity of engineers. Evidently, heuristic elements in the designing of radar systems are inevitable in the future.
3.A choice of the favorite variant of the complex radar system structure depends on the possibility to estimate the effectiveness of each alternative structure and the finances that are necessary to realize this alternative structure. For this purpose, there is a need to use quantitative measures of quality, namely QoS (quality of service). In design problems, the QoS criteria are also called the objective functions of optimal design. The CRS is considered effective if the following main requirements are satisfied:
a.Under given conditions of operation, the CRS solves the assigned tasks completely and at a stated time—this is its technical efficiency.
b.The cost of the problem solved by the CRS is not less than the cost of manufacture and the cost of maintenance during its operation.
The criterion satisfying aforementioned requirements can be presented in the following form:
= − , |
(1.1) |
where
is the positive effect following the use of the CRS for definite purposes
is the designing, development, and exploitation charges of the CRS
Principles of Systems Approach to Design Complex Radar Systems |
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Choice of the performance criterion is the exterior problem, which must be solved based on an analysis of high-level information and control system purposes in comparison with the considered system. Naturally, the designed CRS is a constituent of information and control system.
4.The problem of searching for the best structure of the CRS must be solved by employing a computer-aided design system and using the optimization problems.
5.The CRS model is a physical or abstract model, which can sufficiently represent some aspects of the system operation. Adequacy assumes a reproduction by the system model all features with a sufficient completeness, which are essential to reach the end purpose of a given investigation. In the design of complex radar systems we widely use the following:
a.Mathematical models: a representation of the system operations using a language of mathematical relations and definitions.
b.Simulation models: a reproduction of the system operation by other computer subsystems.
c.Modeling: a process of representation of the investigated system by an adequate model with subsequent test operation to obtain information about system functioning.
6.Preliminary structure of the complex radar system seems uncertain at the initial moment. Solutions made at the beginning of system designing are approximated. Solutions are made clear with accumulation of knowledge. Consequently, the designing process is an iterative process, at each stage of which we search for a solution that is perfect in comparison with the previous one. The iterative character of a designed problem solution is a principal difference between the systems approach and traditional and ordinary approaches under system synthesis and designing.
Thus, the most characteristic feature of the systems approach to design CRSs is a decision searching by iterative optimization based on computer-aided designing systems. Figure 1.1 represents a
Goals and QoS |
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Optimal version |
of radar |
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of radar system |
systems |
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structure choice |
Versions of |
Analysis of radar |
Comparison of |
radar system |
system structure |
versions of radar |
structure |
version efficiency |
system structure |
Financing |
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To repeat |
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optimization |
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charges |
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cycle |
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FIGURE 1.1 Block diagram of choice in optimal decision regarding the CRS structure.
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block diagram to choose the optimal structure. In accordance with this diagram, the main operations of the system designing are carried out in the following order:
•Definition and generation of the end goals, restrictions for number of goals, and problems that must be solved by the system; choice and justification of the system QoS (the efficiency criterion)
•Generation of all possible alternative variants to design the system, including impossible versions, at the first sight
•Definition of investments to realize each alternative version of the system structure
•Designing the models chosen to optimize the alternatives and their software implementation, definition of QoS, and costs of the alternative system structures using the definite model
•Comparison of the alternatives and the decision making: either to recommend one or several versions of the radar system structure for further designing or to repeat the whole cycle of optimization process changing a set of initial statements and defining more exactly the QoS (the criterion of effectiveness)
In conclusion, various mathematical methods and procedures are required at the stage of system designing: the theory of probabilities and mathematical statistics; the theory of linear, nonlinear, and dynamic programming; the theory of modeling; etc.
1.2 MAIN REQUIREMENTS OF COMPLEX RADAR SYSTEMS
There are various aspects to complex radar system design. Before a new CRS that has not existed previously can be manufactured, a conceptual design has to be performed to guide the actual development. A conceptual design is based on the requirements for the system that will satisfy the customer or user. The result of the conceptual design effort is to provide a list of the radar characteristics as found in the general characteristics of the subsystems that might be employed, namely, transmitter, antenna, receiver, signal processing, and so forth.
Automated CRSs are widely used to solve, for instance, the following problems: air-traffic control, military fighter/attack, ballistic missile defense, battlefield surveillance, navigation, target tracking and control, and so on. In accordance with purposes and the nature of problems that we try to solve, these automated systems can be classified into two groups [1]:
•Information radar systems: The main purpose is to collect information about the searched objects (the supervisory radar control systems concerning air, cosmic, and over-water conditions; the meteorological radar systems; the remote sensing radar systems; etc.).
