Non-Adaptive and Adaptive Beam Scheduling …cradpdf.drdc-rddc.gc.ca/PDFS/unc252/p804736_A1b.pdfNon-Adaptive and Adaptive Beam Scheduling Techniques for Phased Array Radar Zhen Ding

Defence Research andDevelopment Canada

Recherche et developpementpour la defense Canada

Non-Adaptive and Adaptive Beam Scheduling Techniques forPhased Array RadarZhen Ding and Peter MooDRDC – Ottawa Research Centre

Defence Research and Development Canada

Scientific ReportDRDC-RDDC-2016-R214November 2016

Non-Adaptive and Adaptive Beam SchedulingTechniques for Phased Array Radar

Zhen Ding and Peter MooDRDC – Ottawa Research Centre

Defence Research and Development CanadaScientific ReportDRDC-RDDC-2016-R214November 2016

c⃝ Her Majesty the Queen in Right of Canada, as represented by the Minister of NationalDefence, 2016

c⃝ Sa Majesté la Reine (en droit du Canada), telle que réprésentée par le ministre de laDéfense nationale, 2016

Abstract

In this report, we study beam scheduling techniques to resolve the radar resourcemanagement (RRM) problem, including non-adaptive and adaptive approaches. Per-formance metrics of beam scheduling are presented, followed by a brief description ofthe simulation tool Adapt_MFR that is used in the study. Both non-adaptive andadaptive techniques are described, and the details of adaptive target prioritization,time-balancing scheduling and track update intervals are quantified. Also presentedare two testing scenarios and the results of the performance comparison. It is shownthat the adaptive approach significantly reduces the tracking occupancy and frametime, leaving more time for radar detection and other functions. At the same time,the adaptive approach is still able to keep the track completeness at the same level.A few research topics are recommended for future work.

Significance for defence and security

Multi-function radar (MFR) needs effective beam scheduling, which is studied andpresented in this report.

A content model is proposed, which has all the elements of a typical RRM problem.

Adapt_MFR, an existing DRDC simulator, has been expanded to simulate bothnon-adaptive and adaptive beam scheduling techniques.

A number of performance metrics are also implemented in Adapt_MFR.

Performance of both non-adaptive and adaptive techniques are simulated and com-pared.

The study is essential for Canadian Surface Combatant (CSC) program, where radarbeam scheduling must be evaluated against chosen performance metrics. It is alsohelpful for other programs, when an MFR is required.

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Résumé

Dans le présent rapport, nous étudions les techniques de programmation des fais-ceaux afin de résoudre le problème de gestion des ressources radar (GRR), y comprisles approches d’adaptation et de non-adaptation. Les mesures de rendement liées àla programmation des faisceaux sont présentées et sont suivies d’une brève descrip-tion de l’outil de simulation Adapt_MFR qui est utilisé dans l’étude. Les techniquesd’adaptation et de non-adaptation sont décrites toutes les deux, et nous fournissonsles détails liés à la quantification des intervalles de sélection des cibles d’adaptation,de programmation propre à la répartition du temps et d’actualisation de la poursuite.Deux scénarios d’essai et les résultats du rendement comparé sont aussi présentés. Ilest démontré que l’approche d’adaptation réduit considérablement le suivi de l’occu-pation et la durée de la trame, ce qui laisse plus de temps pour la détection radaret d’autres fonctions. Au même moment, l’approche d’adaptation permet encore deconserver au même niveau l’intégrité de la poursuite. Quelques travaux de recherchesont recommandés pour des travaux futurs.

Importance pour la défense et la sécurité

Le radar multifonctions (RMF) a besoin d’une programmation efficace des faisceaux,ce qui est étudié et présenté dans ce rapport.

Un modèle de contenu est proposé ; il comporte tous les éléments d’un problème typede GRR.

Les capacités de l’outil Adapt_MFR, un simulateur existant de RDDC, ont été ac-crues afin de simuler les techniques de programmation des faisceaux selon les ap-proches d’adaptation et de non-adaptation.

Un certain nombre de mesures de rendement sont aussi mises en œuvre dans l’outilAdapt_MFR.

Le rendement des techniques d’adaptation et de non-adaptation est simulé et comparé.

L’étude est essentielle au programme de navire de combat de surface canadien (NCSC),où la programmation des faisceaux radar doit être évaluée d’après des mesures derendement choisies. Elle est aussi utile à d’autres programmes lorsqu’un RMF estnécessaire. Ceci est l’importance pour la défense et la sécurité.

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Table of contentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iSignificance for defence and security . . . . . . . . . . . . . . . . . . . . . . . iRésumé . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiImportance pour la défense et la sécurité . . . . . . . . . . . . . . . . . . . . . iiTable of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiList of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Resources of a Phased Array Multi-Function Radar . . . . . . . . . 11.2 Radar Scheduling Terminology . . . . . . . . . . . . . . . . . . . . . 31.3 Description of Phased Array Radar Functions . . . . . . . . . . . . . 41.4 A Radar Resource Management Model . . . . . . . . . . . . . . . . . 5

2 Performance Metrics for Radar Beam Scheduling . . . . . . . . . . . . . . 82.1 Scheduler Performance Metrics . . . . . . . . . . . . . . . . . . . . . 82.2 Detection Performance Metrics . . . . . . . . . . . . . . . . . . . . . 82.3 Tracker Performance Metrics . . . . . . . . . . . . . . . . . . . . . . 8

