LEVERAGING COGNITIVE RADIOS FOR ... - Semantic Scholar

LEVERAGING COGNITIVE RADIOS FOR EFFECTIVE WIRELESS COMMUNICATIONS OVER WATER

by Li Zhang

A project report submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Science

MONTANA STATE UNIVERSITY Bozeman, Montana March 2010

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COPYRIGHT by Li Zhang 2010 All Rights Reserved

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APPROVAL of a project report submitted by Li Zhang

This project report has been read by each member of the committee and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic style, and consistency, and is ready for submission to the College of Graduate Studies. Dr. Jian (Neil) Tang

Approved for the Department of Computer Science

Dr. John Paxton

Approved for the College of Graduate Studies

Dr. Carl A. Fox

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STATEMENT OF PERMISSION TO USE In presenting this project report in partial fulfillment of the requirements for a master’s degree at Montana State University, I agree that the Library shall make it available to borrowers under rules of the Library. If I have indicated my intention to copyright this project report by including a copyright notice page, copying is allowable only for scholarly purposes, consistent with “fair use” as prescribed in the U. S. Copyright Law. Requests for permission for extended quotation from or reproduction of this project report in whole or in parts may be granted only by the copyright holder. Li Zhang

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TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Transmission Over Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction to Cognitive Radio Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The physical architecture of cognitive radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cognitive radio network architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IEEE standards of interest for CR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Our Work and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 3 5 6 8 10

2. RELATED WORK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Previous Work on Overwater Propagation Modeling . . . . . . . . . . . . . . . . . . . . . . . . . Previous Work on Spectrum Allocation and Scheduling. . . . . . . . . . . . . . . . . . . . . .

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3. SYSTEM MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Propagation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4. PROBLEM DEFINITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5. PROPOSED SCHEDULING ALGORITHMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Scheduling Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimal and Heuristic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heavy Traffic Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17 21 23

6. NUMERICAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7. CONCLUSIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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REFERENCES CITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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LIST OF TABLES Table 1. Link Capacity VS. Path Loss Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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LIST OF FIGURES Figure

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1. Overwater path losses on two different frequencies given by the AREPS

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2. Physical architecture of the cognitive radio [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3. The cognitive radio network architecture [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4. Graph models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5. Scenario 1: n = 5 and H = 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6. Scenario 2: n = 15 and H = 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7. Scenario 3: H = 35 and D = 25km . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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8. Scenario 4 (success ratio): n = 15 and H = 35 . . . . . . . . . . . . . . . . . . . . . . . . . . .

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9. Scenario 4(network throughput): n = 15 and H = 35 . . . . . . . . . . . . . . . . . . . .

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GLOSSARY Cognitive Radio — A cognitive radio is a radio that can change its transmitter or receiver parameters based on interaction with the environment in which it operates. 802.22 — IEEE 802.22 is a standard for Wireless Regional Area Network (WRAN) using white spaces in the TV frequency spectrum. 802.22 WG — IEEE 802.22 WG is a working group of IEEE 802 LAN/MAN standards committee which is chartered to write the 802.22 standard. 802.11 — IEEE 802.11 is a set of standards for wireless local area network (WLAN) computer communication in the 5 GHz and 2.4 GHz public spectrum bands. 802.15 — IEEE 802.15 is the 15th working group of the IEEE 802 and specializes in Wireless PAN (Personal Area Network) standards. 802.16 — The IEEE WiMAX standard set. SCC41 — The IEEE Standards Coordinating Committee 41 (SCC41) works on Dynamic Spectrum Access Networks (DySPAN). The objective of this effort is to develop supporting standards dealing with new technologies and techniques being developed for next generation radio and advanced spectrum management. primary users — Primary users are the users who have the license to operate in a certain spectrum band. secondary users — Secondary users have no spectrum license and need additional functionalities to share the licensed spectrum band. co-channel interference — Any two communication links must not use the same channel at the same time if at least of them is in the interference range of the other. white space — White spaces refer to frequencies allocated to a broadcasting service but not used locally. In the United States, it has gained prominence after the FCC ruled that unlicensed devices that can guarantee that they will not interfere with assigned broadcasts can use the empty white spaces in frequency spectrum. AREPS — The Advanced Refractive Effects Prediction System (AREPS) is a sophisticated propagation modeling tool developed by the Space and Naval Warface Systems Center. APM — The Advanced Propagation Model (APM) is a hybrid model using the complimentary strengths of both ray optics and parabolic equation methods.

viii A/D converter — An analog-to-digital converter (A/D) is a device which converts continuous signals to discrete digital numbers.

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ABSTRACT

Wireless communications over water may suffer from serious multipath fading due to strong specular reflections from conducting water surfaces. The effect tends to be temporally variable and frequency selective. Cognitive radios enable dynamic frequency selection which can be used to mitigate this problem. In this project, we study how to leverage cognitive radios for effective communications in wireless networks over water. We formally define the related problem as the Overwater Channel Scheduling Problem (OCSP) which seeks a channel assignment schedule such that a “good” communication link can be maintained between every Mobile Station (MS) and the Base Station (BS) all the time. We present a general scheduling framework for solving the OCSP. Based on the proposed framework, we present an optimal algorithm and several fast heuristic algorithms. The proposed not only work for the MS-BS communications but also will work for the MS-MS communications. In addition, we discuss an extension to the heavy traffic load case and propose two throughput-aware scheduling algorithms. We performed simulation runs based on path loss data provided by the Advanced Refractive Effects Prediction System (AREPS) and present simulation results to justify the efficiency of the proposed scheduling algorithms.

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INTRODUCTION While extensive research has been carried out examining the effects of terrain and mobility on wireless communications in point-to-point, point-to-multipoint and mesh topologies, there have been few instances where the unique effects of propagation over water and their impact on wireless networking have been reported. In this report, we study wireless networks over water, such as a wireless network consisting of ships. U.S. Navy is particularly interested in such networks. Wireless communications over water may suffer from serious multipath fading due to strong specular reflections from conducting water surfaces.

Transmission Over Water Overwater propagation is a special case of the more general ground reflection problem. The large scale fading characteristics for a link whose transmitting and receiving nodes are close to the ground are well captured by the two-ray model, leading to the well known d−4 path loss formula [19], where d is the distance between transmitting and receiving nodes. In the case where the E-field is in the plane of incidence (e.g., vertically polarized) and the surface is a strong reflector, such as a conductor, the exact expression for the received power P is given by Equation ( 1.1) [19].

