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or echo interferences, reflection from the Earth’s surface, various objects, such as trees, buildings, hydrometeors, and so on, transient observations, a variety of problems that are to be solved, and limitations in energy and computational resources of the CRS. Hence, the control subsystem must be considered, first, as the means toward this end assigned for the CRS and, second, as a method to compensate for unwanted changes in environment that are interferences for its optimal functioning [1].

The main requirement to organize the control subsystem in a CRS structure is the knowledge of controlled parameters. If the number of controlled parameters is increased, the possibilities to organize the control system become high. Most control problems can be solved by multifunctional complex radar subsystems [2–7]. Therefore, in this chapter we consider mainly the problem statements and solutions of control problems in CRSs of this kind. Henceforth, all necessary signal and data processing algorithms assigned to reach the given control goal are considered as the control subsystem of a CRS. In doing so, the word control is used to designate both a process to reach the assigned task and in the sense of purposeful impact on parameters and structure of complex radar subsystems.

The first stage of designing the CRS control subsystem is a choice or formalization of goals, which must be attained in the course of controlling. In a general case, a high-level efficacy of CRS functioning is the main aim of a control subsystem. A degree of fulfillment of this aim can be evaluated by estimation of the vector Y(t)—the output parameters of a CRS—that is used to define its efficacy index: = [Y(t)] [8–10]. To realize the control subsystem, there is a need to design control subsystem channels to transfer control signal U(t). Internal parameters and methods of limited resource consumption of CRS are the object of a control subsystem. The figure of merit of required information is a function of an environment statement Z(t), the set of the internal parameters XU(t) corrected by the control system, and special controlling decision U(t):

where F is the vector-operator of the controlled object functioning. In a general case, the goal of a control subsystem is to obtain such values of the vector Y(t) = Y•(t) that ensure a condition

Now, informed about the environment conditions, controlled object, and control subsystem aim, we are able to present the control signal U(t) in the form of an algorithm:

Owing to the complexity of a radar system as a controlled object, the solution of the control problem, in a general form, has some difficulties. On the one hand, these difficulties are caused by the required computer costs and RAM size to solve the control problems within the limits of very short and strictly limited time intervals defined by dynamical changes of environment and CRS functioning. On the other hand, these difficulties have a principal character, since there are no methods of formalization and optimization of the control problem, which allow us to obtain a quantitative assessment as a whole for such a system as the CRS. Hence, in the course of designing the CRS control subsystem, the well-known system engineering procedure of complex system division in individual subsystems is widely used. In doing so, a choice of the structure and dimension of subsystem is carried out in accordance with universally adopted principles to save the backbone connections, and

also taking into consideration the definite stages of CRS signal processing. Naturally, in division we should take into consideration possibilities to ensure the best control process for subsystems and the CRS as a whole. Division or decomposition of the CRS into subsystems assumes that each subsystem has a criterion function to control that is generated from a general objective function of the CRS.

To increase efficiency and decrease work content for the solution of control tasks, a subsystem of control algorithms is designed based on a hierarchical approach [11]. The hierarchical structure of the control subsystem is characterized by the presence of some control levels associated with each other, by which a general task is divided. In doing so, the control algorithms of high levels define and coordinate the working abilities of lower levels. Based on the aforementioned general statements, the CRS, as an object to control, can be divided into controlled subsystems, including the signal detection and signal processing subsystems. The controlled subsystems are as follows:

1.Transmit and receive antenna with controlled parameters:

a.The number of generated beams of transmit Ntr and receive Nr antennas

b.The directional diagram beam width of the transmit (θβtr , θtrε ) and receive (θβr , θrε ) antennas

c.A degree of beam overlapping for the multibeam receive antenna directional diagram (δβr, δεr)

d.Function of changes in the main lobe direction of the transmit antenna directional diagram (β0, ε0)

e.The number and direction of radar antenna directional diagram valleys

2.Transmitter with controlled parameters:

a.The duration of searching signal τs

b.The power of transmitted pulse Pp

c.The carrier frequency fc or sequence of carrier frequencies {fci} under multifrequency operation

d. The spectrum bandwidth of searching signals fs

e.The parameters and way of chirp modulation of searching signals

f.The frequency F of searching signal repetition

3.Receiver with controlled parameters:

a.The optimal structure with a viewpoint of the maximal SNR under conditions of complex noise environment

b.Operation mode

c. The spectrum bandwidth of input linear tract fr

d.The dimension of gated area—the number of elements in the gate and coordinates of the gate center

