Matthieu Boutier
email: boutier@pps.univ-paris-diderot.fr

Juliusz Chroboczek

User-space Multipath UDP in Mosh

. While our work is specific to Mosh, we hope that it is generic enough to serve as a basis for designing UDPbased multipath applications or even more general APIs.

Introduction

Standard networking APIs are mainly designed with the implicit assumption that a client with a single address connects to a server with a single address. This assumption is often incorrect: many hosts have multiple addresses, either because they are multihomed (connected to multiple networks) or connected to a network that is itself multihomed.

WiFi 3G

Figure 1: A multihomed host

Multihomed hosts Many hosts have are connected to multiple networks (Figure 1). The most common case is that of a mobile host connected to the Internet over multiple network technologies (e.g. WiFi and cellular or WiFi and Ethernet), but this is also the case of servers with redundant connectivity. Since hosts do not typically participate in the routing protocol, multihomed hosts have multiple addresses, one per network interface.

A similar situation arises with double-stack hosts, that have both IPv4 and IPv6 addresses. While both addresses are assigned to the same network interface, such hosts are multihomed from the point of view of the higher layers.

ISP 1 ISP 2

Figure 2: A network connected to two providers Source-specific routing and multihomed networks Similar to a multihomed host, a multihomed network (Figure 2) is one that is connected to the Internet over multiple physical links, either for fault tolerance or in order to improve throughput or reduce cost. Classically, such networks are assigned Provider-Independent (PI) addresses that are announced over all links, in which case the dynamic nature of the routing protocol automatically provided for fault-tolerance; improvements in throughput and reductions in cost can be achieved by careful engineering of the routing protocol. PI addresses need to be announced in the Internet's global "Default-Free Zone" and cannot be easily aggregated; they are therefore a costly resource. For smaller networks, it is a natural proposition to announce multiple Provider-Dependent prefixes, one to each provider. In this case, the internal routing protocol must be able to perform source-specific routing (sometimes called SADR), where outgoing packets are routed to the right gateway depending on their source. We describe our experience with source-specific routing elsewhere [START_REF] Boutier | Source-specific routing[END_REF].

Choosing addresses dynamically

In the presence of multiple addresses, hosts must choose a pair of a source and a destination address for every packet that they send. The usual approach is to make this choice at connection establishment: the set of possible (source, destination) pairs is ordered according to a set of static rules [START_REF] Draves | Default Address Selection for Internet Protocol version 6[END_REF], and the first that works is used throughout the lifetime of the connection. This is sometimes slightly refined by probing all of the possible pairs in parallel [START_REF] Wing | Happy Eyeballs: Success with Dual-Stack Hosts[END_REF].

An obvious drawback of such a relatively static approach is that the choice of addresses cannot be changed once a connection has been established, with the consequence that a network hiccup will cause all established connections to drop (or, worse, to hang). A number of researchers have come up with protocols that switch addresses mid-connection; this can be done at the network layer, at the transport layer, or, as in our work, at the application layer.

Network layer Shim6 [START_REF] García-Martínez | The shim6 architecture for ipv6 multihoming[END_REF][START_REF] Nordmark | Level 3 Multihoming Shim Protocol for IPv6[END_REF] is a host-centric layer 3 shim which provides reliability in multihomed networks. When a connection is established by higher layers to a remote host, Shim6 exchanges the local and remote addresses. If the connection is broken, Shim6 finds an alternative working path and changes the source and destination addresses of both the outgoing and incoming packets of the connection. This operation is totally transparent to the higher layers.

Shim6 detects failures based on the natural traffic of the application: if packets are sent without response, then it is likely that a failure has occurred. In that case, Shim6 finds another responsive path using the reachability protocol (REAP) [START_REF] Arkko | Failure Detection and Locator Pair Exploration Protocol for IPv6 Multihoming[END_REF].

REAP builds a list of all possible paths, and probes them to find one that works. REAP probes can be fairly heavyweight, since they contain information about the other probes sent and received, allowing REAP to detect and benefit from unidirectional paths. To limit the overhead of probes, REAP sorts the flows with a number of heuristics before probing them with an exponential backoff interval between two probes. Naderi et al. [START_REF] Naderi | Experience with ipv6 path probing[END_REF] remark that having more aggressive probing is desirable in practice, since it achieves fastest convergence while the overhead will likely be less than the broken connection's traffic.

Transport layer Multiple source and destination addresses can be chosen by the transport protocol, as is the case in Multipath TCP (MPTCP) [START_REF] Raiciu | How hard can it be? designing and implementing a deployable multipath tcp[END_REF] and SCTP [START_REF] Stewart | Stream Control Transmission Protocol[END_REF].

MPTCP is a reliable flow-oriented TCP-compatible protocol which establishes as many alternative paths as possible. These paths are called subflows, and provide both reliability and better performance: MPTCP is able to balance traffic between its subflows, without performance losses due to slow flows. Subflows are continuously estimated by regular TCP messages, which act as probes.

SCTP is a reliable, message-oriented, connectionoriented protocol, designed to achieve reliability in multihomed networks. When a SCTP connection (association) is established, a primary path is selected by each end-point and used to send packets to the other one. A number of mechanisms allow the end-points to exchange their addresses and build alternate paths. These paths are regularly probed at at fixed intervals (heartbeats) to check their reliability. When a failure is detected on the primary path, one of the working alternate paths is selected to be the new primary path. The protocol definition gives no guidelines about the strategy to be used to switch to a better path when the primary path is active but less efficient than other paths.

Application layer A server's addresses are usually stored within the DNS, and the client will try them all, either in turn [START_REF] Draves | Default Address Selection for Internet Protocol version 6[END_REF] or in parallel [START_REF] Wing | Happy Eyeballs: Success with Dual-Stack Hosts[END_REF]. Once a flow is established, it is no longer possible to change the source and destination addresses -from the user's point of view, all connections are broken whenever a link outage forces a change of address.

A TCP connection is bound to a pair of addresses at connection establishment; however, a number of modern applications are based upon UDP and implement their own scheduling and retransmission strategies. This is notably the case of VoIP applications (SIP, Skype, etc.), of some recent peer-to-peer file transfer applications [START_REF] Norberg | uTorrent transport protocol[END_REF], and of Mosh, the Mobile Shell, an SSH replacement designed for lossy and high-latency links [START_REF] Winstein | An interactive remote shell for mobile clients[END_REF].

Since standard Mosh doesn't implement full multipath, it is unable to survive certain classes of topology changes. In the rest of this paper, we describe our implementation of multipath for Mosh, and our experiences with our implementation.

The original Mobile Shell

The Mobile Shell is a lightweight and responsive remote shell. It differs from SSH mainly by two aspects. On the one hand, it predicts what should display the terminal while waiting for a server confirmation, which increase the user experience on slow links, and on the other hand, it uses the UDP transport protocol with an algorithm limiting the impact of packet loss and reordering.

Mosh is composed of multiple layers: the front-end layer, the transport layer and the network layer. The front-end layer is in charge of interaction with the user, The transport layer is in charge of keeping the states of the two peers in sync and of data fragmentation. It is also its responsibility to deal with packet loss and reordering: essentially, it maintains the knowledge of the last acknowledged state, and tries to send deltas from that state to the current local state. If a packet is lost, its content will (probably) be included in the next packet, avoiding the need for a retransmission. Reordering is also not a problem: as newer packets have also the information bring by the older, the older has just to be ignored.

The network layer is in charge to receive and send packets, estimate the Maximum Transmission Unit (MTU), Round Trip Time (RTT) and Retransmission TimeOut (RTO), encrypt and decrypt packets, and keep connection active, even in the presence of NAT. Our modifications to enable multipath are confined to the network layer.

Mosh network protocol

The Mosh network protocol header is described in Figure 3, and consists of 12 octets (96 bits) The first 64 bits contain a cryptographic nonce, a flag indicating the direction of the flow (client to server, or server to client), and the message sequence number (seqno). The rest of the header consists of two timestamp fields used to measure the RTT.

RTT measurement When a packet is about to be sent, the timestamp field is filled with the host's current timestamp, and the timestamp reply field is set to the last timestamp received from the remote peer plus the time elapsed since the packet bringing that timestamp was received. The RTT is computed as the difference of the current timestamp and the timestamp reply field of each packet; and is averaged by an exponential mean to compute the smoothed RTT (SRTT).