P (r) = Pt Gt Gr

h2t h2r d4

(1.1)

In this equation, Pt is the transmit power of the transmitter and d is the distance between the transmitter and receiver. Gt and Gr are the antenna gains of the transmitter and the receiver. ht and hr are the antenna heights of the transmitter and the receiver respectively. This two-ray effect can lead to deep fades under conditions when d = k(4ht hr )/λ (null conditions), where k is an integer and λ is the wavelength. According to Equation ( 1.1), the power decays in an oscillatory fashion, with local minimal approaching −∞dB. Once d is sufficiently large, and the power then falls off

2 asymptotically with the increasing distance. In a practical situation, the reflecting surface is not a perfect conductor and the surface is not flat, yielding power nulls that may reach tens of dBs. Water surfaces tend to be flat and conducting, providing a situation that closely approximates the ideal two-ray model. Ocean water, due to its salinity, is an excellent conductor, with a conductivity of 5S/m, and fresh water has a conductivity in the range of 0.005 to 0.5S/m [14].

(a) 1.7GHz

(b) 2.4GHz

Figure 1. Overwater path losses on two different frequencies given by the AREPS. Fig. 1 shows an example of the two-ray effect and overwater path losses predicted by the Advanced Refractive Effects Prediction System (AREPS) [4]. The AREPS is a sophisticated propagation modeling tool developed by the Space and Naval Warfare Systems Center. It can be used for calculating propagation losses for overwater paths, taking into account surface and atmospheric conditions. The AREPS implements the Advanced Propagation Model (APM) which is a hybrid model using the complimentary strengths of both ray optics and parabolic equation methods to construct a fast, but yet very accurate and composite model. Moreover, the AREPS considers range and bearing-dependent influences from surface features to include terrain elevation, finite conductivity, and dielectric ground constants, and includes the ability to model absorption by oxygen and water vapor. Therefore, the AREPS can provide accurate prediction for overwater path losses. This figure shows the power loss of an path over ocean water on two different operating frequencies, 2.4GHz and 1.7GHz, as a function of distance between transmitting and receiving nodes (labeled as “range”), The heights of both transmitting and receiving antennas are 60m. The power loss predicted by the AREPS (shown by the solid black line) oscillates about the large

3 scale free space power loss( shown by the red line), with extremes ranging up to 30dB. Empirical evidence of this effect has also been reported for an overwater LOS path recently in [6].

Introduction to Cognitive Radio Networks Current wireless networks are characterized by a static spectrum allocation policy, where governmental agencies assign wireless spectrum to license holders on a long-term basis for large geographical regions [26]. However, licensed users do not necessarily use the spectra uniformly. Recently, because of the increase in spectrum demand, this policy faces spectrum scarcity in particular spectrum bands. In contrast, a large portion of the assigned spectrum is used sporadically, leading to underutilization of a significant amount of spectrum [28]. Dynamic spectrum access techniques were proposed to solve these spectrum inefficiency problems. Cognitive Radio Network is considered one of the most possible and efficient approach among these dynamic spectrum access techniques. A cognitive radio (CR) is an intelligent radio capable of accessing the unused spectrum dynamically on a secondary basis without causing harmful interference to the licensed users (primary users), which provides a new possible solution to the current spectrum scarcity problems in the area of wireless communications system. Lots of time and money are pouring into a large number of cognitive radio technology and standards. Technology forecasts predict that CR will be a critical part of many future radio systems and networks. The use of CR technologies is already being considered in some regulatory domains, such as the Federal Communications Commission (FCC) in the United States and the Office of Communications in the United Kingdom [29] [30]. Some standardization organizations such as the international telecommunications union - radio sector (ITU-R) and the software defined radio (SDR) Forum are working in this area [31]. The term cognitive radio was first used publicly in an article [32] by Joseph Mitola where it was defined as: ”The point in which wireless personal digital assistants

4 (PDAs) and the related networks are sufficiently computationally intelligent about radio resources and related computer-to-computer communications to detect user communications needs as a function of use context, and to provide radio resources and wireless services most appropriate to those needs.” A software-defined radio (SDR) was assumed for this definition where the radios can be easily reconfigured to operate on different frequencies with different protocols by software reprogramming. Later the term was reused and reworked to suit different needs by different authors. For example, the IEEE SCC41’s P1900.1 working group on Definitions and Terminology defines a CR as follows: • ”A type of Radio in which communication systems are aware of their environment and internal state and can make decisions about their radio operating behavior based on that information and predefined objectives. NOTE: The environmental information may or may not include location information related to communication systems. • A cognitive radio that utilizes radio, adaptive radio, and other technologies to automatically adjust its behavior or operations to achieve desired objectives [33].” From this definition, two main characteristics of cognitive radio can be defined [34]: • Cognitive capability: Cognitive capability refers to the ability of the radio technology to capture or sense the information from its radio environment. Through real-time interaction with the spectrum that are unused at a specific time or location can be identified. Consequently, the best spectrum can be selected, shared with other users, and exploited without interference with the licensed user. • Reconfigurability: The cognitive capability provides spectrum awareness whereas reconfigurability enables the radio to be dynamically programmed according to the radio environment [35]. More specifically, a CR can be programmed to transmit and receive on a variety of frequencies, and use different access technologies supported by its hardware design. Through this capability, the best

5 spectrum band and the most appropriate operating parameters can be selected and reconfigured. The main objective of the cognitive radio is to obtain the best available spectrum through cognitive capability and reconfigurability as described before. Since most of the spectrum has been assigned to licensed users, the most important challenge is to access the licensed spectrum without interfering with the transmission of other licensed users. The cognitive radio enables the usage of temporally unused spectrum, which is referred to as spectrum hole or white space [34]. If this band is used by a licensed user, the cognitive radio moves to another spectrum hole or stay in the same band, altering its transmission power level or modulation scheme to avoid interference. In the over water case, the cognitive radio is used to select a channel with the best propagation characteristics. In the following subsections, I will describe the physical architecture of cognitive radio, the cognitive radio network architecture, IEEE standards of cognitive radio networks in the following subsections.

The physical architecture of cognitive radio A general architecture of a cognitive radio transceiver with RF/analog front-end is shown in Fig.