4.Signal preprocessing processor of target return signals with controlled parameters:

a.The number of signal processing stages under detection and estimation of target return signal parameters

b.The upper A and lower B detection thresholds under sequential detection of target return signals

c.The truncation threshold ntr under sequential analysis of target return signals

d.The number N of accumulated pulses by detector with the fixed sample number

e.The threshold U0 of binary quantization

f.The logic operations (l, m, k) under detection of binary quantized target return signals

5.Signal reprocessing processor of target return signals and preparation of obtained information for user with controlled parameters:

a.The criterion to begin the target track ("2/m + l/n")

b.The criterion to cancel the target range tracking ktrcan

c.The algorithm and parameters of the linear filter used under the target range tracking

d.The way of refreshment of the tracked target

e.The target range parameters and precision characteristics transmitted to the user

The majority of controlled parameters of the CRS and signal processing subsystems depend on each other. For instance, the duration of the scanning signal τs, the period or frequency of–repeti-

tion T or F, the power of transmitted pulse Pp, and the average power of scanning signal Pscan are related by the evident formula:

–

As the average power of scanning signal Pscan is a constant value, then the power resources of the CRS can be controlled by the following parameters: τs, T, and Pp.

The radar antenna directional diagram beam width depends on the angle between the main axis of radar antenna and antenna beam:

where θ0 is the beam width in the main axis direction of the radar antenna. The radar antenna directional diagram beam broadening under misalignment of radar antenna leads us to a decrease in the coefficient of amplification of radar antenna, and consequently, to increasing the required number N of accumulated target return signals to ensure the given SNR by power. There are other associations that must be taken into consideration under the control process. Interrelating control parameters do not allow us to organize a control process insulatedly by each of the controlled blocks or subsystems of the CRS, which indicates the impossibility of spatial division of the control subsystem. At the same time, a specificity of the CRS operation allows us to organize a control process step by step in time and design a multilevel hierarchical structure of the control subsystem (see Figure 6.2).

The first level is the control of CRS and signal processing subsystem parameters and in the course of searching for the preliminary chosen direction in radar coverage taking into consideration a radar functional operation, namely, searching, target range tracking, and so on. Objective control function at this stage is to ensure a minimal energy consumption to obtain the given effect from searching the chosen direction, namely, the given probability of detection PD, the given accuracy to measure angle coordinates σθ2, and so on. Limitations are acceptance bands of CRS technical parameters and ways to integrate them. During the first stage, a control process is carried out by direct selection of controlled parameters of the CRS and signal preprocessing subsystems in real time.

The second control level is an optimization of CRS functional modes. In the case of radar target detection and target range tracking subsystems, there is a need to optimize a searching of new targets and target range tracking functioning. A way to observe the radar coverage and ability to refresh the tracked targets are the controlled functions. The objective function of an optimal control process is the minimization of specific CRS power resource consumption to detect the target under scanning, refreshment, and estimation of target range track parameters under target tracking. CRS technical parameters and specifications of the high-level system are the main limitations for target range tracking. The control process at the second level is carried out by optimal scheduling of radar coverage element observation in the scanning mode and refreshes each target during the target tracking mode. Periodicity of changes in the control process at this stage is mainly defined by

FIGURE 6.2  Hierarchical control system.

dynamics of dirty data within the limits of radar coverage—the number of targets, importance of targets, environmental noise, and so on.

The third control level is a distribution of limited CRS power resources between functional modes: the detection and target tracking modes in the case of two functional CRSs. The objective functions of optimal control at this stage are the maximization of CRS efficiency criterion for higher hierarchical level, at which the CRS operates as the detection and target tracking system, and the maximization of the processed target number taking into consideration their importance. The control process at the third level is carried out by the redistribution of power resource parts assigned for scanning and target tracking modes. The periodicity of the control process depends on the a priori and a posteriori environment data within the radar range and ability of facilities for target servicing and so on.