3 Adapt_MFR Multi-Function Radar Simulator . . . . . . . . . . . . . . . . 134 Non-Adaptive and Adaptive Beam Scheduling Techniques . . . . . . . . . . 16

4.1 Non-Adaptive Scheduling . . . . . . . . . . . . . . . . . . . . . . . . 164.2 Adaptive Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2.1 Fuzzy Logic Prioritization . . . . . . . . . . . . . . . . . . . 164.2.2 Time-Balancing Scheduling . . . . . . . . . . . . . . . . . . 174.2.3 Adaptive Update Intervals for Tracking . . . . . . . . . . . . 19

5 Performance Comparison of Non-Adaptive and Adaptive Techniques . . . . 245.1 Two Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 32References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

DRDC-RDDC-2016-R214 iii

List of figuresFigure 1: Multiple functions of ship-borne radar systems. . . . . . . . . . . . 2Figure 2: Multifunction radar resources. . . . . . . . . . . . . . . . . . . . . 2Figure 3: A radar resource management model. . . . . . . . . . . . . . . . . 6Figure 4: High-level overview of the simulation mode with IMM tracker in

Adapt_MFR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Figure 5: Decision tree for fuzzy logic adaptive target priority. . . . . . . . . 17Figure 6: Illustration of the relative priority or importance of a target and

the use of this information to drive the resource needs fordedicated tracking. The two examples (for friendly or hostileidentification) are for the same target trajectory. Note that thetransient spikes in update rates and occupancy are due to thetracker declaring a manoeuvre. . . . . . . . . . . . . . . . . . . . . 18

Figure 7: Time-balancing algorithm for Trial 1. . . . . . . . . . . . . . . . . 19Figure 8: Time-balancing algorithm for Trial 2. . . . . . . . . . . . . . . . . 21Figure 9: Target 1 in Scenario 1. . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 10: Track priority for Target 1 in Scenario 1. . . . . . . . . . . . . . . 26Figure 11: Track intervals for Target 1 in Scenario 1. . . . . . . . . . . . . . . 26Figure 12: Number of targets in radar field of regard. . . . . . . . . . . . . . 28Figure 13: Track completeness for Scenario 1. . . . . . . . . . . . . . . . . . . 29Figure 14: Track occupancy for Scenario 1. . . . . . . . . . . . . . . . . . . . 29Figure 15: Frame time for Scenario 1. . . . . . . . . . . . . . . . . . . . . . . 30Figure 16: Track completeness for Scenario 2. . . . . . . . . . . . . . . . . . . 30Figure 17: Track occupancy for Scenario 2. . . . . . . . . . . . . . . . . . . . 31Figure 18: Frame time for Scenario 2. . . . . . . . . . . . . . . . . . . . . . . 31

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1 Introduction

The use of phased array antennas has enhanced the flexibility and effectiveness ofradar. In particular, phased array technology allows the radar beam to be controlledand adapted almost instantaneously. This flexibility enables the radar to carry outmultiple functions simultaneously, such as surveillance, tracking and fire control,where each function carries out a number of looks. The execution of multiple func-tions necessitates the study of radar resource management (RRM), which considersthe prioritization and scheduling of radar looks, as well as task parameter selectionand optimization. Radar resource management is especially important in overloadsituations, when the radar does not have sufficient time to schedule all requestedlooks. In this case, the radar scheduler must decide which looks should be scheduledand which should be delayed or dropped. Additionally, for the looks to be scheduled,a start time for each look must be determined.

In this section, we describe the RRM problem from four perspectives, including radarresources, radar terminology, radar functions and the presentation of a RRM model.

1.1 Resources of a Phased Array Multi-Function Radar

A phased array multifunction radar (MFR) performs many functions previously per-formed by individual, dedicated radars, such as surveillance, tracking and fire control.The radar performs these functions by actively controlling its beam position, dwelltime, waveform and energy. Details of general phased array radars can be found inReferences [1, 2, 3, 4]. An illustration of the multiple functions is depicted in Figure 1.

There are typically several tasks associated with each radar function. All the func-tions and function tasks are coordinated by the RRM in the radar system. This RRMcomponent is critical to the success of an MFR since it maximizes the radar resourceusage in order to achieve optimal performance, where the optimality is defined ac-cording to various cost functions.

There are three major radar resources, as shown in Figure 2. The challenge of RRMarises when the radar resources are not sufficient to carry out all function tasks. Lowerpriority tasks must encounter degraded performance due to less available resources,or the radar may not execute some tasks at all. Each task in the radar requires acertain amount of time, energy and computational resources. The time is characterizedby the tactical requirements, the energy is limited by the transmitter energy, andcomputational resources are limited by the RRM computer. All of these limitationshave impacts on the performance of the radar resource manager.

Among the radar resources, the time budget is the most constraining, since the radarhas only 100% of its timeline. The energy budget is typically limited by the availablepower supply and the cooling system. The processing budget is usually the least

DRDC-RDDC-2016-R214 1

constraining because of the ever-increasing capability of computer processors. A radarscheduler coordinates the usage of all radar resources in carrying out RRM.

1.2 Radar Scheduling Terminology

To accurately state the goal of a radar scheduler, it is necessary to distinguish betweena function, a task and a look.

Function: The radar carries out multiple functions, which include weapon control,target tracking, and surveillance. A detailed description of various functions is givenin Section 1.3.