2. The transceiver and the RF/analog processing unit are the

main components of a cognitive radio. Each component can be reconfigured via a control bus to adapt to the time-varing RF environment [36]. In the RF front-end, the received signal is amplified, down converted and A/D converted. In the baseband processing unit, the signal is modulated/demodulated and encoded/decoded. The baseband processing unit of a cognitive radio is essentially similar to existing transceivers. But the novelty of the cognitive radio is the RF front-end [35] which we will focus on. The novel characteristic of the transceiver is a wideband sensing capability of the RF front-end. This function is mainly related to RF hardware technologies such as wideband antenna, power amplifier and adaptive filter. RF hardware for the cognitive radio should be capable of tuning to any part of a large range of

6 frequency spectrum. Generally, a wideband RF/analog front-end architecture for the cognitive radio has the following components [35] [36]: • RF filter: The RF filter selects the desired band by bandpass filtering the received RF signal. • Low noise amplifier: The low noise amplifier amplifies the desired signal while simultaneously minimizing noise component. • Mixer: In the mixer, the received signal is mixed with locally generated RF signal and converted to the baseband or the intermediate frequency. • Voltage-controlled oscillator (VCO): The VCO generates a signal at a specific frequency for a given voltage to mix with the incoming signal. This procedure converts the incoming signal to baseband or an intermediate frequency. • Phase locked loop: The PLL ensures that a signal is locked on a specific frequency and can also be used to generate precise frequencies with fine resolution. • Channel selection filter: The channel selection filter is used to select the desired channel and to reject the adjacent channels. The direct conversion receiver uses a low-pass filter for the channel selection, while the superheterodyne receiver adopts a bandpass filter. • Automatic gain control (AGC): The AGC maintains the gain or output power level of an amplifier constant over a wide range of input signal levels. In this architecture, a wideband signal is received through the RF front-end, sampled by the high speed A/D converter, and measurements are performed for the detection of the licensed user signal. However, there exist some limitations on developing the cognitive radio front-end. The wideband RF antenna receives signals from various transmitters operating at different power levels, bandwidths and locations. As a result, the RF front-end should have the capability to detect a weak signal on a large dynamic range.

Cognitive radio network architecture The components of the CR network architecture are showed in Fig. 3.

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Figure 2. Physical architecture of the cognitive radio [2]..

The components of the CR network architecture, as show in Fig. 3, can be classified as two groups: the primary network and the CR network. The primary network is referred to as an existing network, in which the users have been assigned a license to operate in a certain spectrum band. Due to their priority in spectrum access, the operations of primary users should not be affected by unlicensed users (secondary users). On the other hand, the CR network users do not have the privilege to operate in a primary users band. CR networks can also be equipped with CR basestations that provide single-hop connection to CR users. Finally, CR networks may include spectrum brokers that play a role in distributing the spectrum resources among different CR networks [26].

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Figure 3. The cognitive radio network architecture [26]..

CR users are capable of accessing both the licensed portions of the spectrum used by the licensed users and the unlicensed portions of the spectrum through wideband access technology. Consequently, the operation types for CR networks can be classified as licensed band operation and unlicensed band operation. • Licensed band operation: The licensed band is primarily used by the primary network. Therefore, the CR networks are focused mainly on the detection of primary users in this case. The channel capacity depends on the interference at nearby primary users. Furthermore, if primary users show up in the spectrum band occupied by CR users, CR users should vacate that spectrum band and move to available spectrum immediately [2] [26] [37]. • Unlicensed band operation: In the absence of primary users, CR users have the same right to access the spectrum. Hence, sophisticated spectrum sharing methods are required for CR users to compete for the unlicensed band [2] [26] [37].

9 IEEE standards of interest for CR Standardization is the key to the success of many technologies. Cognitive radio is not exception. Currently the IEEE has two well-known standards activities in this area - SCC41 (formerly known as P1900) [29] and IEEE 802.22 [38]. Standards Coordinating Committee 41 (SCC41) sponsor standards projects in the area of dynamic spectrum access networks (DySpaN) [27]. The SCC41 activities are co-sponsored by the IEEE Communications and Electromagnetic Compatibility Societies. SCC41 addresses techniques and methods of DSA require managing interference, co-ordination of wireless technologies and include network management and information sharing. SCC41 considers SDR to be a key enabler for CR/DSA [39]. It concentrates on developing architectural concepts and specifications for network management between incompatible wireless networks rather than specific mechanisms that can be added to the physical or MAC protocol layers. IEEE SCC41 will provide vertical and horizontal network reconfiguration management methods for inter-operability in infrastructureless wireless networks. The IEEE 802 LAN/MAN Standards committee created the 802.22 working group on wireless regional area networks (WRAN) in response to the FCC Notice of Proposed Rule Making (NPRM) 04-113 [29] for the use of unlicensed wireless operation in the analog television bands. IEEE 802.22 defines air interface for use by licenseexempt devices on a non-interfering basis in VHF and UHF bands which are also referred to as the TV white spaces [40]. IEEE 802.22 working group defines the system architecture, functionalities of various blocks and their mutual interactions. The proposed protocol reference model separates the system into the cognitive, data/control and management planes. The data/control and management planes look similar to other standards within the IEEE The spectrum-sensing function (SSF) and geolocation function which interface with the RF stage of the device provide information to the spectrum manager (SM) on the presence of incumbent signals as well as its current location. The SM function makes decisions on transmission of the information-bearing signals. The PHY,MAC and converagence layers are essentially the same as in 802.16. Security sub-layers are added between service access points to provide protection.

10 While SCC41 and IEEE 802.22 are the primary cognitive standards efforts today, many completed IEEE 802 standards already include CR/DSA like capabilities or related building blocks. For example, IEEE 802.15 was one of the first standards groups to address co-existence issues since 802.15 protocols needed to share the same unlicensed band (2.4GHz) used by IEEE 802.11 [27]. IEEE802.15.2 contains a collection of collaborative techniques that can be applied to enable the coexistence between IEEE 802.11 and IEEE 802.15. Some other prior IEEE standards work related to CR deals with DFS, dynamic channel selection and TPC, i.e. IEEE 802.11h, IEEE 802.16-2004 and IEEE 802.15.4. These features deal with the fact that other systems may operate in the Unlicensed National Information Infrastructure bands and need protection.

