Netted radar: Network communications design and optimisation

Ad Hoc Networks 9 (2011) 736–751

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Ad Hoc Networks journal homepage: www.elsevier.com/locate/adhoc

Netted radar: Network communications design and optimisation Stephen Hurley a,⇑, M. Imran Khan b a b

School of Computer Science, Cardiff University, Cardiff CF24 3AA, United Kingdom Defence Science and Technology Laboratory, Farnborough, United Kingdom

a r t i c l e

i n f o

Article history: Received 24 May 2010 Received in revised form 18 August 2010 Accepted 28 August 2010 Available online 6 September 2010 Keywords: Optimisation Network design Distributed radar

a b s t r a c t Networks of phased array radars are generally able to provide better counter stealth target detection and classification. Each radar sensor (or node) generates information which requires transmission to a central authority that is able to evaluate the information. This requires a communications network to be established to allow transmission of information to and from any node. Each radar node is limited by range and degree and relies on the formation of a multi-hop network to facilitate these transmissions. This paper presents a model whereby the radar beam itself is used in the formation of a multi-hop network. The phased array’s multi-functional nature allows rapid switching between communications and radar function. A model of how the communication system could operate is presented, and an evolutionary optimisation algorithm based upon the concept of Pareto optimality is used for the topological design of the network. Finally, a simulation environment is presented to show the simulated performance of the communication model and designed networks. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction The advantages and diversity of phased array radar have been known for decades. Fourikis [1] provides a rich overview and discusses the diverse range of applications of phased array based systems. More recent advances in phased arrays allow for inter-continental phased array communication. These radars communicate over large distances and relay information to central operational control centres. This paper uses much smaller radars to form tightly controlled distributed radar networks over small geographical areas. The phased array radar antenna has the ability to form beams in both transmit and receive mode, effectively allowing the radar to maximise its sensitivity in the desired direction while minimising its sensitivity in other directions [2]. This versatility and agility can be used to good effect when trying to implement a communication function using the phased array radar itself. With this ⇑ Corresponding author. Tel.: +44 2920 874749. E-mail address: [email protected] (S. Hurley). 1570-8705/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.adhoc.2010.08.023

communications ability the phased array radar becomes a multi-functional radar (MFR), performing both the ground based air defense (GBAD) and communications functions. The use of phased array radar antenna for communication has several advantages associated with highly directional antenna as compared to their omni-directional counterparts. This results in an increased communications range which in turn allows more connections to be made. Directive antenna also have higher gains and higher capacity. All these factors contribute to having high data rate, low interference and well connected networks. The collective use of a network of phased array antennas also has the advantage of being more difficult to jam because they require lower power than their larger omni equivalents. They also have lower sidelobes and the ability to form adaptive nulls, i.e. place nulling beams in the direction of the jammer. These advantages are further enhanced because of the distributed nature of the radars - jammers are required to interfere over a larger area and in multiple directions [3,4]. It is possible to use a separate dedicated subsystem for communications, however this leads to a

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less robust and less reliable system with more components and slower operation because of potentially increased delays required by crossing multiple subsystems (radar to radio). Also, there may be increased costs in maintaining and supporting two separate subsystems. Most of the published work on networked radars, not necessarily phased arrays, focus on how to combine observations from different radars on the same target to increase sensitivity and/or accuracy, for example [5–8]. Work presented in [9] describes the performance of netted radar in terms of sensitivity and ambiguity function and develops a set of software tools to assess netted radar sensitivity and ambiguity properties in two and three dimensions. This paper does not consider the detection or tracking capability of a target from a single phased array radar network but aims to exploit the directionality of the beam of phased arrays for the design of the network topology and the communication protocols of the network. The results for the network topology design and communications are obtained through the use of an evolutionary algorithm, yielding efficient yet suboptimal solutions. Studies such as [10] consider network topology management and design for large phased array antennas with large ranges. The formation of these networks is based on a straightforward network mesh formation as the large ranges enable easy link establishment between any nodes. These phased array networks are also used solely as high bandwidth backbone nodes with communication a priority. In this paper, the network is used to increase the size of the surveilled region for a given range of radar transceivers and a multi-hop network is designed, using the directional beams of the phased arrays, to form a communications network for the transfer of tactical information. Very little previous work exists on combining the radar and communications functions using the radar beam itself. Giuli et al. [11] briefly mentions this combination by proposing a system of receive sensors based on an ad-hoc network where each element of a multistatic radar performs as both a radar receive sensor and as a communication node, however, no topological design of the ad-hoc network is considered. Other studies involve the use of networked radar for meteorological applications. For example Donovan et al. [12] describes the use of combining energy harvesting techniques in wireless sensor networks with X-band radars, for a rapidly deployable and self sustainable remote sensing of the troposphere. Tracking mobile targets is an important application of multi-hop sensor networks for both military and defense systems [13]. Topology control in multi-hop sensor networks can be used to conserve energy, reduce interference and maximise capacity, and several algorithms have been proposed e.g. [14–16]. In general there are two approaches to topology control in ad-hoc networks - power control (energy conservation) and hierarchical topology organisation [17]. However, dependencies on volatile information, such as node position, signal strength, and angular positions, contribute to potential instability of topology control algorithms based on power control [18]. Hierarchical topology organisation generally involves some form of clustering to form a subset of nodes that have certain characteristics, for example to serve as a network backbone. In

the work presented here there is no reliance on energy conservation in the network and no clustering of nodes is considered. This paper will be organised as follows. Section 2 contains a description of the communications model, Section 3 contains details of the simulation environment used for testing radar network topologies, Section 4 contains details of the optimisation algorithm used for designing phased array networks. Section 5 contains results of numerical simulations used to test network designs and the communications model. Finally, Section 6 contains conclusions and suggestions for future work. 2. Communications model 2.1. The radar node The radar node simulates the basic operations of a radar based on the proximity to a target. Fig. 1 is representative of how targets and radars interact. The nodes also contribute to the formation of an infrastructure-less network and can be considered ad-hoc [19]. The nodes therefore perform the following ad-hoc and radar functions:  Operate as a radar and generate information and messages regarding targets.  Establish directional beams to facilitate communication and formation of a radar network.  Operate as a router and forward packets using the established radar network. Table 1 shows a summary of the important aspects of both the radar and communication characteristics of each node assumed in this paper. 2.2. Radar node subsystem Fig. 2 shows the message processing and associated simulator subsystems of the radar node. Messages can arrive either from other radar nodes through the incoming links or directly from the radar subsystem. Incoming messages are processed depending on whether incoming messages