Tasks: Each function consists of one or more tasks. For the weapon control function,a task involves the control of an individual weapon. Similarly, for the target trackingfunction, a task involves the tracking of an individual target. The surveillance functionmonitors a specified region of interest. A surveillance task may include the monitoringof a subregion within the specified region of interest. The surveillance function canalso be thought of as consisting of a single task, where the task involves monitoringthe entire region of interest.

Looks: Each task consists of several looks, where a look requires one continuous timeinterval of finite duration to be completed. For a tracking task, a look is an attemptto update a track by steering the radar in the direction of the expected location of thetarget. In this case, a look could consist of one or more beam positions of the radar.For a surveillance task, a look could consist of a single beam position or multiplebeam positions. Since a look has been defined to require a continuous time intervalto be completed, it is beneficial to define surveillance looks to be as short in durationas possible. This allows the scheduler the flexibility to interleave looks from multipletasks.

Each task sends look requests to the radar scheduler. For a target tracking task, alook request may consist of an attempt to update a track at a specified time. Thespecified time will depend on the time of the track update, the estimated targetdynamics and the tracking model. For all tasks, look requests are sent to the radarscheduler independently. That is, each task makes look requests based only on itsown requirements. The role of the radar scheduler is to receive all look requests andformulate a schedule for the radar, under the constraint that at any given time, theradar only executes one look. The radar scheduler must decide whether or not toschedule the look request. For example, if two look requests which start at the sametime are received, the scheduler must decide whether to alter the start times of oneor both looks or to not schedule one of the looks.


1.3 Description of Phased Array Radar Functions

The following functions are carried out by a ship-borne MFR.

Horizon search: The objective of horizon search is to detect low flying targets assoon as they cross the radar horizon. Because these threats are perceived to be oneof the major threats to maritime surface ships, horizon search is one of the mainfunctions of the MFR.

Cued search: Other sensors in the ship’s sensor suite may detect targets that arenot yet being tracked by the MFR. This event may occur due to adverse propagationor other conditions for the MFR, a temporary overload of the MFR time budget,or because the target is outside of the coverage area of the MFR. If the target hasnot yet been tracked due to adverse propagation or other conditions, the length ofthe cued search dwell is increased compared to the normal search dwell to improvethe probability of detection. The cued search pattern, which depends on the sourceof the cue, is executed only once. The delay between the detection of the target bythe other sensor and the actual transmission in the MFR must be short to keep thesearch volume, and therefore the load on the time budget, as small as possible.

Confirmation: After a target has been detected in a search dwell and the target isnot yet in track, a dwell is transmitted in the direction measured by the search dwellto confirm the presence of a target. A successful confirmation results in the initiationof a track. The delay in the transmission of a confirmation dwell must be short toensure that the target is still within half of a beamwidth of the direction measuredby the search dwell.

Air target track: After tracks have been initiated, air targets are tracked withdedicated dwells. The update rate and the dwell time are adapted to the behavior ofthe target in such a way that the track is maintained with a minimum load on thetime-energy budget.

Weapon track: Targets that have been selected for an engagement are tracked withan update rate that is high enough to guarantee a track accuracy that is required formissile guidance.

Surface-to-air missile (SAM) acquisition: A search pattern is executed to ac-quire the SAM shortly after launch by the ownship. Knowledge about the SAMtrajectory is used to define a pattern that has a high probability of acquisition andrequires only limited radar time and energy. After a successful acquisition, a track isinitiated.

SAM track: SAMs are tracked to collect information that is required for midcourseguidance and to avoid unnecessary usage of resources due to confirmation or cuedsearch dwells in the direction of the SAM.

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Midcourse guidance: SAMs that have been launched against a target require mid-course guidance to the predicted intercept point. The actual information in a mid-course guidance message is dependent on the missile type.

Terminal illumination: In the terminal phase of an engagement using semi-activeSAMs, targets must be illuminated by the MFR to enable the missile seeker to lock onthe target. It is assumed here that the seeker of the semi-active missile requires illumi-nation dwells at very regular intervals. This requirement results from the synchronousoperation of the processor in the missile seeker.

Kill assessment: Shortly before and after the predicted intercept, the update ratesof the weapon track and SAM-tracks are increased to establish the result of the en-gagement with a high degree of confidence. The result of this assessment is submittedto the combat system to support the decision of launching other missiles.

Each function has a specific demand for a share of the time budget that is determinedby the duration of the function, the average number of dwells per second (the updaterate) and the dwell time. For search function, the update rate is determined by thenumber of beams that are required to scan the search volume (frame) and the timebetween successive dwells in the same direction (frame time).

For the horizon search function, relatively large deviations from the desired timebetween successive dwells are allowed to enable more important functions, such asterminal illumination, to be scheduled. As a result the confirmed detection range willdecrease, but this is acceptable during overload conditions.

For the midcourse guidance and tracking functions, the time between the desiredand actual transmission time of a dwell is more constrained to avoid a significantdegradation of the kill probability of the SAMs and tracking performance, respec-tively. Finally, as has already been noted, the dwells for terminal illumination mustbe transmitted synchronously.