Figure 4 illustrates this process: the client sends a packet destined to the server (destination = 0), with seqno s, timestamp t 0 , and timestamp reply -1, because it has not yet received a timestamp from the server. The server receives the packet at time u 0 , and stores both t 0 and u 0 as the last timestamps received from the client. When it next sends data to the client, at time u 1 , it fills the packet with the right destination field (destination = 1), client server

t 0 u 0 (0 , s, t 0 , -1) ∆ u 1 t 1 (1 , s , u1 , t 0 + ∆ ) ∆ t 2 u 0 (0 , s + 1, t 2 , u 1 + ∆ )
Figure 4: A Mosh network layer exchange its seqno s , the timestamp u 1 , and the timestamp reply t 0 = t 0 + ∆ = t 0 + (u 1u 0 ). On reception, the client computes the value of the RTT as RTT = t 1t 0 , and stores the two timestamps for future messages.

In order to keep accurate measurements, only in-order messages are considered, i.e. messages with a strictly increasing sequence number. The payload of out-of-order packets is still transmitted to the transport layer, but the control information is ignored.

Connection timeout As Mosh uses UDP, an unreliable transport protocol, it must determine when the connection has been lost. Mosh uses the standard RTO computation, as defined in TCP: RTO = SRTT + 4 × SRTTVAR. The timeout value is not used by the network layer, but by the higher layers, so that data are sent at regular intervals to continuously monitor the connection, and to inform the user that the connection has been lost.

Connection loss A connection can be lost due to many causes: network failure, link removal, changing IP addresses, or NAT timeouts. Mosh makes a best effort to keep the connection active, and will never give up without an explicit request from the user.

If the connection times out, data packets are still sent to the server, but at larger intervals. When the network offers connectivity again, the connection recovers almost immediately.

Mosh resists to IP address changes because by using the sendto system call with no explicit source address, leaving the responsibility of choosing the source address to the operating system. It is therefore possible to use the same Mosh session from multiple addresses (e.g. after moving a laptop).

NATs sometimes time out active connections. As NATs associate a connection to the 5-tuple (transport protocol, IP src, IP dst, port src, port dst), a Mosh client switches ports regularly when it has no sign of the server. This is done by creating and using a new socket to send data. Mosh retains a small number of older sockets, in case a packet from the server arrives for a previously used port.

Limitations of Mosh

In some cases, the mechanisms implemented in Mosh are not sufficient to keep a connection, or simply to choose the best connection among multiple possible ones. In a multi-address environment, a Mosh client may have multiple paths to reach the destination; since Mosh lets the system choose the source address, it will not switch to a better path or change protocol familites.

Multipath Mosh

There are potentially as many different paths as pairs (s, d) of addresses, where s is a client address and d a server address. Our implementation of a multipath Mosh continually estimates the latency of each of these paths and selects the best one. We call flow the structure representing a path and its characteristics; this corresponds to MPTCP's subflows or SCTP's paths.

We have added a flag field to the network layer protocol in order to have more types of messages. We use it to differentiate data, probes, and address gathering. Protocol details are described in Section 4.

Address gathering

In order to build all possible flows, the client must gather both its local addresses and the server's addresses. Both the client and the server have access to their local addresses through standard APIs (such as getifaddrs) provided by the system. At bootstrap, the client has a reachable address of the server: in combination with its local addresses, it builds an initial set of flows.

Gathering server's addresses

The client asks the server for its addresses at regular intervals. In particular, it sends an address request at bootstrap to quickly have a complete set of flows. Both the request and the reply messages are tagged with the ADDR_FLAG flag bit.

On reception of a message with the ADDR_FLAG set, the server answers with the set of its local addresses. The message bringing the answer is also tagged with the ADDR_FLAG, and may not contain other data than the server's addresses.

On reception of a message with the ADDR_FLAG set, the client parses the message and extracts the server's local addresses. It then completes the set of flows it has to the server. Existing flows are not modified.

Address pair filtering Some pairs of addresses will not lead to a valid flow: for example, an IPv4 source address cannot be used with an IPv6 destination address. Filtering such incompatible combinations can reduce the number of flows being probed. Of course, determining if combination is valid or not is not always obvious, and it is more desirable to consider too many flows rather than filter out good ones.

We only do very limited filtering in our implementation, such as verifying that the two addresses of the same pair have the same address family, are both loopback addresses or not, and are both link-local or not. While more discrimination would be possible, we prefer to keep a more general implementation, the overhead being tolerable (see Section 3.5).

Sending packets on a flow

To send a datagram on a given flow, we must specify both its source and destination IP addresses. There are three possible implementations:

• using one socket per flow, each bound both to a local address (with bind) and to a remote address (with connect). Sending and receiving messages on a particular flow is then done with the send and recv system calls: the socket parameters indicate without ambiguity which are the local and remote addresses of both outgoing and incoming packets.

• using one socket per local address, in combination with the sendto and recvfrom system calls, which respectively set the destination of outgoing packets, and retrieve the remote peer address of incoming packets. The local address is specified and retrieved as previously, by the socket.

• using one socket per network-layer protocol (IPv4, IPv6), with the sendmsg and recvmsg system calls which allow to specify and retrieve both the source and the destination address of each packet.

After a number of experiments, we have decided to use the third one: it results in a much simpler implementation, especially in the presence of port hopping (see above).

More precisely, messages are sent with the sendmsg system call, with the msg_name and msg_namelen fields providing the destination address. The source address is provided by a control message (msg_control and msg_controllen). In IPv4, we use IP_PKTINFO and IP_SENDSRCADDR, depending on the operating system; IPv6 provides the portable API IPV6_PKTINFO. (We have found out that this only works if the socket is explictly bound to the wildcard address -on some systems, using an unbound socket leads to a kernel panic.)

We did consider using a single hybrid (IPv6 and IPv4) socket. Unfortunately, hybrid sockets' options are a small subset of plain IPv6 options, not sufficient for our needs.

Flow selection

Mosh is an interactive lightweight protocol: the metric we want to optimize is clearly the RTT, and load balancing is not in our scope. To measure the RTT, very small messages, called probes, are regularly sent on flows to estimate their latency. Probe exchanges are only initiated by the client: the server only response to probes.

We consider that paths are bidirectional and symmetric, so the client and the server use the same flow at any one given time. This flow is selected by the client, which chooses the flow with lowest RTT, while the server merely selects the flow of the latest in-order data packet received to send data back.

We didn't implement any mechanism to limit instability, which is not a problem in the case of Mosh. Indeed, having instability with two paths of roughly same RTT will at worst cause packet reordering, which is not a problem for the higher layers of Mosh. Our tests with flows of similar RTT exhibited good behaviour, but more investigation in this area may be needed.

Probing flows

Probing flows consists in periodically sending small messages, known as probes, that carry enough information to estimate the flow's RTT. The interval between two probes is determined dynamically: waiting for a flow RTT update should be of the same order of magnitude as the RTT itself; in effect, faster paths will be probed more often than slower ones. Beyond a certain frequency, however, sending more probes no longer improves the user experience. For that reason, our implementation never sends more than one probe every 500 ms.

An additional issue is that of non-functional flows: since no probes will be received, the RTT will not be naturally increased, while a single packet loss should not be considered as a broken path. We maintain an idle_time field in the flow structure which represents the time during which a flow has not been responsive. The SRTT value of an idle flow is unchanged, but the value used for choosing flows is the sum of the SRTT and the idle time.

A packet loss, or lack of response, is detected using RTO. We use the standard TCP's RTO computation, also taking the idle time into account:

RTO := (SRTT + idle_time) + 4 × SRTTVAR
When a RTO has elapsed with no response from the server, the client immediately sends another probe, even if the next probe for this flow was delayed, and the idle time is increased by one RTO. Increasing by no more than one RTO is important, even if more time elapsed since the last probe sending: the event loop may give us back control after a lot of time, leading to a significant over-estimation of idle time on a simple packet loss. We observed delays of several seconds, leading the mosh client to choose a worst flow. On the other hand, increasing by one RTO is enough: since the computation of the RTO takes the idle time into account, it is the same behaviour on idle flows as doubling the RTT each time: idle_time := idle_time + RTO Mosh uses delayed acknowledgements. To compensate, the Mosh network layer receives the maximum delay interval from the higher layers, and computes a delayed RTO (dRTO). The dRTO is used to compute the probing interval and the actual timeout of packet acknowledgements, but we keep the RTO value to increase the idle time: the delays induced by the delayed acknowledgements are not representative of the real idle time. This leads to the following equations: dRTO := RTO + max_delack probe_interval := max(dRTO, 500 ms) An example of the whole process is described in figure 5: the client sends a probe to the server, and schedules the next probe. The server receives the probe, and delays the acknowledgement before sending back a probe. The client receives the acknowledgement in dRTO, so it waits for the end of the probe interval to send again a probe to the server. This time, the server decides to send back the probe immediately, but the packet is lost. The client notices the loss when the event loop next yields control: it adds RTO to the flow's idle time, and immediately sends back a probe, without waiting for a whole probe interval.