Target Dir

ir al W

ion

ect

Radar Node e

ng

r da

ss

ele

Forward Velocity

Ra

Ra

Range Coverage Fig. 1. Target–node interaction.

k

Lin

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queueing methods such as those discussed in Tanenbaum [20] and more detailed algorithms such as rate-controlled algorithms are not considered.

Table 1 Radar and communication characteristics of a node. Attribute/characteristic

Value/description

Power (mW) : Frequency (GHz) : Wavelength (m) : Radar range, Xcr Radar ID x-Coord y-Coord z-Coord Number of phased arrays

200 15 0.02 3750m 12Bit ID OS reference OS reference Elevation 4

2.3. Radar communication and operation Each radar node is made up of four phased arrays which each cover 90°. Fig. 3 shows how the communication model is intertwined with the radar model. In Fig. 3 when node 1 face 3 detects a target it sends messages to or via node 2 and onto its final destination. It is assumed that the radar performs normal radar function for the majority of the time (90% here) and enters a communication mode for the remainder of the time (10% here). Consequently, each 100 ms timeslot is split as shown in Fig. 3 – 90 ms radar scan followed by 10 ms of communication. Node 2 face 3 has to be pointing in the correct direction and at precisely the same time during communication with node 1 face 1. This highlights the precise time synchronous nature of the operation of the radar nodes. The radars can have up to two communication links per face (LPF). This requires the timeslots to alternate between

are destined for the node or another node in the network. Messages destined for the node are analysed by a separate subsystem. Messages that are destined for a different node in the network are re-packed and placed on an outgoing message queue dictated by the routing table. If required, the outgoing queues can be prioritised depending on message type, e.g. tracking messages could be placed at the front of the queue and surveillance messages moved to the back of the queue. Queueing is based on a FirstCome-First-Serve method unless otherwise stated. Other

System Overview

Radar Node

Radar Scanning Subsystem Radar/Communication Subsystem

Face 3

Face 2

Face 0

Face 0 Links Face 1 Links Face 2 Links Face 3 Links

Face 1

Queue Processing

Routing Table

Face 0 outgoing queue Face 1 outgoing queue Face 2 outgoing queue Face 3 outgoing queue

Frame building/ prioritising

Message Analysis

Fig. 2. Radar node overview.

Target

Radar Node1

Face 3 Face 0 Face 2 Face 1

Radar Node 2

Node 1 radar Coverage

Face 3

Face 0

Face 2

Face 1

Node 2 radar Coverage

Comms Mode

Communication Profile Node 1 Face 1

Radar Scan

100ms

100ms

100ms

100ms

100ms

100ms

100ms

1 Second Fig. 3. Radar operation 1 link per face.

100ms

100ms

100ms

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Target Radar Node1 Face 3

Face 0

Face 2

Face 1

Radar Node 3

Radar Node 2

Comms Mode

Face 0

Face 2

Face 1

Face 0

Face 2

Face 1

Comms Mode

Communication Profile Node 1 Face 1 2 links per face

Radar Scan

100ms

Face 3

Face 3

100ms

100ms

100ms

100ms

100ms

100ms

100ms

100ms

100ms

1 Second Fig. 4. Radar operation 2 links per face.

the different nodes. If, as in Fig. 4, node 1 sends messages to both nodes 2 and 3 on the same face, then the communication time is divided as shown.

– each message is tracked to allow message delays, queuing, and overall message times to be analysed. 3.1. The target

3. Network simulation environment Radar network simulation is used to simulate the interaction between the radar network and potential targets. It is also required to simulate the interaction of radar-to-radar communications in the radar network. It is assumed that all messages generated by the radar nodes in response to targets must be sent to a commander (positioned at a single radar node somewhere in the network) via the radar network itself using the communications model above. This message passing/packet routing is simulated in the form of a routed network to allow an evaluation of the radar network topology design. In order to perform this function the simulator is required to:  Represent the physical aspects of the regional environment, lines-of-sight, terrain, radio propagation model – this aspect of the simulator is incorporated into a geographical information system.  Represent the physical aspects of radars, radar node operations and links – ranges, communications timings, data rate characteristics of radars.  Allow adaptations of the physical aspects of the radar nodes – e.g. one or two links per face used for communication.  Provide abstract representation of the radar – the radar operation is simulated through the generation of messages based on target proximity rather than true radar operation based on the electromagnetic properties of the system.  Use suitable network level protocols including routing – the routing of messages is carried out using routing tables maintained by each radar node. Adaptive delay routing is used in the simulator [21].  Allow quantitative and qualitative information to be extracted from the various components of the system

The simulator generates communication messages based on the proximity of a target (see Fig. 1). An event occurs when an airborne target is detected by a radar node. This event triggers the radar node to carry out operations required to monitor and identify the target. Surveillance and tracking messages are generated and sent to the commander node via an already established wireless link (wireless links are only available during designated timeslots, see Section 2.3). As targets travel through the network, each node attached to the network detects targets within their range and sends the relevant messages to the commander node. Targets are given by a set x, y and z component of velocity. The velocity of the target is set initially and remains unchanged during the simulation. Table 2 outlines the properties of a target. 3.2. The environment The radars are placed in a simulated environment using a geographic information system (GIS) to enable the accurate modelling of spatial characteristics such as distance, elevation, terrain and lines-of-sight. As the radar nodes are highly directional, accurate lines-of-sight are critical