1.4 A Radar Resource Management Model

Due to the nature of RRM for MFRs, a model for RRM will necessarily be complex.A general RRM system model is shown in Figure 3. It performs the following steps:

• Obtain a radar mission profile or function setup;

• Generate radar tasks;

• Assign priorities to tasks by using a prioritization algorithm;

• Manage available resources via a scheduling algorithm so that the system canmeet the requirements of all radar functions;


• For non-surveillance tasks, schedule a re-look if a target was not detected. Thiswill depend on the task priority and elapsed time since the last scheduling ofthe same task.

Figure 3: A radar resource management model.

The radar scheduler takes into account a number of factors, including radar beams,dwell time, carrier frequency, pulse repetition frequency (PRF), and transmitted en-ergy. As can be seen from the above steps, the RRM problem has two key elements:task prioritization and task scheduling. RRM algorithms can address these two ele-ments separately or simultaneously. Task prioritization is an important factor in thetask scheduler. The other factor is the required scheduling time, which is decided bythe environment, the target scenario and the performance requirements of radar func-tions. The required scheduling time may be improved by using advanced algorithms,such as waveform-aided algorithms and adaptive update rate algorithms.

Note that the general sensor management problem is to optimally coordinate theusage of multiple sensors, which is not considered in this report.


The rest of the report is arranged as follows. Performance metrics for radar beamscheduling are presented in Section 2, followed by a description of the Adapt_MFRradar simulator. Adaptive scheduling techniques are proposed in Section 4. A per-formance comparison of adaptive and non-adaptive techniques is given in Section 5.Conclusions and future work are provided in Section 6.


2 Performance Metrics for Radar Beam Scheduling

RRM involves many components of the radar. Its performance is quantified by overallradar performance. To be specific, RRM is evaluated with respect to the scheduler,the detector and the tracker, where detection and tracking are the two primary MFRfunctions.

2.1 Scheduler Performance Metrics

Scheduler performance metrics are those which are directly related to how timely themultifunction beams are scheduled. These metrics are as follows.

Maximum Delay (MD) is the largest delay of all scheduled beams. The MD couldbe applied to different functions, such as Surveillance MD (SMD) and Tracking MD(TMD).

Accumulated Delay (AD) is the summation of delays of all scheduled beams.The AD could be applied to different functions, such as Surveillance AD (SAD) andTracking AD (TAD).

Ratio of Scheduling (RS) is the ratio of the number of scheduled beams to thetotal number of beams of the radar mission.

Surveillance Occupancy (SO) is defined as the ratio of the surveillance time tothe total time.

Tracking Occupancy (TO) is defined as the ratio of the tracking time to the totaltime.

When computing SO and TO, track confirmations are considered as part of thedetection process, confirming detections to decide whether a track shall be initializedfor the target.

2.2 Detection Performance Metrics

Probability of Detection (Pd) is defined as Pd of specific targets.

Frame Time (FT) is defined as the revisit time of the first detection beam position.Typically the radar comes back to the first detection beam after finishing all detectionbeams. The FT can be defined for a specific region when there are regions of differentpriorities.

2.3 Tracker Performance Metrics

Target Indication Accuracies: are a measure of the error between the true targetpositions and the estimated track positions. Target indication accuracy is measured


for range, azimuth and elevation.

TIAR(j, i) = R(j, i) + ˆR[t(j, i + 1) − t(j, i)] − R(j, i), (1)TIAθ(j, i) = θ(j, i) + ˆθ[t(j, i + 1) − t(j, i)] − θ(j, i), (2)TIAφ(j, i) = φ(j, i) + ˆφ[t(j, i + 1) − t(j, i)] − φ(j, i), (3)

where:

• TIA = target indication accuracy per target measurement (m or rad)

• R = range (m)

• θ = azimuth (rad)

• φ = elevation (rad)

• j = target index

• i = measurement index

• x = x estimate (m or rad)

• x = x rate (m/s or rad/s)

Aggregate Target Indication Accuracies Per Target are obtained by takingthe mean and standard deviation of the target indication accuracies for individualtargets. These values show how well individual targets are being tracked.


TIAR(j, i) =

Ii=1

TIAR(j, i)

I, (4)

TIAθ(j, i) =

Ii=1

TIAθ(j, i)

I, (5)

TIAφ(j, i) =

Ii=1

TIAφ(j, i)

I, (6)

TIAσR(j) =

Ii=1

(TIAR(j, i) − TIAR(j, i))2

I − 1 , (7)

TIAσθ(j) =

Ii=1

(TIAθ(j, i) − TIAθ(j, i))2

I − 1 , (8)

TIAσφ(j) =

Ii=1

(TIAφ(j, i) − TIAφ(j, i))2

I − 1 , (9)

where:

• TIA = target indication accuracy per target measurement (m or rad)

• TIA = mean target indication accuracy of all measurements of one target

• R = range (m)




• i = measurement index

• I = number of measurements

Aggregate Target Indication Accuracies for All Target is obtained by takingthe geometric mean of all individual target TIA means. This value shows how wellthe tracker is performing in general for all targets. The aggregates are measured forrange, azimuth and elevation.


GM_TIAR(j, i) = J

Jj=1

TIAR(j), (10)

GM_TIAθ(j, i) = J

Jj=1

TIAθ(j), (11)

GM_TIAφ(j, i) = J

Jj=1

TIAφ(j), (12)

where:

• TIA = mean target indication accuracy of all measurements of one target

• GM_TIA = geometric mean target indication accuracy for all targets

• R = range (m)




• I = number of measurements

Track Completeness is defined as follows:

TC = total time for which any confirmed track number is allocated to the targettotal time that the target is within defined detection region

(13)

where the time interval considered in the numerator of the above expression starts atthe latest of either:

• the time that an confirmed track for the target is first initiated, or

• the time at which the confirmed track enters the defined target detection regionif the target is being tracked before it enters the region,

and ends at the earliest of either:

• the time that an confirmed track with the highest track number for the targetis terminated, or

• the time at which the confirmed track leaves the defined target detection region.