Probe overhead

Our approach will lead to permanent overhead in the network, with regular probes on each flow. As the number of flows is the product of the number of local addresses and the number of remote addresses, it might in principle grow to fairly large values.

Figure 6 shows the overhead induced by one flow, depending on the probe interval. These values are realworld measurements (obtained using wireshark). One probe is contained in an Ethernet frame of less than 90 octets. An idle flow, having a probe interval higher than 10 seconds, will lead to an overhead of less than 10 B/s, while an active and efficient flow will lead to an overhead of less than 200 B/s. Considering a client and a server having 4 (compatible) addresses each, 16 flows will be built. If each of these flows has latency better than 500 ms, we will have an overhead of less that 3 kB/s for the whole network.

Protocol details

In this section, we describe the modifications made to the Mosh network protocol. The new packet header is represented in Figure 7. There are two main modifications: the identification of flows by a flow ID, and the presence of a flags field.

Flow ID In standard mosh, the cryptographic nonce is constituted of the direction and the sequence number. The direction indicates if the message was sent by the client (with a value of 0), or by the server (value of 1), while the sequence number is used by the received to determine whether the packet is the most recent one. As the nonce has double usage, and needs to be unique, mosh gives up when the sequence number overflows (wraps around to 0). Since it is a 63-bit value, this is unlikely to be a serious problem.

We use a separate flow ID, allocated by the client, to identify flows, and sequence numbers increase independently for each flow. Both the flow ID and sequence Flags The Flags field is used to extend the network layer protocol. Two flags are defined: the PROBE_FLAG and the ADDR_FLAG. Currently, the flags serve as a message type: either none or exactly one of the two flags will be set, identifying the type of message.

Because the main objective of a probe is to be lightweight, a probe does not carry any extra data from higher layers, and therefore is exactly 14 bytes long.

An address request message, i.e. a message with ADDR_FLAG set and originated by the client, doesn't carry any extra-information, like a probe. An address response message contains the list of the server's addresses, in the format described in figure 8: 1 octet for the sub-message length (in octets), 1 octet for the address family, 2 octets for the port number, and the rest for the address (4 octets for IPv4 addresses, and 16 octets for IPv6 addresses).

Since an address request is always sent at the beginning of the connection, it may in principle be possible for a malicious program to send duplicates of a message containing an address request; since the server's reply is much larger than the request, this could be used for an amplification attack. For that reason, we ignore address request packets unless they are in-order.

Results

We tested our implementation in a simple testbed illustrated in figure 9: the client and the server are connected to two routers connected by two distinct paths. We use the Linux netem module to simulate variable delay and loss ratios on our links, and unplug an Ethernet cable to Figure 9: Testing mp-mosh on delayed or broken paths simulate a connection loss with no changes. The routing is assured by the Babel routing protocol [START_REF] Chroboczek | The Babel Routing Protocol[END_REF].

In this graph, we only use two flows, and we bound the higher plots to 3 seconds, both for readability purposes. Each of the black segments at the bottom of the graph represents a sent packet, and indicates which flow has been chosen to send the data. The two curves indicate the RTT values computed by Mosh.

Initially, both paths have negligible delay. At time 7 s, we add 300 ms delay on (the path taken by) flow 5: Mosh's estimate converges slowly to that value while data are sent on flow 1. This paths happened to experiment two isolated packet losses, which increased the idle time, but didn't disturb the SRTT value computation.

At time 17 s, we add 200 ms on flow 1: its SRTT computation grows quickly to the expected value, and data continue taking this flow, which still has the lower latency. The convergence of the RTT is faster, since flow 1 received a larger number of packets. Only a small number of probes were sent on flow 5. At time 28 s, we unplug the Ethernet cable used by flow 1. The first data packets are sent on flow 5 roughly one second later, and the RTT of flow 1 grows without bound (bounded at 3 s on the figure).

Finally, at time 38 s, we plug back the Ethernet cable. This time, Mosh takes around 21 seconds to recover, which is the time needed for the lower layers (notably routing) to recover, and to the probing interval which has already reached its maximum value (10 s in our implementation).

Limitations and future work

Mosh doesn't consume much bandwidth. Contrary to MPTCP, we didn't need to balance the load on multi-ple flows, but only choose the most responsive. As the Mosh-transport layer is resilient to packet's reordering, it would be possible to split traffic among multiple flows; we have not investigated this possibility.

Our implementation makes no efforts to avoid instability when multiple flows have similar latency; this did not appear to be a problem in our experiments. In highthroughput scenarios, Mosh may fragment messages into multiple UDP datagrams; in that case, Mosh only buffers a single message; if two different fragmented messages overlap, both might be discarded. Further experimentation is necessary in order to determine if this is a problem in practice, and whether it is more desirable to increase the amount of buffering done by Mosh, or to limit the amount of instability, which might in turn decrease our algorithm's responsivity to link outages (and perhaps the amount of natural load balancing due to instability.)

Mosh is an application designed to have a mobile client and a fixed server. Client and server thus have strongly asymmetric roles. We have used this property, putting all the intelligence on the client side with no choice of the path on the server side. In other applications, both the client and the server might be mobile, which would require smarter server-side algorithms.

Our implementation assumes that the links are symmetric, both in reachability and in delay. Asymmetric protocols such as REAP require larger probes, since each probe needs to carry information about the other flows. It is not clear to us whether this is worthwile in real-world topologies, and whether the overhead can be somehow reduced.

Conclusion

We have designed and implemented a multipath version of mosh, using the assumption that using different source and destination addresses leads to different paths. We use active and continuous probing to estimate the RTT of the flows induced by these paths, while having techniques to (i) limit and adapt the number of probes depending on the performances of the flows, (ii) quickly discriminate idle flows while not being affected by occasional packet loss, and (iii) deal with external time delays to allow delayed acknowledgements and event loop integration.

Our implementation achieves fast re-convergence, small overhead, and does not interrupt the event-loop to generate extra traffic. Our modifications are contained in the Mosh network layer, built as a separate C++ library: it could in principle be used by any UDP-based application that would benefit from multiple paths.

Figure 3 :

 3 Figure 3: Original Mosh packet format

Figure 6 :

 6 Figure 5: Probe scheduling Probe interval (ms) 100 500 1000 10000 IPv6 overhead (B/s) 900 180 90 9 IPv4 overhead (B/s) 720 144 72 7.2 Figure 6: Ethernet probing frame overhead of one flow.

Figure 7 Figure 8 :

 78 Figure 7: Multipath Mosh packet format length family port address 1 1 2 length -3 Figure 8: Address sub-messages format

Available software

Our multipath mosh implementation is available at: http://github.com/boutier/mosh


M Bellec

S Avrillon

P Y Jezequel

S Palud

Ph F Colombel

Pouliguen

G King

Millington

Measurements of Vertically Polarized Electromagnetic Surface Waves Over a Calm Sea in HF Band. Comparison to Planar Earth Theories

Keywords: HF band measurements, surface-wave propagation, ground-wave field, vertical electric dipole, planar Earth model. I

Radio communication over Earth along mixed-paths in the HF band is a relevant subject today. In this paper, we present measurements of electric field propagating over sea water in HF Band compared to K.A. Norton, R.W.P