The fourth control level is an administration to keep the CRS under required operational conditions taking into consideration information about the operation quality of its subsystems, changed environment, information from subsystems of the same levels, and control commands from subsystems of a higher hierarchical level. At this level, a contingency administration is mainly carried out.

Thus, we obtain the multilevel hierarchical structure of a radar control subsystem, the simplest flowchart of which is shown in Figure 6.2. The hierarchy of control process is characterized by a sequential release of information from complex radar subsystem of higher to lower level subsystems. At the same time, the results of particular problem solutions at lower levels are used as the basis to make decisions at the higher level. Thus, information about the energy consumption for scanning in each direction, the number of detected targets, and the energy consumption under target tracking mode comes to the second-level subsystem as a result of the first-level task solutions. The information about the number of tracked targets ntgtrack, their importance, and also about a scanning interval of new target zones is transferred to the subsystem of the third level as a result of solutions of tasks at the second level. Simultaneously, the subsystems of the second and third levels of the control subsystem transfer information about an ability of facilities and quality to solve the tasks to the subsystem of the fourth level, where an administration of the CRS is carried out as a whole.

6.2  DIRECT CONTROL OF COMPLEX RADAR SUBSYSTEM PARAMETERS

6.2.1  Initial Conditions

The control process in the course of scanning the selected direction is carried out by direct choice of controlled parameters of the CRS and signal preprocessing subsystem with the purpose of adapting to dynamical environmental conditions under the given operation mode. The main modes of CRS functioning are as follows:

•Scan new targets in radar coverage.

•Refresh met target tracks or search mode of detected targets.

Other possible functioning modes can be considered as particular cases of the aforementioned modes. Additionally, an extension of the mode numbers does not change control process principles.

The external environment for a CRS is characterized by the presence of targets, noise, and different kinds of interferences such as the following:

•The inadvertent interference—radio radiation of the world network, various radio engineering systems, mobile systems, and so on

•The lumped interference—radiation, the spectrum of which is concentrated in the neighborhood of the central or resonant frequency and, with a spectral bandwidth that is larger in comparison to the spectral bandwidth of the signal at the radar receiver or detector input

•The pulse interference—a sharp short-term increase in the spectral power density of the additive noise that occurs within the spectrum bandwidth limits of the signal

•The deliberate interference—the interference generated specifically for the purpose to reduce the efficiency and noise immunity of the CRS

Henceforth, we assume that all information about target conditions in radar coverage is reconstructed by the a priori and a posteriori data in the course of CRS operation. The noise environment is evaluated by a special signal processing subsystem assigned to analyze changed conditions of the environment. We assume that analysis of additive noise parameters, namely, the type, power level, spectral power density, and so on, is carried out immediately before scanning the chosen direction. Processing and analysis of passive interferences and inclusion of protective equipment against this kind of interferences are carried out by control facilities of signal preprocessing subsystems during scanning the radar coverage.

There is a need to take into consideration that the tasks of choice and task-oriented changes of complex radar subsystem parameters must be solved within the limits of finite time intervals. This requirement is very strong. In the course of the control process, the pulsing rate defined by repetition frequency cannot be changed and must be constant. All processes of decision making should be finished between neighboring scanning. In line with this, the table methods to make a decision can be widely used based on results of noise environment analysis in the radar range.

6.2.2  Control under Directional Scan in Mode of Searched New Targets

In this case, the control process is carried out by two stages. At the first stage, the calculation and choice of scanning signal parameters are carried out. The scanning signals must correspond to the functional mode of searching targets and maximal radar range in the given direction. Additionally, the receiver performance and signal processing algorithms for signal preprocessing subsystems should be defined and computed. This stage is carried out before scanning pulsing in the given direction. Control of accumulated received signals up to making decisions about the target detection/ no detection using all resolution elements in the radar range (the case of sequential analysis) or up

FIGURE 6.3  Logical structure of algorithm to search for a direction in the scanning mode.

to accumulation of a determined number of the target return signals using detectors with the fixed sample sizes is carried out at the second stage. In the course of accumulation of the target return signals, the initial parameter values of scanning signals are the same excepting the carrier frequency fc. In the following, we give a description of a logical algorithmic flowchart to solve the control tasks under direction scanning using the searching mode (see Figure 6.3).