Track Continuity the number of track breakups per a chosen time period of evalu-ation for the same known object.

False Track Rate is defined to be the average number of false tracks per day, wherefalse tracks are any tracks not associated with a known object.


3 Adapt_MFR Multi-Function Radar Simulator

Adapt_MFR is a full radar simulation package that was designed and developedat DRDC Ottawa to model naval radars operating in a littoral environment. Sup-port for both rotating and non-rotating phased array multifunction radars, as wellas conventional rotating dishes such as volume search radars, is included. It incorpo-rates models for land, sea, chaff, and rain clutter, as well as jammers. Adapt_MFRruns sequencially, producing detection output results for one beam at a time. Mul-tiple waveforms and radar operational modes are available, including the dynamicand adaptive switching of waveforms. Adapt_MFR also includes the ability to modelanomalous propagation, and to incorporate real terrain features through the import-ing of Digital Terrain Elevation Data (DTED) files.

An illustration of the high-level Adapt_MFR simulation architecture is presentedin Figure 4. The framework consists of a series of modules (left hand side) thatdescribe the radar(s), target scenario, and environment which are required to provideinput to the simulation. The simulation flow located in the centre section of the figurerepresents the running code, which makes use of the data and associated functionality(algorithms, models, etc.). Adapt_MFR uses a tracker which employs an InteractingMultiple Model algorithm with a constant velocity model and a Singer manoeuvringmodel for estimating target dynamics. The measurement models include range, rangerate, bearing and elevation. Detection-to-track data association is carried out usingNearest Neighbour (NN) JPDA [5].

As a result of the large parameter set and general versatility of the tool, there aremany and varied modes in which it may be operated. There are, however, three basicmodes of operation for Adapt_MFR, which are:

• calculator mode

• simulation mode without tracker

• simulation mode with IMM tracker

The calculator mode allows the user to compute preliminary detection results in anon-causal mode. The simulation modes are causal in nature and provide a completesimulation run, making the functionality of Adapt_MFR available to the user.

In order to analyse the performance of RRM techniques, Adapt_MFR is operatedin the simulation mode with IMM tracker. An overview of this mode is shown inFigure 4. To operate in this mode, user inputs are accepted through a graphical userinterface and stored into corresponding radar, scheduling, environmental, and otherdata structures. Target initial positions and trajectories are set by the user. Thesimulator runs in a loop, with time incremented in each pass by the dwell time of theradar beam, until the simulation time ends. Surveillance continues until a detectionoccurs and a confirmation is scheduled for that detection. For each successful target


• calculate target trajectories

• set measurement resolutions, beam patternspecifications, environmental conditions, etc.

• initialize tracking and scheduler parameters

• compute track update intervals

• implement radar scheduler, including task pri-oritization

• compute full radar range equation and detectionprobabilities

• determine target detection based on MonteCarlo test

• add appropriate random perturbations to detec-tion measurements

Radar

Targets

Environment

Input

Parameters

Simulation

Flow

Interactive MultipleModel Tracker

Detections

Tracks

Figure 4: High-level overview of the simulation mode with IMM tracker inAdapt_MFR.


confirmation, a measurement report is sent to the tracker. Predictions are requestedat specific scheduled times based on user-defined rules to determine track updateintervals. Based on the radar scheduling algorithm being modeled, future surveillanceand tracking beams are assigned at specific times. Adapt_MFR is capable of modelingnetworked radars with an arbitrary number of radars. Multiple-radar tracking is alsoenabled.

Adapt_MFR accurately assesses RRM performance by causally modeling radar op-eration on a beam-by-beam basis. Radar detections are input to an IMM tracker.The tracker is then capable of sending track update requests to the radar scheduler.Tracking performance is analysed by comparing tracker outputs to ground truth data.


4 Non-Adaptive and Adaptive Beam SchedulingTechniques

4.1 Non-Adaptive Scheduling

Current and future defence systems will employ multifunction phased array radars toprovide search, track, weapon control and identification, all under software control.Existing RRM techniques utilize fixed sets of tasks and task priorities. Non-AdaptiveRRM allocates a fixed percentage such as 30% of the radar’s timeline to trackingtasks, with the remainder allocated to surveillance tasks. There is no prioritizationamong the tracking tasks. All detection and tracking beams are scheduled sequen-tially, resulting under-scheduled or over scheduled tasks.

4.2 Adaptive Scheduling

Future RRM techniques are expected to employ adaptivity. The potential benefits ofthese adaptive control techniques and strategies are expected to include:

• Optimization of the available radar timeline (search time vs. other tasks etc.)leading to improved performance, especially when close to overload.

• Adaptive modification of radars performance as the environment changes (e.g.ship moving from Open Ocean to Littoral, ECM).

• Ability to reconfigure the radar for different applications through software con-trol changes (e.g. from medium range air defence to BMD).

• Ability to rapidly reconfigure the radar to counter unforeseen threats, applica-tions and eventualities (e.g. introduction of a different threat into the scenario).