INTRODUCTION

Introduced at the beginning of the last century, surface-wave propagation has been largely investigated starting by Sommerfeld [START_REF] Sommerfeld | Propagation of waves in wireless telegraphy[END_REF] and followed by Norton [START_REF] Norton | The propagation of radio waves over the surface of the earth and upper atmosphere -PART 1[END_REF], [START_REF] Norton | The propagation of radio waves over the surface of the earth and upper atmosphere -PART 2[END_REF], King [START_REF] King | On the radiation efficiency and the electromagnetic field of a vertical electric dipole in the air above a dielectric or conducting half-space[END_REF]- [START_REF] King | Electromagnetic ground-wave field of vertical antennas for communication at 1 to 30 MHz[END_REF], Wait [START_REF] Wait | Electromagnetic Waves in Stratified Media[END_REF], [START_REF] Wait | The ancient and modern history of EM ground-wave propagation[END_REF]. These pioneer researchers provided mainly theoretical studies and analytical solutions to this problem. Sommerfeld started by calculating the EM field radiated by an infinitesimal vertical electric dipole located on the surface of the planar Earth. Then, Norton introduced the attenuation function, the ground effect, and the frequency dependence of the surface wave radiated by a vertical dipole. Based on Maxwell's equations, R.W.P. King established the EM field expression generated by a vertical electric dipole located on or in the vicinity of the surface of a planar Earth and described the surface-wave propagation behavior. King also introduced characteristic distances to explain the attenuation factor variation along the path. In order to model mixed-path surface wave propagation effects, Millington [START_REF] Millington | Ground-wave propagation over an inhomogeneous smooth earth[END_REF], [START_REF] Millington | Ground-wave propagation over an inhomogeneous smooth earth. Part 2: Experimental evidence and practical implications[END_REF] developed an analytical method which takes into account the ground characteristics changes along the path. Recently, L. Sevgi [START_REF] Sevgi | A mixed-path groundwave field-strength prediction virtual tool for digital radio broadcast systems in medium and short wave bands[END_REF]- [START_REF] Sevgi | Groundwave Modeling and Simulation Strategies and Path Loss Prediction Virtual Tools[END_REF] has developed significant contributions which integrate surface-waves propagation along mixed-path. All these studies are mainly theoretical and the measurements are unusual.

This work was supported in part by TDF and the "Direction Générale de l'Armement".

M. Bellec, S. Avrillon and F. Colombel are with the institute of Electronics and Telecommunication of Rennes (IETR), UMR CNRS 6164, University of Rennes 1, Campus de Beaulieu, Rennes Cedex 35042, France. (e-mail: mathilde.bellec@tdf.fr; stephane.avrillon@univ-rennes1.fr; franck.colombel@univ-rennes1.fr) S. Palud and P-Y Jezequel are with TDF, La Haute Galesnais, Centre Mesure d'Antennes, 35340 Liffré, France. (e-mail : sebastien.palud@tdf.fr; pierre-yves.jezequel@tdf.fr) Ph. Pouliguen is with the « Direction Générale de l'armement » (DGA), DGA-DS/MRIS, 7-9, rue des Mathurins, Bagneux Cedex 92221, France (e-mail : philippe.pouliguen@ intradef.gouv.fr) This propagation phenomenon should present attractive and useful features for industrial applications because the surface waves propagate along the surface of Earth and beyond the radio-electric horizon. Few examples already exist mainly operating in VLF, LF and in the HF band. Thanks to these properties, the surface waves allow communication in hard environments (forest…) or target detection at very low elevation and at large distances. This paper presents the measurements of surface waves over the sea in HF band and gives the comparison between the experimental studies and the theoretical models provided in the literature, especially in order to validate the surface wave decrease as 1/d and 1/d² along the path, and the characteristic distances introduced by King.

Section II presents the surface-wave propagation theories proposed by Norton, King, and Millington where the radiating element is a vertically polarized antenna located above the ground. Section III presents measurements realized over the sea. The measurement process is carefully described including the design of the antennas used to radiate the surface waves. Then, section IV provides a comparison between the measurements and the theoretical results.

II. PROPAGATION THEORIES

This section describes theoretical approaches and then provides an interpretation of the surface wave propagation theories on a planar Earth thanks to the research of Sommerfeld [START_REF] Sommerfeld | Propagation of waves in wireless telegraphy[END_REF], K.A. Norton [START_REF] Norton | The propagation of radio waves over the surface of the earth and upper atmosphere -PART 1[END_REF], [START_REF] Norton | The propagation of radio waves over the surface of the earth and upper atmosphere -PART 2[END_REF], R.W.P. King [START_REF] King | On the radiation efficiency and the electromagnetic field of a vertical electric dipole in the air above a dielectric or conducting half-space[END_REF]- [START_REF] King | Electromagnetic ground-wave field of vertical antennas for communication at 1 to 30 MHz[END_REF], and G. Millington [START_REF] Millington | Ground-wave propagation over an inhomogeneous smooth earth[END_REF], [START_REF] Millington | Ground-wave propagation over an inhomogeneous smooth earth. Part 2: Experimental evidence and practical implications[END_REF]. These authors have provided electromagnetic field formulas radiated by an infinitesimal vertical electric dipole located at a specified height h e , over an imperfectly conducting half-space. In this section, we have summarized these theories with a standardized notation system. We have employed a harmonic time factor e -iωt throughout. The infinitesimal dipole is fed by a unit electric moment Idl=1 A.m (current I, infinitesimal length dl). Fig. 2 describes the set of coordinates and the geometry parameters. Since the propagation characteristics are dependent on ground properties, we use the wave numbers k 0 and k g , respectively in the air and in the ground, where ε rg and σ g are respectively the relative permittivity and the conductivity of the ground. These media are assumed to have the same permeability µ 0 as that of free space.

( 1 )

( 2 ) ( 3 )
Where ε c is the complex refractive index of the ground.

A. Norton's Model

The EM field radiated by an infinitesimal vertical electric dipole on the surface of the planar Earth was firstly analyzed by A. Sommerfeld [START_REF] Sommerfeld | Propagation of waves in wireless telegraphy[END_REF]. Then, K.A. Norton simplified the calculation, the formalism and the interpretation [START_REF] Norton | The propagation of radio waves over the surface of the earth and upper atmosphere -PART 1[END_REF], [START_REF] Norton | The propagation of radio waves over the surface of the earth and upper atmosphere -PART 2[END_REF] by introducing the attenuation function. Norton's formalism starts from the Hertz vector and Norton's model is valid for any transmitter or receiver height (h e or h r ). The Hertz vector expression Π z contains 3 terms: a direct wave, a reflected wave and the surface wave. When the transmitter and the receiver are both located on the ground (h e =h r =0 m), the direct and reflected components cancel each other out, and only the surface wave is propagated (third component in ( 4)).

(

) 4
Where Z 0 =120π is the free space impedance, R v the Fresnel's reflection coefficient and F the attenuation function of the surface wave. R v and F(p 0 ) are defined with the following formula:

( 5 )

1- j ( 6 ) ( 7 )
Where p 0 is the Sommerfeld numerical distance.

The parameters b g and p g are respectively a numerical distance and a numerical velocity:

( 8 ) ( 9 )
Where X is the loss tangent of the ground.

The relation between the magnetic field and the Hertz vector is: Based on Norton's theory, we have also investigated the ground type and the frequency dependence of surface waves. Fig. 1 depicts the path loss versus the distance for sea water (ε rg =80 and σ g =4 S/m), and dry ground (ε rg =8 and σ g =0.04 S/m) [START_REF] King | The electromagnetic field of a vertical electric dipole over the Earth or sea[END_REF], each at three frequencies (10 MHz, 20 MHz, and 30 MHz). These results were calculated with L. Sevgi's tool [START_REF] Sevgi | A mixed-path groundwave field-strength prediction virtual tool for digital radio broadcast systems in medium and short wave bands[END_REF]. Whatever the frequency, we notice that the path losses over the sea are lower than over dry ground. As a result, at 30 MHz and for a distance of 50 km, the path loss over dry ground is 44 dB higher than over sea water. Likewise, over any grounds, the path losses of the surface wave become more important when the frequency increases. As a result, over a dry ground at 50 km, the path loss at 30 MHz is 30 dB higher than at 10 MHz.

B. King's Model

R.W.P. King established the EM field expression generated by a vertical electric dipole located on or in the vicinity of Earth surface from Maxwell's equations. According to [START_REF] King | Electromagnetic ground-wave field of vertical antennas for communication at 1 to 30 MHz[END_REF], the transverse magnetic induction B φ and associated electric field E are governed by the formulas:

( 11 ) ( 12 ) ( 13 )
Where P 0 =k 0 3 d/2k g 2 is the Sommerfeld numerical distance and F(P 0 ) is defined by the following formula: [START_REF] Boithias | Propagation des ondes radioélectriques dans l'environnement terrestre[END_REF] Where, C 2 (P 0 )+iS 2 (P 0 ) is the Fresnel integral and ω is the pulsation.

These formulas have been proposed with the following conditions issued from [START_REF] King | On the radiation efficiency and the electromagnetic field of a vertical electric dipole in the air above a dielectric or conducting half-space[END_REF] and [START_REF] King | Electromagnetic ground-wave field of vertical antennas for communication at 1 to 30 MHz[END_REF] respectively:

( 15 ) [START_REF] Iut-R | Calculation of free space attenuation[END_REF] Where r 0 is defined in Fig. 2.