Table 2 Target attribute/operational details. Attribute/operational state

Description

TargetID Velocity Current position

For simulation use only x, y, z components of velocity Current position based on simulator time Starting position of the target

Entry point

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S. Hurley, M. Imran Khan / Ad Hoc Networks 9 (2011) 736–751 Inputs Terrain OS Tile\Tiles Number of Nodes Node Positions Commander Position Radar bandwidth at separation

Inputs Number of Links Per Face

Inputs Number of Targets Target Entry Points Target Velocities

GIS

Outputs Average number of hops Average link length All pairs ST connectivity Averge number of hops to commander Average number of link colour changes to commander

Radar Network Design

Simulation

Outputs Message related stats Average message delay to commander Total number of messages routed Total number of messages sent Full routed path analysis for each message (if required)

Inputs

Outputs

Node related stats Total number of messages sent by each node Total number of messages routed by each node Average message delay from each node Target related stats Average message delay for each target Number of messages regarding each target First detection times Fig. 5. System overview inputs and outputs.

to calculate which radar nodes are visible to each other. This information is then used in the optimisation algorithm (Section 4). Lines of sight are calculated using the GIS system ArcGIS.1 The terrain datasets used are digital elevation models taken directly from the United Kingdom’s Ordnance Survey (OS). The datasets, in NTF2 high resolution terrain format, provide accurate models of the terrain. The radar nodes can be placed on the grid either randomly or at predefined positions and the GIS calculates the lines-ofsight based on three criteria – radar range, node height, interference/propagation.3 Fig. 5 shows the full system in the form of inputs to the system and generated outputs at each stage of the simulation and design optimisation. The system is given access to the GIS component at all times during both the optimisation and simulation stage. The framework can initially call for current lines-of-sight for a given set of nodes or retrieve previously calculated lines-of-sight. Calculations of lines-of-sight on-the-fly re1

See http://www.esri.com/software/arcgis for full details of ArcGIS. UK Ordnance Survey PANORAMA Digital Terrain Model. 3 ArcGIS solution developed includes interfaces for the inclusion of a propagation model. 2

quire large amounts of computational power, consequently the calculations are based on predicted node movements and therefore lines-of-sights can be precomputed. 3.3. Traffic generation Section 3.1 describes the triggering event of a target passing within range of the radar. This section4 describes the three modes of operations and the timings involved with:  Surveillance mode  Tracking mode  Engagement mode 3.3.1. Surveillance mode It is assumed that the radars gather information during the scan phase of the radar operation which accounts for 90% of the radar operating time. After a target is first detected within radar range the target is added to the acquired target list. The node changes to surveillance mode 4

Developed in accordance with QinetiQ recommendations.

S. Hurley, M. Imran Khan / Ad Hoc Networks 9 (2011) 736–751

from the default scan state. After a confidence period of 2 s has elapsed, i.e. the target is tracked to ensure that it is not simply noise, messages regarding the target are sent to the commander via the network at 1 s intervals. After a further five detections/seconds the radar node changes to tracking mode. 3.3.2. Tracking mode In tracking mode the number of messages sent to the commander is increased to two messages per second (1 per 0.5 s). Fig. 6 shows how a target enters the radar range of node 16. After two detections it will enter surveillance mode and send messages as required. After a further five detections, it enters a tracking mode. The commander, assumed to be at node 23, on receiving tracking messages sends messages to nodes along the predicted path. In Fig. 6 these would be nodes 14, 15 and 13, which then enter tracking mode once the target is detected within each node’s range. If another target is detected while in tracking mode some form of data grouping could take place in the communications (see [22] for details of the issues involved in data distribution, data grouping and data sharing in radar networking), however this is not considered in this paper. 3.3.3. Engagement mode After the target has been tracked for some period of time, dictated by the time a commander takes to make a decision to counter the target, the commander issues an order to engage the target, i.e. fire a missile to intercept the incoming target. This involves updating the missile with new target information during the interception and increased detections of the target. This aspect is not considered in this paper. 3.4. Timeslot synchronisation – graph colouring Graph colouring is an important aspect of the simulation when two links per face are assumed. The communication between nodes relies on each link being setup in the correct timeslot, i.e. the timeslots need to be sequenced since both links on a face cannot communicate using the same timeslot. This requires the use of edge-colouring an undirected graph (which represents the connected radar network) to ensure that the nodes are properly synchronised. Each timeslot and associated colour represents a 10 ms connection between two nodes. The number of timeslot colours is dictated by the number of links per face, i.e. if each radar face is allowed two links then two distinct colours are reTarget

Predicted Target Path

Fig. 6. Tracking operation.

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quired and there are two colours in the palette of the colouring algorithm. As the graph colouring problem is a classically computationally hard mathematical problem [23], we use an efficient randomised algorithm since fast execution time is critical in the simulator, and the inherently tight upper and lower bounds make finding an optimal colouring less important [24]. Consequently, since execution time is the critical requirement, a highly randomised algorithm using the Nibble method is used [25]. The Nibble method can be used as either a distributed algorithm or a global algorithm where all edge information is known. The networks considered here do not require all adjacent links on a radar node to be different colours as in traditional edge-colouring – only links on the same face of a radar node require proper edge colouring (for example, in Fig. 4 the two links on node 1 face 1 must be different colours to signify different timeslots). Therefore, a series of edge induced subgraphs is generated which are induced from the adjacent links of each face of each node in turn. These subgraphs require proper edge-colouring in the simulator.