The objective of adaptive techniques is to develop approaches that optimize perfor-mance for an MFR in a dynamically changing environment. This section describesAdaptive RRM, which is characterized by three main techniques:

• Fuzzy Logic Prioritization

• Time-Balancing Scheduling (TBS)

• Adaptive Update Intervals for Tracking

These techniques are described here in more detail.

4.2.1 Fuzzy Logic Prioritization

Figure 5 shows the fuzzy logic decision tree and can be used to rank the relativeimportance of targets detected and tracked by the radar [6]. This method can beused to support task scheduling as well as allowing Adaptive RRM to decide when


track accuracy for low priority targets may be relaxed when the radar is overloaded.The ability of the radar to selectively relax the detection and tracking requirementsfor lower priority radar tasks coupled with the need to adapt the task priority order fortask scheduling provides a tool to support the implementation of graceful degradationof radar performance in extreme overload. Data inputs into the fuzzy logic tool suchas track range, (radial) range rate, and velocity are generated by the track extractor.Target ID may be produced by a high resolution radar (HRR) classification activity.

Figure 5: Decision tree for fuzzy logic adaptive target priority.

Figure 6 below illustrates an example of the output from the fuzzy logic tool and howthis is used to drive the use of tracking resources. The blue plot represents a targetwhich has been classified as hostile while the red plot represents the same targettrajectory when the target is identified as friendly. Clearly, the friendly target hasbeen classified as less important and, therefore, Adaptive RRM uses this informationto request less radar time for dedicated tracking of this target.

4.2.2 Time-Balancing Scheduling

Adaptive RRM uses the time-balancing algorithm for its beam-time allocation [7].Time-balancing is a method that is often used in operating systems to dynamicallyallocate times for different processes. Figure 7 shows a time-balancing graph. A time-balance slope is defined for each beam type. For each time unit of 0.012007 second inthis example, the simulation carries out the algorithm and determines which beamto execute. Once that beam is executed, the time balance is then stepped down.Two trials were performed to verify the accuracy of this algorithm. After running


Figure 6: Illustration of the relative priority or importance of a target and the use ofthis information to drive the resource needs for dedicated tracking. The two examples(for friendly or hostile identification) are for the same target trajectory. Note that thetransient spikes in update rates and occupancy are due to the tracker declaring amanoeuvre.


the program, the values were geometrically verified using the time-balancing graphproduced by the simulation. Proportions were created to convert between the numberof pixels on the screen and the actual units in seconds. The results of the verificationof the algorithm for Trials 1 and 2 are shown in Table 1. The algorithm was alsographically verified as shown in Figures 7 and 8 which illustrate the time-balancingalgorithm graphs for Trials 1 and 2, respectively.

Figure 7: Time-balancing algorithm for Trial 1.

4.2.3 Adaptive Update Intervals for Tracking

This subsection describes the calculation of update intervals for Adaptive RRM. As-sume a track’s state estimate is

X(k) = [x(k), x(k), x(k), y(k), y(k), y(k)], (14)

at time tk in the North-East coordinate system. The covariance matrix is P (k). Forsimplicity, the coordinate z in the North-East-Down coordinate system is ignored.The azimuth position θ, velocity θ and acceleration θ are calculated by a nonlinearfunction [θ, θ, θ] = h(x, x, x, y, y, y) which includes the following equations.

θ = tan−1(y

x), (15)

θ = xy

r2 − yx

r2 , (16)


Table 1: Time-balancing verification.


Figure 8: Time-balancing algorithm for Trial 2.

θ = (xy − yx

r2 )′, (17)

= r2(xy − yx)′ − (xy − yx)(x2 + y2)′

r4 , (18)

≈ (xy − yx)′

r2 , (19)

≈ (xy + xy) − (yx + yx)r2 , (20)

≈ xy − yx

r2 , (21)

where r =√

x2 + y2 is the horizontal range. Equation (19) is an approximation of(18) to simplify the calculation by ignoring the part with much smaller value. With(15) to (21), the Jacobian matrix for the transformation X

h−→ [θ, θ, θ] is defined asfollows:

H(k) = δh

δX

X(k)

=

−y(k)r2(k) 0 0 x(k)

r2(k) 0 0˙y(k)

r2(k)−y(k)r2(k) 0 ˙−x(k)

r2(k)x(k)r2(k) 0

¨y(k)r2(k)

−y(k)r2(k) 0 ¨−x(k)

r2(k)x(k)r2(k) 0

. (22)

The covariance matrix Paz(k) for the estimation error of [θ(k), θ(k), θ(k)] is calculated


as follows:

Paz(k) = H(k)P (k)HT (k). (23)

From Paz(k), three quantities are available: the azimuth variance a(k), azimuth-azimuth rate covariance b(k) and azimuth rate variance d(k). For medium prior-ity targets, the time interval for the next updates is calculated by the followingEquation [8].