In table I, we calculate |k g |/k 0 versus ground characteristics and frequencies. As a result, we notice that the condition |k g |≥3k 0 is verified in the HF band. But over a dry ground (poor conductivity and relative permittivity) in the UHF band, the initial condition ( 15) is not verified.

) ( 17
) 18
Where a is the Earth radius. There are two notions of horizon. First, the optical horizon is close to 37 km at sea level. Secondly, in the field of surface-wave propagation, the radio-electrical horizon d c is the electrical planar Earth boundary. As well as the antenna dimensions, the electrical horizon depends on the wavelength. Fig. 3 sketches the propagation behavior and we can distinguish two main areas:

• Up to the intermediate distance d i , the EM field decreases as 1/d.

•

Starting from d i , the EM field decreases as 1/d².

Physically, the transition between the two areas is smooth. We call this transition area the "smoothly" attenuation. As a result, Fig. 3 sketches three cases of surface-wave propagation:

C. Millington's Model

The Millington's model is applied as soon as the environment contains several ground types along the propagation path. A simple case is sketched in Fig. 4 with two transitions through three media. According to Fig. 4, the semi empirical method can be explained with the following equations ( 19)-( 21) coming from [START_REF] Sevgi | A mixed-path groundwave field-strength prediction virtual tool for digital radio broadcast systems in medium and short wave bands[END_REF] and [START_REF] Boithias | Propagation des ondes radioélectriques dans l'environnement terrestre[END_REF]:

The total field E T along a multi-mixed propagation path at the receiver is defined by: [START_REF] Palud | Large-area broadband surface-wave antenna[END_REF] Where E D and E R are respectively the fields along the direct and reverse paths:

( 20 ) ( 21 )
Where E 1 , E 2 and E 3 are respectively the field over the medium 1, the medium 2 and the medium 3. The Millington's method shows that the EM surface wave field strength is subject to the medium change. According to the modification of electrical ground characteristics, sea-ground or ground-sea, the EM field could respectively increase or decrease from each transition.

III. MEASUREMENT SETUP

1) Global description

This section presents the objectives of the measurements and describes the setup used to measure the attenuation of the electric field over the sea. The goals of our measurements are:

•

To validate the 1/d and 1/d² attenuation of the surface wave propagation in the HF band calculated with the planar model.

•

To validate Millington's model.

In order to check the different attenuation behaviors over the sea, we have selected three frequencies (10 MHz, 20 MHz, and 30 MHz).

The sea has been constantly calm (Sea State 0) all over the experimentation, so no sea roughness parameter has been considered in the theories.

The experimentation took place at the Mediterranean Sea in June 2013, at distances varying from the transmitting antennas. • At 10 MHz, we measure the electric field strength from 9 km until 35 km. Consequently, the "smoothly" attenuation can be observed. At this frequency, the Millington's effect is notable because of the sand transition.

•

At 20 MHz, we measure the electric field strength from 6.5 km until 60 km. Consequently, the 1/d² attenuation can be observed. At this frequency, the Millington's effect is more significant.

•

At 30 MHz, we measure the electric field strength from 6.5 km until 50 km. Consequently, the 1/d² attenuation can be observed. At this frequency, the Millington's effect increases.

2) Antennas used for the measurements

The measurement setup used 2 types of antennas (see Fig. 6 and Fig. 7). The transmitting antenna, a patented surface-wave antenna, called DAR antenna [START_REF] Palud | Large-area broadband surface-wave antenna[END_REF], has been manufactured by TDF (see Fig. 6). The antenna is manufactured with a steel galvanized wire with a diameter of 2.7 mm. Its dimensions have been adjusted according to the selected frequency. The horizontal radiation pattern is omnidirectional. Table III summarizes the horizontal length L t , the vertical height h, and the gap Z e of the DAR-antennas for each frequency. The receiving antenna, a loop (see Fig. 7) installed on a boat, operates across a broad frequency band. The table IV presents the performance of the loop at 10, 20 and 30 MHz. The K-Factor is inversely proportional to the gain. So, the lower the K-factor, the higher the efficiency. The receiver antenna is installed 1 meter above the surface of the sea. A Rohde & Schwarz EB200 is used as the receiver.

Fig. 6. DAR-antenna design and tuning parameters: horizontal length (L t ) and vertical height (h). The discrepancies between theories and measurements are less than 2 dB between 6 km and 10 km. From 30 km, the 1/d² attenuation is observed. At 20 MHz, the effect of the sand transition is more significant than at 10 MHz. At the interface between the sand and the sea water (6 km), we notice small perturbations on the measured electrical fields. The sand transition includes a sand dune. This relief could induce diffraction and it could be the reason of this perturbation. The phenomenon has not been taken into account theoretically; a bigger change of the slope has been predicted. The perturbation, underlined at 20 MHz at the interface between the sand and the sea water, is amplified at 30 MHz because the relief is higher related to the wavelength. V. CONCLUSION

In this paper, the measurements of surface waves propagating along sea water path in the HF band are compared with theories. First of all, we have described briefly the theoretical results proposed by Norton and King. Then, we have presented measurement results at 3 frequencies (10 MHz, 20 MHz and 30 MHz) and compared it to the theories including Millington's modification in order to take into account the interface between the coast and water sea. At 10 MHz, the "smoothly" attenuation is shown and is very well correlated with the theory. The EM field decrease as 1/d² has been clearly observed at 20 MHz and 30 MHz.

A future work is scheduled to measure the electric field strength of the surface wave at larger distances in order to consider the roundness of Earth.

AKNOWLEDGEMENTS

The Authors thank warmly J. Y. Laurent from TDF for his technical support. They also thank TDF and Direction Générale de l'Armement for their funding.

Fig. 2 .

 2 Fig. 2. Set of coordinates and location of an infinitesimal vertical electric dipole (D) at a height he in the air (wave number k0) over the ground (wave number kg).

Fig. 1 .

 1 Fig. 1. Path loss of the field radiated by a vertically polarized dipole at 10 MHz, 20 MHz, and 30 MHz over the sea water (SW) and over a dry ground (DG) versus distance [11].

Fig. 3 .

 3 Fig. 3. Behavior of the surface wave propagation along a path: according to the frequency and the ground type, the surface wave attenuation decreases as 1/d to reach smoothly 1/d². (a) -At 10 MHz over a sea water path, the surface field strength attenuation decreases as 1/d up to di=69 km ~ dc. (b) -At 20 MHz over a sea water path, the surface field strength attenuation decreases as 1/d over up to di=17 km, then decreases as 1/d² up to dc=58 km. (c) -At

Fig. 4 .

 4 Fig. 4. Sketch of the Millington's model: The transmitting antenna (Tx) is located over the medium 1 while the receiver antenna (Rx) is located over the medium 3. The medium 1 represents a segment range of length d1, the medium 2 represents a segment range of length d2 and the medium 3 represents a segment of a variable length d.

  Fig.5depicts the environmental topography of the measurement area. The attenuation of the electric-field strength versus distance from the transmitting antennas was measured at 10, 20, and 30 MHz. Each measurement has been geo-localized and stored with an acquisition software developed by TDF. HF antennas installed on the coast (T x ) have the capability to emit HF signal at each chosen frequency (10, 20, and 30 MHz) and the received signals are carried out with a loop antenna installed on a boat (R x ). The boat followed a southwestward path across the Mediterranean Sea, steering a constant course.The three transmitting antennas operating respectively at 10 MHz, 20 MHz, and 30 MHz are located over salt ponds. A sand zone is located between the sea water and the transmitters. The relative permittivity ε rg1 of the salt ponds is 80, and the conductivity σ g1 is 8.8 S/m. For the sand transition, ε rg2 =8 and σ g2 =0.038 S/m. For the sea water, ε rg2 =80 and σ g2 =5 S/m. The path over the salt ponds and the sand is respectively 1 km and 6 km. These conductivities have been measured thanks to the following commercial devices: • HANNA HI 993310 with HI 76305 probe for ground • HANNA HI 9033 with HI 76302 probe for liquid The measurements have been carried out in Continuous Waves (CW). No sky waves could be received, due to: • A low Sunspot Number of 52.5 observed for June 2013 • A maximal path of 50 km • A monopole shape radiation pattern for the transmitting antennas This medium characteristic change allows observing the Millington's effect.