4. Network design The phased array radar network design can be formalized as follows. We are given a set V of mobile radar nodes. Each node v 2 V is specified by its coordinates {x(v), y(v), z(v)} at a given point in time. Each node has a maximum communications range of Xcr, i.e. the maximum distance for any two nodes to communicate directly is Xcr. Additionally, for each radar node, v 2 V, the GIS component uses position, elevation and terrain information to calculate which radar nodes are visible to v. Let this set of radar nodes visible to v be denoted by Vvisible(v). Therefore we have an induced graph GX cr ¼ ðV; EÞ, where E = {(u, v)jd(u, v) 6 Xcr, u 2 Vvisible(v),v 2 Vvisible(u)} where d(u, v) is the Euclidean distance between u and v. Our goal in performing topological control (network design) is to find an undirected subgraph G of GX cr such that  G consists of all the nodes in GX cr ,  each node in G has a maximum degree, for each of its four faces, equal to the number of links allowed per face (1 or 2),  G is connected. The purpose of optimisation is to find a G such that the average delay of all messages sent to a designated commander node vc 2 V is minimised, regardless of which radar node is designated the commander position. Let AMD (i, j, k) define the average message delay in a network k, for messages destined for command node j generated by target i. A graph G is considered acceptable for a particular command position, vc, if for a number of targets Ntargets

1

NX targets

Ntargets

i¼1

AMDði; v c ; GÞ < l

where l is a specified time threshold, in milliseconds.

ð1Þ

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4.1. Optimisation metrics The optimisation algorithm requires performance metrics to be defined that allow differentiation between different network designs. The most appropriate measure is to use the results from simulation, i.e. Eq. (1) over a range of targets and assess the number of feasible command positions (the higher the number the better the network). However this is computationally too expensive to be used at each iteration of the optimisation algorithm, therefore metrics are needed which, when optimised, generate networks which have good performance under simulation. The metrics investigated in this paper will directly consider number of hops and link length, and indirectly consider vertex connectivity. These metrics are used in an evolutionary algorithm based approach to produce suboptimal solutions that are shown to be effective under simulation, i.e. increase the number of feasible command positions (see Section 5.4). For a graph, G, these metrics are defined as follows. Number of hops is the measure of the path cost from a source node s to a destination node t. Fewer hops in networks paths tend to be considered better as they consume less network resources in total. When a node is not able to establish a direct link to the required node, then there is no option but to use a multiple hop route. The average number of hops is calculated using the total number of minimum hops between each pair of nodes. Minimum hop paths, min(p), are calculated using the shortest path, with each link given a weight of 1. The weight of each minimum path min(p):p(u ? v) for each pair of nodes u, v 2 V is summed and then divided by the total number of node pairs, i.e.

P

u;v 2V minðpÞ : pðu jVjðjVj1Þ 2

Nhops ðGÞ ¼

! vÞ

Average number of hops is minimised during the optimisation process. Average link length (bandwidth) is simply the sum of all link lengths divided by the total number of links. For a network of V nodes and E links, linklength(e) is the length (distance) of the link e which joins two nodes, then

P ALlength ðGÞ ¼

e2E linklength ðeÞ

jEj

Average link length is minimised during the optimisation process – shorter links have higher data rate than longer links. All-pairs ST (source–target) vertex connectivity and more generally vertex connectivity is characterized by Menger’s (1927) Theorem [26] which states that for a graph G with u, v # V then the minimum number of vertices separating u from v in G is equal to the maximum number of vertex disjoint u ? v paths in G. If the number of vertex disjoint paths is known then the vertex connectivity between nodes u and v is known. Let the vertex connectivity between a pair of nodes s and t in G where s, t, 2 V, be defined by jG (s, t), then the average vertex connectivity of a network is

P ST conn ðGÞ ¼

j

s;t;2V G ðs; tÞ jVjðjVj1Þ 2

It is assumed that the higher the connectivity of G, the higher the reliability (robustness) of the related radar network design. 4.2. Optimisation algorithm The optimisation algorithm used in this paper is based on a genetic algorithm, specifically the Strength Pareto Evolutionary Algorithm (SPEA) [27] which uses the notion of domination – a well established concept in multiple objective optimisation used to compare different solutions under multiple objectives (see [28] for further details on domination). Let R ¼ fR1 ; R2 ; . . . ; RNpop g be the set of candidate solutions (network designs) at each generation of the optimisation algorithm, then network design Ri is said to dominate network design Rj if

Nhops ðRi Þ < N hops ðRj Þ and ALlength ðRi Þ < ALlength ðRj Þ Furthermore let Rnondom  R be the set of non-dominated solutions. Applying domination with the objectives of minimising the number of hops and average link length, a set of solutions which are pair-wise non-dominated are desirable in the sense that it is impossible to find another design in the set which improves the value of any objective (i.e. hop length or link length) without simultaneously degrading the quality of the other objective. The set of all possible non-dominated solutions from the entire search space constitutes the Pareto set and any solution from the Pareto set is called Pareto optimal. Network designs which are in the Pareto set represent the best trade-off between number of hops and average link length. The main components of the optimisation for radar network design is as follows: (1) (Initialisation) An initial population of binary encoded represented radar networks is generated. This involves generating a link between a pair of randomly selected radar nodes. To illustrate the encoding consider a network with five radar nodes with one link per face allowed. The total number of potential links is 10 (20 if two links per face), therefore each candidate network in the population is a binary array containing 10 elements. For example, the candidate network 0,1,1,0,1,0,1,1,0,0 would represent a network with communications links existing between node pairs (0, 2), (0, 3), (1, 2), (1, 4), and (2, 3), i.e.

For 2 links per face networks the binary encoding is twice as long with two elements assigned to each node pair, one element for each potential link. Repair operators5 5 Repair operators are methods of removing infeasible elements from a solution by either removing them completely or using a heuristic method to correct the solution.

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are implemented at this initialisation stage to ensure that the radar networks are feasible, i.e. chosen links are within available range and in line of sight. (2) (Update non-dominated set) The set, Rnondom is reevaluated after each new generation. This requires new non-dominated solutions to be added and any, now, dominated solutions in the non dominated set to be removed. There is also a clustering procedure used to ensure that the set does not increase above its maximum number of solutions (see [29] for details). (3) (Assign fitness values) This is the strength element of the algorithm. If we define

8 > < 1 if Nhops ðRi Þ < Nhops ðRj Þ and PDðRi ; Rj Þ ¼ ALlength ðRi Þ < ALlength ðRj Þ > : 0 otherwise

ð2Þ

then the strength of each member of the non-dominated set, Ri 2 Rnondom is calculated based on the number of solutions it dominates, i.e.