τ 2(k) ≤E(k) −

E2(k) − 16A2F (k)

8A2 , (24)

where

E(k) = 4Bhr(k)A + 16r2(k)d(k), (25)

F (k) = r2(k)B2 − 16r2(k)a(k) − 32τ(k)b(k). (26)

Similarly, for high priority targets, the equation is as follows:

τ 2h(k) ≤

Eh(k) −

E2(k) − 16A2Fh(k)8A2 , (27)

where

Eh(k) = 4Bhr(k)A + 16r2(k)d(k), (28)

Fh(k) = r2(k)B2h − 16r2(k)a(k) − 32τh(k)r2(k)b(k), (29)

Bh = 2B

K. (30)

In (24) and (27), τ(k) and τh(k) are approximations of τ(k) and τh(k) . The purposeof the approximations is to simplify the calculation. Note that τh(k) is a sensitiveparameter and a smaller value is needed to generate feasible solutions. To avoidinfeasible solutions, we can simply let it be zero, i.e., τh(k) = 0. τ(k) can be theprevious rate τ(k − 1) for the same target.


The variable A is the maximum acceleration of the target (typically 1g or 2g in metersper second). The variable B is the beamwidth for the target direction. The accuracyfactor K is a tuning parameter between 2 and 10, where 5 or 6 is reasonable value.When K is high (K > 6 for example), the calculation of τh(k) by (29) may becomeunstable. It is suggested to check the positiveness of the values which are to be squarerooted. In addition, a setup of minimum and maximum values for both τ(k) and τh(k)would also be helpful to avoid unrealistic update rates: between 2 and 4 seconds formedium priority targets, and between 0.25 and 2 seconds for high priority targets.

Note that an azimuth has to be converted to an angle relative to the boresight forthe beamwidth calculation.


5 Performance Comparison of Non-Adaptive andAdaptive Techniques

5.1 Two Scenarios

For this comparison, the scenario length is 600 seconds. The radar transmits coherentpulsed waveforms with a peak power of 10 kW.

Two target scenarios are implemented in Adapt_MFR. Scenario 1 has a total of 52targets, where each target is present in the scenario for some portion of the scenariotimeline. Because all targets are not necessarily present at any given time, the totalnumber of targets in the simulation may be less than 52 at any given time. The targetsmay be surface or airborne platforms. Each target is specified by a unique platformidentification, location, velocity, trajectory, and RCS.

Scenario 2 has a total of 152 targets. These targets include the 52 targets fromScenario 1, 50 targets which are replicated from the original 52 targets, and 50 birdtargets.

5.2 Simulation Results

Non-Adaptive RRM allocates 30% of the radar’s timeline to tracking tasks, with the remainder allocated to surveillance tasks. There is no prioritization among the tracking tasks. As described in Section 3.3, Adaptive RRM utilizes Fuzzy Logic Pri-oritization, Time-Balancing Scheduling, and adaptive update rates for tracking. High priority targets are tracked targets with priority greater than 0.7. These targets have a desired track update rate given by (27). Medium priority targets are those with a priority value between 0.3 and 0.7, and have a desired track update rate given by (24). Low priority targets are those with a priority value of less than 0.3. These targets are updated using track-while-scan; that is, there are no dedicated track update beams for low priority targets.

To begin the analysis of this performance comparison, the behavior of a single targetis considered. In Scenario 1, Target 1 is an airborne target that is in the field of regardat the start of the scenario and is initially approaching the radar. At approximately150 seconds, the target starts to travel away from the radar and exits the field ofregard at 300 seconds. The range and azimuth of Target 1 as a function of time areshown in Figure 9. The target track priority, as shown in Figure 10 is 0.85 untilapproximately 100 seconds, and then decreases slightly with time. Target 1 is a highpriority target until 200 seconds and then becomes a medium priority target, as shownby the requested track intervals in Figure 11. As a high priority target, the requestedtrack intervals are between 0.25 seconds and 2 seconds, while as a medium prioritytarget, the requested track intervals are between 2 and 4 seconds.


0 50 100 150 200 250 3002.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3x 104

time, s

targ

et ra

nge,

m

(a) Range vs. time

0 50 100 150 200 250 30080

90

100

110

120

130

140

150

160

time, s

targ

et a

zim

uth,

deg

(b) Azimuth vs. time

Figure 9: Target 1 in Scenario 1.


0 100 200 300 400 500 6000

0.2

0.4

0.6

0.8

1

time, s

prio

rity

Figure 10: Track priority for Target 1 in Scenario 1.

0 100 200 300 400 5000

1

2

3

4

5

6

time, s

track

bea

m in

terv

als,

s

actual track intervalsrequested track intervals

Figure 11: Track intervals for Target 1 in Scenario 1.


Scenario 1 has a total of 52 targets, but not all targets are in the radar’s field of regardat any given time. For Scenario 1, Figure 12a shows the total number of targets in thefield of regard during the simulation. Also shown are the number of high, medium andlow priority targets. The priority value, as calculated by the Fuzzy Logic Prioritizationtechnique, dynamically varies with the characteristics and dynamics of a target. As aresult, the number of high, medium and low priority targets also varies throughout thesimulation. For Scenario 2, Figure 12b shows the total number of targets, includingthe number high, medium and low priority targets.

For Scenario 1, Figure 13 shows track completeness as a function of target index.Adaptive and Non-Adaptive RRM have similar track completeness values for mosttargets, with some minor exceptions. Figure 14 presents track occupancy as a functionof time. Examination of Figures 13 and 14 shows that Adaptive RRM has significantlylower track occupancy than Non-Adaptive RRM, while achieving similar values oftrack completeness. The use of Adaptive RRM allows the radar to allocate less timeto tracking while maintaining the same track completeness as Non-Adaptive RRM.