Fig. 5 .

 5 Fig. 5. The measurement path over the sea by boat from the vicinity of the transmitter (Tx) until the receiver (Rx).

Fig. 7 .

 7 Fig. 7. Receiver-antenna design: copper tube (16/14 mm) loop of 420 mm diameter

Fig. 8

 8 Fig.8presents the theoretical and the measured electric field along a 35 km mixed-path (salt ponds, sand, and sea water) at 10 MHz. 46 points per kilometers have been recorded. The theoretical models (King and Norton) and the measurement results are in good agreement besides a maximal deviation of 1.13 dB. The EM field attenuation slope is between the 1/d and 1/d² slopes. This behavior corresponds to the "smoothly" attenuation because the maximum measured distance (35 km) is lower than King's intermediate distance d i which is equal to 69 km. The decrease of electric field level is due to the sand transition because the sand is a medium which is not suitable to the HF propagation.

2 )

 2 Fig. 9 presents the theoretical and the measured electric field along a 60 km mixed-path (salt ponds, sand, and sea water) at 20 MHz. 40 points per kilometers have been recorded. The theoretical models (King and Norton) and measurement results are in good agreement.The discrepancies between theories and measurements are less than 2 dB between 6 km and 10 km. From 30 km, the 1/d² attenuation is observed.

Fig. 8 .

 8 Fig. 8. Theoretical and measured electric field attenuation at 10 MHz over a mixed path: salt ponds, sand, and sea water. The theoretical results are calculated from Norton's and King's models. The red curve represents the measurements over the sea water.

Fig. 9 .

 9 Fig. 9. Theoretical and measured electric field attenuation at 20 MHz over a mixed path: salt ponds, sand, and sea water. The theoretical results are calculated from Norton's and King's models. The red curve represents the measurements over the sea water.

Fig. 10

 10 Fig. 10 exhibits the theoretical and the measured electric fields along a 50 km mixed-path (salt ponds and sea water) at 30 MHz. 46 points per kilometers have been recorded. The theoretical models (King and Norton) and the measurement results are in good agreement. The maximal deviation between theories and measurements is close to 4 dB between 6 km and 10 km. Starting from 15 km, the 1/d² attenuation behavior is observed.

Fig. 10 .

 10 Fig. 10. Theoretical and measured electric field attenuation at 30 MHz over a mixed path: salt ponds, sand, and sea water. The theoretical results are calculated from Norton's and models. The red curve represents the measurements over the sea water.

TABLE I

 I

	.	CALCULATION OF |KG|/K0VERSUS GROUND CHARACTERISTICS
	(SEA WATER AND DRY GROUND) AND FREQUENCIES IN ORDER TO VERIFY THE
		CONDITION |KG|≥3K0
	|kg|/k0	10 MHz	20 MHz	30 MHz
	Sea Water
	εrg=80 ;	85	27	10
	σg=4 S/m
	Dry Ground
	εrg=8 ;	8	3.3	2.83
	σg=0.04 S/m

King's theory describes physically surface-wave propagation behavior by defining characteristic distances: the critical distance d c , and the intermediate distance d i . The critical distance d c represents the boundary of the planar Earth model and the intermediate distance d i is a baseline which defines the modification of attenuation law of the surface waves.

(

Table

  II contains several characteristic distances d c and d i depending on the environment and frequency. The critical distance d c varies only with frequency, while the intermediate distance d i varies both with frequency and the ground characteristics.

•

  At 10 MHz over sea water, the intermediate distance d i is close to d c . Consequently, the 1/d² field strength attenuation is not achieved, but the "smoothly" attenuation is expected. • At 20 MHz over sea water, the intermediate distance d i is equal to 17 km and the critical distance d c is equal to 58 km. Consequently, the three behaviors (1/d, smoothly, and 1/d² attenuation) are expected. • At 30 MHz over sea water, the intermediate distance d i is equal to 8 km and the critical distance d c is equal to 50 km. Consequently, the three behaviors (1/d, smoothly, and 1/d² attenuation) are expected.

TABLE II

 II

	.	CHARACTERISTIC DISTANCES DI AND (DC) VERSUS SEVERAL
		GROUND TYPES AND FREQUENCIES.
	di (dc)	10 MHz	20 MHz	30 MHz
	Sea εrg=80 ; σg=4 S/m	69 km (73 km)	17 km (58 km)	7.6 km (50 km)
	Dry Ground εrg=8 ; σg=0.04 S/m	690 m (73 km)	176 m (58 km)	80 m (50 km)

TABLE III .

 III DIMENSIONS OF THE DAR-ANTENNAS.

		10 MHz	20 MHz	30 MHz
	Lt	6.37 m	2.52 m	1.83 m
	h	1.8 m	1.8 m	1.5 m
	Ze	0.5 m	0.5 m	0.5 m

TABLE IV .

 IV PERFORMANCES OF LOOP ANTENNA VERSUS FREQUENCY.The antenna gain has been measured in the relevant azimuth in order to calculate the electric field strength. The antenna gains at 10 MHz, 20 MHz, and 30 MHz are respectively 3.3 dBi, 5 dBi, and -1.3 dBi (see table V). The electric field strength E(d 0 ) at 1 km is the reference field used to normalize the theoretical models with the transmitting antenna characteristics. Thus, the reference field E(d 0 =1 km) at 10 MHz, 20 MHz, and 30 MHz is respectively 90.48 dBµV/m, 92.79 dBµV/m, and 88.24 dBµV/m.

		10 MHz	20 MHz	30 MHz
	K -Factor (dB/m)	42	41	43

TABLE V .

 V MEASURED ANTENNA GAINS (DBI) AND THE ASSOCIATED ELECTRIC FIELD STRENGTH AT A DISTANCE D0=1 KM.

	f (MHz)	Antenna Gain (dBi)	Input power (dBm)	E(d0) (dBµV/m)
	10	3.3	45	90.48
	20	5	45	92.79
	30	-1.3	47	88.24
	IV. COMPARISON BETWEEN MEASUREMENTS AND THEORETICAL
	CALCULATION
	1) The "smoothly" attenuation at 10 MHz


Mathilde Bellec

Sébastien Palud

Pierre Yves Jezequel

Stéphane Avrillon

Ph Franck Colombel

Philippe Pouliguen

Pouliguen

Measurements of surface waves radiated by a vertically polarized antenna over planar seawater at 5 MHz. comparison to planar Earth models

Keywords: HF band measurements, surface-wave propagation, ground-wave field, vertical electric dipole, planar Earth model. I

teaching and research institutions in France or abroad, or from public or private research centers.

INTRODUCTION

The surface waves propagation phenomenon presents attractive and useful features for industrial applications because the surface waves propagate along the surface of the Earth and beyond the radio-electric horizon. Thanks to these properties, the surface waves allow communication in hard environments (forest…) or target detection at very low elevation and at large distances. Furthermore, the temporal stability of the surface wave propagation is an attractive feature in a defense or civil context. Few examples already exist mainly operating in VLF, LF and in the HF band [1] [START_REF] Bazin | A general presentation about the OTH-Radar NOSTRADAMUS[END_REF].

This work was supported in part by TDF and the "Direction Générale de l'Armement".