Our Work and Contributions Our approach to mitigating this effect is to shift the operating frequency. A null in power can be avoided by a change in frequency, i.e., using a different channel. If the trajectory and speed of a Mobile Station (MS) are known in advance, predictive techniques can be used to estimate the times and durations of deep fades, and a dynamic channel selection method can be used to switch its radio to an operating frequency where the null conditions are not met. For example, during a period in which a channel on 2.4GHz experiences deep fades, another channel on 1.7GHz can be selected for communications if it may lead to acceptable path losses. It is assumed that the radio of the MS’s can get access to all the channels. The emerging cognitive radio technology enables dynamic spectrum access [2]. With a cognitive radio, an MS can dynamically switch its radio to any available channel whenever it has packets to send. This report briefly summarizes overwater propagation phenomena and then proposes the use of cognitive radios to mitigate the pronounced channel fading effects that are experienced in overwater paths, which, to our best knowledge, has not been well studied before. We formally define the related

11 problem as the Overwater Channel Scheduling Problem (OCSP) which seeks a channel assignment schedule such that a “good” communication link can be maintained between each MS and the BS all the time. Our major contributions are summarized as follows: 1) We present a general scheduling framework which can provide a guideline for designing scheduling algorithms to solve the OCSP. 2) Based on the proposed framework, we present an optimal algorithm and several fast heuristic algorithms for the OCSP. 3) We performed simulation runs based on path loss data provided by the AREPS and present simulation results to justify the efficiency of the proposed algorithms. The rest of this report is organized as follows. We discuss related work in Chapter 2. The system model and problem definition are described in Chapter 3 and Chapter 4 respectively. We present the proposed scheduling framework and algorithms in Chapter 5. We present simulation results in Chapter 6 and conclude the report in Chapter 7.

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RELATED WORK

Previous Work on Overwater Propagation Modeling Path loss effects for LOS paths close to the ground were extensively studied in the early 1970’s with the deployment of point-to-point microwave radio systems. Ground reflection, atmospheric refraction and ducting effects were reported in [16]. Particularly deep fades, exceeding 20dB relative to free space path loss, were observed in overwater paths for radio links between the UK and France [5]. Overwater path loss effects have generally been ignored until recently, as the focus of attention in wireless system design and applications has been toward cellular systems and wireless LANs. Empirical evidence of this effect has recently been reported for an overwater LOS path in [6].

Previous Work on Spectrum Allocation and Scheduling Spectrum allocation (channel assignment) and scheduling are very important problems in cognitive radio networks [2], which have been studied by a few recent works. In a centralized spectrum sharing protocol proposed in [7], spectrum management is conducted in a central server, which can obtain a global view of network by exchanging information with users. In [25], Zheng et al. developed a graph-theoretic model to characterize spectrum access, based on which, they designed several centralized heuristics to find fair spectrum allocation solutions. Distributed methods were presented in [8, 15, 24]. For example, a distributed spectrum allocation algorithm based on local bargaining was presented in [8]. In [24], the authors presented optimal and suboptimal distributed spectrum access strategies under a framework of partially observable Markov decision process. In [15], the authors proposed the Dynamic Open Spectrum Sharing (DOSS) MAC protocol, which provides real-time dynamic spectrum allocation and high spectrum utilization. The authors of [23] introduced the

13 concept of time-spectrum block and proposed algorithms to allocate such blocks to meet certain performance goals. In [22], Tang et al. studied joint spectrum allocation and scheduling problems in cognitive radio networks. They presented a graph model to characterize the interference impact. Based on that model, optimal and heuristic algorithms were presented to find maximum throughput and fair solutions. Channel assignment has also been studied for traditional wireless networks with multiple homogeneous channels. In [17] and [18], the authors proposed one of the first 802.11-based multi-radio mesh network architectures and developed several centralized and distributed heuristic algorithms for channel assignment and routing. In [21], Tang et al. proposed an interference-aware channel assignment algorithm. A constant-bound approximation algorithm was presented in [3] to jointly compute channel assignment, routing and scheduling solutions for fair rate allocation. A similar problem was studied in [13]. The authors derived upper bounds on the achievable throughput using a fast primal-dual algorithm and presented two channel assignment algorithms. In this report, we study channel assignment and scheduling in the context of cognitive radio networks and overwater communications. Our problem is different from those studied in the related works, as the main factor is the channel quality rather than primary or secondary interference.

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SYSTEM MODEL In this chapter, we will describe the network model and the propagation model.

Network Model We consider a wireless network over water, consisting of a Base Station (BS) v0 and n − 1 MSs {v1 , v2 , · · · , vn−1 }, each of which is equipped with a cognitive radio. The BS could be a radio station installed on the shore or carried by a ship. An MS could be a ship, or any object flying over water such as an airplane or a balloon. The available spectrum is divided into H non-overlapping channels. A cognitive radio can be tuned to an available channel to deliver its packets. A radio used by a ship or an airplane can usually transmit packets over a long distance with the help of a powerful amplifier. For example, the SeaLancet radio developed for the U.S. Navy has an amplifier that can increase the transmit power to 10W, which gives a transmission range of approximately 80km [20]. Hence, each MS can directly communicate with the BS. It is also assumed that each radio transmits at the fixed power level. Therefore, in such a network, there are n − 1 MS-BS links and every MS-BS link needs to be assigned a different channel for communications at any time to prevent co-channel interference.

Propagation Model According to the two-ray propagation model given in Equation ( 1.1), this two-ray fading effect can lead to deep fades under conditions when θ∆ = kπ, where k is an integer. Note that θ∆ is a function of the antenna heights of transmitting and receiving nodes, the distance between them and the operating frequency. These conditions can result from movements of the nodes (e.g., changes in distance). We explicitly calculate path losses using the AREPS. Fig. 1 illustrates a calculation of path losses obtained with AREPS for three different operating frequencies, 4.9GHz, 2.4GHz and 1.7GHz.

15 The orange horizontal line in the figure indicates a threshold of 138dB, corresponding to a path loss that would limit the radio link capacity to a certain acceptable level. Note that link capacity is related to path loss and other parameters such as transmit power, antenna gains, channel bandwidth, and so on. Once the values of the other parameters are fixed, link capacity becomes a function of path loss. In other words, given a link capacity threshold, we can obtain the corresponding path loss threshold. We will describe how we set the values of the other parameters in the simulation and explain how we derived the corresponding path loss threshold according to a given capacity threshold in Chapter 6. Fig. 1 shows, as a function of distance between transmitting and receiving nodes, that there are intervals where the path loss exceeds this threshold for a particular operating frequency. Intuitively, a channel assignment and scheduling method could be used to switch the radio to a different “good” channel whenever this happens.