Figure 15 shows the frame time for Scenario 1. Track confirmation beams are al-located to detection for the purpose of computing track occupancy. The schedulingof track confirmation beams increases the time until the first detection beam posi-tion is revisited, which results in increased frame time. In Figure 15, this is seen forAdaptive RRM between 150 seconds and 200 seconds of the simulation when numer-ous confirmation beams are scheduled. The corresponding increase in frame time isevident.

Under Scenario 2, track completeness is shown in Figure 16. Adaptive RRM and Non-Adaptive RRM have similar track completeness values. A notable exception is Target7, for which Adaptive RRM has track completeness of 0.97, while Non-AdaptiveRRM has track completeness of 0.58. Targets 141 and 142, which are both birds,have higher track completeness for Non-Adaptive RRM. Figure 17 presents trackoccupancy as a function of time. As was the case with Scenario 1, Scenario 2 resultsshow that Adaptive RRM has significantly lower track occupancy and similar trackcompleteness compared to Non-Adaptive RRM. Figure 18 illustrates the frame timefor Scenario 2.


0 100 200 300 400 500 6000

5

10

15

20

25

30

35

time, s

num

ber o

f tar

gets

priority>=0.70.3<priority<0.7priority<=0.3all

(a) Scenario 1

0 100 200 300 400 500 6000

10

20

30

40

50

60

70

80

time, s

num

ber o

f tar

gets

priority>=0.70.3<priority<0.7priority<=0.3all

(b) Scenario 2

Figure 12: Number of targets in radar field of regard.


5 10 15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

target index

track

com

plet

enes

s

Non−adaptive RRMAdaptive RRM

Figure 13: Track completeness for Scenario 1.

0 100 200 300 400 500 6000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

time, s

track

occ

upan

cy


Figure 14: Track occupancy for Scenario 1.


0 100 200 300 400 500 6004

5

6

7

8

9

10

time, s

fram

e tim

e, s


Figure 15: Frame time for Scenario 1.

20 40 60 80 100 120 1400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

target index

track

com

plet

enes

s


Figure 16: Track completeness for Scenario 2.


0 100 200 300 400 500 6000

0.05

0.1

0.15

0.2

0.25

0.3

time, s

track

occ

upan

cy


Figure 17: Track occupancy for Scenario 2.

0 100 200 300 400 500 6002

3

4

5

6

7

8

9

10

time, s

fram

e tim

e, s


Figure 18: Frame time for Scenario 2.


6 Conclusions and Future Work

Using a radar simulation tool Adapt_MFR, we compare the performance of an adap-tive radar resource management (RRM) technique to that of a non-Adaptive tech-nique. Performance metrics are presented in three areas: scheduling, detection andtracking. The adaptive RRM technique is described, and the details of its adaptiveprioritization, scheduling and track update intervals are quantified. Finally, we presentthe scenario under consideration and the results of the performance comparison. It isshown that the adaptive approach significantly reduces the tracking occupancy andframe time, leaving more time for radar detection or other functions. At the sametime, the adaptive approach is still able to keep the track completeness at the samelevel. Future research is expected on measures of effectiveness and performance forfuture radar applications, and performance analysis of radar resource managementwhen adaptive waveforms, radar electronic protection, radar cognition and spectrumcongestion are considered.


References

[1] Moo, P. and Ding, Z. (2015), Adaptive radar resource management, AcademicPress.

[2] Jeffrey, T. (2009), Phased array radar design, SciTech.

[3] Sabatini, S. and Tarantino, M. (1994), Multifunction array radar - system designand analysis, Artech House, Boston.

[4] Brookner, E. (2006), Phased arrays and radar: past, present and future, MicrowaveJournal, 49(1), 24–46.

[5] Helmick, R. (2000), IMM estimator with nearest-neighbour joint probabilistic dataassociation, Artech House, Boston.

[6] Miranda, B. (2016), Fuzzy logic approach for prioritization of radar tasks andsectors of surveillance in multifunction radar, IET Radar, Sonar, and Navigation,1(2), 131–141.

[7] Butler, J. (1998), Multi-function radar tracking and control, Ph.D. thesis, Uni-versity College London.

[8] Noyes, S. (1998), Calculation of next time for track update in the MESAR phasedarray radar, In IEE Colloquium on Target Tracking and Data Fusion, Vol. 2, pp. 1–7.


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Non-Adaptive and Adaptive Beam Scheduling Techniques for Phased Array Radar

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Moo, Z. D. a. P.

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In this report, we study beam scheduling techniques to resolve the radar resource management(RRM) problem, including non-adaptive and adaptive approaches. Performance metrics of beamscheduling are presented, followed by a brief description of the simulation tool Adapt_MFR thatis used in the study. Both non-adaptive and adaptive techniques are described, and the details ofadaptive target prioritization, time-balancing scheduling and track update intervals are quantified.Also presented are two testing scenarios and the results of the performance comparison. Itis shown that the adaptive approach significantly reduces the tracking occupancy and frametime, leaving more time for radar detection and other functions. At the same time, the adaptiveapproach is still able to keep the track completeness at the same level. A few research topics arerecommended for future work.

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Performance Evaluation, Adaptive Radar Resource Management, Non-Adaptive Radar Re-source Management, Time-Balancing Algorithm

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Non-Adaptive and Adaptive Beam Scheduling …cradpdf.drdc-rddc.gc.ca/PDFS/unc252/p804736_A1b.pdfNon-Adaptive and Adaptive Beam Scheduling Techniques for Phased Array Radar Zhen Ding