SðRi Þ ¼

PjRj j¼1 PDðRi ; Rj Þ j–i

ð3Þ

Nþ1

Here the number of total number solutions which solution Ri dominates is divided by the population size + one. This value represents the fitness of each non-dominated solution. The strength of the dominated solutions Rj 2 (R  Rnondom) is given by

SðRj Þ ¼ 1 þ

jRnondom X j i¼1

SðRi Þ if PDðRi ; Rj Þ ¼ 1 0

if PDðRi ; Rj Þ ¼ 0

ð4Þ

i.e. the fitness of the dominated individuals is given by summing the strength of all the dominating individuals and adding one. (4) (Selection) A new population is generated by choosing two solutions at random from the non-dominated set and the population and making them compete in binary tournaments, i.e. whichever is the strongest individual from the pair selected survives to the next generation. (5) (Crossover, Mutation and Repair) Pairs of the selected individuals then undergo simple crossover and mutation based on crossover and mutations probabilities (see [30] for specific details). For example, consider that the two networks 0,1,1,0,1,0,1,1,0,0 and 1,1,0,1,1,0,0,1,0,1 were selected for crossover. If the crossover probability was passed, then a random cut point between 1 and 9 would be determined and the sub-arrays either side of the cut point juxtaposed to create two new networks e.g. if the cut point was 3 we would produce new networks 0,1,1,1,1,0,0,1,0,1 and 1,1,0,0,1,0,1,1,0,0. Mutation is applied to each element in each new network – if the mutation rate is passed then the binary element is toggled. The resulting solutions are repaired, if necessary, to ensure they form feasible radar networks. (6) (Termination) If the total number of generations has been reached then the non-dominated set represents

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the final Pareto set. Otherwise the algorithm is repeated from the Update non-dominated set phase. The SPEA algorithm used is almost identical to the original framework set out in [27], apart from the custom encoding of the radar networks, the repair operators, and the optimisation criteria, which are radar specific. Pseudocode for the algorithm is as follows: Algorithm 4.1 (Optimisation algorithm for radar networks). variables Npop Population size Nnondom Maximum size of non-dominated set T Maximum number of generations pc Crossover probability pm Mutation probability Rt Set of candidate solutions in population at time t Rtnondom Set of non-dominated candidate solutions at time t Rtemp Tempory population of maximum size Npop to store next generation of solutions /* Initalisation */ R0nondom 0 /* Set non-dominated set to empty 0 */ for i 0 to Npop do Generate random BERN Rt Rt + BERN for i 0 to T /* Update non-dominated set: */ Find non-dominated solutions in Rt, copy to t Rnondom Remove any newly dominated individuals from Rtnondom If jRtnondom j > N nondom reduce number of candidate solutions in non-dominated set to Nnondom /* Assign population andnon-dominated set strengths: */ Non-dominated set fitness: use Eq. (2) Poplulation set fitness: use Eq. (3) /* Selection: */ for i 0 to Npop Randomly select two individuals Ri ; Rj 2 Rt þ Rtnondom if S(Ri) < S(Rj)Rtemp = Rtemp + Ri else Rtemp = Rtemp + Rj /* Crossover and mutation: */ Crossover solutions from Rtemp with probability pc Mutate each new solution obtained from crossover with probability pm /* Repair population: */ Repair all solutions, if necessary, to ensure feasibility /* Re-Initialize population: */ Copy Rtemp to Rt end for /* Extract final non-dominated set: */ Rnondom ¼ RTnondom Functions: BERN Random Binary Encoded Radar Network

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The algorithm optimises two parameters simultaneously. The following values are used for the experiments:     

Crossover rate 0.7 Mutation rate 0.01 Population size 40 Maximum non-dominated set size 25 Maximum number of generations 1000

The crossover and mutation values are based on results and recommendations of [30]. The non-dominated set and population sizes are as recommended in [31]. The SPEA

algorithm is run with two metrics – average number of hops and average link length to calculate dominance. The solution from the non-dominated set, Rnondom, output at the end of the algorithm is chosen such that it has the highest value for the STconn metric. 5. Numerical simulations and results In this section we present the results of using the optimisation algorithm and communications model for designing phased array radar networks using two links and one link per face. Experiments involve pseudo-randomly placing 32 radar nodes on a 28 km by 28 km region with flat

Fig. 7. Optimised test network 1 with 14 target paths.

Fig. 8. Optimised test network 1 with commander positioned at node 3.

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S. Hurley, M. Imran Khan / Ad Hoc Networks 9 (2011) 736–751 Table 3 Example target statistics and delays. Target ID (x, y) position

i = 1 (220,000, 321,000) i = 2 (220,000, 323,000) i = 3 (220,000, 325,000) i = 4 (220,000, 327,000) i = 5 (220,000, 329,000) i = 6 (220,000, 331,000) i = 7 (220,000, 333,000) i = 8 (220,000, 335,000) i = 9 (220,000, 337,000) i = 10 (220,000, 339,000) i = 11 (220,000, 341,000) i = 12 (220,000, 343,000) i = 13 (220,000, 345,000) i = 14 (220,000, 347,000)

First detection

AMD(i,3,1) (ms)

Delay (ms)