•Control radar systems: The main purpose is to solve the problems to control the objects using the data of radar tracking, observation, and measurements (antiaircraft and missile defense systems, air traffic control systems, navigational systems, and so on).
As an example of the CRS of the second group, consider the classical radar antiaircraft and missile defense and control system [2–4]. The block diagram of this control system is shown in Figure 1.2. Elements of the antiaircraft and missile defense system are as follows:
•Subsystem of target detection and designation assigned to carry out in a good time the detection and estimation of enemy air target motion parameters
•One or several CRSs to fire control assigned to clarification of motion parameters of the annihilation-oriented air targets
•Definition of current values of pointing angles and setting time for time fuse with required accuracy
•Missile launchers assigned to firing
•Facilities to transmit the information-bearing signals between elementary blocks and subsystems of the control system
Principles of Systems Approach to Design Complex Radar Systems |
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Complex radar |
Radar firing |
Missile |
target detection |
control |
launcher |
and designation |
subsubsystem |
subsystem |
subsystem |
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Target designation |
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information |
Radar signal processing |
Firing data |
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and database |
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subsubsystem |
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Complex radar firing |
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control subsystem |
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FIGURE 1.2 Radar control system of antiaircraft and missile complex.
The most general QoS (the criterion of effectiveness) of the considered control system, which is generated based on performance purposes, is the so-called averted harm given by [5]
N |
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L j |
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(1.2) |
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= ob ∏ 1 − ob j ∏(1 − Pij ) , |
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j =1 |
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i=1 |
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where
ob is the importance of the defended objective
ob j is the relative damage of the objective caused by the jth armed attack facility under absence of defense
Pij is the probability of the jth armed attack facility damage by the ith defended facility (e.g., missile) N is the number of the armed attack facilities
Lj is the number of missiles assigned to attack the armed attack facility, where ∑Nj=1 Lj = L0
L0 is the missile resource
To ensure the maximal value of damage prevention we must try to increase the probability of target destruction in accordance with Equation 1.2:
Pij = Ptd j P2 j P3ij , |
(1.3) |
where
Ptd j is the probability of success under the target designation with respect to the jth target by the complex radar detection and target designation system
P2j is the probability of success under the parameter clarification of the jth target and definition of firing data by the complex radar control firing system at the condition that the problem of target designation has been solved successfully
P3ij is the probability of destruction of the jth target at the condition that the problems of target designation and control have been solved successfully
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FIGURE 1.3 in text.)
Target
0 |
Vrel |
ttr |
j |
Vrel |
ttd |
j |
Vrel |
ttr |
j td |
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j |
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j |
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j |
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R0 |
Rtdeff |
Rtdj |
Vrelj t0 |
j |
Vrelj tdj |
Vrelj tlj |
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Emplacement of the complex radar control and target designation systems. (See the notations
Using Equation 1.3, we can define the QoS of the complex radar control and target designation systems and justify limitations for this quality performance. Consider the case when these systems are placed on the same emplacement (see Figure 1.3). The conditional probability of target destruction by missile can be presented in the following form [6]:
dest |
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σmiss2 |
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−1 |
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Psuc |
= |
1 |
+ |
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(1.4) |
2 |
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Reff |
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where
σ2miss is the variance of miss
Reff is the effective radius of target destruction, that is, the radius of sphere, within the limits of which a missile hits and destructs the searched target with the given probability
Based on Equation 1.4, we see that the probability of target destruction Psucdest is inversely proportional to the variance of miss σ2miss to deliver a missile to target area, which is characterized by the following constituents:
•The error variance to hit the target by missile σ2hit
•The error variance of antitarget guidance by launcher σ2launcher
•The error variance of missile flight path σ2missile
Since these constituents are considered as independent and uncorrelated, the variance of total error with respect to each coordinate from the set
θ = {R,β, ε} |
(1.5) |
is defined in the following form:
σmiss2 = σ2hit |
θ |
+ σ2launcher + σmissile2 |
θ |
. |
(1.6) |
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θ |
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Principles of Systems Approach to Design Complex Radar Systems |
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Only the first term in Equation 1.6, the error variance to hit the target by missile σ2hit, depends on the target designation accuracy given by the control system. Under the fixed values of the second
and third terms in Equation 1.6, the error variance of antitarget guidance by launcher σ2launcher and the error variance of missile flight path σ2missile and given before restrictions to the variance of miss σ2miss, we are able to define requirements for the control system in accuracy of the observed target
coordinates.