16

PROBLEM DEFINITION In this chapter, we formally define the scheduling problems to study.Each MS is assumed to know its moving trajectory and speed in the next T seconds. Therefore, the distance between the BS and an MS at any time can be computed in advance. The BS gathers such information periodically from each MS. We define a channel assignment i schedule for each MS vi as Ai = {(τ1i , hi1 ), · · · , (τj−1 , hij−1 ), (τji , hij ), · · · , (T, himi )}, i which specifies the channel (hij ) assigned to vi in each time interval (τj−1 , τji ). Cor-

respondingly, a channel assignment schedule for the network is given by = {Ai : i ∈ {1, 2, · · · , n − 1}}. Given a cognitive radio network over water with a BS, n − 1 MSs and H channels, and a capacity threshold of C, we study the following optimization problem. Definition 1 (OCSP): The Overwater Channel Scheduling Problem (OCSP) seeks a channel assignment schedule for the network such that at any time within [0, T ], the capacity of every MS-BS link is no smaller than C and no two MSs share a common channel. Here, we are basically interested in finding a channel assignment schedule which can always guarantee a good communication link between each MS and the BS all the time. It is assumed that each node has a channel demand for a channel. For simplicity, we assume an MS always keeps using a channel until it becomes unusable, i.e., the corresponding link capacity drops below the threshold C.

17

PROPOSED SCHEDULING ALGORITHMS In this section, we present a general framework to solve the OCSP. Based on the framework, we present an optimal algorithm and several fast heuristic algorithms. As mentioned before, the distance between the BS and an MS vi at any time can be pre-computed. According to the path loss values predicted by the AREPS, hi hi hi we can identify a set Thi of time intervals {(0, thi 1 ), · · · , (tj−1 , tj ), · · · , (tmi −1 , T )} for

each MS-channel pair (i, h), where i ∈ {1, 2, · · · , n − 1} and h ∈ {1, 2, · · · , H}. During each of such intervals, the link capacity that can be supported by channel h for MS vi is no smaller than the given threshold C. Note that usually these time intervals are not continuous. For example, suppose that the BS is a stationary node on the shore, v1 is 16km away from the BS at time 0 and it moves away along a straight line at a speed of 60km/h. C = 10Mbps and the operating frequency is 2.4GHz. The corresponding path loss threshold is 138dB. According to Fig. 1(b), we have

1 1

= {(0, 60), (84, 378), (438, 942), (1098, 2166)}. The unit of time is seconds

throughout the report.

Scheduling Framework First, we introduce a graph model, time-channel graph, to assist computation. We construct a time-channel graph, Gi (V i , E i ) for each MS vi . In Gi , each vertex u corresponds to a pair of time interval and channel (tj−1 , tj , h), where (tj−1 , tj ) ∈ih . There is a directed edge from vertex u = (tj−1 , tj , hj ) to vertex u′ = (tj ′ −1 , tj ′ , hj ′ ) if tj ′ −1 ≤ tj < tj ′ . In this graph, each edge e = (u, u′ ) can be characterized by a 5-tuple (tj−1 , tj , hj , tj ′ , hj ′ ) since it is assumed that channel h is used until it becomes unusable, i.e., channel hj is used until tj then channel hj ′ is used. The direction of an edge is consistent with the time progressing direction. Gi also includes two virtual vertices si and di . There is a directed virtual edge from si to every vertex corresponding to a time interval whose starting time is 0. Moreover, there is a directed virtual edge from every vertex corresponding to a time interval whose ending time

18 is T to di . It is easy to see that a time-channel graph is a Directed Acyclic Graph (DAG). We say an edge ei in Gi corresponding to (tij−1 , tij , hij , tij ′ , hij ′ ) conflicts with an edge ek in Gk (k 6= i) corresponding to (tkl−1 , tkl , hkl , tkl′ , hkl′ ) if there exists a time within S [tij−1 , tij ′ ] [tkl−1 , tkl′ ] in which a common channel is shared by both MSs vi and vk . The conflicting number of an edge ei in Gi (denoted by Nei ) is the number of edges in all

the time-channel graphs other than Gi that conflict with ei . The importance of a timechannel graph Gi lies in the fact that any simple path from si to di corresponds to a channel assignment schedule. It can be obtained by concatenating the time intervals corresponding to edges on the path. Similarly, we say a path pi in Gi conflicts with a path pk in Gk if there exists a time within [0, T ] in which a common channel is shared by both MSs vi and vk . Note that if an edge on a path conflicts with another edge on another path, these two paths may not conflict with each other. Therefore, whether a path pi conflicts with another one pk cannot be simply determined by checking whether any pair of edges (ei , ek ) (where ei ∈ pi and ek ∈ pk ) conflict with each other. Based on time-channel graphs for all the MSs, we can construct a corresponding conflict graph GP (VP , EP ), which is a layered undirected graph. Each layer i corresponds to an MS vi and there are totally n − 1 layers. In each layer i, each vertex z i corresponds to a simple path pi from vertex si to vertex di in Gi . There is an edge between every pair of vertices in layer i. Hence, the subgraph on each layer i is a complete graph. The number of neighbors of vertex z i on layer i is called the intra-layer degree of z i . In addition, there is an edge between a vertex z i in layer i and another vertex z k in layer k 6= i if their corresponding paths (schedules) conflict with each other. The number of neighbors of vertex z i on layers other than layer i is called the inter-layer degree of z i , denoted by Dzi . The proposed scheduling framework is formally presented as Algorithm 1. Next, we use a simple example to demonstrate how the proposed approach works. In this example, we have 2 MSs and 3 channels. Suppose that T = 500s. For v1 , 11 = {(0, 60), (84, 378), (438, 500), 12 = {(30, 90), (300, 470)} and 13 = {(0, 40), (55, 440), (450, 500).

For v2 , 21 = {(50, 100), (270, 440), 22 = {(0, 70), (75, 390), (420, 500)} and 23 = {(60, 280), (305, 470).

19 Algorithm 1 The Scheduling Framework Step 1 forall i = 1 to n − 1 Construct a time-channel graph Gi (V i , E i ); Find a set of paths from si to ti and store them in set P i ; endforall Step 2 Construct a conflict graph GP (VP , EP ) based on the paths P = {P i : i = 1, 2, · · · , n − 1} found in Step 1; Step 3 if There exists a Maximal Independent Set (MIS) S in GP such that |S| = n−1 return the channel assignment schedule corresponding to S; else return “There is no feasible solution!”; endif

(0,60,1)

s1

(84,378,1)

(30,90,2)

(438,500,1)

d1

(300,470,2)

p11 p

(0,40,3)

G1

(55,440,3)

1 2

(450,500,3)

1 2 0 60 90

1

3 2 0 40 90

3

2 3 440 470500

3

1

1

p31

2 378

0 60

G2

(50,100,1)

2 0

(0,70,2)

(75,390,2)

(420,500,2)

d2

p 22 p 33

(305,470,3)

1 70100

2 0

(60,280,3)

p11 p 12

p31

Layer 1

500

(270,440,1) p12

s2

440

1 470500

1 70100

(a) A time-channel graph

Layer 2

1 2 390 440 500

3

2

70 2

0

2

280

3

2 470500

3

2 470500

390

2 390

p12 p 22

p 33

(b) A conflict graph

Figure 4. Graph models.