M. Bellec, S. Avrillon and F. Colombel are with the institute of Electronics and Telecommunication of Rennes (IETR), UMR CNRS 6164, University of Rennes 1, Campus de Beaulieu, Rennes Cedex 35042, France. (e-mail: mathilde.bellec@tdf.fr; stephane.avrillon@univ-rennes1.fr; franck.colombel@univ-rennes1.fr) S. Palud and P-Y Jezequel are with TDF, Centre de Mesure d'Antennes, La Haute Galesnais, 35340 Liffré, France. (e-mail : sebastien.palud@tdf.fr; pierre-yves.jezequel@tdf.fr) Ph. Pouliguen is with the « Direction Générale de l'armement » (DGA), DGA-DS/MRIS, 7-9, rue des Mathurins, Bagneux Cedex 92221, France (e-mail : philippe.pouliguen@dga.defense.gouv.fr) Introduced at the beginning of the last century, surface-wave propagation has been largely investigated starting by Sommerfeld [1] and followed by Norton [START_REF] Norton | The propagation of radio waves over the surface of the Earth and upper atmosphere -PART 1[END_REF] [START_REF] Norton | The propagation of radio waves over the surface of the Earth and upper atmosphere -PART 2[END_REF] and King [START_REF] King | On the radiation efficiency and the electromagnetic field of a vertical electric dipole in the air above a dielectric or conducting half-space[END_REF] [7] [START_REF] King | Electromagnetic groundwave field of vertical antennas for communication at 1 to 30 MHz[END_REF]. These pioneer researchers provided mainly theoretical studies and analytical solutions to this problem. Sommerfeld started by calculating the EM field radiated by an infinitesimal vertical electric dipole located on the surface of the planar Earth. Then, Norton introduced the attenuation function, the ground effect, and the frequency dependence of the surface wave radiated by a vertical dipole. Based on Maxwell's equations, R.W.P. King established the EM field expression generated by a vertical electric dipole placed on or in the vicinity of the surface of a planar Earth and described the surface-wave propagation behavior. King also introduced characteristic distances to explain the attenuation factor variation along the path. To introduce the environmental constraints, Millington developed an analytical method which takes into account the ground characteristics changes along the path [START_REF] Millington | Ground-wave propagation over an inhomogeneous smooth Earth[END_REF]. All these studies are mainly theoretical and the measurements are unusual. This paper presents the measurements of the surface waves over the sea at 5 MHz and gives the comparison between the experimental studies and the theoretical models provided in the literature, especially in order to validate the surface wave decrease as 1/d all along the planar seawater path. In this paper, we first present the surface-wave propagation theories proposed by Norton, King and Millington where the radiating element is a vertically polarized antenna located above the ground. In the second part, we present measurements performed over the sea. Firstly, the measurement process is carefully described including the design of the electrically small antenna used to radiate the surface waves. Secondly, we provide a comparison between the measurements and the theoretical results.

II. PROPAGATION THEORIES

This section describes theoretical approaches and then provides an interpretation of the surface wave propagation theories on a planar Earth thanks to the research of Sommerfeld [1], K.A. Norton [START_REF] Norton | The propagation of radio waves over the surface of the Earth and upper atmosphere -PART 2[END_REF] and R.W.P. King [START_REF] King | On the radiation efficiency and the electromagnetic field of a vertical electric dipole in the air above a dielectric or conducting half-space[END_REF] [7] [START_REF] King | Electromagnetic groundwave field of vertical antennas for communication at 1 to 30 MHz[END_REF]. These authors have provided electromagnetic field formulas radiated by an infinitesimal vertical electric dipole located at a specified height h e , over an imperfectly conducting half-space. In this section, we have summarized these theories with a standardized notation system. We have employed a harmonic time factor e -iωt throughout. The infinitesimal dipole is fed by a unit electric moment Idl=1 A.m (current I, infinitesimal length dl). Fig. 1 describes the set of coordinates and the geometry parameters. Since the propagation characteristics are dependent on ground properties, we use the wave numbers k 0 and k g , respectively in the air and in the ground, where ε rg and σ g are respectively the relative permittivity and the conductivity of the ground. These media are assumed to have the same permeability µ 0 than free space.

(

( 3 )

Where N is the complex refractive index of the ground.

A. Presentation of Norton's Model

The EM field radiated by an infinitesimal vertical electric dipole on the surface of the planar Earth was firstly analyzed by A. Sommerfeld [1]. Then, K.A. Norton simplified the calculation, the formalism and the interpretation [START_REF] Norton | The propagation of radio waves over the surface of the Earth and upper atmosphere -PART 1[END_REF][5] by introducing the attenuation function. Norton's formalism starts from the Hertz vector and Norton's model is valid whatever the transmitter or the receiver height. The Hertz vector expression Π z contains 3 terms: a direct wave, a reflected wave and the surface wave.

( 4 )

Where Z 0 =120π is the free space impedance, R v the Fresnel's reflection coefficient and F the attenuation function of the surface wave. R v and F(p) are defined with the following formula :

( 5 )

1- j ( 6 )
Where p 0 is the Sommerfeld numerical distance.

The relation between the magnetic field and the Hertz vector is:

B. Presentation of King's Model

R.W.P. King established the EM field expression generated by a vertical electric dipole located on or in the vicinity of the Earth surface from Maxwell's equations. According to [START_REF] King | On the radiation efficiency and the electromagnetic field of a vertical electric dipole in the air above a dielectric or conducting half-space[END_REF], the transverse magnetic induction B 2φ and associated electric field

E 2 are: ( 8 ) ( 9 ) ( 10 )
Where P 0 =k 0 3 d/2k g 2 is the Sommerfeld numerical distance and F(P 0 ) is defined by the following formula: [START_REF] Boithias | Propagation des ondes radioélectriques dans l'environnement terrestre[END_REF] Where, C 2 (P 0 )+iS 2 (P 0 ) is the Fresnel integral and ω is the pulsation.

These formulas have been proposed with the following conditions issued from [START_REF] Norton | The propagation of radio waves over the surface of the Earth and upper atmosphere -PART 1[END_REF] and [START_REF] King | On the radiation efficiency and the electromagnetic field of a vertical electric dipole in the air above a dielectric or conducting half-space[END_REF] respectively:

( 12 ) ( 13 )
Where, r 0 is defined in The critical distance d c varies only with frequency, while the intermediate distance d i varies both with frequency and the ground characteristics. There are two notions of horizon. First, the optical horizon which is close to 37 km at sea level. Secondly, in the field of surface-wave propagation, the radioelectrical horizon d c which is the electrical planar Earth boundary. As well as the antenna dimensions, the electrical horizon depends on the wavelength. As sketches in Fig. 2, we can distinguish two main areas of propagation behavior:

• Up to the intermediate distance d i , the EM field decreases as 1/d. • Starting from d i , the EM field decreases as 1/d².

Physically, the transition between the two areas is smooth. We call this transition area the "smoothly" attenuation (dotted zone). Fig. 2. Two mains areas of propagation behavior around the "smoothly" area (dotted zone).

The trans-horizon radar application requires a long coverage (200 nmi). Even if the sea water is a favorable medium to the surface wave propagation, the frequency is an important choice relative to the characteristic distances (d c and d i ). The 5 MHz frequency is a special case (Fig. 2-a): the intermediate distance (d i =270 km) is superior to the critical distance (d c =90km). Knowing that d i >d c , the surface wave propagation decreases as 1/d all along the planar model range (90 km). This behavior is an attractive feature to the need of large coverage and detections at large distances.

C. Millington's Model

The Millington's model is applied as soon as the environment contains several ground types along the propagation path. A simple case is sketched in Fig. 3 with two transitions through three media. According to Fig. 3, the semi empirical method can be explained with the following equations ( 19)-(21) coming from [START_REF] Sevgi | A mixed-path groundwave field-strength prediction virtual tool for digital radio broadcast systems in medium and short wave bands[END_REF] and [START_REF] Boithias | Propagation des ondes radioélectriques dans l'environnement terrestre[END_REF]:

The total field E T along a multi-mixed propagation path at the receiver is defined by: ( 16)

Where E D and E R are respectively the fields along the direct and reverse paths:

( 17 ) ( 18 )
Where E 1 , E 2 and E 3 are respectively the field over the medium 1, the medium 2 and the medium 3. The Millington's method shows that the EM surface wave field strength is subject to the medium change. According to the modification of electrical ground characteristics, seaground or ground-sea, the EM field could respectively increase or decrease from each transition.

III. MEASUREMENTS SETUP

1) Global description

The goal of our measurements is to validate the 1/d attenuation of the surface waves at 5 MHz calculated with the planar Earth models. In this section, we present the measurement objectives and the setup used to measure the attenuation of the Electric field over the sea.

A transmitter has been designed at 5 MHz to check the theoretical propagation results:

-d c = 90 km -d i = 270 km No roughness parameter has been considered because the marine forecast was optimal (calm sea).

The experimentation took place at the Mediterranean Sea in October 2013. Fig. 4 depicts the path carried out over the sea. Transmitting HF antennas are located on the coast (T x ) and the received signals are carried out with loop antennas installed on a boat (R x ). The boat followed a southwestward path across the Mediterranean Sea, steering a constant course. Each measurement was geo-localized and stored with an acquisition software developed by TDF. The transmitting antenna operating at 5 MHz is located over salt ponds. A mixed-path has also been considered (see Fig. The relative permittivity ε rg1 of the salt ponds is 80, and the conductivity σ g1 is 8.8 S/m. For the mudflat transition, ε rg2 =50 and σ g2 =0.4 S/m. For the sea water, ε rg2 =80 and σ g2 =5 S/m. These conductivities have been measured thanks to commercial devices:

• HANNA HI 993310 with HI 76305 probe for ground • HANNA HI 9033 with HI 76302 probe for liquid The measurements have been carried out in Continuous Waves (CW). Knowing that the transmitting antenna has a monopole shape radiation pattern, a preliminary study has been carried out in order to check the ionospheric activity using VOACAP software (HF Propagation Prediction and Ionospheric Communication Analysis). The Observed Sunspot Number during the measurement was 60. A minimal field strength difference of 30 dB at 90 km at 2 p.m. has been observed. This means that only one-thousandth of the received field strength could come from the sky waves. As a result, we assure that no ionospheric activity could disturb the surface electric field strength measurement.