No. of messages

228 109 20 4 2 10 14 8 26 6 16 7 10 74

392 474 573 594 593 457 538 461 501 612 629 584 456 298

431.2 404.6 396.7 392.5 414.2 367.0 477.7 485.2 478.5 515.5 563.2 489.9 489.3 521.3

terrain. The geographical region used is based on the OS grid SH (where SH is the alphabetical grid reference system used by the UK’s Ordnance Survey). Thirty such test networks are constructed for the experiments. Each test network is optimised using the algorithm presented in Section 4.2. In each experiment the optimised network is evaluated for simulation performance, in particular, each

of the 32 possible command positions is simulated and the average message delay calculated. The time threshold, l, used to evaluate the average message delay in the numerical simulations, is set at 500 ms. It is assumed that the data rate available between two communicating nodes is proportional to log(1 + pr), where pr is the received power which in turn is assumed to be inversely proportional to distance squared. The individual message size is 148 bits. Overall this results in a total of 960 (30  32) individual simulation runs over all 30 experiments. In each simulation targets are fired across the network as shown in Fig. 7 on optimised test network 1. In order to keep results consistent the targets are fired simultaneously and at equal separations of 2 km. For the experiments carried out in this paper the straight line speed of all targets is set at 250 m/s for comparison purposes, and the maximum number of expected targets per 5 km  5 km area is five targets [32], i.e. a 28 km  28 km grid would have a maximum of 14 targets. Consider the example shown in Fig. 8 with the commander positioned at node 3. The optimised network assumes 2 links per timeslot. Table 3 details the average delay for messages for each target as it passes over the network. Average delay values tend to be better depending on the proximity of the target to the commander position.

Table 4 Optimisation and simulation results – 2 links per face. Test network (k)

Average link length

Average no. of hops

All-pairs ST connectivity

1 3214

P31 P14 j¼0

i¼1 AMDði; j; kÞ

Standard deviation AMD

(ms) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

5006.33 4995.77 4413.67 4975.81 4916.56 4757.73 5068.6 4889.94 4860.04 4755.85 4904.02 4847.64 4844.97 4857.31 4704.83 4798.76 4846.05 4573.92 4518.14 4884.76 4333.37 4691.97 4526.18 4342.61 4543.94 4566.65 4691.68 4586.58 4624.29 4896.41

3.22 3.13 3.08 3.3 3.24 3.9 3.25 3.35 3.06 2.88 3.09 3.09 2.74 2.88 2.93 2.66 2.84 2.8 3 2.8 3.31 3.15 2.88 2.96 2.92 2.99 2.97 3 3.16 3.04

2.87 2.88 2.31 2.83 2.88 1.66 2.8 2.56 3.08 3.58 3.4 3.3 3.24 3.51 3.65 3.69 3.75 4.09 2.78 3.39 2.54 2.23 3.49 2.59 2.98 2.87 3.05 2.67 2.63 3.13

5660.33 3082.08 2664.83 5011.44 5763.58 10492.84 5047.65 5948.24 6992.08 2000.17 4241.72 4195.76 6305.85 2796.35 1590.2 2834.27 2381.76 3799.27 4356.71 2082.53 7463.03 5602.26 4662.56 6937.76 7364.06 10274.19 6199.08 3351.1 7304.1 2772

Minimum Maximum Average SD

4333.37 5068.60 4740.81 199.61

2.66 3.90 3.05 0.24

1.66 4.09 3.01 0.52

1590.20 10492.84 4972.59 2301.61

11906.24 6126.405 5537.019 11207.64 12389.12 14151.74 10661.08 10524.22 11581.52 5173.588 9980.12 10399.15 11487.78 8694.742 3429.439 8876.109 6438.244 9632.156 12017.82 7005.631 13630.75 7278.614 10267.42 12019.55 10974.23 14039.45 13440.76 6522.425 12592.32 7307.16

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First detection times are the times taken between the detection by a radar node and the commander receiving the first message regarding this target. The mean of the average delay values is 459.27 ms (standard deviation 363.75 ms) which is below the target threshold of 500 ms. In addition 11 of the targets have average delays less than 500 ms.

Table 5 Message delay values for each commander position for test network 13 – 2 links per face.

5.1. Results – 2 links per face Table 4 shows the optimisation and simulation results for each of the 30 test networks. The optimisation results correspond to the network in the non-dominated set with the highest connectivity value. The average message delay values would seem to indicate that the networks have very few commander positions that are within the 500 ms threshold (the average is 4972.59 ms), however the comparatively large average message delay standard deviations (last column in Table 4) indicate the large fluctuations in average message delay values for different command positions. These fluctuations in message delay can be seen using test network 13 in Fig. 9 as an example. Table 5 gives the message delay values for each commander position in network 13. Note that the larger message delay values usually occur when the commander is positioned at an boundary node, since these nodes tend to have fewer adjacent links and hence less capacity/routing opportunities. Table 5 also shows that test network 13 has 20 out of 32 command positions which are within the threshold of 500 ms. The average delay ranges of all command positions in all test networks is shown in Fig. 10, from which we observe that over 60% of command positions have acceptable performance levels, i.e. are within the threshold of 500 ms. However Fig. 10 also highlights a problem area with respect to designing networks for GBAD radar systems that assume 2 links per face – commanders located at difficult command positions would encounter large delays in the

21

11 23 10

30

15

28

6 26 22

9 14

18744.50 3309.98 357.16 291.47 302.53 337.64 291.78 273.68 349.55 368.52 414.24 12945.50 14781.80 451.14 336.57 3956.47 485.63 32679.50 350.39 283.50 408.74 32499.20 307.46 16603.10 380.94 543.48 317.35 521.15 45017.60 485.38 359.40 13031.80

Minimum Maximum Average SD

273.680 45017.600 6305.848 11487.777

(ms)

350

2 Links per face SPEA Designed

300 250 200 150 100 50

7 5

24

2

0

20 19

3

8

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

i¼1 AMDði; j; 13Þ

400

Number of Command Positions

16

1 14

450

31

17

P14

Commander position (j)

0 0 0 0 0 0 0 0 0 0 0 10 20 30 40 50 60 70 80 90 100 100 > 0 − 00 − 00 − 00 − 00 − 00 − 00 − 00 − 00 − 0 − 8 5 1 0 6 7 2 4 3 9

Average Delay Range (ms) 4

27

13 18

0 12 1

25

Fig. 10. Average delay ranges for all commander positions over all networks – 2 links per face.