The corresponding time-channel graph is shown in Fig. 4(a). Suppose an algorithm designed based on our scheduling framework find 3 paths on each time-channel graph: p11 = {(0, 60, 1), (30, 90, 2), (84, 378, 1), (300, 470, 2), (438, 500, 1)} p12 = {(0, 40, 3), (30, 90, 2), (55, 440, 3), (300, 470, 2), (450, 500, 3)} p13 = {(0, 60, 1), (55, 440, 3), (438, 500, 1)} p21 = {(0, 70, 2), (50, 100, 1), (75, 390, 2), (270, 440, 1),

20 (420, 500, 2)} p22 = {(0, 70, 2), (60, 280, 3), (75, 390, 2), (305, 470, 3), (420, 500, 2)} p23 = {(0, 70, 2), (50, 100, 1), (75, 390, 2), (305, 470, 3), (420, 500, 2)} Every path gives a channel assignment schedule. For example, path p11 gives a channel assignment schedule for MS v1 : {(60, 1), (90, 2), (378, 1), (470, 2), (500, 1). All the corresponding channel assignment schedules and the conflict graph are shown in Fig. 4(b) where the black numbers indicate the time and the red numbers are channels. In this example, we can find an MIS including two vertices corresponding to paths p13 and p21 respectively, which gives a feasible channel assignment for this network. Note that this scheduling framework can be implemented in different ways. For example, different methods can be used to find paths in Step 1. Similarly, in Step 3, different algorithms can be used to test if there exists an independent set S in GP such that |S| = n − 1. This will be discussed in detail in the next section. We have the following theorem. Theorem 1: Any channel assignment schedule for the network returned by a scheduling algorithm designed based on this framework is a feasible schedule. Proof: As mentioned before, each simple si -di path in a time-channel Gi corresponds to a channel assignment schedule for MS vi . The feasibility of the returned channel assignment schedule for the network is guaranteed by the ways we construct time-channel graphs and the conflict graph. Specifically, each Gi only includes those vertices whose corresponding channels are usable in the corresponding time intervals, which makes sure that the capacity constraint is satisfied. Moreover, the way we add virtual vertices si and di , and edges into Gi ensures that each si -di path (channel assignment schedule) covers every time interval between 0 and T . In addition, according to the framework, the subgraph on each layer i of the conflict graph GP is a complete graph. Therefore, an MIS in GP can include no more than one si -di path in layer i (a channel assignment schedule for MS vi ). Moreover, the returned schedule for the network corresponds to an MIS in GP , which ensures there

21 is no confliction between any pair of individual channel assignment schedules, i.e., at any time between 0 and T , no two MSs share a common channel. This completes the proof.

Optimal and Heuristic Algorithms In this section, we first present an optimal algorithm based on the proposed framework to solve the OCSP. Then we present several fast heuristic algorithms. All the proposed algorithms follow the scheduling framework described in Section 5. However, they vary in Step 1 and Step 3. To achieve the optimality, the scheduling algorithm needs to find all possible paths from si to di in Gi for each MS vi in Step 1 and enumerate all MISs in GP in Step 3. We call this algorithm the allpaths based scheduling algorithm. It is known that a simple Depth First Search (DFS) based algorithm can be used to find all possible paths between a pair of vertices in a directed graph [9]. In addition, several efficient MIS enumeration algorithms (e.g., the algorithm in [12]) have been proposed in the literature, which can be applied in Step 3 to test if there exists an MIS S in GP such that |S| = n − 1. We can slightly revise such an algorithm by making it stop once an MIS with a cardinality of n − 1 is found. However, it is well-known that both the number of paths between a pair of vertices and the number of MISs in a graph could be exponentially large. It may take a very long time for the optimal scheduling algorithm to solve large cases. Hence, we present several fast heuristic algorithms. The first heuristic algorithm is called K-paths based scheduling algorithm, which is formally presented as follows. In Step 1, this algorithm simply finds K paths (instead of one path) for every timechannel Gi , which hopefully would increase the chance of finding a feasible schedule. Suppose that Gi has N i vertices and M i edges, and N = max{Ni : i ∈ {1, 2, · · · , n − 1}} and M = max{Mi : i ∈ {1, 2, · · · , n − 1}}. Then Step 1 takes O(n(N + M )K) time. Step 2 can be done within O(N n2 K 2 ) time. In Step 3, a greedy algorithm is used to test if there exists an MIS whose cardinality is n − 1. The algorithm

22 Algorithm 2 The K-paths based scheduling algorithm Step 1 forall i = 1 to n − 1 Construct a time-channel graph Gi (V i , E i ); Find the first K paths from si to di using the DFS-based path enumeration algorithms and store them in set P i ; endforall Step 2 Execute Step 2 in the scheduling framework; Step 3 forall k = 1 to K S := Ø; G := GP ; S := S + {zk1 }, where zk1 is the kth vertex on layer 1 in GP ; Remove all the vertices in layer 1, and the vertices on the other layers that conflict with zk1 from GP ; forall i = 2 to n − 1 if There are vertices left in layer i i i S := S + {zmin }, where zmin is the vertex with the minimum inter-layer degree in GP ; Remove all the vertices in layer i, and the vertices on the other layers that conflict with i zmin from GP ; else break; endif endforall if (|S| = n − 1) return the channel assignment schedule corresponding to S. endif endforall return “There is no feasible solution!”

tries to construct an MIS covering exactly one vertex in each layer of GP , which can done within O(nK) time. This trial is repeated for K times to increase the success ratio. So Step 3 takes O(nK 2 ). The total running time of this algorithm is O(n(N + M )K + n2 N K 2 ).