The effective radar range of the control system can be determined in the following form (see Figure 1.3):
Rtdeffj = R0 + (t0 + ttrj + tl j )Vrel j , |
(1.7) |
where
R0 is the far-field region boundary of destruction area
Vrel j is the relative velocity of the jth target motion with respect to the defended object t0 is the flight time of missile for the range R0
is the time of lock-in of the jth target to track by the firing control system
is the tracking time of the jth target to track by the system of firing control, that is, the time from the lock-in instant to the instant of reaching the required accuracy of the target tracking
Thus, to solve the assigned task successfully, the firing control system has to
•Possess the radar range ensuring the target destruction on the far-field region boundary of the destruction area
•Ensure the smoothed coordinates of the target with accuracy that is sufficient to reach the searched target
In accordance with a character of assigned tasks, the firing control system must possess the pencilbeam pattern of antenna and restricted zone of searching. For this reason, the main assigned task of the target designation system is to provide the coordinates and motion parameters of targets on the target designation line with accuracy allowing the firing control system to accomplish the target lock-in based on the target designation data without any additional searching or, at least, to limit the additional zone searching to a minimum.
Errors in the target designation are defined by the errors of coordinate measurements carried out by the target designation system, total time of smoothing the target coordinates and parameters, time of transmission, receiving, and processing of target designation commands. Let the target designation area be given by the following coordinates Rtd, Δβtd, and Δεtd in the spherical coordinate system. Then the probability to lock-in the target by the control firing system using a single target designation from the CRS of target designation, that is, the probability of success under target designation can be determined in the following form:
0.5 |
Rtd |
0.5 |
βtd |
0.5 εtd |
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Ptd = |
∫ |
∫ |
∫ |
f ( R, β, ε)d Rd βd ε, |
(1.8) |
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−0.5 |
Rtd −0.5 |
βtd −0.5 |
εtd |
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where f( R, Δβ, Δε) is the probability density function of target coordinate deviation from the target designation area center.
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In the case of systematic bias absence of the target designation and the Gaussian normal distribution of random errors with the variances σ2Rtd, σβ2td, and σ2εtd, the probability of success under the target designation takes the following form:
Ptd = Φ0
where
Φ0 (
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Rtd |
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βtd |
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εtd |
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Φ0 |
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Φ0 |
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σR |
σβ |
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σε |
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td |
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td |
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td |
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x) = |
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∫x exp (−0.5t2 )dt |
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2π |
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(1.9)
(1.10)
is the integral of probability. From Equation 1.9 it follows that if the required probability of target designation and the coordinates of target designation area are given before, we are able to formulate the requirements to allowable values of the target designation error variances
σR2 td, σβ2td , and σ2εtd .
The aforementioned statements are correct in the case of a single target designation. If there is a possibility to renew and transmit information about the target designation k times (k > 1), then the probability of success under the target designation is given by
Ptd = 1 − (1 − Ptd1 )(1 − Ptd2 ) (1 − Ptdk ). |
(1.11) |
The repeated target designation data lead to an increase in time of target designation transmission that requires, finally, increasing the radar range of the system. The required radar range is determined by the following formula (the case of a single target designation):
Rtd j |
= Rtdeffj |
+ Vrel j (tdj |
+ ttr j |
+ ttd j ), |
(1.12) |
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td |
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where
tdj is the time required to detect the jth target
ttrjtd is the time of the jth target tracking by the target designation system to ensure the given accuracy of coordinate and parameter definition and estimation at the extrapolated point
for ttdj
is the time required to transmit information about the target designation to the firing control system
From Equations 1.9 and 1.12 it follows that the target designation system has to
1.Possess circular radar scanning
2.Ensure the radar range required to guarantee the target designation on the reassigned target line
3.Provide an accuracy of definition and estimation of the searched target coordinates at the predicted point of target designation, which is sufficient to lock-in the target by the control system without additional searching of the target
Principles of Systems Approach to Design Complex Radar Systems |
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Thus, reasoning from the considered QoS (the criterion of effectiveness) of the antiaircraft defense system, QoS indices of radar subsystems included in the antiaircraft defense system are
1.Radar scanning configuration of the CRS: Requirements and configurations of radar scanning of the target designation system and the control system are different. The radar scanning of the control system in angular coordinates is restricted and a way to scan it is specific (spiral, bitmapped, etc.). The radar scanning of the target designation system is circular, as a rule, or sectored and limited on vertical plane by the special cosecantsquared directional diagram shape.