29

Fig. 9. Optimised test network 13 – 2 links per face.

system, reducing tactical tempo and hence usefulness of the system.

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average message delay values and low standard deviations, i.e. network 10 and 17. In Table 6 the average messages delays are all lower than the 2 links per face networks in Table 4. This indicates that there is an overall improvement in network performance under simulation. Fig. 12 shows designed test network 13 with 1 link per face. All command positions are simulated and results are given in Table 7 which shows that although the average number of hops has increased, the average delay for each command position has decreased. Furthermore, command positions that were above the 500 ms threshold using the 2 links per face assumption have now become viable command positions. All command positions now, apart from node 21, 23 and 28, are viable command positions. Finally, Fig. 13 shows not only an improvement in average message delay ranges but also the number of acceptable command positions. Specifically, the number of command positions with acceptable delay has risen by 20%, this results in a further 137 eligible command positions taken over all 30, 32 node networks.

5.2. Results – 1 link per face The previous section detailed results for designed networks with 2 links per face. The primary advantage with 2 links per face is that it produces more robust networks with higher ST-connectivity values. However the 2 links per face assumption has increased network design and setup requirements such as colouring. Colour changes are also significant in message delay for networks with 2 links per face. A single colour change results in a minimum message delay of 90 ms. Take, for example, the scenario shown in Fig. 11. If node 1 detects a target and the commander is situated at node 4, then at time T1 node 1 sends a message to node 2. The model then dictates that there is another minimum delay of 90 ms, to time T2, before it can send the message via the red link to node 4. Using 1 link per face reduces the effect of swapping timeslots but the connectivity due to the reduction in links is also reduced. As in Section 5.1 the optimisation algorithm is used to design 30 test networks with 1 link per face from the same initial node configurations as those used for 2 links per face. Table 6 shows the optimisation and simulation results for each of the 30 networks. As with Table 4 the average message delay values would seem to indicate that the networks have very few commander positions that are within the 500 ms threshold (the average is 2523.56 ms), however as with Table 4 the comparatively large standard deviations indicate the large fluctuations in average message delay. There are, however, networks that have acceptable

T1

5.3. Performance analysis (1 link per face versus 2 links per face) It is clear that using 1 link per face improves results overall but suffers from reduced connectivity (an average of 3.05 for 2 links compared to an average of 1.79 for 1 link). The designed networks with 1 link per face have connectivity values that vary between 31% and 55% low-

T2 Communication Profile Node 2 Face 0 2 links per face

Radar Scan

100ms

100ms

100ms

100ms

100ms

100ms

100ms

100ms

100ms

100ms

1 Second

Target Radar Node1

Radar Node 3 Face 3

Face 0

Face 2

Face 1

Radar Node5

Face 3

Face 0

Face 2

Face 1 Radar Node 4

Face 3

Face 0

Face 2

Face 1

Radar Node 2

Comms Mode

Comms Mode

Radar Scan

100ms

100ms

100ms

Face 3

Face 0

Face 2

Face 1

Face 3

Face 0

Face 2

Face 1

Communication Profile Node 1 Face 1 2 links per face

100ms

100ms

100ms

1 Second

T1 Fig. 11. Delay caused by 2 links per face.

100ms

100ms

100ms

100ms

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Table 6 Optimisation and simulation results – 1 link per face. Test network (k)

Average link length

Average no. of hops

All-pairs ST connectivity

1 3214

P32 P14 j¼1

i¼1 AMDði; j; kÞ

Standard deviation AMD

(ms) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

4552.70 4169.11 3799.91 4633.65 4387.27 5287.73 4725.18 4064.78 4304.33 3920.61 4321.43 4230.55 4137.24 4273.94 4059.05 3439.01 3920.58 4129.50 3939.30 3914.44 3702.95 3833.46 4112.13 3696.33 3730.51 3022.04 4069.46 3911.80 4294.30 4258.01

4.01 4.47 4.01 4.16 4.14 3.78 3.94 4.52 3.91 4.01 4.08 4.34 3.56 3.78 4.05 4.70 4.00 3.71 4.01 4.21 4.53 4.33 3.87 4.50 4.25 6.11 4.06 4.20 4.02 4.36

1.98 1.70 1.51 1.84 1.80 1.10 1.92 1.65 1.72 2.07 2.09 1.96 2.02 1.90 2.06 1.91 2.04 2.23 1.79 1.85 1.63 1.51 1.94 1.34 1.65 1.30 1.88 1.56 1.70 2.14

1061.97 4748.40 3276.92 3930.01 2145.67 4050.10 474.08 5439.06 2124.92 103.15 857.96 302.78 1499.78 1437.38 2718.11 966.45 117.27 1597.63 2326.52 1045.76 5451.52 3153.51 3772.08 3938.46 3924.40 7778.29 2659.51 3616.78 775.71 412.48

Minimum Maximum Average SD

3022.04 5287.73 4094.71 413.64

3.56 6.11 4.19 0.45

1.10 2.23 1.79 0.26

103.15 7778.29 2523.56 1883.87

3058.63 7784.70 9599.46 7620.11 6424.54 12078.30 2049.61 8951.07 5899.98 42.50 4312.83 1084.25 5076.37 4494.89 5528.33 4215.47 89.60 7376.45 6741.96 4719.65 12243.65 5723.00 10921.96 7998.86 9261.95 10044.12 7264.36 8847.77 1570.44 1640.60

er than the 2 link per face counterpart as shown in Table 8. The average connectivity decrease from 2 links per face to 1 link per face, is 40%. The performance gain is realised by removing the routing delay associated with changing link colours. Higher bandwidth and more direct routes also contribute to lowering the overall delays. Designed networks with 1 link per face allow over 80% of possible command locations to achieve adequate performance. 5.4. Algorithm performance through simulation

Fig. 12. Optimised test network 13 – 1 link per face.