23 The second heuristic algorithm is called the K-shortest-paths based scheduling algorithm, which is different from K-paths based scheduling algorithm in Step 1. Instead of constructing an un-weighted time-channel graph, we construct a weighted time-channel graph Gi for each MS vi in which the weight of each edge is set to its conflicting number, Nei . Then in Step 1, the K-shortest-paths based scheduling algorithm finds K shortest paths for every time-channel graph Gi . The basic design philosophy is to find paths composed of edges with relatively small conflicting numbers in a time-channel graph, which will unlikely conflict with paths found in other time-channel graphs. There are a number of algorithms which can be used to find K shortest paths in a graph in the literature. In the simulation, we implemented a well known algorithm in [10] for this purpose, which has a time complexity of O(N M K 2 log K). Steps 2 and 3 of this algorithm are the same as those of K-paths based scheduling algorithm. Therefore, the overall time complexity of our K-shortestpaths based scheduling algorithm is O(nN M K 2 log K + n2 N K 2 ). The third heuristic algorithm is called the min-max-K-paths based scheduling algorithm, whose first step is different from either the K-path based scheduling algorithm or the K-shortest-paths based scheduling algorithm. As the K-shortest-paths based scheduling algorithm, we construct a weighted time-channel graph Gi for each MS vi . Then we use a binary search to find the minimum edge conflicting number Nmin such that there exist K-paths in a subgraph Gi of Gi which is the same as Gi except that it only includes those edges whose conflicting numbers are no more than Nmin . In the simulation, we also used the algorithm in [10] to test or find K paths in a subgraph Gi . In this way, it can ensure that the maximum edge conflicting number of the K paths found in Step 1 is minimized. The time complexity of this algorithm is O(nN M log M K 2 log K + n2 N K 2 ). Note that usually even if we choose a small value for K, the algorithms can still give decent performance which is quite close to result obtained by the optimal algorithm. For example, it was set to 15 in the simulation. Hence, these algorithms are generally time efficient in practice.

24 Heavy Traffic Case In this section, we discuss how to extend our solutions to the heavy traffic load case. The solutions given by the previous algorithms can ensure that a good communication link (the capacity threshold is satisfied) can always be maintained for each MS all the time. However, the throughput has not been carefully addressed. Specifically, during a certain period, it might be possible that multiple channels are usable. However, they may experience quite different path losses at a particular time, i.e., some of them may be able to support relatively high link capacities and the other can only support relatively low link capacities. If traffic load is light,e.g. less than 10Mbps, it is good enough to only make sure that every selected channel is usable. However, for the heavy traffic load case, a more careful decision should be made for channel assignment to ensure that the channel leading to high throughput is selected among all usable channels. Next, we discuss how to extend the scheduling algorithms proposed in the last section to address the above issue. Similarly, a time-channel graph needs to be constructed for each MS to assist computation. As mentioned before, each edge in this graph e = (u, u′ ) can be characterized by a 5-tuple (tj−1 , tj , hj , tj ′ , hj ′ ). We define a weight function W (·) for each edge in Equation ( 5.1), which gives the maximum number of bits that can be delivered between this MS and the BS in the period [tj−1 , tj ′ ].

W (e) =

Z

tj

tj−1

rhj (t)dt +

Z

tj ′

tj

rhj′ (t)dt

(5.1)

In this equation, rhj (t) and rhj (t) gives the maximum data rates (capacities) that can be supported by channel hj and hj ′ at t respectively, which can be derived based on the corresponding path loss values. In the simulation, we placed a number of sample points on the time axis and obtained the corresponding path loss values using the AREPS. We then calculated the maximum volume of traffic that can delivered in each time interval based on those sample points, which provides a good estimation

25 for the weight function. Similarly, we can define a weight function for an si -di path p in Gi , which gives the maximum number of bits that can be delivered between this MS and the BS in the period [0, T ]. However, note that the path weight is usually less than (not equal to) the summation of weighs of edges on that path. By altering the notation a little bit, we use W (·) to denote the path weight function as well. We propose two throughput-aware heuristic algorithms, which are described in the following. The first heuristic algorithm is called the K-max-throughput-paths based scheduling algorithm, which is similar to the K-shortest-paths based scheduling algorithm. However, in Step 1, we construct a weighted time-channel graph Gi for each MS vi in which the weight of each edge ei is set to W (ei ) according to Equation ( 5.1). Then the algorithm finds K longest paths for every time-channel graph Gi . It is well known that the longest path problem in a general graph is NP-hard. However, every timechannel graph Gi is a DAG. K longest paths in each Gi can be found by changing the weight of every edge ei to −W (ei ) and then applying the K-shortest-path algorithm i in [10]. In addition, in Step 3, instead of adding a vertex zmin with the minimum

inter-layer degree in layer i of the current conflict graph GP (note the conflict graph is updated every time when a vertex is added to S) into the set S every time, we add i i a vertex zmax such that zmax = argmaxz∈VPi

W (z) , Dz

where VPi is set of vertices in layer

i of GP and W (z) gives the weight of the path corresponding to z. The time complexity of this algorithm is the same as that of the K-shortest-paths based scheduling algorithm. The second heuristic algorithm is called the max-min-throughput-K-paths based scheduling algorithm, which is similar to the min-max-K-paths based scheduling algorithm. In Step 1, we construct a weighted time-channel graph Gi for each MS vi in which each edge weight is assigned according to Equation ( 5.1). Then we use a binary search to find the maximum edge weight Wmax such that there exist K paths in a subgraph Gi of Gi which is the same as Gi except that it only includes those edges whose weight is no less than Wmax . We also use the algorithm in [10] to test or find K shortest paths in terms of the edge conflicting number in Gi . In this way, it can

26 ensure that the minimum edge weight of the K paths found in Step 1 is maximized. In Step 3, we use the same greedy method for testing as the K-max-throughput-paths based scheduling algorithm. The time complexity of this algorithm is the same as that of the min-max-K-paths based scheduling algorithm. Note that it is likely that the two throughput-aware scheduling algorithms presented here perform better than the three heuristic algorithms presented in Section 5 in terms of network throughput. However, in terms of the probability of successfully finding a feasible channel assignment schedule (success ratio), the throughput-aware algorithms may not be as good as those in Section 5 which aim for finding paths (schedules) with relatively small conflicting numbers in each time-channel graph Gi . This tradeoff is verified by simulation results in Chapter 6.

27

NUMERICAL RESULTS We evaluated the performance of the proposed algorithms via simulation based on path loss data given by the AREPS.