2.Radar range Rtd (Rtdeff ) is the distance, within the limits of which the task performance of each CRS providing information to the missile firing control subsystem is ensured.
3.Accuracy of information at the given radar range, which is characterized by the covariance matrix of error.
4.QoS index characterizing influence of the external and internal noise and interferences on the considered CRS and that can be defined by numbers of detected decoy targets, which are tracked by the system over a definite period of time.
QoS indices 2 and 3 are related to each other, since the accuracy of obtaining information about the target depends on the distance between the CRS and the searched target. Moreover, there is a need to take into consideration the statistical nature of the QoS 2, 3, and 4, a relationship between them and the probability of target detection, the probability of false alarm, and the accuracy of coordinate measurements by the radar system. Since the probability of target detection, the probability of false alarm, and the accuracy of coordinate measurements depend on technical parameters of the radar systems also, there is a function between the earlier-mentioned statistical performance and the power, duration, bandwidth of scanning signals, dimensions, and type of transmitting and receiving antenna. These parameters of the radar systems must be defined during system designing.
Consider Equation 1.3 again. Taking into consideration the obtained formulas and relations, we can state that the probability of target destruction can be determined and also used to determine the averted harm given by Equation 1.2 under the known QoS of the target designation system, the control system, and the missile launcher. Consequently, the averted harm criterion (the QoS) can be defined, and it is not changed during the system designing. However, this criterion (the QoS) is related to technical parameters of the designed systems by composite and multiple-val- ued function and cannot be used in practice to evaluate and compare the solutions of designing. Meanwhile, according to the systems approach under the radar system designing there is a need to take into account the QoS criteria possessing a physical sense, the ability to be determined, and associated with technical parameters of the designed CRS. The criterion, which we have just considered and analyzed, does not satisfy these conditions.
Under designing the CRSs, it is difficult to define a general criterion (QoS) satisfying the aforementioned requirements owing to the complicated mathematical model of target searching by the system. For this reason, it is worthwhile to introduce an intermediate QoS instead of the general criterion (QoS) with the purpose to relate the main parameters of the radar systems and signal processing subsystems that are designed.
As a basis for the generalized criterion, we can consider the signal-to-noise ratio (SNR) given by
q2 = |
2Es |
, |
(1.13) |
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NN+I |
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where
Es is the energy of the received signal
NN+I is the power spectral density of the total noise and interferences
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In accordance with the general radar formula for the case of matched signal processing in free space in set noise, we can write [7–11]
q2 = 2Ptavt0GtGrλ2Stef , (4π)3 Rt4kT0 N0
where
Ptav is the transmit power t0 is the observation time
Gt is the transmitting antenna gain Gr is the receiving antenna gain
λ is the wavelength
Stef is the effective target reflective surface Rt is the distance to the target
k = 1.38 × 10−23 W/Hz is the Boltzmann constant T0 is the absolute temperature of signal source N0 is the power spectral density of set noise
is the total loss factor
In the case of pulsed radar we can write
Ptav = PpτsF,
where
Pp is the transmit pulse power
τs is the duration of scanning signal
F is the repetition frequency of scanning signals
(1.14)
(1.15)
Under conditions of conflict radar in practice, interferences generated by the enemy are the main noise. The power spectral density of deliberate interference is determined by [12,13]
Nd = |
αPdI |
, |
(1.16) |
4πRdI2 fdI |
where
PdI is the power of noise source
αis the coefficient depending on the direction to the noise source and the performance of the noise source directional diagram and CRS directional diagram
RdI is the distance between the CRS and the noise source (the generator of deliberate interference) fdI is the noise bandwidth
From Equations 1.14 through 1.16 it follows that SNR depends on the main parameters of the CRSs, environment, and target. On the other hand, the main QoS indices of radar signal processing are also expressed by SNR. For instance, the probability of signal detection under the Rayleigh distribution of amplitude and uniform distribution of phase of the signal can be written in the following form:
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γ 2rel |
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PD = exp |
− |
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(1.17) |
2(1 + 0.5q |
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