Step 1: After setting transmit and receive antenna beams along the given direction βi, εi, we carry out an analysis of active interferences received along this direction (block 1). First of all, we should define the power σ2n and the power spectral density (f) of the noise. Evaluation of the noise power is used further to make a decision to power on that or other protection equipment from active interferences and, also, to determine predetection SNR. Estimation of power spectral density of active interferences allows us to define the “spectrum troubles” of interference within the limits of considered frequency bandwidth and select the scanning signal carrier frequency on the interval where an action of interference is weakest. In a general case, under analysis of interference there is a need to distinguish and classify the active interferences with definite integrity to create a possibility to use the obtained results to tune and learn the radar receiving channel.

Step 2: At this stage, we solve the problems of the scanning signal parameter selection (block 2). For this purpose, first of all, there is a need to determine a distance εi from the radar to the radar coverage bound under the given elevation angle value εi. Computation is carried out taking into consideration the shape of radar antenna directional diagram. For scanning and tracking radar, a vertical cross section of idealized zone of target searching is shown in Figure 6.4. All searching zone characteristics are considered unknown.

2.1 As it follows from the geometry presented in Figure 6.4, if εmax > εn > ε0, we have

Step 4: This SNR is used later to adjust a control of the CRS signal preprocessing subsystem detectors, that is, to define the required number of scans to reach the given probability of detection PD and the probability of false alarm PF for detectors with the fixed sample size or to define the weights of units and zeros under sequential analysis of binary quantized target return signals (block 4, Figure 6.3). There is a need to note that a realization of the a priori operations discussed earlier on selection of parameters for transmitter, receiver, and signal processing subsystems must be carried out within the limits of finite time intervals or the so-called free running of sweep time equal to (T − τmaxd ). Because of this, we can employ the tables of parameters and settings corresponding to discrete values of noise characteristics, elevation angles, and other given parameters that are kept in a memory device instead of detailed computations.

Step 5: After finishing the preliminary stage, we can start the process of directional scanning and accumulation of target return signals (block 5, Figure 6.3) taking into account the results of distinguishing the passive interferences and using the protection facilities against the passive interferences (block 6, Figure 6.3). At this stage, the control process is carried out by the signal preprocessing subsystem algorithms in accordance with the operations realized by blocks 7 and 8, Figure 6.3.

After finishing the accumulation stage and making a decision about the scanned direction, the results of decision making are issued and expenditure of energy and timetable are computed to observe the scanned direction (block 9, Figure 6.3). The radar antenna beam control is assigned for an algorithm of scanning management in the searching mode or mode controller. In conclusion, we note once more that the discussed logical flowchart is the way only to assign a control process under the searching new target mode. Naturally, there are possibly other ways, but a general idea to control, namely parametric matching of CRS subsystems and signal and data processing subsystems with environmental parameters and solved problems and tasks is the same.

6.2.3  Control Process under Refreshment of Target in Target Tracing Mode

Consider a possible way to design a control algorithm to detect and measure target coordinates in the course of target tracking using information that is discretely refreshed in the CRS with a controlled radar antenna beam. At the same time, we use the following assumptions:

•Time instants of regular refreshment of target tracking are computed each time after clarification of target tracing parameters at the previous step. Time intervals between the previous and next measurements are determined based on the condition of nonrotating radar.

•Owing to possible overlapping of location intervals of the tracked targets and under stimulus of more foreground modes, delays of instruction executions, for example, the target coordinate measure, are possible. Probability and delay time are high, a loading of the CRS is high, or the number of targets in the radar coverage is high. To exclude cancellations of target tracking owing to the delays mentioned earlier, the possibility to expand a searching zone of regular renewed target pip by the angle coordinates and radar range is provided. Expanding in the searching zone by angular coordinates is carried out by assigning some additional directions of scanning around an extrapolated direction taking into consideration the target track parameters, the so-called additional target searching. The number of directions of the additional target searching is not high—from 3 to 5. Expanding in the

searching zone by the radar range is carried out by increasing the dimensions of gate rgate.

•Expanding in the searching zone is carried out also if there are misses of the target pips on target tracing during one or several scanning jobs.