Table 1. Link Capacity VS. Path Loss Threshold. Modulation Minimum Link Capacity Path Loss CNR(dB) (Mbps) Threshold (dB) QPSK 1/2 10 10 138 16QAM 1/2 14.5 20 133.5 16QAM 3/4 17.25 30 130.75 64QAM 2/3 21.75 40 126.5 64QAM 3/4 23 45 125

The simulation runs were performed based on scenarios where the BS had a 12dBi antenna with a height of 60m and each MS had a 2dBi antenna with a height of 60m. The transmit power was assumed to be 10W. Moreover, the channel bandwidth and the receiver noise figure were chosen as 10Mhz and 5dB respectively. An implementation loss of 3dB was also assumed at both the BS and MSs. The threshold Carrier to Noise Ratio (CNR) values given in the IEEE 802.16 [1] standard for a bit error rate of 10−6 were used in a link budget calculation with the parameters given above to establish the maximum allowable path loss (path loss threshold) for a given modulation index and forward error correction rate. The corresponding link capacity for each modulation index, as shown in Table 1, was obtained by combining the channel bandwidth with the maximum supported symbol rate. In all the simulation scenarios, the link capacity threshold was set to 10Mbps. From this table, we obtained a maximum path loss threshold of 138dB. In addition, the method described in Section 5 was used to calculate edge and path weights based on values from Table 1 for the throughput-aware algorithms and the corresponding scenarios. In these simulations, a static BS was always placed at (0, 0). In each run, each MS was assumed to move away from the BS along a direction randomly chosen and

28 at a random constant speed uniformly distributed in [56, 65]km/s (typical speed of a warship). The schedule duration T was set to 600s for all the scenarios. At the beginning of each run, each MS was randomly placed in a circular strip specified by a small circle with a radius of Dkm and a large circle with a radius of D + 5km. We call D the minimum initial distance. All the channels were divided into three groups, each of which includes approximately the same number of channels. The first, second and third groups of channels were chosen from the 700MHz, 1.7GHz and 2.4GHz bands respectively with a step size of 20MHz. Intuitively, the following parameters play a key role in system performance: the number of MSs nM = n − 1, the number of channels H, and the minimum initial distance D. We conducted our performance evaluation by setting those parameters to different values in different scenarios. Since the objective of the OCSP is to find a feasible channel assignment schedule for the network, the success ratio was used as a performance metric. Specifically, we performed 20 simulation runs and counted the number of times a feasible schedule was successfully found by a proposed algorithm. For the throughput-aware algorithms (i.e, the K-max-throughput-paths based algorithm and the max-min-throughput-K-paths based algorithm), network throughput was used as the performance metric, which is the summation of the throughput given by the channel assignment schedule of each MS. In addition, K was always set to 15. Scenario 1 was designed to compare the proposed heuristic algorithms against the optimal algorithm in small cases. In this scenario, nM = 5, H = 10 and D was changed from 20km to 40km with a step size of 5km. In scenarios 2 and 3, we tested our algorithms in larger cases. In scenario 2, nM = 15, H = 35 and D was increased from 20km to 40km. In scenario 3, H = 35, D = 25km and nM was increased from 5 to 25. The corresponding results are presented in Figs. 5 to 7. Scenario 4 has the same settings as as scenario 2. However, we compared the max-min-K-paths based algorithm with the throughput-aware algorithms in terms of the success ratio. Moreover, we randomly picked a trial in which every algorithm can find a feasible channel assignment schedule and then compared their performance with regards to network throughput. The corresponding results are presented in Figs. 8 to 9.

29 1

The Success Ratio

0.9 0.8 0.7 0.6 0.5 0.4 0.3 20

Optimal K−paths K−shortest−paths min−max−K−paths 25

30

35

40

The Minimum Initial Distance (km) Figure 5. Scenario 1: n = 5 and H = 10.

1

The Success Ratio

0.9 0.8 0.7 0.6 0.5 0.4 20

K−paths K−shortest−paths min−max−K−paths 25

30

35

The Minimum Initial Distance (km) Figure 6. Scenario 2: n = 15 and H = 35.

40

30

The Success Ratio

1

0.9

0.8

0.7

K−paths K−shortest−paths min−max−K−paths

0.6

0.5 5

10

15

20

25

The Number of MSs (nM) Figure 7. Scenario 3: H = 35 and D = 25km.

1

The Success Ratio

0.9 0.8 0.7 0.6 0.5 0.4 20

K−max−thru−paths max−min−thru−K−paths min−max−K−paths 25

30

35

40

The Minimum Initial Distance (km) Figure 8. Scenario 4 (success ratio): n = 15 and H = 35.

31

Network Throughput (Mbps)

650 K−max−thru−paths max−min−thru−K−paths min−max−K−paths

600 550 500 450 400 350 300 20

25

30

35

40

The Minimum Initial Distance (km) Figure 9. Scenario 4(network throughput): n = 15 and H = 35.

We can make the following observations from these results: 1) In terms of the success ratio, the max-min-K-paths based algorithms always performs best among all the heuristic algorithms. In small size networks, the average difference between its success ratios and the optimal values is only 5%. On average, it outperforms the K-shortest-paths based algorithm by 2.7% and the K-paths based algorithm by 12.7%. 2) From Fig. 6, we can see the success ratio decreases with the minimum initial distance no matter which algorithm is used. A large minimum initial distance usually leads to large distances between MSs and the BS throughout the whole simulation run thus a poor success ratio. We can also see from Fig. 7, the success ratio decreases with the number of MSs. It is easy to understand this. With the number of channels fixed, it becomes harder to satisfy every MS’s requirement in a larger network since no two MSs can share a common channel. 3) As expected, we can see from Fig. 9 the two throughput-aware scheduling algorithms provide higher network throughput than the max-min-K-paths based algorithm which has been shown to be the best algorithm in terms of the success ratio.

32 However, from Fig. 8, we find out that in terms of the success ratio, the throughputaware algorithms are not as good as the max-min-K-paths based algorithm. This is because the two throughput-aware scheduling algorithms focus more on throughput than conflicting numbers in the first step, which may lead to finding a path (schedule) that is likely to conflict with other paths.

33

CONCLUSIONS In this report, we studied overwater communications in wireless networks with cognitive radios. We formally defined the related problem as the Overwater Channel Scheduling Problem (OCSP). We presented a general scheduling framework for solving the OCSP. Based on the proposed framework, we presented an optimal algorithm and several fast heuristic algorithms. In addition, we discussed an extension to the heavy traffic load case and proposed two throughput-aware scheduling algorithms. AREPSbased simulation results have been shown to justify the efficiency of the proposed algorithms.

34

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