For each experiment the optimisation algorithm produces up to 25 different solutions (the maximum nondominated set size) and from these, the network chosen has the highest connectivity value. A question arises as to whether the performance of the networks, in terms of evaluation under simulation, improves as the optimisation algorithm progresses, i.e. do the performance criteria used in evaluating networks via simulation improve as the optimisation metrics improve? Results were checked at different generations of the algorithm (generation 1, 50, 250, 500 and 1000) and the current best network design was chosen for each of the 30 test networks. Fig. 14 shows

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S. Hurley, M. Imran Khan / Ad Hoc Networks 9 (2011) 736–751 Table 7 Message delay values for each commander position for test network 13 – 1 link per face. 1 14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

183.96 96.99 76.79 74.85 95.75 76.22 65.77 65.78 80.23 78.51 77.28 96.49 136.75 122.50 81.38 126.38 88.93 150.21 95.85 72.04 75.37 10246.90 67.82 8821.17 70.86 97.70 67.89 87.72 26228.00 90.35 86.22 110.39

Minimum Maximum Average SD

65.77 26228.00 1499.78 5076.87

i¼1 AMDði; j; 13Þ

(ms)

how the percentage of viable command positions varies against average message delay for each generation considered, assuming 1 link per face. From Fig. 14 we observe that as the optimisation progresses, a larger percentage of command positions attain average message delays of less than 500 ms for each generation. In particular, at our target threshold of 500 ms we observe that the percentage of viable command positions increases from 24% at generation 1, to 45% at generation 50, to 58% at generation 250, to 78% at generation 500 and finally to 81% at generation 1000. This suggests that even though the optimisation algorithm does not optimise performance directly (as used in simulation), the metrics used in the design process (average link length and number of hops) are sympathetic to better performing networks, i.e. increasing the number of feasible command positions.

6. Conclusion This paper presents a model and algorithm for topology design of phased array radar networks such that communications between radar nodes are effective. The optimisation algorithm uses two metrics, average number

400

Number of Command Positions

P14

Commander position (j)

450 1 Link per face SPEA Designed

350 300 250 200 150 100 50 0

0 0 0 0 0 0 0 0 0 0 0 10 20 30 40 50 60 70 80 90 100 100 > 0 − 00 − 00 − 00 − 00 − 00 − 00 − 00 − 00 − 0 − 8 7 5 6 2 4 1 3 90

Average Delay Range (ms) Fig. 13. Average delay ranges for all commander positions over all networks – 1 link per face.

Table 8 Comparison of connectivity values of optimised networks. Test network

Connectivity

Percentage decrease (%)

2 Links per face

1 Link per face

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

2.87 2.88 2.31 2.83 2.88 1.66 2.80 2.56 3.08 3.58 3.40 3.30 3.24 3.51 3.65 3.69 3.75 4.09 2.78 3.39 2.54 2.23 3.49 2.59 2.98 2.87 3.05 2.67 2.63 3.13

1.98 1.70 1.51 1.84 1.80 1.10 1.92 1.65 1.72 2.07 2.09 1.96 2.02 1.90 2.06 1.91 2.04 2.23 1.79 1.85 1.63 1.51 1.94 1.34 1.65 1.30 1.88 1.56 1.70 2.14

30.90 40.90 34.60 34.80 37.50 33.70 31.70 35.60 44.10 42.10 38.70 40.70 37.50 45.80 43.70 48.40 45.70 45.50 35.80 45.30 36.00 32.40 44.60 48.40 44.80 54.50 38.30 41.70 35.20 31.60

Minimum Maximum Average SD

1.66 4.09 3.01 0.52

1.10 2.23 1.79 0.26

30.90 54.50 40.02 5.95

of hops and average link length as optimisation performance criteria. Simulation is used to test the performance

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100

Percentage of Command Positions

90 80 70 60 50 40 30 20 Generation 1 Generation 50 Generation 250 Generation 500 Generation 1000

10 0

5

10

100

500

Average delay x100ms Fig. 14. Algorithm performance.

of the designed networks against the objective of having an average message delay of less than 500 ms for messages sent to a command position. The metrics are shown to sympathetic to the simulation objective of increasing the number of feasible command positions. Two scenarios are tested which relate to the number of links that a radar node face can facilitate – either one or two. It is shown, through the experimental results, that the 1 link per face produces better simulation performance, in terms of an increase of approximately 20% in the number of viable command positions. However, this comes at a cost of decreased network connectivity and hence network resilience. Currently the optimisation algorithm used is centralised in nature, i.e. it assumes global information in the design process, for future work it would be desirable to develop a decentralised algorithm that only has access to local information. In addition, the current model assumes a fixed timeslot of 10 ms for communications, it would be instructive to allow variable timeslots, i.e. test the effect of increasing the communication time of any radar node in line with its with additional traffic requirements (e.g. because of multiple targets in one area). Finally, additional work could be carried out to investigate the use of different optimisation metrics which directly or indirectly maximise the number of feasible command positions, and to evaluate the effect of optimising communications topology on detection and tracking performance. Acknowledgments The authors would like to thank Dr. Steve Harman and Dr. Andrew Hume of QinetiQ UK for their support and

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Stephen Hurley is a Professor in the School of Computer Science at Cardiff University, where he has worked since 1990. Previously he has worked for Ferranti Computer Systems, Numercial Algorithms Group and the Atomic Energy Authority in the UK. In 1998 he became Head of the Mobile Communications Research Group at the University. His research interests lie in the areas of combinatorial optimisation, heuristic algorithm design, wireless network optimisation, frequency assignment and spectrum management. He has published widely on these topics.

Imran Khan is a research scientist working at the Defence Science and Technology Laboratory in Farnborough, United Kingdom. He has B.Sc. and PhD degrees in Computer Systems and Computer Science from Cardiff University.