2) Antennas used for the measurements

The measurement setup used two types of antennas:

• DAR antennas as transmitter • Shielded loop antennas as receiver A DAR-antennas, and a shielded loops have been manufactured at TDF.

3) Transmitters: DAR-antennas

The transmitting antenna, based on a patented surface-waves antenna, called DAR antenna [START_REF] Palud | Large-aera broadband surface-wave antenna[END_REF], has been optimized, realized, and installed in salt ponds (see Fig. 5). The antenna is manufactured with a steel galvanized wire with a diameter of 2.7 mm. The dimensions have been adjusted according to the selected frequency. The length L t is equal to 20.4 meters; the vertical height h is 1.8 meters with a gap Z e of 0.5 meters. The horizontal radiation patterns are omnidirectional, and the vertical radiation pattern is quite similar to a monopole over an extremely good conductor. The antenna gain has been measured in the relevant azimuth in order to calculate the radiated electric field strength. The antenna gain at 5 MHz is -3.8 dBi. The input power is 45 dBm.

4) Receivers: Shielded-loop antennas

The receiving antennas are narrow-band shielded-loops. The frequency selectivity and the shield have been used in order to improve the signal to noise ratio (SNR), especially when the measurement distance increases.

Generally, the shield takes the form of a tube around the wire, made of conductive but nonmagnetic material (such as copper or aluminum). Antennas have been manufactured with flexible coaxial cables (see Erreur ! Source du renvoi introuvable.). The inner copper conductor (1) is the power fed element and the outer copper conductor (3) is the shield. Usually, the insulated break is located in the opposite side of the feed point to maintain the symmetry. Baluns have been realized in order to maintain loop balance and to match the impedance of the antenna to 50 Ω. It is important to consider the effect of the antenna shield because, by using a flexible coaxial cable, some additional capacitive components have been involved. This loop design limits the loop's higher frequency tuning range with a fixed diameter d l . As a result, the antenna configuration has been optimized according to the frequency. At 5 MHz, a 1''5/8 coaxial cable has been used to manufacture a loop with a diameter d l of 1.05 meters. Then, the frequency tuning is realized manually with variable air capacitors C controlled by a network analyzer. It is useful in field strength measurements to characterize the receiving antenna by its conversion factor K a as well as by the antenna gain. The relationship between them is described here.

The electrical field E is derived from the measured voltage U and the conversion factor K a of the antenna: The antenna bandwidths at 5 MHz is 0.4% at -3 dB. The Kafactor is inversely proportional to the gain. So, the lower the K-factor, the higher the efficiency. The realized shielded-loop antennas are tested to measure the radiation efficiency thanks to:

• A broadband transmitter

• A calibrated active loop antenna (from Rhode & Schwarz [START_REF] Rhode | loop antenna HF H2-Z2[END_REF]) in order to measure the electrical field E

• Shielded-loop antennas realized in order to measure the voltage U

• Receiver ESH3 (from Rhode & Schwarz) which is able to measure an electrical field and a voltage.

So, the radiation efficiencies (written in the form of Kfactor) is 10 dB/m at 5 MHz. As a result, the selective Fig. 9. Theoretical and measured Electric field attenuation at 5 MHz over a mixed path: marsh and sea water. The theoretical results are calculated from Norton's and King's models. The Millington's solution is considered over the mixed path in order to take into account the environmental constraints. The red curve represents the measurements over the sea water.

shielded-loop antennas allow to increase the measurement sensitivity around 30 dB compared with a broadband loop antenna. This improvement was necessary for the faraway measurements.

IV. COMPARISON BETWEEN MEASUREMENTS AND THEORETICAL CALCULATION. Fig. 9 presents the theoretical and the measured Electric field along a 90 km mixed-path (salt pond, mudflat and sea water) at 5 MHz. 11 points per kilometers have been recorded. The theoretical models (King and Norton) and the measurement results are in good agreement. The maximal discrepancy between measured data and theoretical models is 2 dB. The average error is less than 1 dB. The average deviation error is around to 0.45 dB. The EM field attenuation slope is the 1/d attenuation as predicted by the characteristic distances of King. It appears that around the critical distance d c (planar Earth model boundary), the slope of the measured and theoretical data tends to change smoothly from the 1/d variation but don't reach the 1/d² variation (see black curves on Fig. 9). Further, the topography has optimum electrical characteristics along the three mixed paths with salt ponds (very high conductivity), mudflat (good conductivity), and sea water (high conductivity). At 5 MHz, this mixed path has not a visible effect on the propagation curves, but has to be considered to respect the topography of the measurement area.

I. CONCLUSION

In this paper, the measurement of surface waves propagating along sea water path in the HF band at 5 MHz is compared with theories. First of all, we have described briefly the theoretical results proposed by Norton, King, and Millington. Then, we have presented measurement results at 5 MHz and compared it to the theories including Millington's modification in order to take into account the interface between the coast and water sea. At 5 MHz, the 1/d attenuation is shown and is very well correlated with the theory.

A future work is scheduled to measure the electric field strength of the surface wave at larger distances and at other frequencies in order to consider the roundness of the Earth.

Fig. 1 .

 1 Fig. 1. Set of coordinates and location of an infinitesimal vertical electric dipole (D) at a height h e in the air (wave number k 0 ) over the ground (wave number k g ).

  Fig. 1. The King's theory describes physically surface-wave propagation behavior by defining characteristic distances: the critical distance d c , and the intermediate distance d i . The critical distance d c represents the boundary of the planar Earth model and the intermediate distance d i is a baseline which defines the modification of attenuation law of the surface waves. Where a is the Earth radius.

Fig. 3 .

 3 Fig. 3. Sketch of the Millington's model: The transmitting antenna (T x ) is located over the medium 1 while the receiver antenna (R x ) is located over the medium 3. The medium 1 represents a segment range of length d 1 , the medium 2 represents a segment range of length d 2 and the medium 3 represents a segment of a variable length d.

  Fig. 1. Sketch of the experimental path: The transmitting antenna (Tx) is located over salt ponds while the receiver antenna (Rx) is located over the sea. The salt ponds represent a segment range of length d 1 =2 km, the mudflat represents a segment range of length d 2 =1 km and the sea represents a segment of a maximal length d 3 =220 km.

Fig. 4 .

 4 Fig. 4. Typical round of measurement over the sea by boat from the vicinity of the transmitter (Tx) until the receiver (Rx).

Fig. 5 .

 5 Fig. 5. DAR-antenna design and tuning parameters: horizontal length (L t ), vertical gap (Z e ), and vertical height (h).

Fig. 6 .

 6 Fig. 6. Coaxial cable design: inner copper conductor (1), dielectric (2), outer copper conductor (3) and outer jacket (4).

Fig. 7

 7 Fig. 7 sketched the shielded-loop design and their tuning parameters (loop diameter d L , variable air capacitors C).Usually, the insulated break is located in the opposite side of the feed point to maintain the symmetry. Baluns have been realized in order to maintain loop balance and to match the impedance of the antenna to 50 Ω. It is important to consider the effect of the antenna shield because, by using a flexible coaxial cable, some additional capacitive components have been involved. This loop design limits the loop's higher frequency tuning range with a fixed diameter d l . As a result, the antenna configuration has been optimized according to the frequency. At 5 MHz, a 1''5/8 coaxial cable has been used to manufacture a loop with a diameter d l of 1.05 meters. Then, the frequency tuning is realized manually with variable air capacitors C controlled by a network analyzer.

Fig. 7 .

 7 Fig. 7. Shielded-loop design and tuning parameters: diameter d L , variable capacitors C.

Fig. 8 .

 8 Fig. 8. Realized shielded-loops, installed on the boat.

ACKNOWLEDGMENTS

The authors warmly thank Jean-Yves Laurent from TDF for the antenna manufacturing and for participating in the measurements.